Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(881,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.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: | \(10.0611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.3 | ||
Root | \(0.874032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.881 |
Dual form | 1260.2.d.a.881.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.23607 | − | 1.41421i | 0.845154 | − | 0.534522i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.74806i | − | 0.484826i | −0.970173 | − | 0.242413i | \(-0.922061\pi\) | ||
0.970173 | − | 0.242413i | \(-0.0779389\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.74806i | − | 0.401033i | −0.979690 | − | 0.200517i | \(-0.935738\pi\) | ||
0.979690 | − | 0.200517i | \(-0.0642621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.16228i | − | 0.659380i | −0.944089 | − | 0.329690i | \(-0.893056\pi\) | ||
0.944089 | − | 0.329690i | \(-0.106944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.08191i | 0.386602i | 0.981140 | + | 0.193301i | \(0.0619194\pi\) | ||||
−0.981140 | + | 0.193301i | \(0.938081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.57649i | − | 0.821962i | −0.911644 | − | 0.410981i | \(-0.865186\pi\) | ||
0.911644 | − | 0.410981i | \(-0.134814\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.23607 | + | 1.41421i | −0.377964 | + | 0.239046i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.52786 | 0.251179 | 0.125590 | − | 0.992082i | \(-0.459918\pi\) | ||||
0.125590 | + | 0.992082i | \(0.459918\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.472136 | −0.0737352 | −0.0368676 | − | 0.999320i | \(-0.511738\pi\) | ||||
−0.0368676 | + | 0.999320i | \(0.511738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.472136 | −0.0720001 | −0.0360000 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360000 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.47214 | −0.360598 | −0.180299 | − | 0.983612i | \(-0.557707\pi\) | ||||
−0.180299 | + | 0.983612i | \(0.557707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 6.32456i | 0.428571 | − | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.81913i | − | 1.21140i | −0.795693 | − | 0.605700i | \(-0.792893\pi\) | ||
0.795693 | − | 0.605700i | \(-0.207107\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41421i | 0.190693i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.52786 | −0.198911 | −0.0994555 | − | 0.995042i | \(-0.531710\pi\) | ||||
−0.0994555 | + | 0.995042i | \(0.531710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.49613i | − | 0.447633i | −0.974631 | − | 0.223817i | \(-0.928148\pi\) | ||
0.974631 | − | 0.223817i | \(-0.0718517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.74806i | 0.216821i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.73877i | − | 0.918423i | −0.888327 | − | 0.459211i | \(-0.848132\pi\) | ||
0.888327 | − | 0.459211i | \(-0.151868\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 16.5579i | − | 1.93796i | −0.247148 | − | 0.968978i | \(-0.579493\pi\) | ||
0.247148 | − | 0.968978i | \(-0.420507\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | − | 3.16228i | −0.227921 | − | 0.360375i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.94427 | 1.00631 | 0.503155 | − | 0.864196i | \(-0.332173\pi\) | ||||
0.503155 | + | 0.864196i | \(0.332173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.52786 | 0.606762 | 0.303381 | − | 0.952869i | \(-0.401885\pi\) | ||||
0.303381 | + | 0.952869i | \(0.401885\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.47214 | 0.485071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.9443 | −1.16009 | −0.580045 | − | 0.814584i | \(-0.696965\pi\) | ||||
−0.580045 | + | 0.814584i | \(0.696965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.47214 | − | 3.90879i | −0.259150 | − | 0.409753i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.74806i | 0.179348i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.412662i | 0.0418995i | 0.999781 | + | 0.0209497i | \(0.00666900\pi\) | ||||
−0.999781 | + | 0.0209497i | \(0.993331\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.47214 | −0.843009 | −0.421505 | − | 0.906826i | \(-0.638498\pi\) | ||||
−0.421505 | + | 0.906826i | \(0.638498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.49613i | 0.344484i | 0.985055 | + | 0.172242i | \(0.0551011\pi\) | ||||
−0.985055 | + | 0.172242i | \(0.944899\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.16228i | 0.305709i | 0.988249 | + | 0.152854i | \(0.0488466\pi\) | ||||
−0.988249 | + | 0.152854i | \(0.951153\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.94427 | 0.856706 | 0.428353 | − | 0.903612i | \(-0.359094\pi\) | ||||
0.428353 | + | 0.903612i | \(0.359094\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.65841i | − | 0.626370i | −0.949692 | − | 0.313185i | \(-0.898604\pi\) | ||
0.949692 | − | 0.313185i | \(-0.101396\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.16228i | 0.294884i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.0000 | + | 6.32456i | −0.916698 | + | 0.579771i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4164 | 1.34694 | 0.673469 | − | 0.739216i | \(-0.264804\pi\) | ||||
