Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7500,2,Mod(1,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7500.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7500.a (trivial) |
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: | yes |
Analytic conductor: | \(59.8878015160\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 11 x^{10} + 94 x^{9} + 27 x^{8} - 460 x^{7} + 55 x^{6} + 812 x^{5} - 127 x^{4} + \cdots - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 5^{3} \) |
Twist minimal: | no (minimal twist has level 300) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.62661\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7500.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.80992 | −1.44001 | −0.720006 | − | 0.693968i | \(-0.755861\pi\) | ||||
−0.720006 | + | 0.693968i | \(0.755861\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.190733 | 0.0575081 | 0.0287541 | − | 0.999587i | \(-0.490846\pi\) | ||||
0.0287541 | + | 0.999587i | \(0.490846\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.67943 | −0.465791 | −0.232896 | − | 0.972502i | \(-0.574820\pi\) | ||||
−0.232896 | + | 0.972502i | \(0.574820\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.60324 | 1.11645 | 0.558225 | − | 0.829690i | \(-0.311483\pi\) | ||||
0.558225 | + | 0.829690i | \(0.311483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.64126 | −0.605946 | −0.302973 | − | 0.952999i | \(-0.597979\pi\) | ||||
−0.302973 | + | 0.952999i | \(0.597979\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.80992 | 0.831392 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.35567 | 1.32525 | 0.662625 | − | 0.748951i | \(-0.269442\pi\) | ||||
0.662625 | + | 0.748951i | \(0.269442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.52008 | 0.467966 | 0.233983 | − | 0.972241i | \(-0.424824\pi\) | ||||
0.233983 | + | 0.972241i | \(0.424824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.74937 | 0.673407 | 0.336704 | − | 0.941611i | \(-0.390688\pi\) | ||||
0.336704 | + | 0.941611i | \(0.390688\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.190733 | −0.0332023 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8626 | −1.95019 | −0.975097 | − | 0.221778i | \(-0.928814\pi\) | ||||
−0.975097 | + | 0.221778i | \(0.928814\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.67943 | 0.268925 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.18953 | −1.12282 | −0.561408 | − | 0.827539i | \(-0.689740\pi\) | ||||
−0.561408 | + | 0.827539i | \(0.689740\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.22619 | −1.40698 | −0.703491 | − | 0.710705i | \(-0.748376\pi\) | ||||
−0.703491 | + | 0.710705i | \(0.748376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.54848 | −0.663464 | −0.331732 | − | 0.943374i | \(-0.607633\pi\) | ||||
−0.331732 | + | 0.943374i | \(0.607633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.51545 | 1.07364 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60324 | −0.644583 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.43006 | 1.29532 | 0.647659 | − | 0.761930i | \(-0.275748\pi\) | ||||
0.647659 | + | 0.761930i | \(0.275748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.64126 | 0.349843 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.14057 | 0.929623 | 0.464812 | − | 0.885410i | \(-0.346122\pi\) | ||||
0.464812 | + | 0.885410i | \(0.346122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.53012 | 1.22021 | 0.610103 | − | 0.792322i | \(-0.291128\pi\) | ||||
0.610103 | + | 0.792322i | \(0.291128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.80992 | −0.480004 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.05168 | 0.739330 | 0.369665 | − | 0.929165i | \(-0.379472\pi\) | ||||
0.369665 | + | 0.929165i | \(0.379472\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.35567 | −0.765133 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2983 | 1.57822 | 0.789110 | − | 0.614252i | \(-0.210542\pi\) | ||||
0.789110 | + | 0.614252i | \(0.210542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.21152 | −0.609963 | −0.304981 | − | 0.952358i | \(-0.598650\pi\) | ||||
−0.304981 | + | 0.952358i | \(0.598650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.726676 | −0.0828124 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.11168 | −0.350092 | −0.175046 | − | 0.984560i | \(-0.556007\pi\) | ||||
−0.175046 | + | 0.984560i | \(0.556007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.67837 | 0.513518 | 0.256759 | − | 0.966475i | \(-0.417345\pi\) | ||||
0.256759 | + | 0.966475i | \(0.417345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.52008 | −0.270181 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.9423 | 1.47788 | 0.738939 | − | 0.673772i | \(-0.235327\pi\) | ||||
0.738939 | + | 0.673772i | \(0.235327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.39850 | 0.670745 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.74937 | −0.388792 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.69507 | 0.679782 | 0.339891 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339891 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.190733 | 0.0191694 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5147 | 1.04625 | 0.523127 | − | 0.852255i | \(-0.324765\pi\) | ||||
0.523127 | + | 0.852255i | \(0.324765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.9648 | −1.27746 | −0.638732 | − | 0.769429i | \(-0.720541\pi\) | ||||
−0.638732 | + | 0.769429i | \(0.720541\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.64606 | −0.932520 | −0.466260 | − | 0.884648i | \(-0.654399\pi\) | ||||
