Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.44400625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.01887\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.01887 | 1.42756 | 0.713778 | − | 0.700372i | \(-0.246982\pi\) | ||||
0.713778 | + | 0.700372i | \(0.246982\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.07584 | 1.03792 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.01887 | 0.824200 | ||||||||
\(7\) | −1.01887 | −0.385097 | −0.192548 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192548 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(8\) | 0.153106 | 0.0541311 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.75961 | 1.43508 | 0.717538 | − | 0.696519i | \(-0.245269\pi\) | ||||
0.717538 | + | 0.696519i | \(0.245269\pi\) | |||||||
\(12\) | 2.07584 | 0.599243 | ||||||||
\(13\) | 0.103837 | 0.0287992 | 0.0143996 | − | 0.999896i | \(-0.495416\pi\) | ||||
0.0143996 | + | 0.999896i | \(0.495416\pi\) | |||||||
\(14\) | −2.05697 | −0.549748 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.84257 | −0.960643 | ||||||||
\(17\) | 5.83776 | 1.41587 | 0.707933 | − | 0.706280i | \(-0.249628\pi\) | ||||
0.707933 | + | 0.706280i | \(0.249628\pi\) | |||||||
\(18\) | 2.01887 | 0.475852 | ||||||||
\(19\) | −0.724404 | −0.166190 | −0.0830949 | − | 0.996542i | \(-0.526480\pi\) | ||||
−0.0830949 | + | 0.996542i | \(0.526480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.01887 | −0.222336 | ||||||||
\(22\) | 9.60904 | 2.04865 | ||||||||
\(23\) | 9.07152 | 1.89154 | 0.945771 | − | 0.324834i | \(-0.105308\pi\) | ||||
0.945771 | + | 0.324834i | \(0.105308\pi\) | |||||||
\(24\) | 0.153106 | 0.0312526 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.209634 | 0.0411126 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.11501 | −0.399699 | ||||||||
\(29\) | −3.98847 | −0.740641 | −0.370320 | − | 0.928904i | \(-0.620752\pi\) | ||||
−0.370320 | + | 0.928904i | \(0.620752\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.06662 | 0.191571 | 0.0957857 | − | 0.995402i | \(-0.469464\pi\) | ||||
0.0957857 | + | 0.995402i | \(0.469464\pi\) | |||||||
\(32\) | −8.06387 | −1.42550 | ||||||||
\(33\) | 4.75961 | 0.828542 | ||||||||
\(34\) | 11.7857 | 2.02123 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.07584 | 0.345973 | ||||||||
\(37\) | −4.02621 | −0.661905 | −0.330953 | − | 0.943647i | \(-0.607370\pi\) | ||||
−0.330953 | + | 0.943647i | \(0.607370\pi\) | |||||||
\(38\) | −1.46248 | −0.237245 | ||||||||
\(39\) | 0.103837 | 0.0166273 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.20977 | 1.12598 | 0.562988 | − | 0.826465i | \(-0.309652\pi\) | ||||
0.562988 | + | 0.826465i | \(0.309652\pi\) | |||||||
\(42\) | −2.05697 | −0.317397 | ||||||||
\(43\) | −8.62791 | −1.31574 | −0.657872 | − | 0.753130i | \(-0.728543\pi\) | ||||
−0.657872 | + | 0.753130i | \(0.728543\pi\) | |||||||
\(44\) | 9.88018 | 1.48949 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.3142 | 2.70028 | ||||||||
\(47\) | 8.19797 | 1.19580 | 0.597899 | − | 0.801572i | \(-0.296003\pi\) | ||||
0.597899 | + | 0.801572i | \(0.296003\pi\) | |||||||
\(48\) | −3.84257 | −0.554628 | ||||||||
\(49\) | −5.96190 | −0.851700 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.83776 | 0.817451 | ||||||||
\(52\) | 0.215549 | 0.0298913 | ||||||||
\(53\) | 4.36719 | 0.599880 | 0.299940 | − | 0.953958i | \(-0.403033\pi\) | ||||
0.299940 | + | 0.953958i | \(0.403033\pi\) | |||||||