0.673469 | + | 0.739216i | \(0.264804\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.47214 | − | 3.90879i | −0.214361 | − | 0.338935i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.99070i | − | 0.511820i | −0.966701 | − | 0.255910i | \(-0.917625\pi\) | ||
0.966701 | − | 0.255910i | \(-0.0823751\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.5471i | 1.82760i | 0.406168 | + | 0.913799i | \(0.366865\pi\) | ||||
−0.406168 | + | 0.913799i | \(0.633135\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.47214 | −0.206730 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.08191i | − | 0.172894i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.8918i | 1.38383i | 0.721981 | + | 0.691913i | \(0.243232\pi\) | ||||
−0.721981 | + | 0.691913i | \(0.756768\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.9443 | −1.21615 | −0.608074 | − | 0.793881i | \(-0.708058\pi\) | ||||
−0.608074 | + | 0.793881i | \(0.708058\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.57649i | 0.367593i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.3941i | − | 0.989155i | −0.869134 | − | 0.494577i | \(-0.835323\pi\) | ||
0.869134 | − | 0.494577i | \(-0.164677\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.47214 | − | 7.07107i | −0.352454 | − | 0.557278i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.9443 | −1.64048 | −0.820241 | − | 0.572018i | \(-0.806161\pi\) | ||||
−0.820241 | + | 0.572018i | \(0.806161\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.8885 | 1.69379 | 0.846893 | − | 0.531763i | \(-0.178470\pi\) | ||||
0.846893 | + | 0.531763i | \(0.178470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.94427 | 0.764944 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.0000 | 1.06440 | 0.532200 | − | 0.846619i | \(-0.321365\pi\) | ||||
0.532200 | + | 0.846619i | \(0.321365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.23607 | − | 1.41421i | 0.169031 | − | 0.106904i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.5595i | 1.31246i | 0.754563 | + | 0.656228i | \(0.227849\pi\) | ||||
−0.754563 | + | 0.656228i | \(0.772151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6383i | 1.31104i | 0.755177 | + | 0.655521i | \(0.227551\pi\) | ||||
−0.755177 | + | 0.655521i | \(0.772449\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.52786 | −0.112331 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.32456i | 0.462497i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.74962i | − | 0.198955i | −0.995040 | − | 0.0994776i | \(-0.968283\pi\) | ||
0.995040 | − | 0.0994776i | \(-0.0317172\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.41641 | −0.533845 | −0.266922 | − | 0.963718i | \(-0.586007\pi\) | ||||
−0.266922 | + | 0.963718i | \(0.586007\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.99070i | − | 0.426820i | −0.976963 | − | 0.213410i | \(-0.931543\pi\) | ||
0.976963 | − | 0.213410i | \(-0.0684570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3972i | 1.02059i | 0.860000 | + | 0.510294i | \(0.170464\pi\) | ||||
−0.860000 | + | 0.510294i | \(0.829536\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.94427 | + | 4.65530i | 0.206647 | + | 0.326738i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.472136 | 0.0329754 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.47214 | −0.171001 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.0000 | −0.963800 | −0.481900 | − | 0.876226i | \(-0.660053\pi\) | ||||
−0.481900 | + | 0.876226i | \(0.660053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.472136 | 0.0321994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.47214 | − | 10.2333i | −0.439357 | − | 0.694685i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.81758i | 0.525867i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.1344i | 1.41526i | 0.706581 | + | 0.707632i | \(0.250236\pi\) | ||||
−0.706581 | + | 0.707632i | \(0.749764\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.52786 | −0.101408 | −0.0507039 | − | 0.998714i | \(-0.516146\pi\) | ||||
−0.0507039 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.6383i | 1.16557i | 0.812627 | + | 0.582785i | \(0.198037\pi\) | ||||
−0.812627 | + | 0.582785i | \(0.801963\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 27.1251i | − | 1.77702i | −0.458853 | − | 0.888512i | \(-0.651740\pi\) | ||
0.458853 | − | 0.888512i | \(-0.348260\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.47214 | 0.161264 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.2055i | 1.82446i | 0.409679 | + | 0.912230i | \(0.365641\pi\) | ||||
−0.409679 | + | 0.912230i | \(0.634359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 19.7990i | − | 1.27537i | −0.770299 | − | 0.637683i | \(-0.779893\pi\) | ||
0.770299 | − | 0.637683i | \(-0.220107\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | + | 6.32456i | −0.191663 | + | 0.404061i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.05573 | −0.194431 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5279 | 1.35883 | 0.679413 | − | 0.733756i | \(-0.262234\pi\) | ||||
