Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(4409,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.4409");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4409.5 | ||
Character | \(\chi\) | \(=\) | 4410.4409 |
Dual form | 4410.2.d.c.4409.6 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.60367 | − | 1.55828i | −0.717184 | − | 0.696884i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.60367 | + | 1.55828i | 0.507125 | + | 0.492772i | ||||
\(11\) | − | 4.10672i | − | 1.23822i | −0.785303 | − | 0.619112i | \(-0.787493\pi\) | ||
0.785303 | − | 0.619112i | \(-0.212507\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.67732 | 0.742555 | 0.371277 | − | 0.928522i | \(-0.378920\pi\) | ||||
0.371277 | + | 0.928522i | \(0.378920\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 1.29539i | − | 0.314178i | −0.987584 | − | 0.157089i | \(-0.949789\pi\) | ||
0.987584 | − | 0.157089i | \(-0.0502110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.96705i | 1.59835i | 0.601097 | + | 0.799176i | \(0.294730\pi\) | ||||
−0.601097 | + | 0.799176i | \(0.705270\pi\) | |||||||
\(20\) | −1.60367 | − | 1.55828i | −0.358592 | − | 0.348442i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.10672i | 0.875556i | ||||||||
\(23\) | 3.53283 | 0.736645 | 0.368323 | − | 0.929698i | \(-0.379932\pi\) | ||||
0.368323 | + | 0.929698i | \(0.379932\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.143525 | + | 4.99794i | 0.0287050 | + | 0.999588i | ||||
\(26\) | −2.67732 | −0.525065 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.22563i | 0.598984i | 0.954099 | + | 0.299492i | \(0.0968172\pi\) | ||||
−0.954099 | + | 0.299492i | \(0.903183\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.38019i | − | 1.50513i | −0.658520 | − | 0.752563i | \(-0.728817\pi\) | ||
0.658520 | − | 0.752563i | \(-0.271183\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.29539i | 0.222158i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.3287i | 1.86243i | 0.364470 | + | 0.931215i | \(0.381250\pi\) | ||||
−0.364470 | + | 0.931215i | \(0.618750\pi\) | |||||||
\(38\) | − | 6.96705i | − | 1.13021i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.60367 | + | 1.55828i | 0.253563 | + | 0.246386i | ||||
\(41\) | 1.99657 | 0.311811 | 0.155906 | − | 0.987772i | \(-0.450170\pi\) | ||||
0.155906 | + | 0.987772i | \(0.450170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0984652i | 0.0150158i | 0.999972 | + | 0.00750790i | \(0.00238986\pi\) | ||||
−0.999972 | + | 0.00750790i | \(0.997610\pi\) | |||||||
\(44\) | − | 4.10672i | − | 0.619112i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.53283 | −0.520887 | ||||||||
\(47\) | 9.68213i | 1.41228i | 0.708071 | + | 0.706142i | \(0.249566\pi\) | ||||
−0.708071 | + | 0.706142i | \(0.750434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.143525 | − | 4.99794i | −0.0202975 | − | 0.706815i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.67732 | 0.371277 | ||||||||
\(53\) | 11.8037 | 1.62136 | 0.810679 | − | 0.585491i | \(-0.199098\pi\) | ||||
0.810679 | + | 0.585491i | \(0.199098\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.39943 | + | 6.58584i | −0.862899 | + | 0.888034i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 3.22563i | − | 0.423546i | ||||||
\(59\) | −0.796801 | −0.103735 | −0.0518673 | − | 0.998654i | \(-0.516517\pi\) | ||||
−0.0518673 | + | 0.998654i | \(0.516517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.69258i | 0.344749i | 0.985031 | + | 0.172375i | \(0.0551440\pi\) | ||||
−0.985031 | + | 0.172375i | \(0.944856\pi\) | |||||||
\(62\) | 8.38019i | 1.06429i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.29354 | − | 4.17201i | −0.532548 | − | 0.517475i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.696631i | − | 0.0851070i | −0.999094 | − | 0.0425535i | \(-0.986451\pi\) | ||
0.999094 | − | 0.0425535i | \(-0.0135493\pi\) | |||||||
\(68\) | − | 1.29539i | − | 0.157089i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.32893i | − | 1.10714i | −0.832802 | − | 0.553570i | \(-0.813265\pi\) | ||
0.832802 | − | 0.553570i | \(-0.186735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.26042 | −0.849768 | −0.424884 | − | 0.905248i | \(-0.639685\pi\) | ||||
−0.424884 | + | 0.905248i | \(0.639685\pi\) | |||||||
\(74\) | − | 11.3287i | − | 1.31694i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.96705i | 0.799176i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.73016 | 0.307168 | 0.153584 | − | 0.988136i | \(-0.450919\pi\) | ||||
0.153584 | + | 0.988136i | \(0.450919\pi\) | |||||||
\(80\) | −1.60367 | − | 1.55828i | −0.179296 | − | 0.174221i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.99657 | −0.220484 | ||||||||
\(83\) | 6.79144i | 0.745457i | 0.927940 | + | 0.372728i | \(0.121578\pi\) | ||||
−0.927940 | + | 0.372728i | \(0.878422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.01858 | + | 2.07738i | −0.218946 | + | 0.225324i | ||||
\(86\) | − | 0.0984652i | − | 0.0106178i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.10672i | 0.437778i | ||||||||
\(89\) | −8.03812 | −0.852039 | −0.426019 | − | 0.904714i | \(-0.640084\pi\) | ||||
−0.426019 | + | 0.904714i | \(0.640084\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.53283 | 0.368323 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 9.68213i | − | 0.998635i | ||||||
\(95\) | 10.8566 | − | 11.1729i | 1.11387 | − | 1.14631i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.29039 | −0.638692 | −0.319346 | − | 0.947638i | \(-0.603463\pi\) | ||||
−0.319346 | + | 0.947638i | \(0.603463\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.143525 | + | 4.99794i | 0.0143525 | + | 0.499794i | ||||
\(101\) | −12.0292 | −1.19695 | −0.598477 | − | 0.801140i | \(-0.704227\pi\) | ||||
−0.598477 | + | 0.801140i | \(0.704227\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.1612 | 1.49388 | 0.746939 | − | 0.664892i | \(-0.231523\pi\) | ||||
0.746939 | + | 0.664892i | \(0.231523\pi\) | |||||||
\(104\) | −2.67732 | −0.262533 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.8037 | −1.14647 | ||||||||
\(107\) | 5.95843 | 0.576023 | 0.288011 | − | 0.957627i | \(-0.407006\pi\) | ||||
0.288011 | + | 0.957627i | \(0.407006\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.1027 | 1.44657 | 0.723287 | − | 0.690547i | \(-0.242630\pi\) | ||||
0.723287 | + | 0.690547i | \(0.242630\pi\) | |||||||
\(110\) | 6.39943 | − | 6.58584i | 0.610161 | − | 0.627935i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.471895 | 0.0443922 | 0.0221961 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221961 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.66549 | − | 5.50513i | −0.528310 | − | 0.513356i | ||||
