Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(505,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.505");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.r (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.508277025.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1009.3 | ||
Root | \(1.86526 + 0.199842i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1009 |
Dual form | 1512.2.r.d.505.3 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.468293 | − | 0.811107i | 0.209427 | − | 0.362738i | −0.742107 | − | 0.670281i | \(-0.766173\pi\) |
0.951534 | + | 0.307543i | \(0.0995068\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.48741 | + | 4.30833i | 0.749983 | + | 1.29901i | 0.947830 | + | 0.318776i | \(0.103272\pi\) |
−0.197847 | + | 0.980233i | \(0.563395\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.622156 | + | 1.07761i | −0.172555 | + | 0.298874i | −0.939312 | − | 0.343063i | \(-0.888536\pi\) |
0.766757 | + | 0.641937i | \(0.221869\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.22446 | −1.26712 | −0.633559 | − | 0.773694i | \(-0.718407\pi\) | ||||
−0.633559 | + | 0.773694i | \(0.718407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.18622 | 1.18980 | 0.594900 | − | 0.803800i | \(-0.297192\pi\) | ||||
0.594900 | + | 0.803800i | \(0.297192\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00266 | + | 1.73666i | −0.209069 | + | 0.362118i | −0.951422 | − | 0.307891i | \(-0.900377\pi\) |
0.742352 | + | 0.670010i | \(0.233710\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.06140 | + | 3.57046i | 0.412281 | + | 0.714091i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.43925 | + | 5.95695i | 0.638652 | + | 1.10618i | 0.985729 | + | 0.168341i | \(0.0538410\pi\) |
−0.347077 | + | 0.937837i | \(0.612826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.86526 | − | 4.96277i | 0.514615 | − | 0.891340i | −0.485241 | − | 0.874381i | \(-0.661268\pi\) |
0.999856 | − | 0.0169594i | \(-0.00539860\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.936586 | −0.158312 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.73051 | 1.59969 | 0.799843 | − | 0.600209i | \(-0.204916\pi\) | ||||
0.799843 | + | 0.600209i | \(0.204916\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.73705 | + | 9.93686i | −0.895976 | + | 1.55188i | −0.0633848 | + | 0.997989i | \(0.520190\pi\) |
−0.832592 | + | 0.553887i | \(0.813144\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.80184 | − | 8.31704i | −0.732274 | − | 1.26834i | −0.955909 | − | 0.293663i | \(-0.905126\pi\) |
0.223635 | − | 0.974673i | \(-0.428208\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.984753 | − | 1.70564i | −0.143641 | − | 0.248793i | 0.785224 | − | 0.619212i | \(-0.212548\pi\) |
−0.928865 | + | 0.370418i | \(0.879214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.63418 | 1.04864 | 0.524318 | − | 0.851523i | \(-0.324320\pi\) | ||||
0.524318 | + | 0.851523i | \(0.324320\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.65935 | 0.628267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.43925 | − | 4.22490i | 0.317563 | − | 0.550035i | −0.662416 | − | 0.749136i | \(-0.730469\pi\) |
0.979979 | + | 0.199101i | \(0.0638022\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.52178 | + | 2.63580i | 0.194844 | + | 0.337480i | 0.946849 | − | 0.321677i | \(-0.104247\pi\) |
−0.752005 | + | 0.659157i | \(0.770913\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.582703 | + | 1.00927i | 0.0722754 | + | 0.125185i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.573990 | − | 0.994179i | 0.0701240 | − | 0.121458i | −0.828831 | − | 0.559498i | \(-0.810994\pi\) |
0.898955 | + | 0.438040i | \(0.144327\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.83749 | 1.04882 | 0.524409 | − | 0.851467i | \(-0.324286\pi\) | ||||
0.524409 | + | 0.851467i | \(0.324286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.10698 | 0.714768 | 0.357384 | − | 0.933958i | \(-0.383669\pi\) | ||||
0.357384 | + | 0.933958i | \(0.383669\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.48741 | − | 4.30833i | 0.283467 | − | 0.490979i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.05414 | + | 10.4861i | 0.681144 | + | 1.17978i | 0.974632 | + | 0.223813i | \(0.0718505\pi\) |
−0.293488 | + | 0.955963i | \(0.594816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.431332 | − | 0.747088i | −0.0473448 | − | 0.0820036i | 0.841382 | − | 0.540441i | \(-0.181743\pi\) |
−0.888727 | + | 0.458438i | \(0.848409\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.44658 | + | 4.23760i | −0.265369 | + | 0.459632i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8480 | 1.14989 | 0.574943 | − | 0.818194i | \(-0.305024\pi\) | ||||
0.574943 | + | 0.818194i | \(0.305024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.24431 | 0.130439 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.42867 | − | 4.20658i | 0.249176 | − | 0.431586i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.78521 | − | 6.55618i | −0.384330 | − | 0.665680i | 0.607346 | − | 0.794438i | \(-0.292234\pi\) |
−0.991676 | + | 0.128758i | \(0.958901\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.52970 | + | 4.38156i | 0.251714 | + | 0.435982i | 0.963998 | − | 0.265910i | \(-0.0856724\pi\) |
−0.712284 | + | 0.701892i | \(0.752339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.119496 | + | 0.206973i | −0.0117743 | + | 0.0203936i | −0.871853 | − | 0.489769i | \(-0.837081\pi\) |
0.860078 | + | 0.510162i | \(0.170415\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.25496 | −0.894710 | −0.447355 | − | 0.894356i | \(-0.647634\pi\) | ||||
−0.447355 | + | 0.894356i | \(0.647634\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5453 | −1.01005 | −0.505026 | − | 0.863104i | \(-0.668517\pi\) | ||||