0.679413 | + | 0.733756i | \(0.262234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.47214 | −0.281161 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.4721 | 1.02750 | 0.513752 | − | 0.857939i | \(-0.328255\pi\) | ||||
0.513752 | + | 0.857939i | \(0.328255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.41641 | − | 2.16073i | 0.212285 | − | 0.134261i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 19.3075i | − | 1.19055i | −0.803521 | − | 0.595276i | \(-0.797043\pi\) | ||
0.803521 | − | 0.595276i | \(-0.202957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.81913i | 0.541755i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.5279 | −1.19063 | −0.595317 | − | 0.803491i | \(-0.702974\pi\) | ||||
−0.595317 | + | 0.803491i | \(0.702974\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5687i | 0.702751i | 0.936235 | + | 0.351376i | \(0.114286\pi\) | ||||
−0.936235 | + | 0.351376i | \(0.885714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.41421i | − | 0.0852803i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.00000 | −0.360505 | −0.180253 | − | 0.983620i | \(-0.557691\pi\) | ||||
−0.180253 | + | 0.983620i | \(0.557691\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.40337i | − | 0.381993i | −0.981591 | − | 0.190996i | \(-0.938828\pi\) | ||
0.981591 | − | 0.190996i | \(-0.0611719\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.49302i | − | 0.0887511i | −0.999015 | − | 0.0443756i | \(-0.985870\pi\) | ||
0.999015 | − | 0.0443756i | \(-0.0141298\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.05573 | + | 0.667701i | −0.0623177 | + | 0.0394131i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.4164 | 1.71852 | 0.859262 | − | 0.511535i | \(-0.170923\pi\) | ||||
0.859262 | + | 0.511535i | \(0.170923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.52786 | 0.0889557 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.52786 | −0.319685 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05573 | + | 0.667701i | −0.0608512 | + | 0.0384856i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.49613i | 0.200188i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.4481i | 1.85191i | 0.377633 | + | 0.925955i | \(0.376738\pi\) | ||||
−0.377633 | + | 0.925955i | \(0.623262\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.3607 | 1.38137 | 0.690684 | − | 0.723157i | \(-0.257310\pi\) | ||||
0.690684 | + | 0.723157i | \(0.257310\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.08036i | 0.0610657i | 0.999534 | + | 0.0305329i | \(0.00972042\pi\) | ||||
−0.999534 | + | 0.0305329i | \(0.990280\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.49768i | − | 0.252615i | −0.991991 | − | 0.126307i | \(-0.959687\pi\) | ||
0.991991 | − | 0.126307i | \(-0.0403126\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.94427 | 0.164848 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.81758i | 0.434982i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.74806i | − | 0.0969651i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.52786 | + | 3.49613i | −0.304761 | + | 0.192748i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8885 | −0.653453 | −0.326727 | − | 0.945119i | \(-0.605946\pi\) | ||||
−0.326727 | + | 0.945119i | \(0.605946\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4164 | −0.621891 | −0.310946 | − | 0.950428i | \(-0.600646\pi\) | ||||
−0.310946 | + | 0.950428i | \(0.600646\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.47214 | −0.350486 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.23607 | − | 18.3848i | −0.120736 | − | 0.992685i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.9613i | 1.23263i | 0.787502 | + | 0.616313i | \(0.211374\pi\) | ||||
−0.787502 | + | 0.616313i | \(0.788626\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.6274i | 1.21122i | 0.795762 | + | 0.605609i | \(0.207070\pi\) | ||||
−0.795762 | + | 0.605609i | \(0.792930\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.73877i | 0.410731i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.2272i | 0.961992i | 0.876723 | + | 0.480996i | \(0.159725\pi\) | ||||
−0.876723 | + | 0.480996i | \(0.840275\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9443 | 0.839172 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.5579i | 0.866680i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.82843i | 0.147643i | 0.997271 | + | 0.0738213i | \(0.0235195\pi\) | ||||
−0.997271 | + | 0.0738213i | \(0.976481\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.4721 | − | 19.7202i | −0.647521 | − | 1.02382i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.9443 | −1.39512 | −0.697561 | − | 0.716526i | \(-0.745731\pi\) | ||||
−0.697561 | + | 0.716526i | \(0.745731\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.63932 | 0.187435 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8885 | 0.610673 | 0.305337 | − | 0.952244i | \(-0.401231\pi\) | ||||
0.305337 | + | 0.952244i | \(0.401231\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9443 | 0.865812 | 0.432906 | − | 0.901439i | \(-0.357488\pi\) | ||||