−0.466260 | + | 0.884648i | \(0.654399\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.4454 | 1.95831 | 0.979157 | − | 0.203103i | \(-0.0651025\pi\) | ||||
0.979157 | + | 0.203103i | \(0.0651025\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.8626 | 1.12595 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.04417 | −0.380444 | −0.190222 | − | 0.981741i | \(-0.560921\pi\) | ||||
−0.190222 | + | 0.981741i | \(0.560921\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.67943 | −0.155264 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.5380 | −1.60770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9636 | −0.996693 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.18953 | 0.648258 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7537 | −1.48665 | −0.743327 | − | 0.668928i | \(-0.766753\pi\) | ||||
−0.743327 | + | 0.668928i | \(0.766753\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.22619 | 0.812321 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.30750 | −0.288978 | −0.144489 | − | 0.989506i | \(-0.546154\pi\) | ||||
−0.144489 | + | 0.989506i | \(0.546154\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0630 | 0.872570 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.09916 | −0.179343 | −0.0896717 | − | 0.995971i | \(-0.528582\pi\) | ||||
−0.0896717 | + | 0.995971i | \(0.528582\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2849 | −1.12681 | −0.563404 | − | 0.826181i | \(-0.690509\pi\) | ||||
−0.563404 | + | 0.826181i | \(0.690509\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.54848 | 0.383051 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.320323 | −0.0267868 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.51545 | −0.619864 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.79913 | −0.229313 | −0.114657 | − | 0.993405i | \(-0.536577\pi\) | ||||
−0.114657 | + | 0.993405i | \(0.536577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.71330 | −0.546320 | −0.273160 | − | 0.961969i | \(-0.588069\pi\) | ||||
−0.273160 | + | 0.961969i | \(0.588069\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.60324 | 0.372150 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.9495 | −1.11329 | −0.556646 | − | 0.830750i | \(-0.687912\pi\) | ||||
−0.556646 | + | 0.830750i | \(0.687912\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.43006 | −0.747853 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.2146 | −1.90838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.87503 | 0.695146 | 0.347573 | − | 0.937653i | \(-0.387006\pi\) | ||||
0.347573 | + | 0.937653i | \(0.387006\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.5944 | −1.90318 | −0.951588 | − | 0.307378i | \(-0.900548\pi\) | ||||
−0.951588 | + | 0.307378i | \(0.900548\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1795 | −0.783039 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.64126 | −0.201982 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.9350 | 1.28755 | 0.643774 | − | 0.765216i | \(-0.277368\pi\) | ||||
0.643774 | + | 0.765216i | \(0.277368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.14057 | −0.536718 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.7497 | 1.10244 | 0.551222 | − | 0.834358i | \(-0.314162\pi\) | ||||
0.551222 | + | 0.834358i | \(0.314162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9888 | −0.816791 | −0.408396 | − | 0.912805i | \(-0.633912\pi\) | ||||
−0.408396 | + | 0.912805i | \(0.633912\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.53012 | −0.704486 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.877989 | 0.0642049 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.80992 | 0.277131 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.0355 | −1.73915 | −0.869575 | − | 0.493801i | \(-0.835607\pi\) | ||||
−0.869575 | + | 0.493801i | \(0.835607\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50843 | 0.540469 | 0.270234 | − | 0.962795i | \(-0.412899\pi\) | ||||
0.270234 | + | 0.962795i | \(0.412899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.5522 | −0.894306 | −0.447153 | − | 0.894457i | \(-0.647562\pi\) | ||||
−0.447153 | + | 0.894457i | \(0.647562\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.7618 | −1.40088 | −0.700440 | − | 0.713711i | \(-0.747013\pi\) | ||||
−0.700440 | + | 0.713711i | \(0.747013\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.05168 | −0.426852 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.60128 | −0.673877 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.35567 | 0.441750 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.503774 | −0.0348468 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2479 | −0.774336 | −0.387168 | − | 0.922009i | \(-0.626547\pi\) | ||||
−0.387168 | + | 0.922009i | \(0.626547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.2983 | −0.911186 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.2848 | −0.969715 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.21152 | 0.352162 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.73084 | −0.520033 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.27196 | −0.486967 | −0.243483 | − | 0.969905i | \(-0.578290\pi\) | ||||
−0.243483 | + | 0.969905i | \(0.578290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.46929 | 0.628499 | 0.314249 | − | 0.949340i | \(-0.398247\pi\) | ||||
0.314249 | + | 0.949340i | \(0.398247\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2301 | 1.40292 | 0.701461 | − | 0.712708i | \(-0.252531\pi\) | ||||
0.701461 | + | 0.712708i | \(0.252531\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.726676 | 0.0478118 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.08932 | 0.464437 | 0.232218 | − | 0.972664i | \(-0.425402\pi\) | ||||
