Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(127,1440)]
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, 0, 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("1440.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.x (of order \(4\), degree \(2\), 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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.127 |
Dual form | 1440.2.x.p.703.2 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 2.22474 | − | 0.224745i | 0.994936 | − | 0.100509i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.44949 | + | 1.44949i | −0.547856 | + | 0.547856i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) |
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949i | 0.738549i | 0.929320 | + | 0.369274i | \(0.120394\pi\) | ||||
−0.929320 | + | 0.369274i | \(0.879606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 2.00000i | 0.554700 | − | 0.554700i | −0.373094 | − | 0.927794i | \(-0.621703\pi\) |
0.927794 | + | 0.373094i | \(0.121703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.449490 | + | 0.449490i | 0.109017 | + | 0.109017i | 0.759511 | − | 0.650494i | \(-0.225438\pi\) |
−0.650494 | + | 0.759511i | \(0.725438\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.449490 | + | 0.449490i | 0.0937251 | + | 0.0937251i | 0.752415 | − | 0.658690i | \(-0.228889\pi\) |
−0.658690 | + | 0.752415i | \(0.728889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89898 | − | 1.00000i | 0.979796 | − | 0.200000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.449490i | − | 0.0834681i | −0.999129 | − | 0.0417341i | \(-0.986712\pi\) | ||
0.999129 | − | 0.0417341i | \(-0.0132882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.89898i | 1.59830i | 0.601129 | + | 0.799152i | \(0.294718\pi\) | ||||
−0.601129 | + | 0.799152i | \(0.705282\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.89898 | + | 3.55051i | −0.490017 | + | 0.600146i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.89898 | + | 2.89898i | 0.476589 | + | 0.476589i | 0.904039 | − | 0.427450i | \(-0.140588\pi\) |
−0.427450 | + | 0.904039i | \(0.640588\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89898 | −0.765092 | −0.382546 | − | 0.923936i | \(-0.624953\pi\) | ||||
−0.382546 | + | 0.923936i | \(0.624953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | + | 6.00000i | 0.914991 | + | 0.914991i | 0.996660 | − | 0.0816682i | \(-0.0260248\pi\) |
−0.0816682 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.34847 | − | 9.34847i | 1.36361 | − | 1.36361i | 0.494353 | − | 0.869261i | \(-0.335405\pi\) |
0.869261 | − | 0.494353i | \(-0.164595\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.79796i | 0.399708i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.89898 | + | 2.89898i | −0.398205 | + | 0.398205i | −0.877600 | − | 0.479394i | \(-0.840856\pi\) |
0.479394 | + | 0.877600i | \(0.340856\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.550510 | + | 5.44949i | 0.0742308 | + | 0.734809i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.3485 | −1.47744 | −0.738722 | − | 0.674010i | \(-0.764571\pi\) | ||||
−0.738722 | + | 0.674010i | \(0.764571\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7980 | 1.51057 | 0.755287 | − | 0.655394i | \(-0.227498\pi\) | ||||
0.755287 | + | 0.655394i | \(0.227498\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | − | 4.89898i | 0.496139 | − | 0.607644i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.89898 | + | 6.89898i | −0.842844 | + | 0.842844i | −0.989228 | − | 0.146383i | \(-0.953237\pi\) |
0.146383 | + | 0.989228i | \(0.453237\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.89898 | − | 7.89898i | 0.924506 | − | 0.924506i | −0.0728382 | − | 0.997344i | \(-0.523206\pi\) |
0.997344 | + | 0.0728382i | \(0.0232057\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.55051 | − | 3.55051i | −0.404618 | − | 0.404618i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.10102 | 0.348892 | 0.174446 | − | 0.984667i | \(-0.444187\pi\) | ||||
0.174446 | + | 0.984667i | \(0.444187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.55051 | + | 5.55051i | 0.609248 | + | 0.609248i | 0.942749 | − | 0.333502i | \(-0.108230\pi\) |
−0.333502 | + | 0.942749i | \(0.608230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.10102 | + | 0.898979i | 0.119422 | + | 0.0975080i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000i | 1.27200i | 0.771690 | + | 0.635999i | \(0.219412\pi\) | ||||
−0.771690 | + | 0.635999i | \(0.780588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.79796i | 0.607791i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.44949 | − | 0.449490i | 0.456508 | − | 0.0461167i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | + | 3.00000i | 0.304604 | + | 0.304604i | 0.842812 | − | 0.538208i | \(-0.180899\pi\) |
−0.538208 | + | 0.842812i | \(0.680899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.44949 | −0.840756 | −0.420378 | − | 0.907349i | \(-0.638102\pi\) | ||||
−0.420378 | + | 0.907349i | \(0.638102\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.550510 | − | 0.550510i | −0.0542434 | − | 0.0542434i | 0.679465 | − | 0.733708i | \(-0.262212\pi\) |
−0.733708 | + | 0.679465i | \(0.762212\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.34847 | + | 7.34847i | −0.710403 | + | 0.710403i | −0.966620 | − | 0.256216i | \(-0.917524\pi\) |
0.256216 | + | 0.966620i | \(0.417524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.7980i | − | 1.13004i | −0.825077 | − | 0.565020i | \(-0.808869\pi\) | ||