−0.505026 | + | 0.863104i | \(0.668517\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.06406 | + | 8.77122i | −0.476387 | + | 0.825127i | −0.999634 | − | 0.0270545i | \(-0.991387\pi\) |
0.523247 | + | 0.852181i | \(0.324721\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.939078 | + | 1.62653i | 0.0875695 | + | 0.151675i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.61223 | + | 4.52452i | 0.239463 | + | 0.414762i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.87445 | + | 11.9069i | −0.624950 | + | 1.08245i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.54429 | 0.764225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.52720 | 0.579196 | 0.289598 | − | 0.957148i | \(-0.406478\pi\) | ||||
0.289598 | + | 0.957148i | \(0.406478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.76748 | + | 3.06136i | −0.154425 | + | 0.267472i | −0.932850 | − | 0.360266i | \(-0.882686\pi\) |
0.778424 | + | 0.627738i | \(0.216019\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.59311 | − | 4.49140i | −0.224851 | − | 0.389454i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.48603 | + | 4.30593i | 0.212396 | + | 0.367881i | 0.952464 | − | 0.304651i | \(-0.0985400\pi\) |
−0.740068 | + | 0.672532i | \(0.765207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.87566 | + | 8.44490i | −0.413548 | + | 0.716287i | −0.995275 | − | 0.0970976i | \(-0.969044\pi\) |
0.581726 | + | 0.813385i | \(0.302377\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.19024 | −0.517654 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.44230 | 0.535004 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.39108 | + | 11.0697i | −0.523578 | + | 0.906863i | 0.476046 | + | 0.879421i | \(0.342070\pi\) |
−0.999623 | + | 0.0274426i | \(0.991264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4781 | − | 19.8807i | −0.934078 | − | 1.61787i | −0.776271 | − | 0.630400i | \(-0.782891\pi\) |
−0.157807 | − | 0.987470i | \(-0.550442\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.68356 | − | 4.64806i | −0.215549 | − | 0.373341i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.25489 | + | 14.2979i | −0.658812 | + | 1.14110i | 0.322112 | + | 0.946702i | \(0.395607\pi\) |
−0.980924 | + | 0.194394i | \(0.937726\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00532 | 0.158041 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.2245 | 1.34912 | 0.674562 | − | 0.738218i | \(-0.264333\pi\) | ||||
0.674562 | + | 0.738218i | \(0.264333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.56406 | − | 11.3693i | 0.507943 | − | 0.879782i | −0.492015 | − | 0.870587i | \(-0.663740\pi\) |
0.999958 | − | 0.00919564i | \(-0.00292711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.72584 | + | 9.91745i | 0.440449 | + | 0.762881i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.49412 | − | 16.4443i | −0.721824 | − | 1.25024i | −0.960268 | − | 0.279080i | \(-0.909971\pi\) |
0.238444 | − | 0.971156i | \(-0.423363\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.06140 | − | 3.57046i | 0.155827 | − | 0.269901i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.61835 | −0.569422 | −0.284711 | − | 0.958613i | \(-0.591898\pi\) | ||||
−0.284711 | + | 0.958613i | \(0.591898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.27737 | −0.689581 | −0.344791 | − | 0.938680i | \(-0.612050\pi\) | ||||
−0.344791 | + | 0.938680i | \(0.612050\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.55673 | − | 7.89249i | 0.335018 | − | 0.580267i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.9954 | − | 22.5087i | −0.950317 | − | 1.64600i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.80119 | + | 8.31591i | 0.347402 | + | 0.601718i | 0.985787 | − | 0.167999i | \(-0.0537306\pi\) |
−0.638385 | + | 0.769717i | \(0.720397\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.54155 | − | 13.0624i | 0.542853 | − | 0.940249i | −0.455886 | − | 0.890038i | \(-0.650677\pi\) |
0.998739 | − | 0.0502103i | \(-0.0159892\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.0712 | 0.788788 | 0.394394 | − | 0.918942i | \(-0.370955\pi\) | ||||
0.394394 | + | 0.918942i | \(0.370955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.3368 | 1.29986 | 0.649929 | − | 0.759995i | \(-0.274799\pi\) | ||||
0.649929 | + | 0.759995i | \(0.274799\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.43925 | − | 5.95695i | 0.241388 | − | 0.418096i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.37324 | + | 9.30672i | 0.375283 | + | 0.650010i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.9003 | + | 22.3439i | 0.892331 | + | 1.54556i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.30911 | + | 2.26744i | −0.0901227 | + | 0.156097i | −0.907563 | − | 0.419917i | \(-0.862059\pi\) |
0.817440 | + | 0.576014i | \(0.195393\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.99468 | −0.613432 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.73051 | −0.389013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.25043 | − | 5.62991i | 0.218648 | − | 0.378709i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5442 | + | 21.7272i | 0.840023 | + | 1.45496i | 0.889875 | + | 0.456205i | \(0.150792\pi\) |
−0.0498520 | + | 0.998757i | \(0.515875\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.7781 | − | 22.1323i | −0.848113 | − | 1.46898i | −0.882890 | − | 0.469581i | \(-0.844405\pi\) |
0.0347761 | − | 0.999395i | \(-0.488928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.73657 | + | 4.73987i | −0.180837 | + | 0.313220i | −0.942166 | − | 0.335147i | \(-0.891214\pi\) |
0.761329 | + | 0.648366i | \(0.224547\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.6774 | −0.699500 | −0.349750 | − | 0.936843i | \(-0.613733\pi\) | ||||