\(116\) | 3.22563i | 0.299492i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.796801 | 0.0733515 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.86518 | −0.533198 | ||||||||
\(122\) | − | 2.69258i | − | 0.243775i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 8.38019i | − | 0.752563i | ||||||
\(125\) | 7.55802 | − | 8.23871i | 0.676010 | − | 0.736892i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.2712i | − | 0.911426i | −0.890127 | − | 0.455713i | \(-0.849384\pi\) | ||
0.890127 | − | 0.455713i | \(-0.150616\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.29354 | + | 4.17201i | 0.376568 | + | 0.365910i | ||||
\(131\) | −7.93947 | −0.693675 | −0.346838 | − | 0.937925i | \(-0.612744\pi\) | ||||
−0.346838 | + | 0.937925i | \(0.612744\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.696631i | 0.0601797i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.29539i | 0.111079i | ||||||||
\(137\) | 14.2024 | 1.21339 | 0.606695 | − | 0.794935i | \(-0.292495\pi\) | ||||
0.606695 | + | 0.794935i | \(0.292495\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.26467i | − | 0.192087i | −0.995377 | − | 0.0960433i | \(-0.969381\pi\) | ||
0.995377 | − | 0.0960433i | \(-0.0306187\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.32893i | 0.782867i | ||||||||
\(143\) | − | 10.9950i | − | 0.919449i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.02643 | − | 5.17285i | 0.417423 | − | 0.429582i | ||||
\(146\) | 7.26042 | 0.600877 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.3287i | 0.931215i | ||||||||
\(149\) | − | 23.6322i | − | 1.93602i | −0.250906 | − | 0.968012i | \(-0.580728\pi\) | ||
0.250906 | − | 0.968012i | \(-0.419272\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5657 | 1.42948 | 0.714740 | − | 0.699391i | \(-0.246545\pi\) | ||||
0.714740 | + | 0.699391i | \(0.246545\pi\) | |||||||
\(152\) | − | 6.96705i | − | 0.565103i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.0587 | + | 13.4391i | −1.04890 | + | 1.07945i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7736 | 1.25887 | 0.629436 | − | 0.777052i | \(-0.283286\pi\) | ||||
0.629436 | + | 0.777052i | \(0.283286\pi\) | |||||||
\(158\) | −2.73016 | −0.217200 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.60367 | + | 1.55828i | 0.126781 | + | 0.123193i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.18877i | 0.641394i | 0.947182 | + | 0.320697i | \(0.103917\pi\) | ||||
−0.947182 | + | 0.320697i | \(0.896083\pi\) | |||||||
\(164\) | 1.99657 | 0.155906 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 6.79144i | − | 0.527118i | ||||||
\(167\) | 25.5577i | 1.97771i | 0.148866 | + | 0.988857i | \(0.452438\pi\) | ||||
−0.148866 | + | 0.988857i | \(0.547562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.83196 | −0.448613 | ||||||||
\(170\) | 2.01858 | − | 2.07738i | 0.154818 | − | 0.159328i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0984652i | 0.00750790i | ||||||||
\(173\) | 4.41919i | 0.335985i | 0.985788 | + | 0.167992i | \(0.0537284\pi\) | ||||
−0.985788 | + | 0.167992i | \(0.946272\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.10672i | − | 0.309556i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.03812 | 0.602482 | ||||||||
\(179\) | 5.56112i | 0.415657i | 0.978165 | + | 0.207829i | \(0.0666397\pi\) | ||||
−0.978165 | + | 0.207829i | \(0.933360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.88829i | 0.214685i | 0.994222 | + | 0.107343i | \(0.0342342\pi\) | ||||
−0.994222 | + | 0.107343i | \(0.965766\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.53283 | −0.260443 | ||||||||
\(185\) | 17.6533 | − | 18.1675i | 1.29790 | − | 1.33570i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.31981 | −0.389023 | ||||||||
\(188\) | 9.68213i | 0.706142i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.8566 | + | 11.1729i | −0.787622 | + | 0.810565i | ||||
\(191\) | − | 16.5552i | − | 1.19789i | −0.800788 | − | 0.598947i | \(-0.795586\pi\) | ||
0.800788 | − | 0.598947i | \(-0.204414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.8202i | 1.78660i | 0.449465 | + | 0.893298i | \(0.351615\pi\) | ||||
−0.449465 | + | 0.893298i | \(0.648385\pi\) | |||||||
\(194\) | 6.29039 | 0.451624 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.94419 | 0.423506 | 0.211753 | − | 0.977323i | \(-0.432083\pi\) | ||||
0.211753 | + | 0.977323i | \(0.432083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.95485i | − | 0.351240i | −0.984458 | − | 0.175620i | \(-0.943807\pi\) | ||
0.984458 | − | 0.175620i | \(-0.0561929\pi\) | |||||||
\(200\) | −0.143525 | − | 4.99794i | −0.0101487 | − | 0.353408i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0292 | 0.846374 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.20183 | − | 3.11121i | −0.223626 | − | 0.217296i | ||||
\(206\) | −15.1612 | −1.05633 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.67732 | 0.185639 | ||||||||
\(209\) | 28.6118 | 1.97912 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.8746 | 1.64360 | 0.821798 | − | 0.569779i | \(-0.192971\pi\) | ||||
0.821798 | + | 0.569779i | \(0.192971\pi\) | |||||||
\(212\) | 11.8037 | 0.810679 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.95843 | −0.407310 | ||||||||
\(215\) | 0.153436 | − | 0.157906i | 0.0104643 | − | 0.0107691i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −15.1027 | −1.02288 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.39943 | + | 6.58584i | −0.431449 | + | 0.444017i | ||||
\(221\) | − | 3.46818i | − | 0.233295i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.4667 | −1.50448 | −0.752241 | − | 0.658888i | \(-0.771027\pi\) | ||||
−0.752241 | + | 0.658888i | \(0.771027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.471895 | −0.0313900 | ||||||||
\(227\) | − | 7.98520i | − | 0.529996i | −0.964249 | − | 0.264998i | \(-0.914629\pi\) | ||
0.964249 | − | 0.264998i | \(-0.0853714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.04775i | 0.531810i | 0.963999 | + | 0.265905i | \(0.0856708\pi\) | ||||
−0.963999 | + | 0.265905i | \(0.914329\pi\) | |||||||
\(230\) | 5.66549 | + | 5.50513i | 0.373572 | + | 0.362998i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 3.22563i | − | 0.211773i | ||||||
\(233\) | 15.4065 | 1.00932 | 0.504658 | − | 0.863319i | \(-0.331618\pi\) | ||||
0.504658 | + | 0.863319i | \(0.331618\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.0875 | − | 15.5270i | 0.984198 | − | 1.01287i | ||||
\(236\) | −0.796801 | −0.0518673 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.54137i | 0.293757i | 0.989155 | + | 0.146878i | \(0.0469226\pi\) | ||||
−0.989155 | + | 0.146878i | \(0.953077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.0641i | − | 1.29244i | −0.763150 | − | 0.646222i | \(-0.776348\pi\) | ||