0.825077 | − | 0.565020i | \(-0.191131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.44949 | − | 8.44949i | 0.794861 | − | 0.794861i | −0.187419 | − | 0.982280i | \(-0.560012\pi\) |
0.982280 | + | 0.187419i | \(0.0600122\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.10102 | + | 0.898979i | 0.102671 | + | 0.0838303i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.30306 | −0.119451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6742 | − | 3.32577i | 0.954733 | − | 0.297465i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.44949 | − | 7.44949i | 0.661035 | − | 0.661035i | −0.294589 | − | 0.955624i | \(-0.595183\pi\) |
0.955624 | + | 0.294589i | \(0.0951827\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.44949i | 0.563495i | 0.959489 | + | 0.281747i | \(0.0909140\pi\) | ||||
−0.959489 | + | 0.281747i | \(0.909086\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.89898 | + | 2.89898i | −0.251373 | + | 0.251373i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.44949 | − | 4.44949i | −0.380146 | − | 0.380146i | 0.491009 | − | 0.871155i | \(-0.336628\pi\) |
−0.871155 | + | 0.491009i | \(0.836628\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7980 | −1.33997 | −0.669983 | − | 0.742377i | \(-0.733698\pi\) | ||||
−0.669983 | + | 0.742377i | \(0.733698\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.89898 | + | 4.89898i | 0.409673 | + | 0.409673i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.101021 | − | 1.00000i | −0.00838930 | − | 0.0830455i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.4495i | 1.67529i | 0.546217 | + | 0.837644i | \(0.316067\pi\) | ||||
−0.546217 | + | 0.837644i | \(0.683933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.79796i | − | 0.309074i | −0.987987 | − | 0.154537i | \(-0.950611\pi\) | ||
0.987987 | − | 0.154537i | \(-0.0493885\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | + | 19.7980i | 0.160644 | + | 1.59021i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.89898 | + | 4.89898i | 0.390981 | + | 0.390981i | 0.875037 | − | 0.484056i | \(-0.160837\pi\) |
−0.484056 | + | 0.875037i | \(0.660837\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.30306 | −0.102696 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.89898 | + | 8.89898i | 0.697022 | + | 0.697022i | 0.963767 | − | 0.266745i | \(-0.0859482\pi\) |
−0.266745 | + | 0.963767i | \(0.585948\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.5505 | − | 11.5505i | 0.893805 | − | 0.893805i | −0.101074 | − | 0.994879i | \(-0.532228\pi\) |
0.994879 | + | 0.101074i | \(0.0322278\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.2474 | − | 16.2474i | 1.23527 | − | 1.23527i | 0.273358 | − | 0.961912i | \(-0.411866\pi\) |
0.961912 | − | 0.273358i | \(-0.0881345\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.65153 | + | 8.55051i | −0.427216 | + | 0.646358i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.2474 | −1.81234 | −0.906170 | − | 0.422914i | \(-0.861007\pi\) | ||||
−0.906170 | + | 0.422914i | \(0.861007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.10102 | + | 5.79796i | 0.522077 | + | 0.426274i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.10102 | + | 1.10102i | −0.0805146 | + | 0.0805146i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 20.8990i | − | 1.51220i | −0.654458 | − | 0.756099i | \(-0.727103\pi\) | ||
0.654458 | − | 0.756099i | \(-0.272897\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.89898 | + | 9.89898i | −0.712544 | + | 0.712544i | −0.967067 | − | 0.254523i | \(-0.918082\pi\) |
0.254523 | + | 0.967067i | \(0.418082\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.79796 | − | 7.79796i | −0.555582 | − | 0.555582i | 0.372465 | − | 0.928046i | \(-0.378513\pi\) |
−0.928046 | + | 0.372465i | \(0.878513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7980 | 1.11989 | 0.559944 | − | 0.828531i | \(-0.310823\pi\) | ||||
0.559944 | + | 0.828531i | \(0.310823\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.651531 | + | 0.651531i | 0.0457285 | + | 0.0457285i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.8990 | + | 1.10102i | −0.761218 | + | 0.0768986i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.89898i | 0.338869i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.5959i | − | 1.21135i | −0.795711 | − | 0.605676i | \(-0.792903\pi\) | ||
0.795711 | − | 0.605676i | \(-0.207097\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.6969 | + | 12.0000i | 1.00232 | + | 0.818393i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.8990 | − | 12.8990i | −0.875640 | − | 0.875640i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.79796 | 0.120944 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3485 | − | 18.3485i | −1.22870 | − | 1.22870i | −0.964454 | − | 0.264250i | \(-0.914876\pi\) |
−0.264250 | − | 0.964454i | \(-0.585124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.10102 | − | 3.10102i | 0.205822 | − | 0.205822i | −0.596667 | − | 0.802489i | \(-0.703509\pi\) |
0.802489 | + | 0.596667i | \(0.203509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000i | 0.660819i | 0.943838 | + | 0.330409i | \(0.107187\pi\) | ||||
−0.943838 | + | 0.330409i | \(0.892813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.34847 | + | 9.34847i | −0.612439 | + | 0.612439i | −0.943581 | − | 0.331142i | \(-0.892566\pi\) |
0.331142 | + | 0.943581i | \(0.392566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.6969 | − | 22.8990i | 1.21965 | − | 1.49376i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.2020 | −0.659915 | −0.329958 | − | 0.943996i | \(-0.607034\pi\) | ||||