−0.349750 | + | 0.936843i | \(0.613733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.84461 | −0.120329 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.50000 | − | 4.33013i | 0.161712 | − | 0.280093i | −0.773771 | − | 0.633465i | \(-0.781632\pi\) |
0.935483 | + | 0.353373i | \(0.114965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1684 | − | 17.6121i | −0.655003 | − | 1.13450i | −0.981893 | − | 0.189436i | \(-0.939334\pi\) |
0.326890 | − | 0.945062i | \(-0.393999\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.468293 | + | 0.811107i | 0.0299181 | + | 0.0518197i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.22664 | + | 5.58871i | −0.205306 | + | 0.355601i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.8151 | −1.25072 | −0.625358 | − | 0.780338i | \(-0.715047\pi\) | ||||
−0.625358 | + | 0.780338i | \(0.715047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.97613 | −0.627194 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.969506 | + | 1.67923i | −0.0604761 | + | 0.104748i | −0.894678 | − | 0.446711i | \(-0.852595\pi\) |
0.834202 | + | 0.551459i | \(0.185929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.86526 | − | 8.42687i | −0.302312 | − | 0.523620i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.67768 | − | 11.5661i | −0.411763 | − | 0.713195i | 0.583320 | − | 0.812243i | \(-0.301754\pi\) |
−0.995083 | + | 0.0990481i | \(0.968420\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.57503 | − | 6.19214i | 0.219613 | − | 0.380380i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.15040 | −0.253055 | −0.126527 | − | 0.991963i | \(-0.540383\pi\) | ||||
−0.126527 | + | 0.991963i | \(0.540383\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.6050 | −1.00868 | −0.504341 | − | 0.863505i | \(-0.668264\pi\) | ||||
−0.504341 | + | 0.863505i | \(0.668264\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.2551 | + | 17.7624i | −0.618407 | + | 1.07111i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.55414 | − | 14.8162i | −0.513968 | − | 0.890219i | −0.999869 | − | 0.0162051i | \(-0.994842\pi\) |
0.485900 | − | 0.874014i | \(-0.338492\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.49007 | − | 12.9732i | −0.446820 | − | 0.773916i | 0.551357 | − | 0.834270i | \(-0.314110\pi\) |
−0.998177 | + | 0.0603541i | \(0.980777\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.00580 | − | 15.5985i | 0.535339 | − | 0.927235i | −0.463807 | − | 0.885936i | \(-0.653517\pi\) |
0.999147 | − | 0.0412990i | \(-0.0131496\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.4741 | 0.677294 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.2950 | 0.605588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.8362 | + | 23.9650i | −0.808320 | + | 1.40005i | 0.105707 | + | 0.994397i | \(0.466290\pi\) |
−0.914027 | + | 0.405654i | \(0.867044\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.28456 | − | 3.95698i | −0.133012 | − | 0.230384i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.24762 | − | 2.16095i | −0.0721519 | − | 0.124971i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.80184 | + | 8.31704i | −0.276774 | + | 0.479386i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.85056 | 0.163222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.10040 | −0.348168 | −0.174084 | − | 0.984731i | \(-0.555696\pi\) | ||||
−0.174084 | + | 0.984731i | \(0.555696\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.3277 | − | 23.0842i | 0.755743 | − | 1.30898i | −0.189262 | − | 0.981927i | \(-0.560609\pi\) |
0.945004 | − | 0.327058i | \(-0.106057\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0681 | − | 20.9026i | −0.682130 | − | 1.18148i | −0.974330 | − | 0.225126i | \(-0.927721\pi\) |
0.292200 | − | 0.956357i | \(-0.405613\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.80046 | − | 15.2428i | −0.494283 | − | 0.856124i | 0.505695 | − | 0.862712i | \(-0.331236\pi\) |
−0.999978 | + | 0.00658868i | \(0.997903\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.1097 | + | 29.6348i | −0.957957 | + | 1.65923i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.0952 | −1.50762 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.13006 | −0.284565 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.984753 | + | 1.70564i | −0.0542912 | + | 0.0940351i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.1497 | − | 21.0440i | −0.667810 | − | 1.15668i | −0.978515 | − | 0.206175i | \(-0.933898\pi\) |
0.310705 | − | 0.950506i | \(-0.399435\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.537591 | − | 0.931135i | −0.0293717 | − | 0.0508733i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4722 | + | 19.8704i | −0.624929 | + | 1.08241i | 0.363626 | + | 0.931545i | \(0.381539\pi\) |
−0.988555 | + | 0.150863i | \(0.951795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.5083 | 1.54381 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.36930 | + | 11.0319i | −0.341922 | + | 0.592226i | −0.984790 | − | 0.173751i | \(-0.944411\pi\) |
0.642868 | + | 0.765977i | \(0.277744\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.99468 | + | 6.91899i | 0.213830 | + | 0.370365i | 0.952910 | − | 0.303253i | \(-0.0980727\pi\) |
−0.739080 | + | 0.673618i | \(0.764739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.9781 | − | 19.0147i | −0.584307 | − | 1.01205i | −0.994961 | − | 0.100259i | \(-0.968033\pi\) |
0.410654 | − | 0.911791i | \(-0.365300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.13854 | − | 7.16815i | 0.219651 | − | 0.380446i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.4673 | −1.08022 | −0.540112 | − | 0.841593i | \(-0.681618\pi\) | ||||
−0.540112 | + | 0.841593i | \(0.681618\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.89688 | 0.415625 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.85985 | − | 4.95341i | 0.149692 | − | 0.259273i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.94174 | + | 17.2196i | 0.518955 | + | 0.898856i | 0.999757 | + | 0.0220269i | \(0.00701195\pi\) |