0.432906 | + | 0.901439i | \(0.357488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | + | 3.16228i | 0.101929 | + | 0.161165i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.7202i | 0.999853i | 0.866068 | + | 0.499926i | \(0.166640\pi\) | ||||
−0.866068 | + | 0.499926i | \(0.833360\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.1421i | 0.715199i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.94427 | −0.450035 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.7295i | 0.689063i | 0.938775 | + | 0.344531i | \(0.111962\pi\) | ||||
−0.938775 | + | 0.344531i | \(0.888038\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.2055i | 1.40851i | 0.709945 | + | 0.704257i | \(0.248720\pi\) | ||||
−0.709945 | + | 0.704257i | \(0.751280\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | −0.398508 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.16073i | − | 0.107103i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 35.9442i | − | 1.77733i | −0.458559 | − | 0.888664i | \(-0.651634\pi\) | ||
0.458559 | − | 0.888664i | \(-0.348366\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.41641 | + | 2.16073i | −0.168110 | + | 0.106322i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.52786 | −0.271352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.8328 | 1.11546 | 0.557728 | − | 0.830024i | \(-0.311673\pi\) | ||||
0.557728 | + | 0.830024i | \(0.311673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.8885 | −0.969308 | −0.484654 | − | 0.874706i | \(-0.661055\pi\) | ||||
−0.484654 | + | 0.874706i | \(0.661055\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.47214 | −0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.94427 | − | 7.81758i | −0.239270 | − | 0.378319i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.5595i | − | 0.845809i | −0.906174 | − | 0.422905i | \(-0.861011\pi\) | ||
0.906174 | − | 0.422905i | \(-0.138989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.255039i | − | 0.0122564i | −0.999981 | − | 0.00612820i | \(-0.998049\pi\) | ||
0.999981 | − | 0.00612820i | \(-0.00195068\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.52786 | −0.264434 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0618i | 0.623404i | 0.950180 | + | 0.311702i | \(0.100899\pi\) | ||||
−0.950180 | + | 0.311702i | \(0.899101\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 33.6073i | − | 1.59673i | −0.602174 | − | 0.798365i | \(-0.705699\pi\) | ||
0.602174 | − | 0.798365i | \(-0.294301\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.9443 | 0.518808 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.5563i | − | 0.734150i | −0.930191 | − | 0.367075i | \(-0.880359\pi\) | ||
0.930191 | − | 0.367075i | \(-0.119641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.667701i | 0.0314408i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.47214 | + | 3.90879i | 0.115896 | + | 0.183247i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.4721 | 1.05120 | 0.525601 | − | 0.850731i | \(-0.323840\pi\) | ||||
0.525601 | + | 0.850731i | \(0.323840\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.8885 | 0.740003 | 0.370002 | − | 0.929031i | \(-0.379357\pi\) | ||||
0.370002 | + | 0.929031i | \(0.379357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.05573 | 0.327907 | 0.163954 | − | 0.986468i | \(-0.447575\pi\) | ||||
0.163954 | + | 0.986468i | \(0.447575\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.4164 | −1.45378 | −0.726889 | − | 0.686755i | \(-0.759035\pi\) | ||||
−0.726889 | + | 0.686755i | \(0.759035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.667701i | 0.0307009i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.74806i | − | 0.0802067i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.3607 | −1.11307 | −0.556534 | − | 0.830825i | \(-0.687869\pi\) | ||||
−0.556534 | + | 0.830825i | \(0.687869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 2.67080i | − | 0.121778i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 0.412662i | − | 0.0187380i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.52786 | 0.159863 | 0.0799314 | − | 0.996800i | \(-0.474530\pi\) | ||||
0.0799314 | + | 0.996800i | \(0.474530\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 23.2163i | − | 1.04774i | −0.851799 | − | 0.523869i | \(-0.824488\pi\) | ||
0.851799 | − | 0.523869i | \(-0.175512\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.31061i | − | 0.419329i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.9443 | − | 17.3044i | −0.490918 | − | 0.776209i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.9443 | 0.668997 | 0.334499 | − | 0.942396i | \(-0.391433\pi\) | ||||
0.334499 | + | 0.942396i | \(0.391433\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.0557 | 0.671302 | 0.335651 | − | 0.941986i | \(-0.391044\pi\) | ||||
0.335651 | + | 0.941986i | \(0.391044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.47214 | 0.377005 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.3607 | 1.16842 | 0.584208 | − | 0.811604i | \(-0.301405\pi\) | ||||