−0.329958 | + | 0.943996i | \(0.607034\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7980 | −0.888805 | −0.444402 | − | 0.895827i | \(-0.646584\pi\) | ||||
−0.444402 | + | 0.895827i | \(0.646584\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.628827 | + | 6.22474i | 0.0401743 | + | 0.397684i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | − | 4.00000i | 0.254514 | − | 0.254514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 17.1464i | − | 1.08227i | −0.840935 | − | 0.541136i | \(-0.817994\pi\) | ||
0.840935 | − | 0.541136i | \(-0.182006\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.10102 | + | 1.10102i | −0.0692206 | + | 0.0692206i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.3485 | − | 21.3485i | −1.33168 | − | 1.33168i | −0.903867 | − | 0.427814i | \(-0.859284\pi\) |
−0.427814 | − | 0.903867i | \(-0.640716\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.40408 | −0.522204 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.24745 | − | 6.24745i | −0.385234 | − | 0.385234i | 0.487749 | − | 0.872984i | \(-0.337818\pi\) |
−0.872984 | + | 0.487749i | \(0.837818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.79796 | + | 7.10102i | −0.356166 | + | 0.436212i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.44949i | 0.271290i | 0.990757 | + | 0.135645i | \(0.0433107\pi\) | ||||
−0.990757 | + | 0.135645i | \(0.956689\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.20204i | − | 0.255256i | −0.991822 | − | 0.127628i | \(-0.959264\pi\) | ||
0.991822 | − | 0.127628i | \(-0.0407363\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.44949 | + | 12.0000i | 0.147710 | + | 0.723627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.69694 | − | 8.69694i | −0.522548 | − | 0.522548i | 0.395792 | − | 0.918340i | \(-0.370470\pi\) |
−0.918340 | + | 0.395792i | \(0.870470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.6969 | −1.11537 | −0.557683 | − | 0.830054i | \(-0.688309\pi\) | ||||
−0.557683 | + | 0.830054i | \(0.688309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.69694 | − | 8.69694i | −0.516979 | − | 0.516979i | 0.399677 | − | 0.916656i | \(-0.369122\pi\) |
−0.916656 | + | 0.399677i | \(0.869122\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.10102 | − | 7.10102i | 0.419160 | − | 0.419160i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.5959i | − | 0.976230i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.89898 | + | 6.89898i | −0.403043 | + | 0.403043i | −0.879304 | − | 0.476261i | \(-0.841992\pi\) |
0.476261 | + | 0.879304i | \(0.341992\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.2474 | + | 2.55051i | −1.46996 | + | 0.148496i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.79796 | 0.103979 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.3939 | −1.00257 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.2474 | − | 2.65153i | 1.50292 | − | 0.151826i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.79796 | − | 7.79796i | 0.445053 | − | 0.445053i | −0.448653 | − | 0.893706i | \(-0.648096\pi\) |
0.893706 | + | 0.448653i | \(0.148096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.79796i | − | 0.328772i | −0.986396 | − | 0.164386i | \(-0.947436\pi\) | ||
0.986396 | − | 0.164386i | \(-0.0525643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.89898 | + | 7.89898i | −0.446477 | + | 0.446477i | −0.894181 | − | 0.447705i | \(-0.852242\pi\) |
0.447705 | + | 0.894181i | \(0.352242\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.65153 | − | 8.65153i | −0.485918 | − | 0.485918i | 0.421097 | − | 0.907016i | \(-0.361645\pi\) |
−0.907016 | + | 0.421097i | \(0.861645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.10102 | 0.0616453 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.898979 | + | 0.898979i | 0.0500206 | + | 0.0500206i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.79796 | − | 11.7980i | 0.432553 | − | 0.654433i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.1010i | 1.49413i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 18.0000i | − | 0.989369i | −0.869072 | − | 0.494685i | \(-0.835284\pi\) | ||
0.869072 | − | 0.494685i | \(-0.164716\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.7980 | + | 16.8990i | −0.753863 | + | 0.923290i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.10102 | + | 8.10102i | 0.441291 | + | 0.441291i | 0.892446 | − | 0.451155i | \(-0.148988\pi\) |
−0.451155 | + | 0.892446i | \(0.648988\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.7980 | −1.18043 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2020 | − | 14.2020i | −0.766838 | − | 0.766838i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0000 | − | 12.0000i | 0.644194 | − | 0.644194i | −0.307390 | − | 0.951584i | \(-0.599456\pi\) |
0.951584 | + | 0.307390i | \(0.0994556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.5959i | 1.15600i | 0.816036 | + | 0.578001i | \(0.196167\pi\) | ||||
−0.816036 | + | 0.578001i | \(0.803833\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.2474 | − | 18.2474i | 0.971214 | − | 0.971214i | −0.0283834 | − | 0.999597i | \(-0.509036\pi\) |
0.999597 | + | 0.0283834i | \(0.00903593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.69694 | − | 26.6969i | −0.143139 | − | 1.41693i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.6969 | −0.564563 | −0.282281 | − | 0.959332i | \(-0.591091\pi\) | ||||
−0.282281 | + | 0.959332i | \(0.591091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.7980 | − | 19.3485i | 0.826903 | − | 1.01275i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.34847 | − | 8.34847i | 0.435787 | − | 0.435787i | −0.454805 | − | 0.890591i | \(-0.650291\pi\) |