0.232218 | + | 0.972664i | \(0.425402\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.11168 | 0.202126 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0117 | −1.29445 | −0.647224 | − | 0.762300i | \(-0.724070\pi\) | ||||
−0.647224 | + | 0.762300i | \(0.724070\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.8240 | 1.34139 | 0.670696 | − | 0.741732i | \(-0.265995\pi\) | ||||
0.670696 | + | 0.741732i | \(0.265995\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.43582 | 0.282244 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.67837 | −0.296480 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.7741 | −1.87932 | −0.939662 | − | 0.342104i | \(-0.888861\pi\) | ||||
−0.939662 | + | 0.342104i | \(0.888861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.21224 | 0.0762126 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.2853 | −1.32774 | −0.663869 | − | 0.747849i | \(-0.731087\pi\) | ||||
−0.663869 | + | 0.747849i | \(0.731087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 45.1954 | 2.80830 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.52008 | 0.155989 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.8653 | 1.34827 | 0.674135 | − | 0.738608i | \(-0.264517\pi\) | ||||
0.674135 | + | 0.738608i | \(0.264517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.9423 | −0.853253 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.56132 | −0.278109 | −0.139054 | − | 0.990285i | \(-0.544406\pi\) | ||||
−0.139054 | + | 0.990285i | \(0.544406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.9193 | −0.784791 | −0.392395 | − | 0.919797i | \(-0.628354\pi\) | ||||
−0.392395 | + | 0.919797i | \(0.628354\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.39850 | −0.387255 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.83521 | 0.530856 | 0.265428 | − | 0.964131i | \(-0.414487\pi\) | ||||
0.265428 | + | 0.964131i | \(0.414487\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.74937 | 0.224469 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0305495 | 0.00182243 | 0.000911215 | − | 1.00000i | \(-0.499710\pi\) | ||||
0.000911215 | 1.00000i | \(0.499710\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.80719 | −0.285758 | −0.142879 | − | 0.989740i | \(-0.545636\pi\) | ||||
−0.142879 | + | 0.989740i | \(0.545636\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.3915 | 1.61687 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.18984 | 0.246461 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.69507 | −0.392472 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9705 | 0.874587 | 0.437294 | − | 0.899319i | \(-0.355937\pi\) | ||||
0.437294 | + | 0.899319i | \(0.355937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.190733 | −0.0110674 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.6739 | −0.617290 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.1510 | 2.02607 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.5147 | −0.604055 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.47622 | −0.255472 | −0.127736 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127736 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9648 | 0.737544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.296114 | 0.0167911 | 0.00839554 | − | 0.999965i | \(-0.497328\pi\) | ||||
0.00839554 | + | 0.999965i | \(0.497328\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1569 | 1.19586 | 0.597930 | − | 0.801548i | \(-0.295990\pi\) | ||||
0.597930 | + | 0.801548i | \(0.295990\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.9166 | −1.45562 | −0.727812 | − | 0.685777i | \(-0.759463\pi\) | ||||
−0.727812 | + | 0.685777i | \(0.759463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.480661 | 0.0269119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.64606 | 0.538391 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.1583 | −0.676509 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.4454 | −1.13063 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.3293 | 0.955397 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.07039 | −0.168764 | −0.0843819 | − | 0.996433i | \(-0.526892\pi\) | ||||
−0.0843819 | + | 0.996433i | \(0.526892\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.8626 | −0.650065 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.2521 | −1.53899 | −0.769495 | − | 0.638652i | \(-0.779492\pi\) | ||||
−0.769495 | + | 0.638652i | \(0.779492\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.04417 | 0.219649 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.715129 | 0.0387264 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.96383 | −0.106037 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.6011 | −1.64275 | −0.821376 | − | 0.570387i | \(-0.806793\pi\) | ||||
−0.821376 | + | 0.570387i | \(0.806793\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.1178 | −0.862764 | −0.431382 | − | 0.902169i | \(-0.641974\pi\) | ||||
−0.431382 | + | 0.902169i | \(0.641974\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.67943 | 0.0896416 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.431010 | 0.0229404 | 0.0114702 | − | 0.999934i | \(-0.496349\pi\) | ||||
0.0114702 | + | 0.999934i | \(0.496349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.5380 | 0.928207 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.4738 | 0.975008 | 0.487504 | − | 0.873121i | \(-0.337907\pi\) | ||||