0.763150 | − | 0.646222i | \(-0.223652\pi\) | |||||||
\(242\) | 5.86518 | 0.377028 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.69258i | 0.172375i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.6530i | 1.18686i | ||||||||
\(248\) | 8.38019i | 0.532143i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.55802 | + | 8.23871i | −0.478011 | + | 0.521062i | ||||
\(251\) | 16.3967 | 1.03495 | 0.517476 | − | 0.855698i | \(-0.326872\pi\) | ||||
0.517476 | + | 0.855698i | \(0.326872\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 14.5083i | − | 0.912132i | ||||||
\(254\) | 10.2712i | 0.644476i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 18.5675i | − | 1.15821i | −0.815254 | − | 0.579103i | \(-0.803403\pi\) | ||
0.815254 | − | 0.579103i | \(-0.196597\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.29354 | − | 4.17201i | −0.266274 | − | 0.258737i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.93947 | 0.490502 | ||||||||
\(263\) | −9.17316 | −0.565642 | −0.282821 | − | 0.959173i | \(-0.591270\pi\) | ||||
−0.282821 | + | 0.959173i | \(0.591270\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.9292 | − | 18.3934i | −1.16281 | − | 1.12990i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 0.696631i | − | 0.0425535i | ||||||
\(269\) | −23.5057 | −1.43317 | −0.716583 | − | 0.697502i | \(-0.754295\pi\) | ||||
−0.716583 | + | 0.697502i | \(0.754295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 24.3044i | − | 1.47639i | −0.674590 | − | 0.738193i | \(-0.735680\pi\) | ||
0.674590 | − | 0.738193i | \(-0.264320\pi\) | |||||||
\(272\) | − | 1.29539i | − | 0.0785446i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.2024 | −0.857997 | ||||||||
\(275\) | 20.5252 | − | 0.589417i | 1.23771 | − | 0.0355432i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.89198i | − | 0.233847i | −0.993141 | − | 0.116923i | \(-0.962697\pi\) | ||
0.993141 | − | 0.116923i | \(-0.0373032\pi\) | |||||||
\(278\) | 2.26467i | 0.135826i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.5692i | 0.749813i | 0.927063 | + | 0.374907i | \(0.122325\pi\) | ||||
−0.927063 | + | 0.374907i | \(0.877675\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7033 | 0.636248 | 0.318124 | − | 0.948049i | \(-0.396947\pi\) | ||||
0.318124 | + | 0.948049i | \(0.396947\pi\) | |||||||
\(284\) | − | 9.32893i | − | 0.553570i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.9950i | 0.650148i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.3220 | 0.901292 | ||||||||
\(290\) | −5.02643 | + | 5.17285i | −0.295162 | + | 0.303760i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.26042 | −0.424884 | ||||||||
\(293\) | − | 13.3118i | − | 0.777681i | −0.921305 | − | 0.388841i | \(-0.872876\pi\) | ||
0.921305 | − | 0.388841i | \(-0.127124\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.27781 | + | 1.24164i | 0.0743968 | + | 0.0722910i | ||||
\(296\) | − | 11.3287i | − | 0.658469i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 23.6322i | 1.36897i | ||||||||
\(299\) | 9.45850 | 0.546999 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −17.5657 | −1.01079 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.96705i | 0.399588i | ||||||||
\(305\) | 4.19579 | − | 4.31801i | 0.240250 | − | 0.247249i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.7191 | 1.01128 | 0.505641 | − | 0.862744i | \(-0.331256\pi\) | ||||
0.505641 | + | 0.862744i | \(0.331256\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.0587 | − | 13.4391i | 0.741684 | − | 0.763288i | ||||
\(311\) | −11.6990 | −0.663391 | −0.331695 | − | 0.943387i | \(-0.607621\pi\) | ||||
−0.331695 | + | 0.943387i | \(0.607621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.0112 | 1.30067 | 0.650336 | − | 0.759647i | \(-0.274628\pi\) | ||||
0.650336 | + | 0.759647i | \(0.274628\pi\) | |||||||
\(314\) | −15.7736 | −0.890157 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.73016 | 0.153584 | ||||||||
\(317\) | −31.0601 | −1.74451 | −0.872254 | − | 0.489052i | \(-0.837343\pi\) | ||||
−0.872254 | + | 0.489052i | \(0.837343\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.2468 | 0.741677 | ||||||||
\(320\) | −1.60367 | − | 1.55828i | −0.0896480 | − | 0.0871105i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.02506 | 0.502168 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.384262 | + | 13.3811i | 0.0213150 | + | 0.742249i | ||||
\(326\) | − | 8.18877i | − | 0.453534i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.99657 | −0.110242 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.57625 | 0.306498 | 0.153249 | − | 0.988188i | \(-0.451026\pi\) | ||||
0.153249 | + | 0.988188i | \(0.451026\pi\) | |||||||
\(332\) | 6.79144i | 0.372728i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 25.5577i | − | 1.39846i | ||||||
\(335\) | −1.08555 | + | 1.11717i | −0.0593097 | + | 0.0610374i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 29.5071i | − | 1.60735i | −0.595066 | − | 0.803677i | \(-0.702874\pi\) | ||
0.595066 | − | 0.803677i | \(-0.297126\pi\) | |||||||
\(338\) | 5.83196 | 0.317217 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.01858 | + | 2.07738i | −0.109473 | + | 0.112662i | ||||
\(341\) | −34.4151 | −1.86368 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 0.0984652i | − | 0.00530889i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 4.41919i | − | 0.237577i | ||||||
\(347\) | 31.2172 | 1.67583 | 0.837914 | − | 0.545803i | \(-0.183775\pi\) | ||||
0.837914 | + | 0.545803i | \(0.183775\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.9313i | 0.799252i | 0.916678 | + | 0.399626i | \(0.130860\pi\) | ||||
−0.916678 | + | 0.399626i | \(0.869140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.10672i | 0.218889i | ||||||||
\(353\) | − | 4.79695i | − | 0.255316i | −0.991818 | − | 0.127658i | \(-0.959254\pi\) | ||
0.991818 | − | 0.127658i | \(-0.0407460\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.5371 | + | 14.9605i | −0.771549 | + | 0.794023i | ||||
\(356\) | −8.03812 | −0.426019 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 5.56112i | − | 0.293914i | ||||||
\(359\) | 11.5464i | 0.609396i | 0.952449 | + | 0.304698i | \(0.0985555\pi\) | ||||
−0.952449 | + | 0.304698i | \(0.901445\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.5398 | −1.55473 | ||||||||
\(362\) | − | 2.88829i | − | 0.151805i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.6433 | + | 11.3138i | 0.609440 | + | 0.592190i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.57159 | 0.343034 | 0.171517 | − | 0.985181i | \(-0.445133\pi\) | ||||
0.171517 | + | 0.985181i | \(0.445133\pi\) | |||||||