0.890591 | + | 0.454805i | \(0.150291\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 8.40408i | − | 0.436318i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.10102 | + | 7.10102i | −0.367677 | + | 0.367677i | −0.866629 | − | 0.498952i | \(-0.833718\pi\) |
0.498952 | + | 0.866629i | \(0.333718\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.898979 | − | 0.898979i | −0.0462998 | − | 0.0462998i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.202041 | −0.0103782 | −0.00518908 | − | 0.999987i | \(-0.501652\pi\) | ||||
−0.00518908 | + | 0.999987i | \(0.501652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.34847 | + | 9.34847i | 0.477684 | + | 0.477684i | 0.904390 | − | 0.426706i | \(-0.140326\pi\) |
−0.426706 | + | 0.904390i | \(0.640326\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.69694 | − | 7.10102i | −0.443237 | − | 0.361902i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.1464i | 1.78199i | 0.454009 | + | 0.890997i | \(0.349994\pi\) | ||||
−0.454009 | + | 0.890997i | \(0.650006\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.404082i | 0.0204353i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.89898 | − | 0.696938i | 0.347125 | − | 0.0350668i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.5959 | − | 27.5959i | −1.38500 | − | 1.38500i | −0.835483 | − | 0.549517i | \(-0.814812\pi\) |
−0.549517 | − | 0.835483i | \(-0.685188\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.5959 | 1.17832 | 0.589162 | − | 0.808015i | \(-0.299458\pi\) | ||||
0.589162 | + | 0.808015i | \(0.299458\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.7980 | + | 17.7980i | 0.886579 | + | 0.886579i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.10102 | + | 7.10102i | −0.351985 | + | 0.351985i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.0000i | 0.988936i | 0.869196 | + | 0.494468i | \(0.164637\pi\) | ||||
−0.869196 | + | 0.494468i | \(0.835363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.4495 | − | 16.4495i | 0.809426 | − | 0.809426i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.5959 | + | 11.1010i | 0.667397 | + | 0.544928i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.7526 | −0.574150 | −0.287075 | − | 0.957908i | \(-0.592683\pi\) | ||||
−0.287075 | + | 0.957908i | \(0.592683\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.65153 | + | 1.75255i | 0.128618 | + | 0.0850112i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.1010 | + | 17.1010i | −0.827576 | + | 0.827576i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.4949i | 0.987204i | 0.869688 | + | 0.493602i | \(0.164320\pi\) | ||||
−0.869688 | + | 0.493602i | \(0.835680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.79796 | − | 2.79796i | 0.134461 | − | 0.134461i | −0.636673 | − | 0.771134i | \(-0.719690\pi\) |
0.771134 | + | 0.636673i | \(0.219690\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.898979 | + | 0.898979i | 0.0430040 | + | 0.0430040i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7980 | 0.944905 | 0.472453 | − | 0.881356i | \(-0.343369\pi\) | ||||
0.472453 | + | 0.881356i | \(0.343369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.8990 | + | 12.8990i | 0.612849 | + | 0.612849i | 0.943687 | − | 0.330838i | \(-0.107332\pi\) |
−0.330838 | + | 0.943687i | \(0.607332\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.69694 | + | 26.6969i | 0.127847 | + | 1.26556i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.4949i | − | 0.967214i | −0.875285 | − | 0.483607i | \(-0.839326\pi\) | ||
0.875285 | − | 0.483607i | \(-0.160674\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.0000i | − | 0.565058i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.30306 | + | 12.8990i | 0.0610885 | + | 0.604713i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.797959 | + | 0.797959i | 0.0373269 | + | 0.0373269i | 0.725524 | − | 0.688197i | \(-0.241598\pi\) |
−0.688197 | + | 0.725524i | \(0.741598\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.75255 | −0.0816245 | −0.0408122 | − | 0.999167i | \(-0.512995\pi\) | ||||
−0.0408122 | + | 0.999167i | \(0.512995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.2474 | − | 23.2474i | −1.08040 | − | 1.08040i | −0.996472 | − | 0.0839288i | \(-0.973253\pi\) |
−0.0839288 | − | 0.996472i | \(-0.526747\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.1464 | − | 21.1464i | 0.978540 | − | 0.978540i | −0.0212345 | − | 0.999775i | \(-0.506760\pi\) |
0.999775 | + | 0.0212345i | \(0.00675967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 20.0000i | − | 0.923514i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.6969 | + | 14.6969i | −0.675766 | + | 0.675766i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.79796 | − | 2.00000i | 0.449561 | − | 0.0917663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −41.3939 | −1.89133 | −0.945667 | − | 0.325136i | \(-0.894590\pi\) | ||||
−0.945667 | + | 0.325136i | \(0.894590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.5959 | 0.528728 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.34847 | + | 6.00000i | 0.333677 | + | 0.272446i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.4495 | − | 23.4495i | 1.06260 | − | 1.06260i | 0.0646926 | − | 0.997905i | \(-0.479393\pi\) |
0.997905 | − | 0.0646926i | \(-0.0206067\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.6515i | − | 0.570956i | −0.958385 | − | 0.285478i | \(-0.907848\pi\) | ||
0.958385 | − | 0.285478i | \(-0.0921523\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.202041 | − | 0.202041i | 0.00909947 | − | 0.00909947i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.3939 | + | 17.3939i | 0.780222 | + | 0.780222i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.5959 | −1.32490 | −0.662448 | − | 0.749108i | \(-0.730482\pi\) | ||||