\(54\) | 2.01887 | 0.274733 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.155995 | −0.0208457 | ||||||||
\(57\) | −0.724404 | −0.0959497 | ||||||||
\(58\) | −8.05221 | −1.05731 | ||||||||
\(59\) | −4.91285 | −0.639599 | −0.319799 | − | 0.947485i | \(-0.603616\pi\) | ||||
−0.319799 | + | 0.947485i | \(0.603616\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.96435 | 0.891694 | 0.445847 | − | 0.895109i | \(-0.352903\pi\) | ||||
0.445847 | + | 0.895109i | \(0.352903\pi\) | |||||||
\(62\) | 2.15338 | 0.273479 | ||||||||
\(63\) | −1.01887 | −0.128366 | ||||||||
\(64\) | −8.59476 | −1.07435 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.60904 | 1.18279 | ||||||||
\(67\) | 9.91998 | 1.21192 | 0.605959 | − | 0.795496i | \(-0.292790\pi\) | ||||
0.605959 | + | 0.795496i | \(0.292790\pi\) | |||||||
\(68\) | 12.1183 | 1.46955 | ||||||||
\(69\) | 9.07152 | 1.09208 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7866 | −1.28013 | −0.640065 | − | 0.768320i | \(-0.721093\pi\) | ||||
−0.640065 | + | 0.768320i | \(0.721093\pi\) | |||||||
\(72\) | 0.153106 | 0.0180437 | ||||||||
\(73\) | −8.63115 | −1.01020 | −0.505100 | − | 0.863061i | \(-0.668544\pi\) | ||||
−0.505100 | + | 0.863061i | \(0.668544\pi\) | |||||||
\(74\) | −8.12840 | −0.944907 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.50375 | −0.172491 | ||||||||
\(77\) | −4.84943 | −0.552644 | ||||||||
\(78\) | 0.209634 | 0.0237363 | ||||||||
\(79\) | 2.48291 | 0.279350 | 0.139675 | − | 0.990197i | \(-0.455394\pi\) | ||||
0.139675 | + | 0.990197i | \(0.455394\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.5556 | 1.60740 | ||||||||
\(83\) | −4.24385 | −0.465823 | −0.232911 | − | 0.972498i | \(-0.574825\pi\) | ||||
−0.232911 | + | 0.972498i | \(0.574825\pi\) | |||||||
\(84\) | −2.11501 | −0.230766 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −17.4186 | −1.87830 | ||||||||
\(87\) | −3.98847 | −0.427609 | ||||||||
\(88\) | 0.728724 | 0.0776823 | ||||||||
\(89\) | −18.3752 | −1.94777 | −0.973884 | − | 0.227047i | \(-0.927093\pi\) | ||||
−0.973884 | + | 0.227047i | \(0.927093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.105797 | −0.0110905 | ||||||||
\(92\) | 18.8310 | 1.96327 | ||||||||
\(93\) | 1.06662 | 0.110604 | ||||||||
\(94\) | 16.5506 | 1.70707 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.06387 | −0.823015 | ||||||||
\(97\) | −6.69876 | −0.680156 | −0.340078 | − | 0.940397i | \(-0.610454\pi\) | ||||
−0.340078 | + | 0.940397i | \(0.610454\pi\) | |||||||
\(98\) | −12.0363 | −1.21585 | ||||||||
\(99\) | 4.75961 | 0.478359 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.66147 | 0.563337 | 0.281669 | − | 0.959512i | \(-0.409112\pi\) | ||||
0.281669 | + | 0.959512i | \(0.409112\pi\) | |||||||
\(102\) | 11.7857 | 1.16696 | ||||||||
\(103\) | −0.594489 | −0.0585767 | −0.0292884 | − | 0.999571i | \(-0.509324\pi\) | ||||
−0.0292884 | + | 0.999571i | \(0.509324\pi\) | |||||||
\(104\) | 0.0158981 | 0.00155893 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.81680 | 0.856363 | ||||||||
\(107\) | −1.38651 | −0.134039 | −0.0670193 | − | 0.997752i | \(-0.521349\pi\) | ||||
−0.0670193 | + | 0.997752i | \(0.521349\pi\) | |||||||
\(108\) | 2.07584 | 0.199748 | ||||||||
\(109\) | −8.85677 | −0.848325 | −0.424162 | − | 0.905586i | \(-0.639431\pi\) | ||||
−0.424162 | + | 0.905586i | \(0.639431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.02621 | −0.382151 | ||||||||