\(368\) | 3.53283 | 0.184161 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17.6533 | + | 18.1675i | −0.917753 | + | 0.944486i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.2318i | − | 0.892227i | −0.894976 | − | 0.446113i | \(-0.852808\pi\) | ||
0.894976 | − | 0.446113i | \(-0.147192\pi\) | |||||||
\(374\) | 5.31981 | 0.275081 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 9.68213i | − | 0.499318i | ||||||
\(377\) | 8.63604i | 0.444779i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.90232 | −0.0977157 | −0.0488579 | − | 0.998806i | \(-0.515558\pi\) | ||||
−0.0488579 | + | 0.998806i | \(0.515558\pi\) | |||||||
\(380\) | 10.8566 | − | 11.1729i | 0.556933 | − | 0.573156i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.5552i | 0.847039i | ||||||||
\(383\) | 8.85433i | 0.452435i | 0.974077 | + | 0.226218i | \(0.0726360\pi\) | ||||
−0.974077 | + | 0.226218i | \(0.927364\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 24.8202i | − | 1.26331i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.29039 | −0.319346 | ||||||||
\(389\) | − | 33.9348i | − | 1.72056i | −0.509821 | − | 0.860280i | \(-0.670288\pi\) | ||
0.509821 | − | 0.860280i | \(-0.329712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.57639i | − | 0.231438i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.94419 | −0.299464 | ||||||||
\(395\) | −4.37829 | − | 4.25436i | −0.220296 | − | 0.214060i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.6819 | 1.84101 | 0.920507 | − | 0.390726i | \(-0.127776\pi\) | ||||
0.920507 | + | 0.390726i | \(0.127776\pi\) | |||||||
\(398\) | 4.95485i | 0.248364i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.143525 | + | 4.99794i | 0.00717625 | + | 0.249897i | ||||
\(401\) | 32.2327i | 1.60962i | 0.593530 | + | 0.804812i | \(0.297734\pi\) | ||||
−0.593530 | + | 0.804812i | \(0.702266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 22.4364i | − | 1.11764i | ||||||
\(404\) | −12.0292 | −0.598477 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 46.5239 | 2.30611 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3827i | 0.711177i | 0.934643 | + | 0.355589i | \(0.115720\pi\) | ||||
−0.934643 | + | 0.355589i | \(0.884280\pi\) | |||||||
\(410\) | 3.20183 | + | 3.11121i | 0.158127 | + | 0.153652i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.1612 | 0.746939 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5830 | − | 10.8912i | 0.519497 | − | 0.534630i | ||||
\(416\) | −2.67732 | −0.131266 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −28.6118 | −1.39945 | ||||||||
\(419\) | −5.32282 | −0.260037 | −0.130018 | − | 0.991512i | \(-0.541504\pi\) | ||||
−0.130018 | + | 0.991512i | \(0.541504\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.3672 | 0.748953 | 0.374476 | − | 0.927236i | \(-0.377822\pi\) | ||||
0.374476 | + | 0.927236i | \(0.377822\pi\) | |||||||
\(422\) | −23.8746 | −1.16220 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.8037 | −0.573237 | ||||||||
\(425\) | 6.47429 | − | 0.185921i | 0.314049 | − | 0.00901849i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.95843 | 0.288011 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.153436 | + | 0.157906i | −0.00739936 | + | 0.00761489i | ||||
\(431\) | 32.3577i | 1.55862i | 0.626641 | + | 0.779308i | \(0.284429\pi\) | ||||
−0.626641 | + | 0.779308i | \(0.715571\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.1611 | −1.25722 | −0.628610 | − | 0.777720i | \(-0.716376\pi\) | ||||
−0.628610 | + | 0.777720i | \(0.716376\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.1027 | 0.723287 | ||||||||
\(437\) | 24.6134i | 1.17742i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.2993i | 1.06429i | 0.846655 | + | 0.532143i | \(0.178613\pi\) | ||||
−0.846655 | + | 0.532143i | \(0.821387\pi\) | |||||||
\(440\) | 6.39943 | − | 6.58584i | 0.305081 | − | 0.313967i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.46818i | 0.164964i | ||||||||
\(443\) | 31.7237 | 1.50724 | 0.753619 | − | 0.657312i | \(-0.228307\pi\) | ||||
0.753619 | + | 0.657312i | \(0.228307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.8905 | + | 12.5256i | 0.611068 | + | 0.593772i | ||||
\(446\) | 22.4667 | 1.06383 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.85438i | 0.229092i | 0.993418 | + | 0.114546i | \(0.0365414\pi\) | ||||
−0.993418 | + | 0.114546i | \(0.963459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8.19934i | − | 0.386092i | ||||||
\(452\) | 0.471895 | 0.0221961 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.98520i | 0.374764i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.94478i | 0.324863i | 0.986720 | + | 0.162432i | \(0.0519337\pi\) | ||||
−0.986720 | + | 0.162432i | \(0.948066\pi\) | |||||||
\(458\) | − | 8.04775i | − | 0.376046i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.66549 | − | 5.50513i | −0.264155 | − | 0.256678i | ||||
\(461\) | −0.734361 | −0.0342026 | −0.0171013 | − | 0.999854i | \(-0.505444\pi\) | ||||
−0.0171013 | + | 0.999854i | \(0.505444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7420i | 0.824542i | 0.911061 | + | 0.412271i | \(0.135264\pi\) | ||||
−0.911061 | + | 0.412271i | \(0.864736\pi\) | |||||||
\(464\) | 3.22563i | 0.149746i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.4065 | −0.713695 | ||||||||
\(467\) | − | 17.9353i | − | 0.829947i | −0.909834 | − | 0.414973i | \(-0.863791\pi\) | ||
0.909834 | − | 0.414973i | \(-0.136209\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −15.0875 | + | 15.5270i | −0.695933 | + | 0.716205i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.796801 | 0.0366757 | ||||||||
\(473\) | 0.404369 | 0.0185929 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.8209 | + | 0.999946i | −1.59769 | + | 0.0458807i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 4.54137i | − | 0.207717i | ||||||
\(479\) | 29.8425 | 1.36354 | 0.681769 | − | 0.731567i | \(-0.261211\pi\) | ||||
0.681769 | + | 0.731567i | \(0.261211\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.3306i | 1.38296i | ||||||||
\(482\) | 20.0641i | 0.913896i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.86518 | −0.266599 | ||||||||
\(485\) | 10.0877 | + | 9.80219i | 0.458060 | + | 0.445095i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.3967i | − | 1.06021i | −0.847934 | − | 0.530103i | \(-0.822153\pi\) | ||
0.847934 | − | 0.530103i | \(-0.177847\pi\) | |||||||
\(488\) | − | 2.69258i | − | 0.121887i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.854553i | 0.0385654i | 0.999814 | + | 0.0192827i | \(0.00613826\pi\) | ||||
−0.999814 | + | 0.0192827i | \(0.993862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.17845 | 0.188188 | ||||||||