−0.480803 | + | 0.876829i | \(0.659655\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.81709 | − | 6.61139i | −0.198173 | − | 0.343246i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1438 | + | 29.6939i | −0.887672 | + | 1.53749i | −0.0450513 | + | 0.998985i | \(0.514345\pi\) |
−0.842620 | + | 0.538508i | \(0.818988\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.55900 | −0.440811 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.6248 | 0.956694 | 0.478347 | − | 0.878171i | \(-0.341236\pi\) | ||||
0.478347 | + | 0.878171i | \(0.341236\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.4360 | − | 28.4680i | 0.839842 | − | 1.45465i | −0.0501852 | − | 0.998740i | \(-0.515981\pi\) |
0.890027 | − | 0.455908i | \(-0.150686\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.32968 | − | 4.03512i | −0.118731 | − | 0.205649i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.8250 | − | 18.7495i | −0.548850 | − | 0.950635i | −0.998354 | − | 0.0573571i | \(-0.981733\pi\) |
0.449504 | − | 0.893278i | \(-0.351601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.23836 | − | 9.07311i | 0.264915 | − | 0.458847i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3404 | 0.570600 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2721 | 0.816673 | 0.408336 | − | 0.912832i | \(-0.366109\pi\) | ||||
0.408336 | + | 0.912832i | \(0.366109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.57133 | + | 7.91777i | −0.228281 | + | 0.395395i | −0.957299 | − | 0.289100i | \(-0.906644\pi\) |
0.729018 | + | 0.684495i | \(0.239977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.56528 | + | 6.17524i | 0.177599 | + | 0.307611i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.2038 | + | 41.9222i | 1.19974 | + | 2.07801i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0976 | − | 19.2217i | 0.548743 | − | 0.950450i | −0.449618 | − | 0.893221i | \(-0.648440\pi\) |
0.998361 | − | 0.0572294i | \(-0.0182266\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.87849 | −0.240055 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.807958 | −0.0396611 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.9601 | − | 24.1795i | 0.681994 | − | 1.18125i | −0.292378 | − | 0.956303i | \(-0.594447\pi\) |
0.974372 | − | 0.224945i | \(-0.0722202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0441 | − | 20.8611i | −0.586996 | − | 1.01671i | −0.994623 | − | 0.103558i | \(-0.966977\pi\) |
0.407628 | − | 0.913148i | \(-0.366356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.7697 | − | 18.6537i | −0.522408 | − | 0.904838i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.52178 | − | 2.63580i | 0.0736442 | − | 0.127555i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.1623 | 1.26020 | 0.630098 | − | 0.776516i | \(-0.283015\pi\) | ||||
0.630098 | + | 0.776516i | \(0.283015\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5630 | −0.892082 | −0.446041 | − | 0.895013i | \(-0.647166\pi\) | ||||
−0.446041 | + | 0.895013i | \(0.647166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.20002 | + | 9.00670i | −0.248751 | + | 0.430849i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.85395 | − | 6.67524i | −0.183939 | − | 0.318592i | 0.759279 | − | 0.650765i | \(-0.225552\pi\) |
−0.943218 | + | 0.332173i | \(0.892218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5204 | + | 28.6142i | 0.784909 | + | 1.35950i | 0.929053 | + | 0.369945i | \(0.120624\pi\) |
−0.144145 | + | 0.989557i | \(0.546043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.08004 | − | 8.79889i | 0.240817 | − | 0.417107i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.9283 | −0.940477 | −0.470238 | − | 0.882540i | \(-0.655832\pi\) | ||||
−0.470238 | + | 0.882540i | \(0.655832\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −57.0816 | −2.68787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.582703 | − | 1.00927i | 0.0273175 | − | 0.0473154i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.9326 | + | 29.3282i | 0.792075 | + | 1.37191i | 0.924680 | + | 0.380745i | \(0.124333\pi\) |
−0.132605 | + | 0.991169i | \(0.542334\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.25351 | − | 12.5634i | −0.337830 | − | 0.585138i | 0.646195 | − | 0.763173i | \(-0.276359\pi\) |
−0.984024 | + | 0.178035i | \(0.943026\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.5348 | + | 21.7110i | −0.582544 | + | 1.00900i | 0.412633 | + | 0.910897i | \(0.364609\pi\) |
−0.995177 | + | 0.0980981i | \(0.968724\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.102955 | 0.00476419 | 0.00238209 | − | 0.999997i | \(-0.499242\pi\) | ||||
0.00238209 | + | 0.999997i | \(0.499242\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.14798 | −0.0530088 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.8883 | − | 41.3758i | 1.09839 | − | 1.90246i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.6909 | + | 18.5172i | 0.490532 | + | 0.849626i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.62668 | + | 4.54954i | 0.120016 | + | 0.207874i | 0.919774 | − | 0.392449i | \(-0.128372\pi\) |
−0.799758 | + | 0.600323i | \(0.795039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.05390 | + | 10.4857i | −0.276034 | + | 0.478105i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.09036 | −0.321957 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.7319 | −1.39260 | −0.696299 | − | 0.717752i | \(-0.745171\pi\) | ||||
−0.696299 | + | 0.717752i | \(0.745171\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.35920 | + | 4.08626i | −0.106469 | + | 0.184410i | −0.914338 | − | 0.404953i | \(-0.867288\pi\) |