\(112\) | 3.91508 | 0.369941 | ||||||||
\(113\) | −6.59039 | −0.619971 | −0.309986 | − | 0.950741i | \(-0.600324\pi\) | ||||
−0.309986 | + | 0.950741i | \(0.600324\pi\) | |||||||
\(114\) | −1.46248 | −0.136974 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.27942 | −0.768725 | ||||||||
\(117\) | 0.103837 | 0.00959975 | ||||||||
\(118\) | −9.91841 | −0.913064 | ||||||||
\(119\) | −5.94793 | −0.545245 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.6539 | 1.05945 | ||||||||
\(122\) | 14.0601 | 1.27294 | ||||||||
\(123\) | 7.20977 | 0.650083 | ||||||||
\(124\) | 2.21414 | 0.198836 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.05697 | −0.183249 | ||||||||
\(127\) | 7.29144 | 0.647011 | 0.323505 | − | 0.946226i | \(-0.395139\pi\) | ||||
0.323505 | + | 0.946226i | \(0.395139\pi\) | |||||||
\(128\) | −1.22397 | −0.108184 | ||||||||
\(129\) | −8.62791 | −0.759645 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.55386 | −0.834725 | −0.417362 | − | 0.908740i | \(-0.637045\pi\) | ||||
−0.417362 | + | 0.908740i | \(0.637045\pi\) | |||||||
\(132\) | 9.88018 | 0.859959 | ||||||||
\(133\) | 0.738074 | 0.0639991 | ||||||||
\(134\) | 20.0271 | 1.73008 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.893796 | 0.0766424 | ||||||||
\(137\) | 6.19984 | 0.529688 | 0.264844 | − | 0.964291i | \(-0.414680\pi\) | ||||
0.264844 | + | 0.964291i | \(0.414680\pi\) | |||||||
\(138\) | 18.3142 | 1.55901 | ||||||||
\(139\) | −0.906531 | −0.0768910 | −0.0384455 | − | 0.999261i | \(-0.512241\pi\) | ||||
−0.0384455 | + | 0.999261i | \(0.512241\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.19797 | 0.690394 | ||||||||
\(142\) | −21.7767 | −1.82746 | ||||||||
\(143\) | 0.494225 | 0.0413291 | ||||||||
\(144\) | −3.84257 | −0.320214 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.4252 | −1.44212 | ||||||||
\(147\) | −5.96190 | −0.491729 | ||||||||
\(148\) | −8.35776 | −0.687004 | ||||||||
\(149\) | −4.89808 | −0.401267 | −0.200633 | − | 0.979666i | \(-0.564300\pi\) | ||||
−0.200633 | + | 0.979666i | \(0.564300\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2626 | −0.835161 | −0.417581 | − | 0.908640i | \(-0.637122\pi\) | ||||
−0.417581 | + | 0.908640i | \(0.637122\pi\) | |||||||
\(152\) | −0.110911 | −0.00899603 | ||||||||
\(153\) | 5.83776 | 0.471955 | ||||||||
\(154\) | −9.79036 | −0.788930 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.215549 | 0.0172577 | ||||||||
\(157\) | 8.89537 | 0.709928 | 0.354964 | − | 0.934880i | \(-0.384493\pi\) | ||||
0.354964 | + | 0.934880i | \(0.384493\pi\) | |||||||
\(158\) | 5.01268 | 0.398788 | ||||||||
\(159\) | 4.36719 | 0.346341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.24270 | −0.728427 | ||||||||
\(162\) | 2.01887 | 0.158617 | ||||||||
\(163\) | −11.7791 | −0.922607 | −0.461304 | − | 0.887242i | \(-0.652618\pi\) | ||||
−0.461304 | + | 0.887242i | \(0.652618\pi\) | |||||||
\(164\) | 14.9663 | 1.16867 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.56778 | −0.664989 | ||||||||
\(167\) | −17.3762 | −1.34461 | −0.672306 | − | 0.740274i | \(-0.734696\pi\) | ||||
−0.672306 | + | 0.740274i | \(0.734696\pi\) | |||||||
\(168\) | −0.155995 | −0.0120353 | ||||||||
\(169\) | −12.9892 | −0.999171 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.724404 | −0.0553966 | ||||||||
\(172\) | −17.9101 | −1.36564 | ||||||||
\(173\) | 12.9596 | 0.985298 | 0.492649 | − | 0.870228i | \(-0.336029\pi\) | ||||