\(494\) | − | 18.6530i | − | 0.839239i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.38019i | − | 0.376282i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.5425 | 1.14344 | 0.571719 | − | 0.820450i | \(-0.306277\pi\) | ||||
0.571719 | + | 0.820450i | \(0.306277\pi\) | |||||||
\(500\) | 7.55802 | − | 8.23871i | 0.338005 | − | 0.368446i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.3967 | −0.731822 | ||||||||
\(503\) | 3.40477i | 0.151811i | 0.997115 | + | 0.0759055i | \(0.0241847\pi\) | ||||
−0.997115 | + | 0.0759055i | \(0.975815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.2909 | + | 18.7449i | 0.858435 | + | 0.834138i | ||||
\(506\) | 14.5083i | 0.644975i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 10.2712i | − | 0.455713i | ||||||
\(509\) | 33.4991 | 1.48482 | 0.742410 | − | 0.669945i | \(-0.233682\pi\) | ||||
0.742410 | + | 0.669945i | \(0.233682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.5675i | 0.818975i | ||||||||
\(515\) | −24.3136 | − | 23.6254i | −1.07139 | − | 1.04106i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.7618 | 1.74872 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.29354 | + | 4.17201i | 0.188284 | + | 0.182955i | ||||
\(521\) | −29.6835 | −1.30046 | −0.650230 | − | 0.759738i | \(-0.725327\pi\) | ||||
−0.650230 | + | 0.759738i | \(0.725327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.2177 | −0.840333 | −0.420167 | − | 0.907447i | \(-0.638028\pi\) | ||||
−0.420167 | + | 0.907447i | \(0.638028\pi\) | |||||||
\(524\) | −7.93947 | −0.346838 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.17316 | 0.399969 | ||||||||
\(527\) | −10.8556 | −0.472879 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5191 | −0.457354 | ||||||||
\(530\) | 18.9292 | + | 18.3934i | 0.822232 | + | 0.798959i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.34544 | 0.231537 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.55536 | − | 9.28490i | −0.413114 | − | 0.401421i | ||||
\(536\) | 0.696631i | 0.0300899i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 23.5057 | 1.01340 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0941 | 0.734934 | 0.367467 | − | 0.930036i | \(-0.380225\pi\) | ||||
0.367467 | + | 0.930036i | \(0.380225\pi\) | |||||||
\(542\) | 24.3044i | 1.04396i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.29539i | 0.0555394i | ||||||||
\(545\) | −24.2197 | − | 23.5342i | −1.03746 | − | 1.00810i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 42.5352i | − | 1.81867i | −0.416061 | − | 0.909337i | \(-0.636590\pi\) | ||
0.416061 | − | 0.909337i | \(-0.363410\pi\) | |||||||
\(548\) | 14.2024 | 0.606695 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.5252 | + | 0.589417i | −0.875196 | + | 0.0251328i | ||||
\(551\) | −22.4731 | −0.957388 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.89198i | 0.165354i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 2.26467i | − | 0.0960433i | ||||||
\(557\) | −10.8670 | −0.460450 | −0.230225 | − | 0.973137i | \(-0.573946\pi\) | ||||
−0.230225 | + | 0.973137i | \(0.573946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.263623i | 0.0111500i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 12.5692i | − | 0.530198i | ||||||
\(563\) | − | 28.4240i | − | 1.19793i | −0.800776 | − | 0.598964i | \(-0.795579\pi\) | ||
0.800776 | − | 0.598964i | \(-0.204421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.756765 | − | 0.735345i | −0.0318373 | − | 0.0309362i | ||||
\(566\) | −10.7033 | −0.449895 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.32893i | 0.391433i | ||||||||
\(569\) | − | 19.6809i | − | 0.825068i | −0.910942 | − | 0.412534i | \(-0.864644\pi\) | ||
0.910942 | − | 0.412534i | \(-0.135356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7887 | 1.12107 | 0.560537 | − | 0.828129i | \(-0.310595\pi\) | ||||
0.560537 | + | 0.828129i | \(0.310595\pi\) | |||||||
\(572\) | − | 10.9950i | − | 0.459724i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.507049 | + | 17.6569i | 0.0211454 | + | 0.736342i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.9657 | 1.99684 | 0.998419 | − | 0.0562078i | \(-0.0179009\pi\) | ||||
0.998419 | + | 0.0562078i | \(0.0179009\pi\) | |||||||
\(578\) | −15.3220 | −0.637310 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.02643 | − | 5.17285i | 0.208711 | − | 0.214791i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 48.4744i | − | 2.00760i | ||||||
\(584\) | 7.26042 | 0.300438 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.3118i | 0.549904i | ||||||||
\(587\) | − | 29.2950i | − | 1.20913i | −0.796554 | − | 0.604567i | \(-0.793346\pi\) | ||
0.796554 | − | 0.604567i | \(-0.206654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 58.3853 | 2.40572 | ||||||||
\(590\) | −1.27781 | − | 1.24164i | −0.0526065 | − | 0.0511175i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.3287i | 0.465608i | ||||||||
\(593\) | 0.573952i | 0.0235694i | 0.999931 | + | 0.0117847i | \(0.00375127\pi\) | ||||
−0.999931 | + | 0.0117847i | \(0.996249\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 23.6322i | − | 0.968012i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.45850 | −0.386787 | ||||||||
\(599\) | 46.2445i | 1.88950i | 0.327790 | + | 0.944750i | \(0.393696\pi\) | ||||
−0.327790 | + | 0.944750i | \(0.606304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.5615i | − | 1.16505i | −0.812813 | − | 0.582525i | \(-0.802065\pi\) | ||
0.812813 | − | 0.582525i | \(-0.197935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.5657 | 0.714740 | ||||||||
\(605\) | 9.40582 | + | 9.13959i | 0.382401 | + | 0.371577i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.8214 | −1.45394 | −0.726972 | − | 0.686667i | \(-0.759073\pi\) | ||||
−0.726972 | + | 0.686667i | \(0.759073\pi\) | |||||||
\(608\) | − | 6.96705i | − | 0.282551i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.19579 | + | 4.31801i | −0.169883 | + | 0.174831i | ||||
\(611\) | 25.9221i | 1.04870i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 4.39427i | − | 0.177483i | −0.996055 | − | 0.0887414i | \(-0.971716\pi\) | ||
0.996055 | − | 0.0887414i | \(-0.0282845\pi\) | |||||||
\(614\) | −17.7191 | −0.715084 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.19978 | −0.0885599 | −0.0442799 | − | 0.999019i | \(-0.514099\pi\) | ||||
−0.0442799 | + | 0.999019i | \(0.514099\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.6408i | 0.427688i | 0.976868 | + | 0.213844i | \(0.0685985\pi\) | ||||
−0.976868 | + | 0.213844i | \(0.931402\pi\) | |||||||
\(620\) | −13.0587 | + | 13.4391i | −0.524450 | + | 0.539726i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.6990 | 0.469088 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9588 | + | 1.43466i | −0.998352 | + | 0.0573863i | ||||