0.487504 | + | 0.873121i | \(0.337907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0238 | −0.632829 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9636 | 0.575441 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2757 | −0.536386 | −0.268193 | − | 0.963365i | \(-0.586427\pi\) | ||||
−0.268193 | + | 0.963365i | \(0.586427\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.18953 | −0.374272 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.9277 | −1.86528 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.6433 | −0.758201 | −0.379100 | − | 0.925356i | \(-0.623767\pi\) | ||||
−0.379100 | + | 0.925356i | \(0.623767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.23230 | −0.217975 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7051 | −0.549884 | −0.274942 | − | 0.961461i | \(-0.588659\pi\) | ||||
−0.274942 | + | 0.961461i | \(0.588659\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.7537 | 0.858320 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.3174 | −1.34476 | −0.672378 | − | 0.740208i | \(-0.734727\pi\) | ||||
−0.672378 | + | 0.740208i | \(0.734727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.22619 | −0.468994 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.291780 | 0.0147938 | 0.00739692 | − | 0.999973i | \(-0.497645\pi\) | ||||
0.00739692 | + | 0.999973i | \(0.497645\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.2567 | 1.47958 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.30750 | 0.166841 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.01611 | −0.101185 | −0.0505927 | − | 0.998719i | \(-0.516111\pi\) | ||||
−0.0505927 | + | 0.998719i | \(0.516111\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.0630 | −0.503778 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.88760 | 0.493763 | 0.246882 | − | 0.969046i | \(-0.420594\pi\) | ||||
0.246882 | + | 0.969046i | \(0.420594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.29683 | −0.313667 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.26258 | −0.112152 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.6809 | −1.86320 | −0.931601 | − | 0.363483i | \(-0.881587\pi\) | ||||
−0.931601 | + | 0.363483i | \(0.881587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.09916 | 0.103544 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.2050 | −1.33867 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.2849 | 0.650563 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.6537 | −0.764734 | −0.382367 | − | 0.924011i | \(-0.624891\pi\) | ||||
−0.382367 | + | 0.924011i | \(0.624891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5277 | 0.708036 | 0.354018 | − | 0.935239i | \(-0.384815\pi\) | ||||
0.354018 | + | 0.935239i | \(0.384815\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.54848 | −0.221155 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.3089 | −1.75711 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.320323 | 0.0154653 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.6264 | −0.608192 | −0.304096 | − | 0.952641i | \(-0.598354\pi\) | ||||
−0.304096 | + | 0.952641i | \(0.598354\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.49014 | 0.167725 | 0.0838626 | − | 0.996477i | \(-0.473274\pi\) | ||||
0.0838626 | + | 0.996477i | \(0.473274\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.7870 | −0.803030 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.5630 | −0.933689 | −0.466844 | − | 0.884340i | \(-0.654609\pi\) | ||||
−0.466844 | + | 0.884340i | \(0.654609\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.51545 | 0.357879 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.77485 | 0.131837 | 0.0659185 | − | 0.997825i | \(-0.479002\pi\) | ||||
0.0659185 | + | 0.997825i | \(0.479002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.79913 | 0.132394 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.4261 | −1.81344 | −0.906721 | − | 0.421732i | \(-0.861422\pi\) | ||||
−0.906721 | + | 0.421732i | \(0.861422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.37128 | −0.0645710 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.71330 | 0.315418 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.0296 | 1.68539 | 0.842696 | − | 0.538389i | \(-0.180967\pi\) | ||||
0.842696 | + | 0.538389i | \(0.180967\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.60324 | −0.214861 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.857592 | 0.0399421 | 0.0199710 | − | 0.999801i | \(-0.493643\pi\) | ||||
0.0199710 | + | 0.999801i | \(0.493643\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.4068 | −0.483643 | −0.241822 | − | 0.970321i | \(-0.577745\pi\) | ||||
−0.241822 | + | 0.970321i | \(0.577745\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.5705 | 0.951889 | 0.475944 | − | 0.879475i | \(-0.342106\pi\) | ||||
0.475944 | + | 0.879475i | \(0.342106\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.0564 | −1.06464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.9495 | 0.642759 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.75974 | −0.0809128 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.43006 | 0.431773 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.9380 | 1.45929 | 0.729643 | − | 0.683828i | \(-0.239686\pi\) | ||||
0.729643 | + | 0.683828i | \(0.239686\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.9224 | 0.908383 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.2146 | 1.10180 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.6815 | −0.710599 | −0.355299 | − | 0.934753i | \(-0.615621\pi\) | ||||
−0.355299 | + | 0.934753i | \(0.615621\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.87503 | −0.401343 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4831 | 0.743870 | 0.371935 | − | 0.928259i | \(-0.378694\pi\) | ||||