0.584208 | + | 0.811604i | \(0.301405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.4164 | − | 37.0246i | −1.03588 | − | 1.63787i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3.49613i | − | 0.154058i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.49613i | 0.153760i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −42.3607 | −1.85586 | −0.927928 | − | 0.372761i | \(-0.878411\pi\) | ||||
−0.927928 | + | 0.372761i | \(0.878411\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 27.4589i | − | 1.20070i | −0.799739 | − | 0.600348i | \(-0.795029\pi\) | ||
0.799739 | − | 0.600348i | \(-0.204971\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.4667i | 0.891543i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.825324i | 0.0357487i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.16228i | − | 0.136717i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.94427 | − | 4.24264i | −0.385257 | − | 0.182743i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.8885 | 1.19902 | 0.599511 | − | 0.800366i | \(-0.295362\pi\) | ||||
0.599511 | + | 0.800366i | \(0.295362\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.94427 | −0.383131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.8328 | 0.976261 | 0.488130 | − | 0.872771i | \(-0.337679\pi\) | ||||
0.488130 | + | 0.872771i | \(0.337679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.63932 | 0.155040 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.0000 | − | 12.6491i | 0.850487 | − | 0.537895i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15.1437i | − | 0.641659i | −0.947137 | − | 0.320829i | \(-0.896038\pi\) | ||
0.947137 | − | 0.320829i | \(-0.103962\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.825324i | 0.0349075i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.8885 | 0.922492 | 0.461246 | − | 0.887272i | \(-0.347403\pi\) | ||||
0.461246 | + | 0.887272i | \(0.347403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.65841i | 0.280121i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 11.2349i | − | 0.470991i | −0.971875 | − | 0.235496i | \(-0.924329\pi\) | ||
0.971875 | − | 0.235496i | \(-0.0756714\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | 0.669579 | 0.334790 | − | 0.942293i | \(-0.391335\pi\) | ||||
0.334790 | + | 0.942293i | \(0.391335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.16228i | − | 0.131876i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 36.3569i | − | 1.51356i | −0.653671 | − | 0.756779i | \(-0.726772\pi\) | ||
0.653671 | − | 0.756779i | \(-0.273228\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.3607 | − | 7.81758i | 0.512807 | − | 0.324328i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.4721 | −0.516543 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.8328 | −0.777313 | −0.388657 | − | 0.921383i | \(-0.627061\pi\) | ||||
−0.388657 | + | 0.921383i | \(0.627061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.8885 | −0.980985 | −0.490492 | − | 0.871445i | \(-0.663183\pi\) | ||||
−0.490492 | + | 0.871445i | \(0.663183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | − | 6.32456i | 0.409960 | − | 0.259281i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.41421i | − | 0.0577832i | −0.999583 | − | 0.0288916i | \(-0.990802\pi\) | ||
0.999583 | − | 0.0288916i | \(-0.00919776\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.33540i | − | 0.0544722i | −0.999629 | − | 0.0272361i | \(-0.991329\pi\) | ||
0.999629 | − | 0.0272361i | \(-0.00867059\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.00000 | −0.365902 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.9659i | − | 1.05392i | −0.849889 | − | 0.526962i | \(-0.823331\pi\) | ||
0.849889 | − | 0.526962i | \(-0.176669\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.32145i | 0.174827i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.9443 | −0.603593 | −0.301797 | − | 0.953372i | \(-0.597586\pi\) | ||||
−0.301797 | + | 0.953372i | \(0.597586\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.8114i | − | 0.636543i | −0.948000 | − | 0.318271i | \(-0.896898\pi\) | ||
0.948000 | − | 0.318271i | \(-0.103102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 22.0571i | − | 0.886551i | −0.896385 | − | 0.443275i | \(-0.853816\pi\) | ||
0.896385 | − | 0.443275i | \(-0.146184\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.4721 | + | 15.4775i | −0.980455 | + | 0.620094i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.83282 | −0.272442 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.94427 | −0.356066 | −0.178033 | − | 0.984025i | \(-0.556973\pi\) | ||||
−0.178033 | + | 0.984025i | \(0.556973\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.0557 | − | 5.24419i | −0.438044 | − | 0.207782i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.8949i | 0.746302i | 0.927771 | + | 0.373151i | \(0.121723\pi\) | ||||
−0.927771 | + | 0.373151i | \(0.878277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.6460i | 0.419838i | 0.977719 | + | 0.209919i | \(0.0673200\pi\) | ||||
−0.977719 | + | 0.209919i | \(0.932680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.00000 | −0.314512 | −0.157256 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157256 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.16073i | 0.0848159i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 32.1142i | − | 1.25673i | −0.777920 | − | 0.628364i | \(-0.783725\pi\) | ||