\(626\) | −23.0112 | −0.919714 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.7736 | 0.629436 | ||||||||
\(629\) | 14.6751 | 0.585136 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.0363 | −0.399540 | −0.199770 | − | 0.979843i | \(-0.564020\pi\) | ||||
−0.199770 | + | 0.979843i | \(0.564020\pi\) | |||||||
\(632\) | −2.73016 | −0.108600 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.0601 | 1.23355 | ||||||||
\(635\) | −16.0055 | + | 16.4717i | −0.635158 | + | 0.653660i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.2468 | −0.524444 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.60367 | + | 1.55828i | 0.0633907 | + | 0.0615964i | ||||
\(641\) | 8.44410i | 0.333522i | 0.985997 | + | 0.166761i | \(0.0533308\pi\) | ||||
−0.985997 | + | 0.166761i | \(0.946669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.4190 | 0.805248 | 0.402624 | − | 0.915366i | \(-0.368098\pi\) | ||||
0.402624 | + | 0.915366i | \(0.368098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.02506 | −0.355086 | ||||||||
\(647\) | 15.9942i | 0.628796i | 0.949291 | + | 0.314398i | \(0.101803\pi\) | ||||
−0.949291 | + | 0.314398i | \(0.898197\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.27224i | 0.128447i | ||||||||
\(650\) | −0.384262 | − | 13.3811i | −0.0150720 | − | 0.524849i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.18877i | 0.320697i | ||||||||
\(653\) | −29.6701 | −1.16108 | −0.580541 | − | 0.814231i | \(-0.697159\pi\) | ||||
−0.580541 | + | 0.814231i | \(0.697159\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.7323 | + | 12.3719i | 0.497492 | + | 0.483411i | ||||
\(656\) | 1.99657 | 0.0779528 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.28916i | 0.244991i | 0.992469 | + | 0.122495i | \(0.0390897\pi\) | ||||
−0.992469 | + | 0.122495i | \(0.960910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.26725i | 0.204872i | 0.994740 | + | 0.102436i | \(0.0326638\pi\) | ||||
−0.994740 | + | 0.102436i | \(0.967336\pi\) | |||||||
\(662\) | −5.57625 | −0.216727 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 6.79144i | − | 0.263559i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3956i | 0.441239i | ||||||||
\(668\) | 25.5577i | 0.988857i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.08555 | − | 1.11717i | 0.0419383 | − | 0.0431599i | ||||
\(671\) | 11.0577 | 0.426877 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.10722i | 0.235416i | 0.993048 | + | 0.117708i | \(0.0375547\pi\) | ||||
−0.993048 | + | 0.117708i | \(0.962445\pi\) | |||||||
\(674\) | 29.5071i | 1.13657i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.83196 | −0.224306 | ||||||||
\(677\) | 10.3238i | 0.396777i | 0.980123 | + | 0.198389i | \(0.0635708\pi\) | ||||
−0.980123 | + | 0.198389i | \(0.936429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.01858 | − | 2.07738i | 0.0774091 | − | 0.0796640i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 34.4151 | 1.31782 | ||||||||
\(683\) | 19.3208 | 0.739291 | 0.369646 | − | 0.929173i | \(-0.379479\pi\) | ||||
0.369646 | + | 0.929173i | \(0.379479\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.7759 | − | 22.1313i | −0.870224 | − | 0.845592i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.0984652i | 0.00375395i | ||||||||
\(689\) | 31.6022 | 1.20395 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 50.5898i | − | 1.92453i | −0.272122 | − | 0.962263i | \(-0.587726\pi\) | ||
0.272122 | − | 0.962263i | \(-0.412274\pi\) | |||||||
\(692\) | 4.41919i | 0.167992i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.2172 | −1.18499 | ||||||||
\(695\) | −3.52899 | + | 3.63178i | −0.133862 | + | 0.137761i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.58633i | − | 0.0979643i | ||||||
\(698\) | − | 14.9313i | − | 0.565157i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.85900i | − | 0.183522i | −0.995781 | − | 0.0917610i | \(-0.970750\pi\) | ||
0.995781 | − | 0.0917610i | \(-0.0292496\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −78.9278 | −2.97682 | ||||||||
\(704\) | − | 4.10672i | − | 0.154778i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.79695i | 0.180536i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.3199 | −1.47669 | −0.738344 | − | 0.674424i | \(-0.764392\pi\) | ||||
−0.738344 | + | 0.674424i | \(0.764392\pi\) | |||||||
\(710\) | 14.5371 | − | 14.9605i | 0.545567 | − | 0.561459i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.03812 | 0.301241 | ||||||||
\(713\) | − | 29.6058i | − | 1.10874i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.1333 | + | 17.6324i | −0.640749 | + | 0.659414i | ||||
\(716\) | 5.56112i | 0.207829i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 11.5464i | − | 0.430908i | ||||||
\(719\) | 31.9349 | 1.19097 | 0.595486 | − | 0.803366i | \(-0.296960\pi\) | ||||
0.595486 | + | 0.803366i | \(0.296960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 29.5398 | 1.09936 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.88829i | 0.107343i | ||||||||
\(725\) | −16.1215 | + | 0.462958i | −0.598737 | + | 0.0171938i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.5695 | 1.83843 | 0.919216 | − | 0.393754i | \(-0.128824\pi\) | ||||
0.919216 | + | 0.393754i | \(0.128824\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.6433 | − | 11.3138i | −0.430939 | − | 0.418741i | ||||
\(731\) | 0.127551 | 0.00471764 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.7160 | −0.839036 | −0.419518 | − | 0.907747i | \(-0.637801\pi\) | ||||
−0.419518 | + | 0.907747i | \(0.637801\pi\) | |||||||
\(734\) | −6.57159 | −0.242562 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.53283 | −0.130222 | ||||||||
\(737\) | −2.86087 | −0.105382 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.2098 | −1.25843 | −0.629213 | − | 0.777233i | \(-0.716623\pi\) | ||||
−0.629213 | + | 0.777233i | \(0.716623\pi\) | |||||||
\(740\) | 17.6533 | − | 18.1675i | 0.648949 | − | 0.667852i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.7338 | −0.723961 | −0.361981 | − | 0.932186i | \(-0.617899\pi\) | ||||
−0.361981 | + | 0.932186i | \(0.617899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.8255 | + | 37.8982i | −1.34918 | + | 1.38848i | ||||
\(746\) | 17.2318i | 0.630900i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.31981 | −0.194512 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.1064 | −1.46350 | −0.731752 | − | 0.681571i | \(-0.761297\pi\) | ||||
−0.731752 | + | 0.681571i | \(0.761297\pi\) | |||||||
\(752\) | 9.68213i | 0.353071i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 8.63604i | − | 0.314506i | ||||||