0.371935 | + | 0.928259i | \(0.378694\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.6005 | 0.522461 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −50.6655 | −2.27266 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4339 | 0.556618 | 0.278309 | − | 0.960492i | \(-0.410226\pi\) | ||||
0.278309 | + | 0.960492i | \(0.410226\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.5944 | 1.09880 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.33327 | −0.193211 | −0.0966055 | − | 0.995323i | \(-0.530799\pi\) | ||||
−0.0966055 | + | 0.995323i | \(0.530799\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.1795 | 0.452088 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0120 | 0.621072 | 0.310536 | − | 0.950562i | \(-0.399492\pi\) | ||||
0.310536 | + | 0.950562i | \(0.399492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.8555 | 0.878354 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.64126 | 0.116614 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.867545 | −0.0381546 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.9350 | −0.743366 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.92829 | 0.0844801 | 0.0422400 | − | 0.999107i | \(-0.486551\pi\) | ||||
0.0422400 | + | 0.999107i | \(0.486551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.95894 | 0.0856583 | 0.0428291 | − | 0.999082i | \(-0.486363\pi\) | ||||
0.0428291 | + | 0.999082i | \(0.486363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.2593 | 0.751826 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.3946 | 0.756287 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.14057 | 0.309874 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0743 | 0.522998 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.7497 | −0.636497 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.43344 | 0.0617428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.6132 | −1.48814 | −0.744069 | − | 0.668103i | \(-0.767107\pi\) | ||||
−0.744069 | + | 0.668103i | \(0.767107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.9888 | 0.471575 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.9494 | −0.681947 | −0.340973 | − | 0.940073i | \(-0.610757\pi\) | ||||
−0.340973 | + | 0.940073i | \(0.610757\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.53012 | 0.406735 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.65617 | −0.283562 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8552 | 0.504136 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.0343 | −1.82342 | −0.911711 | − | 0.410831i | \(-0.865239\pi\) | ||||
−0.911711 | + | 0.410831i | \(0.865239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.4948 | 0.655359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.877989 | −0.0370687 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.8560 | −0.794686 | −0.397343 | − | 0.917670i | \(-0.630068\pi\) | ||||
−0.397343 | + | 0.917670i | \(0.630068\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.80992 | −0.160001 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.3652 | −1.02144 | −0.510721 | − | 0.859747i | \(-0.670621\pi\) | ||||
−0.510721 | + | 0.859747i | \(0.670621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.3391 | 0.641923 | 0.320962 | − | 0.947092i | \(-0.395994\pi\) | ||||
0.320962 | + | 0.947092i | \(0.395994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.0355 | 1.00410 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.3401 | −0.596985 | −0.298493 | − | 0.954412i | \(-0.596484\pi\) | ||||
−0.298493 | + | 0.954412i | \(0.596484\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.50843 | −0.312040 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.8242 | −0.739472 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.79862 | 0.0744913 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.7026 | 0.441744 | 0.220872 | − | 0.975303i | \(-0.429110\pi\) | ||||
0.220872 | + | 0.975303i | \(0.429110\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.90306 | −0.408048 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.5522 | 0.516328 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.5756 | −0.968135 | −0.484067 | − | 0.875031i | \(-0.660841\pi\) | ||||
−0.484067 | + | 0.875031i | \(0.660841\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.7618 | 0.808798 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.8055 | 0.564078 | 0.282039 | − | 0.959403i | \(-0.408989\pi\) | ||||
0.282039 | + | 0.959403i | \(0.408989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.61536 | 0.392219 | 0.196109 | − | 0.980582i | \(-0.437169\pi\) | ||||
0.196109 | + | 0.980582i | \(0.437169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.05168 | 0.246443 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.7884 | −0.965539 | −0.482770 | − | 0.875747i | \(-0.660369\pi\) | ||||
−0.482770 | + | 0.875747i | \(0.660369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.60128 | 0.389063 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.63888 | 0.309036 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0716 | 0.649127 | 0.324563 | − | 0.945864i | \(-0.394783\pi\) | ||||
0.324563 | + | 0.945864i | \(0.394783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.34595 | 0.376254 | 0.188127 | − | 0.982145i | \(-0.439758\pi\) | ||||
0.188127 | + | 0.982145i | \(0.439758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.4768 | −0.742645 | −0.371323 | − | 0.928504i | \(-0.621096\pi\) | ||||