0.777920 | − | 0.628364i | \(-0.216275\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.4164 | −0.602369 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.588890i | 0.0229399i | 0.999934 | + | 0.0114699i | \(0.00365108\pi\) | ||||
−0.999934 | + | 0.0114699i | \(0.996349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.16073i | − | 0.0840425i | −0.999117 | − | 0.0420213i | \(-0.986620\pi\) | ||
0.999117 | − | 0.0420213i | \(-0.0133797\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.47214 | + | 3.90879i | 0.0958653 | + | 0.151576i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.58359 | 0.254918 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.94427 | −0.190872 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.4721 | 1.32880 | 0.664402 | − | 0.747376i | \(-0.268686\pi\) | ||||
0.664402 | + | 0.747376i | \(0.268686\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.4164 | 1.43803 | 0.719015 | − | 0.694995i | \(-0.244593\pi\) | ||||
0.719015 | + | 0.694995i | \(0.244593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.583592 | + | 0.922740i | 0.0223962 | + | 0.0354115i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.9690i | − | 0.611037i | −0.952186 | − | 0.305519i | \(-0.901170\pi\) | ||
0.952186 | − | 0.305519i | \(-0.0988298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.99070i | 0.228893i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.4164 | −0.587318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 25.8685i | − | 0.984084i | −0.870571 | − | 0.492042i | \(-0.836251\pi\) | ||
0.870571 | − | 0.492042i | \(-0.163749\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 21.5471i | − | 0.817326i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.11146 | 0.0799771 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7.89639i | − | 0.298243i | −0.988819 | − | 0.149121i | \(-0.952356\pi\) | ||
0.988819 | − | 0.149121i | \(-0.0476445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.67080i | − | 0.100731i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.9443 | + | 11.9814i | −0.712473 | + | 0.450607i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.944272 | 0.0354629 | 0.0177314 | − | 0.999843i | \(-0.494356\pi\) | ||||
0.0177314 | + | 0.999843i | \(0.494356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.4721 | −0.541986 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.47214 | 0.0924526 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.4721 | −0.838069 | −0.419035 | − | 0.907970i | \(-0.637631\pi\) | ||||
−0.419035 | + | 0.907970i | \(0.637631\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.94427 | + | 7.81758i | 0.184134 | + | 0.291142i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.08191i | 0.0773204i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9706i | 0.629403i | 0.949191 | + | 0.314702i | \(0.101904\pi\) | ||||
−0.949191 | + | 0.314702i | \(0.898096\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.11146 | 0.0780950 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.5579i | 0.611580i | 0.952099 | + | 0.305790i | \(0.0989206\pi\) | ||||
−0.952099 | + | 0.305790i | \(0.901079\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.05573 | 0.112407 | 0.0562034 | − | 0.998419i | \(-0.482100\pi\) | ||||
0.0562034 | + | 0.998419i | \(0.482100\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.2564i | 1.69698i | 0.529210 | + | 0.848491i | \(0.322489\pi\) | ||||
−0.529210 | + | 0.848491i | \(0.677511\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 16.8918i | − | 0.618866i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.47214 | + | 7.07107i | 0.163408 | + | 0.258371i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.0000 | 1.24068 | 0.620339 | − | 0.784334i | \(-0.286995\pi\) | ||||
0.620339 | + | 0.784334i | \(0.286995\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.9443 | 0.543878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.4721 | −0.671381 | −0.335691 | − | 0.941972i | \(-0.608970\pi\) | ||||
−0.335691 | + | 0.941972i | \(0.608970\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.8885 | −0.430959 | −0.215480 | − | 0.976508i | \(-0.569132\pi\) | ||||
−0.215480 | + | 0.976508i | \(0.569132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0000 | − | 12.6491i | 0.724049 | − | 0.457929i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.67080i | 0.0964372i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 16.9706i | − | 0.611974i | −0.952036 | − | 0.305987i | \(-0.901014\pi\) | ||
0.952036 | − | 0.305987i | \(-0.0989864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0000 | −0.647415 | −0.323708 | − | 0.946157i | \(-0.604929\pi\) | ||||
−0.323708 | + | 0.946157i | \(0.604929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.57649i | − | 0.164392i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.825324i | 0.0295703i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.9443 | −0.391617 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.3941i | 0.442363i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.32145i | 0.154043i | 0.997029 | + | 0.0770216i | \(0.0245410\pi\) | ||||