\(755\) | −28.1697 | − | 27.3723i | −1.02520 | − | 0.996182i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 41.6404i | − | 1.51345i | −0.653735 | − | 0.756724i | \(-0.726799\pi\) | ||
0.653735 | − | 0.756724i | \(-0.273201\pi\) | |||||||
\(758\) | 1.90232 | 0.0690954 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.8566 | + | 11.1729i | −0.393811 | + | 0.405282i | ||||
\(761\) | −1.12253 | −0.0406916 | −0.0203458 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203458 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 16.5552i | − | 0.598947i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 8.85433i | − | 0.319920i | ||||||
\(767\) | −2.13329 | −0.0770286 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 43.4547i | − | 1.56702i | −0.621382 | − | 0.783508i | \(-0.713429\pi\) | ||
0.621382 | − | 0.783508i | \(-0.286571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24.8202i | 0.893298i | ||||||||
\(773\) | 23.7066i | 0.852668i | 0.904566 | + | 0.426334i | \(0.140195\pi\) | ||||
−0.904566 | + | 0.426334i | \(0.859805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.8837 | − | 1.20277i | 1.50451 | − | 0.0432047i | ||||
\(776\) | 6.29039 | 0.225812 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.9348i | 1.21662i | ||||||||
\(779\) | 13.9102i | 0.498384i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.3113 | −1.37089 | ||||||||
\(782\) | 4.57639i | 0.163651i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.2957 | − | 24.5797i | −0.902843 | − | 0.877288i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.8300 | 0.564279 | 0.282140 | − | 0.959373i | \(-0.408956\pi\) | ||||
0.282140 | + | 0.959373i | \(0.408956\pi\) | |||||||
\(788\) | 5.94419 | 0.211753 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.37829 | + | 4.25436i | 0.155772 | + | 0.151363i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.20889i | 0.255995i | ||||||||
\(794\) | −36.6819 | −1.30179 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 4.95485i | − | 0.175620i | ||||||
\(797\) | 34.8696i | 1.23514i | 0.786515 | + | 0.617571i | \(0.211883\pi\) | ||||
−0.786515 | + | 0.617571i | \(0.788117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.5421 | 0.443709 | ||||||||
\(800\) | −0.143525 | − | 4.99794i | −0.00507437 | − | 0.176704i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 32.2327i | − | 1.13818i | ||||||
\(803\) | 29.8165i | 1.05220i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 22.4364i | 0.790290i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.0292 | 0.423187 | ||||||||
\(809\) | 35.1888i | 1.23717i | 0.785716 | + | 0.618587i | \(0.212295\pi\) | ||||
−0.785716 | + | 0.618587i | \(0.787705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.5831i | 0.617428i | 0.951155 | + | 0.308714i | \(0.0998985\pi\) | ||||
−0.951155 | + | 0.308714i | \(0.900101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −46.5239 | −1.63066 | ||||||||
\(815\) | 12.7604 | − | 13.1321i | 0.446977 | − | 0.459997i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.686012 | −0.0240005 | ||||||||
\(818\) | − | 14.3827i | − | 0.502878i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.20183 | − | 3.11121i | −0.111813 | − | 0.108648i | ||||
\(821\) | − | 38.9656i | − | 1.35991i | −0.733255 | − | 0.679954i | \(-0.762000\pi\) | ||
0.733255 | − | 0.679954i | \(-0.238000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.8786i | − | 0.658065i | −0.944319 | − | 0.329033i | \(-0.893277\pi\) | ||
0.944319 | − | 0.329033i | \(-0.106723\pi\) | |||||||
\(824\) | −15.1612 | −0.528166 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.7654 | 0.895950 | 0.447975 | − | 0.894046i | \(-0.352145\pi\) | ||||
0.447975 | + | 0.894046i | \(0.352145\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 9.10894i | − | 0.316366i | −0.987410 | − | 0.158183i | \(-0.949436\pi\) | ||
0.987410 | − | 0.158183i | \(-0.0505637\pi\) | |||||||
\(830\) | −10.5830 | + | 10.8912i | −0.367340 | + | 0.378040i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.67732 | 0.0928193 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.8261 | − | 40.9862i | 1.37824 | − | 1.41838i | ||||
\(836\) | 28.6118 | 0.989559 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.32282 | 0.183874 | ||||||||
\(839\) | −11.5225 | −0.397800 | −0.198900 | − | 0.980020i | \(-0.563737\pi\) | ||||
−0.198900 | + | 0.980020i | \(0.563737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.5953 | 0.641218 | ||||||||
\(842\) | −15.3672 | −0.529590 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.8746 | 0.821798 | ||||||||
\(845\) | 9.35255 | + | 9.08783i | 0.321738 | + | 0.312631i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.8037 | 0.405339 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.47429 | + | 0.185921i | −0.222066 | + | 0.00637704i | ||||
\(851\) | 40.0224i | 1.37195i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.2713 | −1.55006 | −0.775030 | − | 0.631925i | \(-0.782265\pi\) | ||||
−0.775030 | + | 0.631925i | \(0.782265\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.95843 | −0.203655 | ||||||||
\(857\) | 53.1721i | 1.81632i | 0.418620 | + | 0.908161i | \(0.362514\pi\) | ||||
−0.418620 | + | 0.908161i | \(0.637486\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.0126i | 0.580462i | 0.956957 | + | 0.290231i | \(0.0937322\pi\) | ||||
−0.956957 | + | 0.290231i | \(0.906268\pi\) | |||||||
\(860\) | 0.153436 | − | 0.157906i | 0.00523214 | − | 0.00538454i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 32.3577i | − | 1.10211i | ||||||
\(863\) | −32.7306 | −1.11416 | −0.557080 | − | 0.830459i | \(-0.688079\pi\) | ||||
−0.557080 | + | 0.830459i | \(0.688079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.88633 | − | 7.08692i | 0.234142 | − | 0.240963i | ||||
\(866\) | 26.1611 | 0.888989 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 11.2120i | − | 0.380342i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.86510i | − | 0.0631966i | ||||||
\(872\) | −15.1027 | −0.511441 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 24.6134i | − | 0.832560i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.3164i | 1.56399i | 0.623283 | + | 0.781996i | \(0.285798\pi\) | ||||
−0.623283 | + | 0.781996i | \(0.714202\pi\) | |||||||
\(878\) | − | 22.2993i | − | 0.752564i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.39943 | + | 6.58584i | −0.215725 | + | 0.222008i | ||||
\(881\) | −48.6850 | −1.64024 | −0.820119 | − | 0.572193i | \(-0.806093\pi\) | ||||
−0.820119 | + | 0.572193i | \(0.806093\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 40.9532i | − | 1.37818i | −0.724674 | − | 0.689092i | \(-0.758010\pi\) | ||
0.724674 | − | 0.689092i | \(-0.241990\pi\) | |||||||