−0.662448 | + | 0.749108i | \(0.730482\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.2474 | + | 26.2474i | 1.17032 | + | 1.17032i | 0.982134 | + | 0.188182i | \(0.0602594\pi\) |
0.188182 | + | 0.982134i | \(0.439741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.7980 | + | 1.89898i | −0.836498 | + | 0.0845035i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16.0454i | − | 0.711200i | −0.934638 | − | 0.355600i | \(-0.884277\pi\) | ||
0.934638 | − | 0.355600i | \(-0.115723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.8990i | 1.01299i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.34847 | − | 1.10102i | −0.0594207 | − | 0.0485168i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.8990 | + | 22.8990i | 1.00710 | + | 1.00710i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.4949 | −1.59887 | −0.799435 | − | 0.600752i | \(-0.794868\pi\) | ||||
−0.799435 | + | 0.600752i | \(0.794868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.8990 | + | 26.8990i | 1.17621 | + | 1.17621i | 0.980702 | + | 0.195508i | \(0.0626356\pi\) |
0.195508 | + | 0.980702i | \(0.437364\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.00000 | + | 4.00000i | −0.174243 | + | 0.174243i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.5959i | − | 0.982431i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.79796 | + | 9.79796i | −0.424397 | + | 0.424397i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.6969 | + | 18.0000i | −0.635404 | + | 0.778208i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.85357 | −0.295204 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7980 | 0.679207 | 0.339604 | − | 0.940569i | \(-0.389707\pi\) | ||||
0.339604 | + | 0.940569i | \(0.389707\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.65153 | − | 26.2474i | −0.113579 | − | 1.12432i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.5959 | + | 25.5959i | −1.09440 | + | 1.09440i | −0.0993499 | + | 0.995053i | \(0.531676\pi\) |
−0.995053 | + | 0.0993499i | \(0.968324\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.898979i | − | 0.0382978i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.49490 | + | 4.49490i | −0.191142 | + | 0.191142i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.10102 | − | 1.10102i | −0.0466517 | − | 0.0466517i | 0.683396 | − | 0.730048i | \(-0.260502\pi\) |
−0.730048 | + | 0.683396i | \(0.760502\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.20204 | − | 2.20204i | −0.0928050 | − | 0.0928050i | 0.659180 | − | 0.751985i | \(-0.270903\pi\) |
−0.751985 | + | 0.659180i | \(0.770903\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.8990 | − | 20.6969i | 0.710945 | − | 0.870727i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.3939i | 1.39994i | 0.714170 | + | 0.699972i | \(0.246804\pi\) | ||||
−0.714170 | + | 0.699972i | \(0.753196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.59592i | 0.234182i | 0.993121 | + | 0.117091i | \(0.0373569\pi\) | ||||
−0.993121 | + | 0.117091i | \(0.962643\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.65153 | + | 1.75255i | 0.110576 | + | 0.0730864i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.6969 | + | 11.6969i | 0.486950 | + | 0.486950i | 0.907342 | − | 0.420392i | \(-0.138108\pi\) |
−0.420392 | + | 0.907342i | \(0.638108\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.0908 | −0.667560 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.10102 | − | 7.10102i | −0.294094 | − | 0.294094i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.1464 | − | 25.1464i | 1.03790 | − | 1.03790i | 0.0386514 | − | 0.999253i | \(-0.487694\pi\) |
0.999253 | − | 0.0386514i | \(-0.0123062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.7980i | 0.733352i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.5505 | − | 19.5505i | 0.802843 | − | 0.802843i | −0.180696 | − | 0.983539i | \(-0.557835\pi\) |
0.983539 | + | 0.180696i | \(0.0578349\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.89898 | + | 0.292856i | −0.118847 | + | 0.0120059i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.4949 | −1.16427 | −0.582135 | − | 0.813092i | \(-0.697782\pi\) | ||||
−0.582135 | + | 0.813092i | \(0.697782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.0000 | 1.38689 | 0.693444 | − | 0.720510i | \(-0.256092\pi\) | ||||
0.693444 | + | 0.720510i | \(0.256092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.1237 | − | 1.12372i | 0.452244 | − | 0.0456859i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.55051 | − | 6.55051i | 0.265877 | − | 0.265877i | −0.561559 | − | 0.827436i | \(-0.689798\pi\) |
0.827436 | + | 0.561559i | \(0.189798\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 37.3939i | − | 1.51279i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5959 | − | 19.5959i | 0.791472 | − | 0.791472i | −0.190262 | − | 0.981733i | \(-0.560934\pi\) |
0.981733 | + | 0.190262i | \(0.0609337\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.34847 | − | 9.34847i | −0.376355 | − | 0.376355i | 0.493430 | − | 0.869785i | \(-0.335743\pi\) |
−0.869785 | + | 0.493430i | \(0.835743\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.3939 | −1.26183 | −0.630913 | − | 0.775853i | \(-0.717320\pi\) | ||||
−0.630913 | + | 0.775853i | \(0.717320\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.3939 | − | 17.3939i | −0.696871 | − | 0.696871i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0000 | − | 9.79796i | 0.920000 | − | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.60612i | 0.103913i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.8990i | 0.513500i | 0.966478 | + | 0.256750i | \(0.0826517\pi\) | ||||