0.492649 | + | 0.870228i | \(0.336029\pi\) | |||||||
\(174\) | −8.05221 | −0.610436 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −18.2892 | −1.37860 | ||||||||
\(177\) | −4.91285 | −0.369273 | ||||||||
\(178\) | −37.0971 | −2.78055 | ||||||||
\(179\) | 1.09897 | 0.0821409 | 0.0410704 | − | 0.999156i | \(-0.486923\pi\) | ||||
0.0410704 | + | 0.999156i | \(0.486923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9797 | −1.11343 | −0.556716 | − | 0.830703i | \(-0.687939\pi\) | ||||
−0.556716 | + | 0.830703i | \(0.687939\pi\) | |||||||
\(182\) | −0.213590 | −0.0158323 | ||||||||
\(183\) | 6.96435 | 0.514820 | ||||||||
\(184\) | 1.38890 | 0.102391 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.15338 | 0.157893 | ||||||||
\(187\) | 27.7855 | 2.03188 | ||||||||
\(188\) | 17.0177 | 1.24114 | ||||||||
\(189\) | −1.01887 | −0.0741119 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7404 | −0.921862 | −0.460931 | − | 0.887436i | \(-0.652484\pi\) | ||||
−0.460931 | + | 0.887436i | \(0.652484\pi\) | |||||||
\(192\) | −8.59476 | −0.620273 | ||||||||
\(193\) | 4.38386 | 0.315557 | 0.157779 | − | 0.987475i | \(-0.449567\pi\) | ||||
0.157779 | + | 0.987475i | \(0.449567\pi\) | |||||||
\(194\) | −13.5239 | −0.970962 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.3759 | −0.883996 | ||||||||
\(197\) | −3.22165 | −0.229533 | −0.114767 | − | 0.993392i | \(-0.536612\pi\) | ||||
−0.114767 | + | 0.993392i | \(0.536612\pi\) | |||||||
\(198\) | 9.60904 | 0.682885 | ||||||||
\(199\) | −2.70518 | −0.191765 | −0.0958825 | − | 0.995393i | \(-0.530567\pi\) | ||||
−0.0958825 | + | 0.995393i | \(0.530567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.91998 | 0.699701 | ||||||||
\(202\) | 11.4298 | 0.804196 | ||||||||
\(203\) | 4.06374 | 0.285218 | ||||||||
\(204\) | 12.1183 | 0.848447 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.20020 | −0.0836216 | ||||||||
\(207\) | 9.07152 | 0.630514 | ||||||||
\(208\) | −0.399002 | −0.0276658 | ||||||||
\(209\) | −3.44788 | −0.238495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.4435 | 1.82044 | 0.910222 | − | 0.414122i | \(-0.135911\pi\) | ||||
0.910222 | + | 0.414122i | \(0.135911\pi\) | |||||||
\(212\) | 9.06559 | 0.622627 | ||||||||
\(213\) | −10.7866 | −0.739084 | ||||||||
\(214\) | −2.79918 | −0.191348 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.153106 | 0.0104175 | ||||||||
\(217\) | −1.08675 | −0.0737736 | ||||||||
\(218\) | −17.8807 | −1.21103 | ||||||||
\(219\) | −8.63115 | −0.583239 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.606177 | 0.0407759 | ||||||||
\(222\) | −8.12840 | −0.545543 | ||||||||
\(223\) | 8.03245 | 0.537893 | 0.268946 | − | 0.963155i | \(-0.413325\pi\) | ||||
0.268946 | + | 0.963155i | \(0.413325\pi\) | |||||||
\(224\) | 8.21604 | 0.548957 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.3051 | −0.885044 | ||||||||
\(227\) | −16.4576 | −1.09233 | −0.546166 | − | 0.837677i | \(-0.683913\pi\) | ||||
−0.546166 | + | 0.837677i | \(0.683913\pi\) | |||||||
\(228\) | −1.50375 | −0.0995880 | ||||||||
\(229\) | 0.409285 | 0.0270463 | 0.0135231 | − | 0.999909i | \(-0.495695\pi\) | ||||
0.0135231 | + | 0.999909i | \(0.495695\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.84943 | −0.319069 | ||||||||
\(232\) | −0.610658 | −0.0400917 | ||||||||
\(233\) | 18.4641 | 1.20962 | 0.604811 | − | 0.796369i | \(-0.293249\pi\) | ||||
0.604811 | + | 0.796369i | \(0.293249\pi\) | |||||||