−0.997029 | + | 0.0770216i | \(0.975459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.41641 | − | 14.8886i | −0.334809 | − | 0.529379i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.11146 | −0.217024 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.8328 | 0.879623 | 0.439812 | − | 0.898090i | \(-0.355045\pi\) | ||||
0.439812 | + | 0.898090i | \(0.355045\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0557 | 0.391124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.4164 | −0.826347 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.47214 | + | 7.07107i | 0.157622 | + | 0.249222i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 30.2086i | − | 1.06208i | −0.847348 | − | 0.531038i | \(-0.821802\pi\) | ||
0.847348 | − | 0.531038i | \(-0.178198\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 9.40802i | − | 0.330360i | −0.986263 | − | 0.165180i | \(-0.947179\pi\) | ||
0.986263 | − | 0.165180i | \(-0.0528206\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.9443 | 0.733646 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.825324i | 0.0288744i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.9936i | 1.84949i | 0.380588 | + | 0.924745i | \(0.375722\pi\) | ||||
−0.380588 | + | 0.924745i | \(0.624278\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.11146 | −0.0736007 | −0.0368004 | − | 0.999323i | \(-0.511717\pi\) | ||||
−0.0368004 | + | 0.999323i | \(0.511717\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 24.4543i | − | 0.850359i | −0.905109 | − | 0.425180i | \(-0.860211\pi\) | ||
0.905109 | − | 0.425180i | \(-0.139789\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.81448i | − | 0.201945i | −0.994889 | − | 0.100973i | \(-0.967805\pi\) | ||
0.994889 | − | 0.100973i | \(-0.0321954\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.4164 | + | 28.2843i | −0.464851 | + | 0.979992i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.8885 | −0.757484 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.8885 | −0.755676 | −0.377838 | − | 0.925872i | \(-0.623332\pi\) | ||||
−0.377838 | + | 0.925872i | \(0.623332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.6656 | 0.850539 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.94427 | −0.342093 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.1246 | − | 12.7279i | 0.691490 | − | 0.437337i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.83153i | − | 0.165623i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.5687i | 0.396106i | 0.980191 | + | 0.198053i | \(0.0634619\pi\) | ||||
−0.980191 | + | 0.198053i | \(0.936538\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.94427 | 0.100574 | 0.0502872 | − | 0.998735i | \(-0.483986\pi\) | ||||
0.0502872 | + | 0.998735i | \(0.483986\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 30.0323i | − | 1.02469i | −0.858780 | − | 0.512345i | \(-0.828777\pi\) | ||
0.858780 | − | 0.512345i | \(-0.171223\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 42.7603i | − | 1.45558i | −0.685802 | − | 0.727788i | \(-0.740548\pi\) | ||
0.685802 | − | 0.727788i | \(-0.259452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.0000 | −0.476014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 12.6491i | − | 0.429092i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.23607 | + | 1.41421i | −0.0755929 | + | 0.0478091i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.7771 | −1.14057 | −0.570286 | − | 0.821446i | \(-0.693167\pi\) | ||||
−0.570286 | + | 0.821446i | \(0.693167\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.8328 | 0.432349 | 0.216174 | − | 0.976355i | \(-0.430642\pi\) | ||||
0.216174 | + | 0.976355i | \(0.430642\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.4721 | 0.688942 | 0.344471 | − | 0.938797i | \(-0.388058\pi\) | ||||
0.344471 | + | 0.938797i | \(0.388058\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.3050 | 0.581043 | 0.290522 | − | 0.956868i | \(-0.406171\pi\) | ||||
0.290522 | + | 0.956868i | \(0.406171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.94427 | + | 5.65685i | −0.299981 | + | 0.189725i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.32145i | 0.144612i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 17.5595i | − | 0.586948i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.52786 | 0.317772 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.4404i | 1.31395i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 17.6383i | − | 0.586316i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.1935 | 1.50063 | 0.750313 | − | 0.661083i | \(-0.229903\pi\) | ||||
0.750313 | + | 0.661083i | \(0.229903\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.1760i | − | 1.49675i | −0.663277 | − | 0.748374i | \(-0.730835\pi\) | ||
0.663277 | − | 0.748374i | \(-0.269165\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7.81758i | − | 0.258724i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 34.4721 | − | 21.8021i | 1.13837 | − | 0.719969i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.94427 | −0.0971226 | −0.0485613 | − | 0.998820i | \(-0.515464\pi\) | ||||