−0.966478 | + | 0.256750i | \(0.917348\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.8990 | − | 18.2474i | 0.591248 | − | 0.724128i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.59592 | + | 5.59592i | 0.221718 | + | 0.221718i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.7980 | −1.33494 | −0.667470 | − | 0.744637i | \(-0.732623\pi\) | ||||
−0.667470 | + | 0.744637i | \(0.732623\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.1010 | + | 23.1010i | 0.911015 | + | 0.911015i | 0.996352 | − | 0.0853368i | \(-0.0271966\pi\) |
−0.0853368 | + | 0.996352i | \(0.527197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.2474 | + | 10.2474i | −0.402869 | + | 0.402869i | −0.879243 | − | 0.476374i | \(-0.841951\pi\) |
0.476374 | + | 0.879243i | \(0.341951\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 27.7980i | − | 1.09117i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.55051 | − | 1.55051i | 0.0606762 | − | 0.0606762i | −0.676118 | − | 0.736794i | \(-0.736339\pi\) |
0.736794 | + | 0.676118i | \(0.236339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.44949 | + | 14.3485i | 0.0566363 | + | 0.560641i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.2474 | 1.56782 | 0.783909 | − | 0.620876i | \(-0.213223\pi\) | ||||
0.783909 | + | 0.620876i | \(0.213223\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.20204 | 0.319022 | 0.159511 | − | 0.987196i | \(-0.449008\pi\) | ||||
0.159511 | + | 0.987196i | \(0.449008\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.79796 | + | 7.10102i | −0.224835 | + | 0.275366i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.202041 | − | 0.202041i | 0.00782306 | − | 0.00782306i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.8990i | 1.11563i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.79796 | − | 8.79796i | 0.339136 | − | 0.339136i | −0.516906 | − | 0.856042i | \(-0.672916\pi\) |
0.856042 | + | 0.516906i | \(0.172916\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.65153 | + | 4.65153i | 0.178773 | + | 0.178773i | 0.790821 | − | 0.612048i | \(-0.209654\pi\) |
−0.612048 | + | 0.790821i | \(0.709654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.69694 | −0.333758 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.6515 | − | 12.6515i | −0.484097 | − | 0.484097i | 0.422340 | − | 0.906437i | \(-0.361209\pi\) |
−0.906437 | + | 0.422340i | \(0.861209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.8990 | − | 8.89898i | −0.416429 | − | 0.340013i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.5959i | 0.441769i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 7.79796i | − | 0.296648i | −0.988939 | − | 0.148324i | \(-0.952612\pi\) | ||
0.988939 | − | 0.148324i | \(-0.0473879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.1464 | + | 3.55051i | −1.33318 | + | 0.134679i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.20204 | − | 2.20204i | −0.0834083 | − | 0.0834083i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.7423 | 1.01004 | 0.505022 | − | 0.863106i | \(-0.331484\pi\) | ||||
0.505022 | + | 0.863106i | \(0.331484\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.79796 | + | 5.79796i | 0.218674 | + | 0.218674i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.2474 | − | 12.2474i | 0.460613 | − | 0.460613i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 8.20204i | − | 0.308034i | −0.988068 | − | 0.154017i | \(-0.950779\pi\) | ||
0.988068 | − | 0.154017i | \(-0.0492211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.00000 | + | 4.00000i | −0.149801 | + | 0.149801i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | + | 9.79796i | 0.448775 | + | 0.366423i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.7980 | 0.962102 | 0.481051 | − | 0.876693i | \(-0.340255\pi\) | ||||
0.481051 | + | 0.876693i | \(0.340255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.59592 | 0.0594351 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.449490 | − | 2.20204i | −0.0166936 | − | 0.0817818i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.14643 | + | 8.14643i | −0.302134 | + | 0.302134i | −0.841848 | − | 0.539714i | \(-0.818532\pi\) |
0.539714 | + | 0.841848i | \(0.318532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.39388i | 0.199500i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.1010 | − | 13.1010i | 0.483897 | − | 0.483897i | −0.422477 | − | 0.906374i | \(-0.638839\pi\) |
0.906374 | + | 0.422477i | \(0.138839\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.8990 | − | 16.8990i | −0.622482 | − | 0.622482i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.3939 | 1.00770 | 0.503850 | − | 0.863791i | \(-0.331916\pi\) | ||||
0.503850 | + | 0.863791i | \(0.331916\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.44949 | − | 8.44949i | −0.309982 | − | 0.309982i | 0.534921 | − | 0.844902i | \(-0.320342\pi\) |
−0.844902 | + | 0.534921i | \(0.820342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.59592 | + | 45.4949i | 0.168381 | + | 1.66680i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 21.3031i | − | 0.778397i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.6969i | 1.55803i | 0.627003 | + | 0.779017i | \(0.284281\pi\) | ||||
−0.627003 | + | 0.779017i | \(0.715719\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.853572 | − | 8.44949i | −0.0310647 | − | 0.307508i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.6969 | + | 16.6969i | 0.606861 | + | 0.606861i | 0.942124 | − | 0.335264i | \(-0.108825\pi\) |