\(234\) | 0.209634 | 0.0137042 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.1983 | −0.663852 | ||||||||
\(237\) | 2.48291 | 0.161283 | ||||||||
\(238\) | −12.0081 | −0.778369 | ||||||||
\(239\) | −4.61682 | −0.298637 | −0.149319 | − | 0.988789i | \(-0.547708\pi\) | ||||
−0.149319 | + | 0.988789i | \(0.547708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.2022 | −1.88108 | −0.940540 | − | 0.339682i | \(-0.889681\pi\) | ||||
−0.940540 | + | 0.339682i | \(0.889681\pi\) | |||||||
\(242\) | 23.5277 | 1.51242 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 14.4569 | 0.925506 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.5556 | 0.928030 | ||||||||
\(247\) | −0.0752201 | −0.00478614 | ||||||||
\(248\) | 0.163307 | 0.0103700 | ||||||||
\(249\) | −4.24385 | −0.268943 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.389664 | 0.0245954 | 0.0122977 | − | 0.999924i | \(-0.496085\pi\) | ||||
0.0122977 | + | 0.999924i | \(0.496085\pi\) | |||||||
\(252\) | −2.11501 | −0.133233 | ||||||||
\(253\) | 43.1769 | 2.71451 | ||||||||
\(254\) | 14.7205 | 0.923645 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.7185 | 0.919906 | ||||||||
\(257\) | −8.03324 | −0.501100 | −0.250550 | − | 0.968104i | \(-0.580611\pi\) | ||||
−0.250550 | + | 0.968104i | \(0.580611\pi\) | |||||||
\(258\) | −17.4186 | −1.08444 | ||||||||
\(259\) | 4.10219 | 0.254898 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.98847 | −0.246880 | ||||||||
\(262\) | −19.2880 | −1.19162 | ||||||||
\(263\) | 24.2131 | 1.49304 | 0.746522 | − | 0.665360i | \(-0.231722\pi\) | ||||
0.746522 | + | 0.665360i | \(0.231722\pi\) | |||||||
\(264\) | 0.728724 | 0.0448499 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.49008 | 0.0913624 | ||||||||
\(267\) | −18.3752 | −1.12454 | ||||||||
\(268\) | 20.5923 | 1.25787 | ||||||||
\(269\) | 26.4063 | 1.61002 | 0.805009 | − | 0.593263i | \(-0.202161\pi\) | ||||
0.805009 | + | 0.593263i | \(0.202161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4088 | −0.632287 | −0.316144 | − | 0.948711i | \(-0.602388\pi\) | ||||
−0.316144 | + | 0.948711i | \(0.602388\pi\) | |||||||
\(272\) | −22.4320 | −1.36014 | ||||||||
\(273\) | −0.105797 | −0.00640310 | ||||||||
\(274\) | 12.5167 | 0.756160 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 18.8310 | 1.13349 | ||||||||
\(277\) | 24.5207 | 1.47330 | 0.736652 | − | 0.676272i | \(-0.236405\pi\) | ||||
0.736652 | + | 0.676272i | \(0.236405\pi\) | |||||||
\(278\) | −1.83017 | −0.109766 | ||||||||
\(279\) | 1.06662 | 0.0638572 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4228 | −0.860393 | −0.430197 | − | 0.902735i | \(-0.641556\pi\) | ||||
−0.430197 | + | 0.902735i | \(0.641556\pi\) | |||||||
\(282\) | 16.5506 | 0.985576 | ||||||||
\(283\) | −2.14925 | −0.127760 | −0.0638798 | − | 0.997958i | \(-0.520347\pi\) | ||||
−0.0638798 | + | 0.997958i | \(0.520347\pi\) | |||||||
\(284\) | −22.3912 | −1.32867 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.997775 | 0.0589997 | ||||||||
\(287\) | −7.34582 | −0.433610 | ||||||||
\(288\) | −8.06387 | −0.475168 | ||||||||
\(289\) | 17.0795 | 1.00468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.69876 | −0.392688 | ||||||||
\(292\) | −17.9169 | −1.04851 | ||||||||
\(293\) | 9.02970 | 0.527521 | 0.263760 | − | 0.964588i | \(-0.415037\pi\) | ||||
0.263760 | + | 0.964588i | \(0.415037\pi\) | |||||||
\(294\) | −12.0363 | −0.701972 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.616437 | −0.0358297 | ||||||||