\(884\) | − | 3.46818i | − | 0.116647i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.7237 | −1.06578 | ||||||||
\(887\) | 47.8647i | 1.60714i | 0.595210 | + | 0.803570i | \(0.297069\pi\) | ||||
−0.595210 | + | 0.803570i | \(0.702931\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.8905 | − | 12.5256i | −0.432091 | − | 0.419860i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.4667 | −0.752241 | ||||||||
\(893\) | −67.4559 | −2.25733 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.66578 | − | 8.91821i | 0.289665 | − | 0.298103i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 4.85438i | − | 0.161993i | ||||||
\(899\) | 27.0314 | 0.901547 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.2904i | − | 0.509396i | ||||||
\(902\) | 8.19934i | 0.273008i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.471895 | −0.0156950 | ||||||||
\(905\) | 4.50077 | − | 4.63187i | 0.149611 | − | 0.153969i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 44.4729i | − | 1.47670i | −0.674418 | − | 0.738350i | \(-0.735605\pi\) | ||
0.674418 | − | 0.738350i | \(-0.264395\pi\) | |||||||
\(908\) | − | 7.98520i | − | 0.264998i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 27.7147i | − | 0.918230i | −0.888377 | − | 0.459115i | \(-0.848167\pi\) | ||
0.888377 | − | 0.459115i | \(-0.151833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.8905 | 0.923042 | ||||||||
\(914\) | − | 6.94478i | − | 0.229713i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.04775i | 0.265905i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.16663 | −0.0384837 | −0.0192418 | − | 0.999815i | \(-0.506125\pi\) | ||||
−0.0192418 | + | 0.999815i | \(0.506125\pi\) | |||||||
\(920\) | 5.66549 | + | 5.50513i | 0.186786 | + | 0.181499i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.734361 | 0.0241849 | ||||||||
\(923\) | − | 24.9765i | − | 0.822112i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −56.6203 | + | 1.62595i | −1.86166 | + | 0.0534611i | ||||
\(926\) | − | 17.7420i | − | 0.583040i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 3.22563i | − | 0.105886i | ||||||
\(929\) | 8.12440 | 0.266553 | 0.133276 | − | 0.991079i | \(-0.457450\pi\) | ||||
0.133276 | + | 0.991079i | \(0.457450\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.4065 | 0.504658 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.9353i | 0.586861i | ||||||||
\(935\) | 8.53123 | + | 8.28976i | 0.279001 | + | 0.271104i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.2806 | 0.368521 | 0.184260 | − | 0.982877i | \(-0.441011\pi\) | ||||
0.184260 | + | 0.982877i | \(0.441011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.0875 | − | 15.5270i | 0.492099 | − | 0.506433i | ||||
\(941\) | 18.0948 | 0.589872 | 0.294936 | − | 0.955517i | \(-0.404702\pi\) | ||||
0.294936 | + | 0.955517i | \(0.404702\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.05352 | 0.229694 | ||||||||
\(944\) | −0.796801 | −0.0259337 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.404369 | −0.0131472 | ||||||||
\(947\) | −43.2000 | −1.40381 | −0.701906 | − | 0.712270i | \(-0.747667\pi\) | ||||
−0.701906 | + | 0.712270i | \(0.747667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.4385 | −0.630999 | ||||||||
\(950\) | 34.8209 | − | 0.999946i | 1.12974 | − | 0.0324425i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.86393 | −0.254738 | −0.127369 | − | 0.991855i | \(-0.540653\pi\) | ||||
−0.127369 | + | 0.991855i | \(0.540653\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.7977 | + | 26.5492i | −0.834794 | + | 0.859110i | ||||
\(956\) | 4.54137i | 0.146878i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.8425 | −0.964167 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39.2276 | −1.26541 | ||||||||
\(962\) | − | 30.3306i | − | 0.977898i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 20.0641i | − | 0.646222i | ||||||
\(965\) | 38.6768 | − | 39.8034i | 1.24505 | − | 1.28132i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.4858i | 1.46273i | 0.681989 | + | 0.731363i | \(0.261115\pi\) | ||||
−0.681989 | + | 0.731363i | \(0.738885\pi\) | |||||||
\(968\) | 5.86518 | 0.188514 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.0877 | − | 9.80219i | −0.323897 | − | 0.314729i | ||||
\(971\) | 35.3116 | 1.13320 | 0.566601 | − | 0.823992i | \(-0.308258\pi\) | ||||
0.566601 | + | 0.823992i | \(0.308258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.3967i | 0.749678i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.69258i | 0.0861873i | ||||||||
\(977\) | −36.9189 | −1.18114 | −0.590570 | − | 0.806987i | \(-0.701097\pi\) | ||||
−0.590570 | + | 0.806987i | \(0.701097\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.0103i | 1.05501i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 0.854553i | − | 0.0272699i | ||||||
\(983\) | 36.6036i | 1.16747i | 0.811943 | + | 0.583737i | \(0.198410\pi\) | ||||
−0.811943 | + | 0.583737i | \(0.801590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.53253 | − | 9.26272i | −0.303732 | − | 0.295135i | ||||
\(986\) | −4.17845 | −0.133069 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.6530i | 0.593432i | ||||||||
\(989\) | 0.347860i | 0.0110613i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.5134 | 0.524565 | 0.262283 | − | 0.964991i | \(-0.415525\pi\) | ||||
0.262283 | + | 0.964991i | \(0.415525\pi\) | |||||||
\(992\) | 8.38019i | 0.266071i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.72104 | + | 7.94594i | −0.244773 | + | 0.251903i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.6792 | −1.22498 | −0.612492 | − | 0.790477i | \(-0.709833\pi\) | ||||
−0.612492 | + | 0.790477i | \(0.709833\pi\) | |||||||
\(998\) | −25.5425 | −0.808532 | ||||||||
\(999\) | 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 | 4410.2.d.c.4409.5 | ✓ | 24 | |
3.2 | odd | 2 | 4410.2.d.d.4409.20 | yes | 24 | ||
5.4 | even | 2 | 4410.2.d.d.4409.6 | yes | 24 | ||
7.6 | odd | 2 | inner | 4410.2.d.c.4409.20 | yes | 24 | |
15.14 | odd | 2 | inner | 4410.2.d.c.4409.19 | yes | 24 | |
21.20 | even | 2 | 4410.2.d.d.4409.5 | yes | 24 | ||
35.34 | odd | 2 | 4410.2.d.d.4409.19 | yes | 24 | ||
105.104 | even | 2 | inner | 4410.2.d.c.4409.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4410.2.d.c.4409.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
4410.2.d.c.4409.6 | yes | 24 | 105.104 | even | 2 | inner | |
4410.2.d.c.4409.19 | yes | 24 | 15.14 | odd | 2 | inner | |
4410.2.d.c.4409.20 | yes | 24 | 7.6 | odd | 2 | inner | |
4410.2.d.d.4409.5 | yes | 24 | 21.20 | even | 2 | ||
4410.2.d.d.4409.6 | yes | 24 | 5.4 | even | 2 | ||
4410.2.d.d.4409.19 | yes | 24 | 35.34 | odd | 2 | ||
4410.2.d.d.4409.20 | yes | 24 | 3.2 | odd | 2 |