−0.371323 | + | 0.928504i | \(0.621096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.35567 | −0.255044 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −53.1189 | −2.12816 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.503774 | 0.0201188 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −54.6063 | −2.17729 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.5690 | 1.53541 | 0.767704 | − | 0.640804i | \(-0.221399\pi\) | ||||
0.767704 | + | 0.640804i | \(0.221399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.2479 | 0.447063 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.6217 | −0.500090 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.2983 | 0.526073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8461 | −0.507389 | −0.253695 | − | 0.967284i | \(-0.581646\pi\) | ||||
−0.253695 | + | 0.967284i | \(0.581646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.1030 | 0.792784 | 0.396392 | − | 0.918081i | \(-0.370262\pi\) | ||||
0.396392 | + | 0.918081i | \(0.370262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.1895 | 1.54070 | 0.770350 | − | 0.637622i | \(-0.220082\pi\) | ||||
0.770350 | + | 0.637622i | \(0.220082\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.36194 | 0.0534609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.2848 | 0.559865 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9894 | 1.01704 | 0.508522 | − | 0.861049i | \(-0.330192\pi\) | ||||
0.508522 | + | 0.861049i | \(0.330192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.21152 | −0.203321 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.42356 | −0.250226 | −0.125113 | − | 0.992142i | \(-0.539929\pi\) | ||||
−0.125113 | + | 0.992142i | \(0.539929\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.5875 | 0.839657 | 0.419829 | − | 0.907603i | \(-0.362090\pi\) | ||||
0.419829 | + | 0.907603i | \(0.362090\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.73084 | 0.300241 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0168 | 0.620172 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.27196 | 0.281150 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.81771 | 0.0701718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.94040 | 0.228986 | 0.114493 | − | 0.993424i | \(-0.463476\pi\) | ||||
0.114493 | + | 0.993424i | \(0.463476\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.1784 | 1.42888 | 0.714441 | − | 0.699696i | \(-0.246681\pi\) | ||||
0.714441 | + | 0.699696i | \(0.246681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.5077 | −0.978894 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.46929 | −0.362864 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.1024 | −1.72580 | −0.862899 | − | 0.505377i | \(-0.831353\pi\) | ||||
−0.862899 | + | 0.505377i | \(0.831353\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.2301 | −0.809977 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.8372 | −0.603348 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5713 | −1.08691 | −0.543453 | − | 0.839440i | \(-0.682883\pi\) | ||||
−0.543453 | + | 0.839440i | \(0.682883\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.726676 | −0.0276041 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.0952 | −1.25357 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.08932 | −0.268143 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.2636 | −1.67181 | −0.835907 | − | 0.548871i | \(-0.815058\pi\) | ||||
−0.835907 | + | 0.548871i | \(0.815058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.3321 | 1.18171 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40.0602 | −1.50662 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0124 | 0.638913 | 0.319457 | − | 0.947601i | \(-0.396500\pi\) | ||||
0.319457 | + | 0.947601i | \(0.396500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.11168 | −0.116697 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.8298 | 0.892433 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.0117 | 0.747350 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.29496 | 0.309350 | 0.154675 | − | 0.987965i | \(-0.450567\pi\) | ||||
0.154675 | + | 0.987965i | \(0.450567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.3950 | 1.83956 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.8240 | −0.774454 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.46319 | −0.276794 | −0.138397 | − | 0.990377i | \(-0.544195\pi\) | ||||
−0.138397 | + | 0.990377i | \(0.544195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.4704 | −1.57082 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0201 | −0.443973 | −0.221987 | − | 0.975050i | \(-0.571254\pi\) | ||||
−0.221987 | + | 0.975050i | \(0.571254\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.15425 | 0.0425175 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.3335 | 0.931908 | 0.465954 | − | 0.884809i | \(-0.345711\pi\) | ||||
0.465954 | + | 0.884809i | \(0.345711\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.43582 | −0.162954 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.0959 | −0.773935 | −0.386968 | − | 0.922093i | \(-0.626477\pi\) | ||||
−0.386968 | + | 0.922093i | \(0.626477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.67837 | 0.171173 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.7507 | 1.34284 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.3897 | −1.25490 | −0.627449 | − | 0.778658i | \(-0.715901\pi\) | ||||
−0.627449 | + | 0.778658i | \(0.715901\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.7741 | 1.08503 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.9762 | 1.23488 | 0.617442 | − | 0.786616i | \(-0.288169\pi\) | ||||
0.617442 | + | 0.786616i | \(0.288169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.21224 | −0.0440014 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.3872 | −0.485284 | −0.242642 | − | 0.970116i | \(-0.578014\pi\) | ||||