−0.335264 | + | 0.942124i | \(0.608825\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.6969 | 1.25776 | 0.628882 | − | 0.777501i | \(-0.283513\pi\) | ||||
0.628882 | + | 0.777501i | \(0.283513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.1010 | + | 17.1010i | 0.619099 | + | 0.619099i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.6969 | + | 22.6969i | −0.819539 | + | 0.819539i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.1918i | 0.908441i | 0.890889 | + | 0.454220i | \(0.150082\pi\) | ||||
−0.890889 | + | 0.454220i | \(0.849918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.3485 | + | 23.3485i | −0.839786 | + | 0.839786i | −0.988830 | − | 0.149044i | \(-0.952380\pi\) |
0.149044 | + | 0.988830i | \(0.452380\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.89898 | + | 43.5959i | 0.319661 | + | 1.56601i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.79796 | −0.351048 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.3939 | 1.05180 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.0000 | + | 9.79796i | 0.428298 | + | 0.349704i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.1010 | + | 25.1010i | −0.894755 | + | 0.894755i | −0.994966 | − | 0.100211i | \(-0.968048\pi\) |
0.100211 | + | 0.994966i | \(0.468048\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.4949i | 0.870938i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.5959 | − | 23.5959i | 0.837916 | − | 0.837916i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.4495 | − | 10.4495i | −0.370140 | − | 0.370140i | 0.497388 | − | 0.867528i | \(-0.334292\pi\) |
−0.867528 | + | 0.497388i | \(0.834292\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.40408 | 0.297315 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.3485 | + | 19.3485i | 0.682793 | + | 0.682793i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.89898 | + | 0.292856i | −0.102176 | + | 0.0103218i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9.79796i | − | 0.344478i | −0.985055 | − | 0.172239i | \(-0.944900\pi\) | ||
0.985055 | − | 0.172239i | \(-0.0551001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.7980i | 0.554741i | 0.960763 | + | 0.277371i | \(0.0894630\pi\) | ||||
−0.960763 | + | 0.277371i | \(0.910537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.7980 | + | 17.7980i | 0.763549 | + | 0.623435i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | + | 12.0000i | 0.419827 | + | 0.419827i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.55051 | −0.263515 | −0.131757 | − | 0.991282i | \(-0.542062\pi\) | ||||
−0.131757 | + | 0.991282i | \(0.542062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3485 | − | 10.3485i | −0.360725 | − | 0.360725i | 0.503355 | − | 0.864080i | \(-0.332099\pi\) |
−0.864080 | + | 0.503355i | \(0.832099\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.00000 | + | 8.00000i | −0.278187 | + | 0.278187i | −0.832385 | − | 0.554198i | \(-0.813025\pi\) |
0.554198 | + | 0.832385i | \(0.313025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.79796i | − | 0.131909i | −0.997823 | − | 0.0659543i | \(-0.978991\pi\) | ||
0.997823 | − | 0.0659543i | \(-0.0210092\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.25765 | + | 1.25765i | −0.0435751 | + | 0.0435751i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.1010 | − | 28.2929i | 0.799444 | − | 0.979115i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.69694 | 0.0931087 | 0.0465543 | − | 0.998916i | \(-0.485176\pi\) | ||||
0.0465543 | + | 0.998916i | \(0.485176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7980 | 0.993033 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.12372 | + | 11.1237i | 0.0386573 | + | 0.382668i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.24745 | + | 7.24745i | −0.249025 | + | 0.249025i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.60612i | 0.0893367i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.7980 | + | 21.7980i | −0.746348 | + | 0.746348i | −0.973791 | − | 0.227443i | \(-0.926963\pi\) |
0.227443 | + | 0.973791i | \(0.426963\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.5505 | + | 23.5505i | 0.804470 | + | 0.804470i | 0.983791 | − | 0.179321i | \(-0.0573899\pi\) |
−0.179321 | + | 0.983791i | \(0.557390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.20204 | −0.143372 | −0.0716859 | − | 0.997427i | \(-0.522838\pi\) | ||||
−0.0716859 | + | 0.997427i | \(0.522838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.3485 | + | 21.3485i | 0.726710 | + | 0.726710i | 0.969963 | − | 0.243253i | \(-0.0782144\pi\) |
−0.243253 | + | 0.969963i | \(0.578214\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.4949 | − | 39.7980i | 1.10486 | − | 1.35317i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.59592i | 0.257674i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.5959i | 0.935052i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.6515 | + | 20.2929i | −0.360087 | + | 0.686024i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.10102 | − | 7.10102i | −0.239784 | − | 0.239784i | 0.576976 | − | 0.816761i | \(-0.304232\pi\) |
−0.816761 | + | 0.576976i | \(0.804232\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.7980 | 1.81250 | 0.906250 | − | 0.422743i | \(-0.138933\pi\) | ||||
0.906250 | + | 0.422743i | \(0.138933\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.6969 | + | 22.6969i | 0.763813 | + | 0.763813i | 0.977009 | − | 0.213197i | \(-0.0683875\pi\) |