−0.0485613 | + | 0.998820i | \(0.515464\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.5279 | −0.445275 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.52786 | 0.0502359 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.0557 | 1.21576 | 0.607880 | − | 0.794029i | \(-0.292020\pi\) | ||||
0.607880 | + | 0.794029i | \(0.292020\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.0557 | − | 5.24419i | −0.362337 | − | 0.171871i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 6.32456i | − | 0.206835i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 21.5471i | − | 0.703912i | −0.936017 | − | 0.351956i | \(-0.885517\pi\) | ||
0.936017 | − | 0.351956i | \(-0.114483\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.83282 | 0.157545 | 0.0787726 | − | 0.996893i | \(-0.474900\pi\) | ||||
0.0787726 | + | 0.996893i | \(0.474900\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.49302i | 0.0486196i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.9272i | 1.58992i | 0.606662 | + | 0.794960i | \(0.292508\pi\) | ||||
−0.606662 | + | 0.794960i | \(0.707492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.9443 | −0.939571 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.9194i | 1.81141i | 0.423910 | + | 0.905704i | \(0.360657\pi\) | ||||
−0.423910 | + | 0.905704i | \(0.639343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.74962i | 0.0889755i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.47214 | − | 13.3956i | −0.273580 | − | 0.432567i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.0557 | 0.324378 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.41641 | 0.238743 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.8885 | −0.961151 | −0.480575 | − | 0.876953i | \(-0.659572\pi\) | ||||
−0.480575 | + | 0.876953i | \(0.659572\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.0000 | −1.02693 | −0.513464 | − | 0.858111i | \(-0.671638\pi\) | ||||
−0.513464 | + | 0.858111i | \(0.671638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.4721 | + | 48.1807i | 0.976892 | + | 1.54460i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 28.4605i | − | 0.910532i | −0.890355 | − | 0.455266i | \(-0.849544\pi\) | ||
0.890355 | − | 0.455266i | \(-0.150456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.4775i | 0.494664i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.583592 | 0.0186137 | 0.00930685 | − | 0.999957i | \(-0.497037\pi\) | ||||
0.00930685 | + | 0.999957i | \(0.497037\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.99070i | 0.190880i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.49302i | 0.0474754i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.05573 | 0.0335363 | 0.0167682 | − | 0.999859i | \(-0.494662\pi\) | ||||
0.0167682 | + | 0.999859i | \(0.494662\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 14.3972i | − | 0.456421i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.7217i | 0.656264i | 0.944632 | + | 0.328132i | \(0.106419\pi\) | ||||
−0.944632 | + | 0.328132i | \(0.893581\pi\) | |||||||
\(998\) | 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 | 1260.2.d.a.881.3 | ✓ | 4 | |
3.2 | odd | 2 | 1260.2.d.b.881.3 | yes | 4 | ||
4.3 | odd | 2 | 5040.2.f.b.881.2 | 4 | |||
5.2 | odd | 4 | 6300.2.f.c.3149.7 | 8 | |||
5.3 | odd | 4 | 6300.2.f.c.3149.1 | 8 | |||
5.4 | even | 2 | 6300.2.d.b.3401.2 | 4 | |||
7.6 | odd | 2 | 1260.2.d.b.881.4 | yes | 4 | ||
12.11 | even | 2 | 5040.2.f.d.881.2 | 4 | |||
15.2 | even | 4 | 6300.2.f.a.3149.8 | 8 | |||
15.8 | even | 4 | 6300.2.f.a.3149.2 | 8 | |||
15.14 | odd | 2 | 6300.2.d.a.3401.2 | 4 | |||
21.20 | even | 2 | inner | 1260.2.d.a.881.4 | yes | 4 | |
28.27 | even | 2 | 5040.2.f.d.881.1 | 4 | |||
35.13 | even | 4 | 6300.2.f.a.3149.5 | 8 | |||
35.27 | even | 4 | 6300.2.f.a.3149.3 | 8 | |||
35.34 | odd | 2 | 6300.2.d.a.3401.1 | 4 | |||
84.83 | odd | 2 | 5040.2.f.b.881.1 | 4 | |||
105.62 | odd | 4 | 6300.2.f.c.3149.4 | 8 | |||
105.83 | odd | 4 | 6300.2.f.c.3149.6 | 8 | |||
105.104 | even | 2 | 6300.2.d.b.3401.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1260.2.d.a.881.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1260.2.d.a.881.4 | yes | 4 | 21.20 | even | 2 | inner | |
1260.2.d.b.881.3 | yes | 4 | 3.2 | odd | 2 | ||
1260.2.d.b.881.4 | yes | 4 | 7.6 | odd | 2 | ||
5040.2.f.b.881.1 | 4 | 84.83 | odd | 2 | |||
5040.2.f.b.881.2 | 4 | 4.3 | odd | 2 | |||
5040.2.f.d.881.1 | 4 | 28.27 | even | 2 | |||
5040.2.f.d.881.2 | 4 | 12.11 | even | 2 | |||
6300.2.d.a.3401.1 | 4 | 35.34 | odd | 2 | |||
6300.2.d.a.3401.2 | 4 | 15.14 | odd | 2 | |||
6300.2.d.b.3401.1 | 4 | 105.104 | even | 2 | |||
6300.2.d.b.3401.2 | 4 | 5.4 | even | 2 | |||
6300.2.f.a.3149.2 | 8 | 15.8 | even | 4 | |||
6300.2.f.a.3149.3 | 8 | 35.27 | even | 4 | |||
6300.2.f.a.3149.5 | 8 | 35.13 | even | 4 | |||
6300.2.f.a.3149.8 | 8 | 15.2 | even | 4 | |||
6300.2.f.c.3149.1 | 8 | 5.3 | odd | 4 | |||
6300.2.f.c.3149.4 | 8 | 105.62 | odd | 4 | |||
6300.2.f.c.3149.6 | 8 | 105.83 | odd | 4 | |||
6300.2.f.c.3149.7 | 8 | 5.2 | odd | 4 |