−0.242642 | + | 0.970116i | \(0.578014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −77.8953 | −2.82000 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.9921 | −0.433010 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.94485 | −0.214377 | −0.107188 | − | 0.994239i | \(-0.534185\pi\) | ||||
−0.107188 | + | 0.994239i | \(0.534185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.2853 | 0.766570 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.0966 | 1.22637 | 0.613184 | − | 0.789940i | \(-0.289888\pi\) | ||||
0.613184 | + | 0.789940i | \(0.289888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −45.1954 | −1.62138 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.9894 | 0.680366 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.53643 | 0.0907604 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.52008 | −0.0900602 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.97301 | −0.0703301 | −0.0351651 | − | 0.999382i | \(-0.511196\pi\) | ||||
−0.0351651 | + | 0.999382i | \(0.511196\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.8653 | −0.778424 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.4079 | 0.547843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.0052 | −0.568361 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.5512 | 1.04676 | 0.523379 | − | 0.852100i | \(-0.324671\pi\) | ||||
0.523379 | + | 0.852100i | \(0.324671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.9378 | −0.740725 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.9423 | 0.492626 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.994009 | −0.0350778 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.56132 | 0.160566 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.94507 | 0.279334 | 0.139667 | − | 0.990199i | \(-0.455397\pi\) | ||||
0.139667 | + | 0.990199i | \(0.455397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.5021 | 0.649698 | 0.324849 | − | 0.945766i | \(-0.394687\pi\) | ||||
0.324849 | + | 0.945766i | \(0.394687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9193 | 0.453099 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.3687 | 0.852555 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.39850 | 0.223582 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4242 | −0.538307 | −0.269154 | − | 0.963097i | \(-0.586744\pi\) | ||||
−0.269154 | + | 0.963097i | \(0.586744\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.5847 | 1.44955 | 0.724775 | − | 0.688986i | \(-0.241944\pi\) | ||||
0.724775 | + | 0.688986i | \(0.241944\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.8857 | 1.21309 | 0.606547 | − | 0.795048i | \(-0.292554\pi\) | ||||
0.606547 | + | 0.795048i | \(0.292554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.6095 | 1.61882 | 0.809408 | − | 0.587247i | \(-0.199788\pi\) | ||||
0.809408 | + | 0.587247i | \(0.199788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.83521 | −0.306490 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.5955 | 1.19866 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.74937 | −0.129597 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.3953 | 1.46365 | 0.731825 | − | 0.681493i | \(-0.238669\pi\) | ||||
0.731825 | + | 0.681493i | \(0.238669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.6492 | −0.781007 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0305495 | −0.00105218 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.7705 | 1.43525 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.80719 | 0.164982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −75.3946 | −2.58449 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.74484 | 0.128221 | 0.0641104 | − | 0.997943i | \(-0.479579\pi\) | ||||
0.0641104 | + | 0.997943i | \(0.479579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.9648 | −1.36517 | −0.682586 | − | 0.730806i | \(-0.739145\pi\) | ||||
−0.682586 | + | 0.730806i | \(0.739145\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −56.1078 | −1.91437 | −0.957186 | − | 0.289472i | \(-0.906520\pi\) | ||||
−0.957186 | + | 0.289472i | \(0.906520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.3915 | −0.933500 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.5927 | −0.632904 | −0.316452 | − | 0.948609i | \(-0.602492\pi\) | ||||
−0.316452 | + | 0.948609i | \(0.602492\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.18984 | −0.142294 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.593500 | −0.0201331 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.1634 | −0.344373 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.69507 | 0.226594 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.8792 | −0.367365 | −0.183682 | − | 0.982986i | \(-0.558802\pi\) | ||||
−0.183682 | + | 0.982986i | \(0.558802\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.9705 | −0.504943 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.9938 | 1.14528 | 0.572641 | − | 0.819806i | \(-0.305919\pi\) | ||||
0.572641 | + | 0.819806i | \(0.305919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.2549 | −0.513367 | −0.256683 | − | 0.966496i | \(-0.582630\pi\) | ||||
−0.256683 | + | 0.966496i | \(0.582630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.5046 | 0.957090 | 0.478545 | − | 0.878063i | \(-0.341164\pi\) | ||||