0.807868 | + | 0.589363i | \(0.200621\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.9682 | − | 31.1219i | −0.809248 | − | 1.40166i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.41875 | − | 7.65349i | −0.198208 | − | 0.343306i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3566 | + | 21.4023i | −0.553158 | + | 0.958098i | 0.444886 | + | 0.895587i | \(0.353244\pi\) |
−0.998044 | + | 0.0625105i | \(0.980089\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.4083 | 0.865371 | 0.432686 | − | 0.901545i | \(-0.357566\pi\) | ||||
0.432686 | + | 0.901545i | \(0.357566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.73856 | 0.210863 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.72850 | − | 4.72591i | 0.120939 | − | 0.209472i | −0.799199 | − | 0.601066i | \(-0.794743\pi\) |
0.920138 | + | 0.391594i | \(0.128076\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.05349 | − | 5.28880i | −0.135078 | − | 0.233963i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.111918 | + | 0.193848i | 0.00493170 | + | 0.00854196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.89897 | − | 8.48527i | 0.215457 | − | 0.373182i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.7683 | 1.08512 | 0.542558 | − | 0.840018i | \(-0.317456\pi\) | ||||
0.542558 | + | 0.840018i | \(0.317456\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.7530 | −1.43219 | −0.716094 | − | 0.698004i | \(-0.754072\pi\) | ||||
−0.716094 | + | 0.698004i | \(0.754072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.9694 | + | 25.9278i | −0.652078 | + | 1.12943i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.48934 | + | 16.4360i | 0.412580 | + | 0.714610i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.13868 | − | 12.3646i | −0.309211 | − | 0.535569i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.33403 | + | 7.50676i | −0.187377 | + | 0.324546i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.97483 | −0.214281 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.8575 | 1.62762 | 0.813811 | − | 0.581130i | \(-0.197389\pi\) | ||||
0.813811 | + | 0.581130i | \(0.197389\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.93827 | + | 8.55333i | −0.211532 | + | 0.366385i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.74835 | − | 3.02824i | −0.0747543 | − | 0.129478i | 0.826225 | − | 0.563340i | \(-0.190484\pi\) |
−0.900979 | + | 0.433862i | \(0.857151\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.8367 | + | 30.8941i | 0.759869 | + | 1.31613i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.05414 | − | 10.4861i | 0.257448 | − | 0.445913i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.1226 | 1.44582 | 0.722911 | − | 0.690941i | \(-0.242803\pi\) | ||||
0.722911 | + | 0.690941i | \(0.242803\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.9500 | 0.505431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.65071 | − | 13.2514i | 0.322439 | − | 0.558481i | −0.658552 | − | 0.752535i | \(-0.728831\pi\) |
0.980991 | + | 0.194055i | \(0.0621640\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.74293 | + | 8.21500i | 0.199537 | + | 0.345608i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.4953 | + | 28.5707i | 0.691520 | + | 1.19775i | 0.971340 | + | 0.237695i | \(0.0763920\pi\) |
−0.279820 | + | 0.960053i | \(0.590275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.7150 | − | 18.5590i | 0.448410 | − | 0.776668i | −0.549873 | − | 0.835248i | \(-0.685324\pi\) |
0.998283 | + | 0.0585801i | \(0.0186573\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.26755 | −0.344781 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.4188 | −1.59939 | −0.799697 | − | 0.600404i | \(-0.795007\pi\) | ||||
−0.799697 | + | 0.600404i | \(0.795007\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.431332 | + | 0.747088i | −0.0178947 | + | 0.0309944i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.9894 | + | 32.8905i | 0.786459 | + | 1.36219i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.43772 | − | 14.6146i | −0.348262 | − | 0.603207i | 0.637679 | − | 0.770302i | \(-0.279895\pi\) |
−0.985941 | + | 0.167095i | \(0.946561\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8599 | − | 25.7380i | 0.612290 | − | 1.06052i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.7817 | −0.894467 | −0.447233 | − | 0.894417i | \(-0.647591\pi\) | ||||
−0.447233 | + | 0.894417i | \(0.647591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.89316 | 0.200600 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.3778 | + | 23.1710i | −0.546601 | + | 0.946740i | 0.451904 | + | 0.892067i | \(0.350745\pi\) |
−0.998504 | + | 0.0546732i | \(0.982588\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5615 | + | 21.7571i | 0.512393 | + | 0.887491i | 0.999897 | + | 0.0143699i | \(0.00457423\pi\) |
−0.487504 | + | 0.873121i | \(0.662092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.43852 | + | 11.1518i | 0.261763 | + | 0.453387i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.31975 | + | 7.48203i | −0.175333 | + | 0.303686i | −0.940277 | − | 0.340411i | \(-0.889434\pi\) |
0.764943 | + | 0.644098i | \(0.222767\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.45068 | 0.0991440 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.1789 | 1.86515 | 0.932575 | − | 0.360977i | \(-0.117557\pi\) | ||||
0.932575 | + | 0.360977i | \(0.117557\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.76222 | + | 9.98046i | −0.231978 | + | 0.401798i | −0.958390 | − | 0.285461i | \(-0.907853\pi\) |
0.726412 | + | 0.687260i | \(0.241186\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.6325 | − | 34.0045i | −0.789096 | − | 1.36675i | −0.926521 | − | 0.376242i | \(-0.877216\pi\) |