−0.213197 | + | 0.977009i | \(0.568387\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.14643 | + | 3.14643i | −0.105647 | + | 0.105647i | −0.757954 | − | 0.652308i | \(-0.773801\pi\) |
0.652308 | + | 0.757954i | \(0.273801\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.5959i | 0.724304i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.6969 | − | 18.6969i | 0.625669 | − | 0.625669i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −53.9444 | + | 5.44949i | −1.80316 | + | 0.182156i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00000 | 0.133407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.60612 | −0.0868225 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.2474 | + | 2.24745i | −0.739530 | + | 0.0747077i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.79796 | − | 9.79796i | 0.325336 | − | 0.325336i | −0.525474 | − | 0.850810i | \(-0.676112\pi\) |
0.850810 | + | 0.525474i | \(0.176112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 40.0908i | − | 1.32827i | −0.747614 | − | 0.664134i | \(-0.768800\pi\) | ||
0.747614 | − | 0.664134i | \(-0.231200\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5959 | + | 13.5959i | −0.449959 | + | 0.449959i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.34847 | − | 9.34847i | −0.308714 | − | 0.308714i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.8990 | 1.34913 | 0.674566 | − | 0.738214i | \(-0.264331\pi\) | ||||
0.674566 | + | 0.738214i | \(0.264331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.0000 | − | 24.0000i | −0.789970 | − | 0.789970i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.1010 | + | 11.3031i | 0.562278 | + | 0.371642i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 56.0908i | − | 1.84028i | −0.391590 | − | 0.920140i | \(-0.628075\pi\) | ||
0.391590 | − | 0.920140i | \(-0.371925\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.59592i | 0.183399i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.20204 | + | 2.69694i | −0.0720144 | + | 0.0881993i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.5959 | − | 22.5959i | −0.738176 | − | 0.738176i | 0.234048 | − | 0.972225i | \(-0.424803\pi\) |
−0.972225 | + | 0.234048i | \(0.924803\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.1464 | 0.884948 | 0.442474 | − | 0.896781i | \(-0.354101\pi\) | ||||
0.442474 | + | 0.896781i | \(0.354101\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.20204 | − | 2.20204i | −0.0717083 | − | 0.0717083i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.4949 | + | 20.4949i | −0.665995 | + | 0.665995i | −0.956786 | − | 0.290792i | \(-0.906081\pi\) |
0.290792 | + | 0.956786i | \(0.406081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 31.5959i | − | 1.02565i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.34847 | + | 1.34847i | −0.0436812 | + | 0.0436812i | −0.728610 | − | 0.684929i | \(-0.759833\pi\) |
0.684929 | + | 0.728610i | \(0.259833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.69694 | − | 46.4949i | −0.151989 | − | 1.50454i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.8990 | 0.416530 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −48.1918 | −1.55458 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.7980 | + | 24.2474i | −0.637319 | + | 0.780553i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.34847 | + | 6.34847i | −0.204153 | + | 0.204153i | −0.801777 | − | 0.597624i | \(-0.796112\pi\) |
0.597624 | + | 0.801777i | \(0.296112\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 6.04541i | − | 0.194006i | −0.995284 | − | 0.0970032i | \(-0.969074\pi\) | ||
0.995284 | − | 0.0970032i | \(-0.0309257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.8990 | − | 22.8990i | 0.734108 | − | 0.734108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.4495 | + | 20.4495i | 0.654237 | + | 0.654237i | 0.954010 | − | 0.299773i | \(-0.0969110\pi\) |
−0.299773 | + | 0.954010i | \(0.596911\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.3939 | −0.939432 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.2474 | − | 26.2474i | −0.837164 | − | 0.837164i | 0.151321 | − | 0.988485i | \(-0.451647\pi\) |
−0.988485 | + | 0.151321i | \(0.951647\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.1010 | − | 15.5959i | −0.608609 | − | 0.496927i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.39388i | 0.171515i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24.2020i | − | 0.768803i | −0.923166 | − | 0.384402i | \(-0.874408\pi\) | ||
0.923166 | − | 0.384402i | \(-0.125592\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.1464 | − | 3.55051i | 1.11422 | − | 0.112559i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.2020 | + | 20.2020i | 0.639805 | + | 0.639805i | 0.950507 | − | 0.310702i | \(-0.100564\pi\) |
−0.310702 | + | 0.950507i | \(0.600564\pi\) | |||||||
\(998\) | 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.x.p.127.2 | yes | 4 | |
3.2 | odd | 2 | 1440.2.x.l.127.1 | yes | 4 | ||
4.3 | odd | 2 | 1440.2.x.o.127.2 | yes | 4 | ||
5.3 | odd | 4 | 1440.2.x.o.703.2 | yes | 4 | ||
12.11 | even | 2 | 1440.2.x.k.127.1 | ✓ | 4 | ||
15.8 | even | 4 | 1440.2.x.k.703.1 | yes | 4 | ||
20.3 | even | 4 | inner | 1440.2.x.p.703.2 | yes | 4 | |
60.23 | odd | 4 | 1440.2.x.l.703.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.x.k.127.1 | ✓ | 4 | 12.11 | even | 2 | ||
1440.2.x.k.703.1 | yes | 4 | 15.8 | even | 4 | ||
1440.2.x.l.127.1 | yes | 4 | 3.2 | odd | 2 | ||
1440.2.x.l.703.1 | yes | 4 | 60.23 | odd | 4 | ||
1440.2.x.o.127.2 | yes | 4 | 4.3 | odd | 2 | ||
1440.2.x.o.703.2 | yes | 4 | 5.3 | odd | 4 | ||
1440.2.x.p.127.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1440.2.x.p.703.2 | yes | 4 | 20.3 | even | 4 | inner |