0.478545 | + | 0.878063i | \(0.341164\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 63.8303 | 2.14080 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.190733 | 0.00638979 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0137 | 0.402024 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.6739 | 0.356392 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.44871 | 0.315132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.4089 | 1.44616 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35.1510 | −1.16975 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.1919 | 0.736868 | 0.368434 | − | 0.929654i | \(-0.379894\pi\) | ||||
0.368434 | + | 0.929654i | \(0.379894\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.5147 | 0.348751 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.6047 | 1.34529 | 0.672647 | − | 0.739963i | \(-0.265157\pi\) | ||||
0.672647 | + | 0.739963i | \(0.265157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.892319 | 0.0295314 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.6013 | 0.416132 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5514 | 0.414031 | 0.207016 | − | 0.978338i | \(-0.433625\pi\) | ||||
0.207016 | + | 0.978338i | \(0.433625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.47622 | 0.147497 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.3336 | −0.735121 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.9648 | −0.425821 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.4129 | −1.85085 | −0.925424 | − | 0.378932i | \(-0.876291\pi\) | ||||
−0.925424 | + | 0.378932i | \(0.876291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.8502 | −0.650565 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.296114 | −0.00969434 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.1247 | 1.37616 | 0.688078 | − | 0.725637i | \(-0.258455\pi\) | ||||
0.688078 | + | 0.725637i | \(0.258455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.1569 | −0.690430 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.7834 | −1.00351 | −0.501755 | − | 0.865010i | \(-0.667312\pi\) | ||||
−0.501755 | + | 0.865010i | \(0.667312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −45.6943 | −1.48801 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.741722 | −0.0241027 | −0.0120514 | − | 0.999927i | \(-0.503836\pi\) | ||||
−0.0120514 | + | 0.999927i | \(0.503836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.75241 | 0.284115 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.9166 | 0.840405 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.3063 | −1.27326 | −0.636628 | − | 0.771171i | \(-0.719671\pi\) | ||||
−0.636628 | + | 0.771171i | \(0.719671\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.480661 | −0.0155376 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.99763 | 0.258257 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.9422 | −0.546522 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.64606 | −0.310840 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.7793 | −1.56864 | −0.784319 | − | 0.620358i | \(-0.786987\pi\) | ||||
−0.784319 | + | 0.620358i | \(0.786987\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.1583 | 0.390582 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −61.2669 | −1.96615 | −0.983074 | − | 0.183210i | \(-0.941351\pi\) | ||||
−0.983074 | + | 0.183210i | \(0.941351\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.6143 | 1.62262 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.1646 | −0.357186 | −0.178593 | − | 0.983923i | \(-0.557155\pi\) | ||||
−0.178593 | + | 0.983923i | \(0.557155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.65925 | 0.0849900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.4454 | 0.652772 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.0074 | 0.988983 | 0.494492 | − | 0.869182i | \(-0.335354\pi\) | ||||
0.494492 | + | 0.869182i | \(0.335354\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.3293 | −0.551599 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −58.6387 | −1.86460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5575 | 0.938926 | 0.469463 | − | 0.882952i | \(-0.344447\pi\) | ||||
0.469463 | + | 0.882952i | \(0.344447\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.07039 | 0.0974358 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.0506 | 1.71180 | 0.855899 | − | 0.517142i | \(-0.173004\pi\) | ||||
0.855899 | + | 0.517142i | \(0.173004\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.8626 | 0.375315 |
(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 | 7500.2.a.m.1.3 | 12 | ||
5.2 | odd | 4 | 7500.2.d.g.1249.15 | 24 | |||
5.3 | odd | 4 | 7500.2.d.g.1249.10 | 24 | |||
5.4 | even | 2 | 7500.2.a.n.1.10 | 12 | |||
25.2 | odd | 20 | 1500.2.o.c.649.4 | 24 | |||
25.9 | even | 10 | 1500.2.m.c.901.5 | 24 | |||
25.11 | even | 5 | 1500.2.m.d.601.2 | 24 | |||
25.12 | odd | 20 | 300.2.o.a.169.3 | ✓ | 24 | ||
25.13 | odd | 20 | 1500.2.o.c.349.4 | 24 | |||
25.14 | even | 10 | 1500.2.m.c.601.5 | 24 | |||
25.16 | even | 5 | 1500.2.m.d.901.2 | 24 | |||
25.23 | odd | 20 | 300.2.o.a.229.3 | yes | 24 | ||
75.23 | even | 20 | 900.2.w.c.829.1 | 24 | |||
75.62 | even | 20 | 900.2.w.c.469.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.3 | ✓ | 24 | 25.12 | odd | 20 | ||
300.2.o.a.229.3 | yes | 24 | 25.23 | odd | 20 | ||
900.2.w.c.469.1 | 24 | 75.62 | even | 20 | |||
900.2.w.c.829.1 | 24 | 75.23 | even | 20 | |||
1500.2.m.c.601.5 | 24 | 25.14 | even | 10 | |||
1500.2.m.c.901.5 | 24 | 25.9 | even | 10 | |||
1500.2.m.d.601.2 | 24 | 25.11 | even | 5 | |||
1500.2.m.d.901.2 | 24 | 25.16 | even | 5 | |||
1500.2.o.c.349.4 | 24 | 25.13 | odd | 20 | |||
1500.2.o.c.649.4 | 24 | 25.2 | odd | 20 | |||
7500.2.a.m.1.3 | 12 | 1.1 | even | 1 | trivial | ||
7500.2.a.n.1.10 | 12 | 5.4 | even | 2 | |||
7500.2.d.g.1249.10 | 24 | 5.3 | odd | 4 | |||
7500.2.d.g.1249.15 | 24 | 5.2 | odd | 4 |