0.137425 | − | 0.990512i | \(-0.456117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.42400 | − | 9.39464i | −0.217308 | − | 0.376388i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.30578 | + | 10.9219i | −0.252231 | + | 0.436877i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.8367 | −2.02699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.8387 | 0.909193 | 0.454596 | − | 0.890698i | \(-0.349784\pi\) | ||||
0.454596 | + | 0.890698i | \(0.349784\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.05664 | − | 5.29426i | 0.121299 | − | 0.210096i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.622156 | − | 1.07761i | −0.0246507 | − | 0.0426963i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.04899 | − | 15.6733i | −0.357413 | − | 0.619058i | 0.630114 | − | 0.776502i | \(-0.283008\pi\) |
−0.987528 | + | 0.157444i | \(0.949675\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.0416 | − | 26.0529i | 0.593184 | − | 1.02742i | −0.400616 | − | 0.916246i | \(-0.631204\pi\) |
0.993800 | − | 0.111179i | \(-0.0354627\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.1323 | 0.988054 | 0.494027 | − | 0.869447i | \(-0.335524\pi\) | ||||
0.494027 | + | 0.869447i | \(0.335524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.2697 | 0.952668 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.24884 | − | 9.09125i | 0.205403 | − | 0.355768i | −0.744858 | − | 0.667223i | \(-0.767483\pi\) |
0.950261 | + | 0.311455i | \(0.100816\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.65539 | + | 2.86722i | 0.0646815 | + | 0.112032i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.04138 | − | 6.99988i | −0.157430 | − | 0.272677i | 0.776511 | − | 0.630103i | \(-0.216988\pi\) |
−0.933941 | + | 0.357427i | \(0.883654\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4530 | − | 23.3012i | 0.523260 | − | 0.906312i | −0.476374 | − | 0.879243i | \(-0.658049\pi\) |
0.999634 | − | 0.0270695i | \(-0.00861755\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.85734 | −0.188360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.7936 | −0.534090 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.57060 | + | 13.1127i | −0.292260 | + | 0.506209i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.11160 | + | 10.5856i | 0.235585 | + | 0.408045i | 0.959443 | − | 0.281904i | \(-0.0909661\pi\) |
−0.723858 | + | 0.689949i | \(0.757633\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.34015 | + | 5.78531i | 0.128372 | + | 0.222348i | 0.923046 | − | 0.384689i | \(-0.125691\pi\) |
−0.794674 | + | 0.607037i | \(0.792358\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.78521 | + | 6.55618i | −0.145263 | + | 0.251603i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.2125 | −0.735146 | −0.367573 | − | 0.929995i | \(-0.619811\pi\) | ||||
−0.367573 | + | 0.929995i | \(0.619811\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.65677 | 0.177926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.74966 | + | 8.22664i | −0.180947 | + | 0.313410i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.72706 | + | 9.91955i | 0.217867 | + | 0.377357i | 0.954156 | − | 0.299310i | \(-0.0967566\pi\) |
−0.736288 | + | 0.676668i | \(0.763423\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.56648 | + | 7.90937i | 0.173216 | + | 0.300020i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.9730 | − | 51.9147i | 1.13531 | − | 1.96641i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.29596 | 0.162256 | 0.0811281 | − | 0.996704i | \(-0.474148\pi\) | ||||
0.0811281 | + | 0.996704i | \(0.474148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.4646 | 1.90331 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.52970 | − | 4.38156i | 0.0951390 | − | 0.164786i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.44506 | − | 11.1632i | −0.242049 | − | 0.419242i | 0.719248 | − | 0.694753i | \(-0.244486\pi\) |
−0.961298 | + | 0.275511i | \(0.911153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.74576 | + | 9.95195i | 0.215180 | + | 0.372703i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.89885 | + | 5.02095i | −0.108411 | + | 0.187773i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.46489 | −0.203806 | −0.101903 | − | 0.994794i | \(-0.532493\pi\) | ||||
−0.101903 | + | 0.994794i | \(0.532493\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.238992 | 0.00890051 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.1793 | + | 24.5594i | −0.526608 | + | 0.912111i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.9300 | + | 43.1800i | 0.924601 | + | 1.60146i | 0.792201 | + | 0.610260i | \(0.208935\pi\) |
0.132401 | + | 0.991196i | \(0.457731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.0870 | + | 43.4520i | 0.927878 | + | 1.60713i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.6123 | − | 30.5054i | 0.650525 | − | 1.12674i | −0.332471 | − | 0.943114i | \(-0.607882\pi\) |
0.982996 | − | 0.183629i | \(-0.0587844\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.71100 | 0.210367 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.7209 | −1.31401 | −0.657007 | − | 0.753885i | \(-0.728178\pi\) | ||||
−0.657007 | + | 0.753885i | \(0.728178\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.53043 | − | 11.3110i | 0.239578 | − | 0.414962i | −0.721015 | − | 0.692919i | \(-0.756324\pi\) |
0.960593 | + | 0.277958i | \(0.0896575\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.98580 | + | 10.3677i | 0.219303 | + | 0.379843i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.62748 | + | 8.01503i | 0.169084 | + | 0.292863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.11223 | − | 1.92644i | 0.0405859 | − | 0.0702968i | −0.845019 | − | 0.534736i | \(-0.820411\pi\) |
0.885605 | + | 0.464440i | \(0.153744\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.5005 | −0.782484 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.27335 | 0.155317 | 0.0776587 | − | 0.996980i | \(-0.475256\pi\) | ||||
0.0776587 | + | 0.996980i | \(0.475256\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.2206 | − | 43.6833i | 0.914245 | − | 1.58352i | 0.106242 | − | 0.994340i | \(-0.466118\pi\) |
0.808003 | − | 0.589179i | \(-0.200549\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.27263 | + | 9.13246i | 0.190882 | + | 0.330617i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.03519 | + | 5.25710i | 0.109594 | + | 0.189823i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.03493 | − | 1.79255i | 0.0373205 | − | 0.0646411i | −0.846762 | − | 0.531972i | \(-0.821451\pi\) |
0.884082 | + | 0.467331i | \(0.154784\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.3739 | 1.02054 | 0.510269 | − | 0.860015i | \(-0.329546\pi\) | ||||
0.510269 | + | 0.860015i | \(0.329546\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.6258 | 0.848664 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.7536 | + | 51.5347i | −1.06603 | + | 1.84642i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.9825 | + | 38.0748i | 0.786595 | + | 1.36242i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.73141 | + | 13.3912i | 0.275946 | + | 0.477952i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.72536 | − | 2.98841i | 0.0615025 | − | 0.106525i | −0.833635 | − | 0.552316i | \(-0.813744\pi\) |
0.895137 | + | 0.445791i | \(0.147077\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.1281 | 0.360115 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.78714 | −0.134485 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.2230 | + | 19.4388i | −0.397540 | + | 0.688559i | −0.993422 | − | 0.114513i | \(-0.963469\pi\) |
0.595882 | + | 0.803072i | \(0.296803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.14480 | + | 8.91106i | 0.182010 | + | 0.315251i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1906 | + | 26.3108i | 0.536064 | + | 0.928490i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.939078 | − | 1.62653i | 0.0330982 | − | 0.0573277i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.2366 | −0.641164 | −0.320582 | − | 0.947221i | \(-0.603878\pi\) | ||||
−0.320582 | + | 0.947221i | \(0.603878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.8280 | 0.590910 | 0.295455 | − | 0.955357i | \(-0.404529\pi\) | ||||
0.295455 | + | 0.955357i | \(0.404529\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.06610 | − | 13.9709i | 0.282543 | − | 0.489379i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.9034 | − | 43.1340i | −0.871260 | − | 1.50907i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.6149 | − | 32.2420i | −0.649665 | − | 1.12525i | −0.983203 | − | 0.182516i | \(-0.941576\pi\) |
0.333538 | − | 0.942737i | \(-0.391757\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.13747 | − | 10.6304i | 0.213939 | − | 0.370553i | −0.739005 | − | 0.673700i | \(-0.764704\pi\) |
0.952944 | + | 0.303147i | \(0.0980374\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.60355 | 0.299175 | 0.149587 | − | 0.988749i | \(-0.452205\pi\) | ||||
0.149587 | + | 0.988749i | \(0.452205\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.2887 | −1.53821 | −0.769105 | − | 0.639123i | \(-0.779298\pi\) | ||||
−0.769105 | + | 0.639123i | \(0.779298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.61223 | − | 4.52452i | 0.0905084 | − | 0.156765i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.14781 | − | 10.6483i | −0.212754 | − | 0.368500i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.6154 | + | 40.9030i | 0.815293 | + | 1.41213i | 0.909117 | + | 0.416540i | \(0.136758\pi\) |
−0.0938240 | + | 0.995589i | \(0.529909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.15684 | + | 15.8601i | −0.315753 | + | 0.546900i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.7255 | 0.368968 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7489 | 0.472418 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.75640 | + | 16.8986i | −0.334445 | + | 0.579276i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9825 | + | 20.7543i | 0.410273 | + | 0.710614i | 0.994919 | − | 0.100674i | \(-0.0321000\pi\) |
−0.584646 | + | 0.811288i | \(0.698767\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.50903 | + | 11.2740i | 0.222344 | + | 0.385111i | 0.955519 | − | 0.294928i | \(-0.0952958\pi\) |
−0.733175 | + | 0.680040i | \(0.761962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.0473685 | − | 0.0820447i | 0.00161619 | − | 0.00279933i | −0.865216 | − | 0.501399i | \(-0.832819\pi\) |
0.866832 | + | 0.498600i | \(0.166152\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.8729 | 0.880723 | 0.440361 | − | 0.897821i | \(-0.354850\pi\) | ||||
0.440361 | + | 0.897821i | \(0.354850\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.7841 | −0.604678 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.1183 | + | 52.1664i | −1.02169 | + | 1.76962i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.714223 | + | 1.23707i | 0.0242005 | + | 0.0419165i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.27215 | − | 7.39958i | −0.144425 | − | 0.250151i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.9042 | − | 46.5994i | 0.908489 | − | 1.57355i | 0.0923254 | − | 0.995729i | \(-0.470570\pi\) |
0.816164 | − | 0.577821i | \(-0.196097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.8689 | 1.44429 | 0.722144 | − | 0.691743i | \(-0.243157\pi\) | ||||
0.722144 | + | 0.691743i | \(0.243157\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.5967 | 1.16427 | 0.582136 | − | 0.813092i | \(-0.302217\pi\) | ||||
0.582136 | + | 0.813092i | \(0.302217\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.2278 | + | 17.7150i | −0.343415 | + | 0.594812i | −0.985064 | − | 0.172186i | \(-0.944917\pi\) |
0.641650 | + | 0.766998i | \(0.278250\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.26360 | − | 5.65272i | −0.109458 | − | 0.189586i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.10714 | − | 8.84583i | −0.170904 | − | 0.296015i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.56762 | + | 6.17930i | −0.119252 | + | 0.206551i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.4173 | 1.31464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.8845 | −1.32874 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.34453 | + | 7.52494i | −0.144417 | + | 0.250137i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.92456 | + | 6.79754i | 0.130313 | + | 0.225709i | 0.923797 | − | 0.382882i | \(-0.125068\pi\) |
−0.793484 | + | 0.608591i | \(0.791735\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.87189 | − | 6.70631i | −0.128282 | − | 0.222190i | 0.794729 | − | 0.606964i | \(-0.207613\pi\) |
−0.923011 | + | 0.384774i | \(0.874279\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.14580 | − | 3.71663i | 0.0710156 | − | 0.123003i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.53495 | 0.116734 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.3702 | 0.638963 | 0.319482 | − | 0.947592i | \(-0.396491\pi\) | ||||
0.319482 | + | 0.947592i | \(0.396491\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.49830 | + | 9.52334i | −0.180979 | + | 0.313464i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0585 | + | 34.7424i | 0.659520 | + | 1.14232i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.77989 | − | 3.08287i | −0.0583964 | − | 0.101146i | 0.835349 | − | 0.549720i | \(-0.185265\pi\) |
−0.893746 | + | 0.448574i | \(0.851932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.59311 | + | 4.49140i | −0.0849858 | + | 0.147200i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.3426 | −0.796089 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.2230 | −1.11802 | −0.559008 | − | 0.829162i | \(-0.688818\pi\) | ||||
−0.559008 | + | 0.829162i | \(0.688818\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.02033 | + | 10.4275i | −0.196257 | + | 0.339928i | −0.947312 | − | 0.320312i | \(-0.896212\pi\) |
0.751055 | + | 0.660240i | \(0.229545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.5046 | − | 19.9266i | −0.374642 | − | 0.648899i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.3623 | − | 19.6802i | −0.369227 | − | 0.639519i | 0.620218 | − | 0.784429i | \(-0.287044\pi\) |
−0.989445 | + | 0.144910i | \(0.953711\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.79949 | + | 6.58092i | −0.123337 | + | 0.213626i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.74488 | 0.218488 | 0.109244 | − | 0.994015i | \(-0.465157\pi\) | ||||
0.109244 | + | 0.994015i | \(0.465157\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.99346 | 0.291022 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.48603 | − | 4.30593i | 0.0802782 | − | 0.139046i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.919395 | − | 1.59244i | −0.0296579 | − | 0.0513690i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.06331 | − | 12.2340i | −0.227376 | − | 0.393827i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8267 | − | 22.2165i | 0.412479 | − | 0.714434i | −0.582681 | − | 0.812701i | \(-0.697996\pi\) |
0.995160 | + | 0.0982664i | \(0.0313297\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.9298 | −1.31350 | −0.656750 | − | 0.754108i | \(-0.728069\pi\) | ||||
−0.656750 | + | 0.754108i | \(0.728069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.75133 | 0.312613 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.2365 | − | 38.5147i | 0.711408 | − | 1.23220i | −0.252920 | − | 0.967487i | \(-0.581391\pi\) |
0.964329 | − | 0.264708i | \(-0.0852756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.9835 | + | 46.7367i | 0.862395 | + | 1.49371i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.4550 | − | 49.2855i | −0.907573 | − | 1.57196i | −0.817425 | − | 0.576035i | \(-0.804599\pi\) |
−0.0901483 | − | 0.995928i | \(-0.528734\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.18455 | − | 8.97990i | 0.165193 | − | 0.286123i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.2585 | 0.612384 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.7331 | −1.42099 | −0.710496 | − | 0.703701i | \(-0.751530\pi\) | ||||
−0.710496 | + | 0.703701i | \(0.751530\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.58698 | − | 14.8731i | 0.272225 | − | 0.471508i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.36681 | + | 16.2238i | 0.296650 | + | 0.513812i | 0.975367 | − | 0.220587i | \(-0.0707973\pi\) |
−0.678718 | + | 0.734399i | \(0.737464\pi\) | |||||||
\(998\) | 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 | 1512.2.r.d.1009.3 | 8 | ||
3.2 | odd | 2 | 504.2.r.d.337.2 | yes | 8 | ||
4.3 | odd | 2 | 3024.2.r.l.1009.3 | 8 | |||
9.2 | odd | 6 | 504.2.r.d.169.2 | ✓ | 8 | ||
9.4 | even | 3 | 4536.2.a.ba.1.2 | 4 | |||
9.5 | odd | 6 | 4536.2.a.x.1.3 | 4 | |||
9.7 | even | 3 | inner | 1512.2.r.d.505.3 | 8 | ||
12.11 | even | 2 | 1008.2.r.m.337.3 | 8 | |||
36.7 | odd | 6 | 3024.2.r.l.2017.3 | 8 | |||
36.11 | even | 6 | 1008.2.r.m.673.3 | 8 | |||
36.23 | even | 6 | 9072.2.a.ce.1.3 | 4 | |||
36.31 | odd | 6 | 9072.2.a.cl.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.d.169.2 | ✓ | 8 | 9.2 | odd | 6 | ||
504.2.r.d.337.2 | yes | 8 | 3.2 | odd | 2 | ||
1008.2.r.m.337.3 | 8 | 12.11 | even | 2 | |||
1008.2.r.m.673.3 | 8 | 36.11 | even | 6 | |||
1512.2.r.d.505.3 | 8 | 9.7 | even | 3 | inner | ||
1512.2.r.d.1009.3 | 8 | 1.1 | even | 1 | trivial | ||
3024.2.r.l.1009.3 | 8 | 4.3 | odd | 2 | |||
3024.2.r.l.2017.3 | 8 | 36.7 | odd | 6 | |||
4536.2.a.x.1.3 | 4 | 9.5 | odd | 6 | |||
4536.2.a.ba.1.2 | 4 | 9.4 | even | 3 | |||
9072.2.a.ce.1.3 | 4 | 36.23 | even | 6 | |||
9072.2.a.cl.1.2 | 4 | 36.31 | odd | 6 |