\(297\) | 4.75961 | 0.276181 | ||||||||
\(298\) | −9.88860 | −0.572831 | ||||||||
\(299\) | 0.941960 | 0.0544750 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.79072 | 0.506689 | ||||||||
\(302\) | −20.7189 | −1.19224 | ||||||||
\(303\) | 5.66147 | 0.325243 | ||||||||
\(304\) | 2.78358 | 0.159649 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.7857 | 0.673743 | ||||||||
\(307\) | −5.03454 | −0.287336 | −0.143668 | − | 0.989626i | \(-0.545890\pi\) | ||||
−0.143668 | + | 0.989626i | \(0.545890\pi\) | |||||||
\(308\) | −10.0666 | −0.573599 | ||||||||
\(309\) | −0.594489 | −0.0338193 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.89158 | −0.277376 | −0.138688 | − | 0.990336i | \(-0.544289\pi\) | ||||
−0.138688 | + | 0.990336i | \(0.544289\pi\) | |||||||
\(312\) | 0.0158981 | 0.000900051 0 | ||||||||
\(313\) | 3.17282 | 0.179338 | 0.0896691 | − | 0.995972i | \(-0.471419\pi\) | ||||
0.0896691 | + | 0.995972i | \(0.471419\pi\) | |||||||
\(314\) | 17.9586 | 1.01346 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.15413 | 0.289942 | ||||||||
\(317\) | 19.9953 | 1.12305 | 0.561524 | − | 0.827461i | \(-0.310215\pi\) | ||||
0.561524 | + | 0.827461i | \(0.310215\pi\) | |||||||
\(318\) | 8.81680 | 0.494422 | ||||||||
\(319\) | −18.9836 | −1.06288 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.38651 | −0.0773872 | ||||||||
\(322\) | −18.6598 | −1.03987 | ||||||||
\(323\) | −4.22890 | −0.235302 | ||||||||
\(324\) | 2.07584 | 0.115324 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.7804 | −1.31707 | ||||||||
\(327\) | −8.85677 | −0.489780 | ||||||||
\(328\) | 1.10386 | 0.0609503 | ||||||||
\(329\) | −8.35267 | −0.460498 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.01724 | 0.330738 | 0.165369 | − | 0.986232i | \(-0.447119\pi\) | ||||
0.165369 | + | 0.986232i | \(0.447119\pi\) | |||||||
\(332\) | −8.80954 | −0.483486 | ||||||||
\(333\) | −4.02621 | −0.220635 | ||||||||
\(334\) | −35.0803 | −1.91951 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.91508 | 0.213585 | ||||||||
\(337\) | −22.8136 | −1.24274 | −0.621369 | − | 0.783518i | \(-0.713423\pi\) | ||||
−0.621369 | + | 0.783518i | \(0.713423\pi\) | |||||||
\(338\) | −26.2235 | −1.42637 | ||||||||
\(339\) | −6.59039 | −0.357941 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.07672 | 0.274920 | ||||||||
\(342\) | −1.46248 | −0.0790818 | ||||||||
\(343\) | 13.2065 | 0.713084 | ||||||||
\(344\) | −1.32098 | −0.0712227 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 26.1637 | 1.40657 | ||||||||
\(347\) | −9.79068 | −0.525591 | −0.262796 | − | 0.964852i | \(-0.584644\pi\) | ||||
−0.262796 | + | 0.964852i | \(0.584644\pi\) | |||||||
\(348\) | −8.27942 | −0.443823 | ||||||||
\(349\) | −1.28648 | −0.0688639 | −0.0344320 | − | 0.999407i | \(-0.510962\pi\) | ||||
−0.0344320 | + | 0.999407i | \(0.510962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.103837 | 0.00554242 | ||||||||
\(352\) | −38.3809 | −2.04571 | ||||||||
\(353\) | −1.16422 | −0.0619654 | −0.0309827 | − | 0.999520i | \(-0.509864\pi\) | ||||
−0.0309827 | + | 0.999520i | \(0.509864\pi\) | |||||||
\(354\) | −9.91841 | −0.527158 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −38.1439 | −2.02162 | ||||||||
\(357\) | −5.94793 | −0.314798 | ||||||||
\(358\) | 2.21868 | 0.117261 | ||||||||
\(359\) | 19.0504 | 1.00544 | 0.502720 | − | 0.864449i | \(-0.332333\pi\) | ||||
0.502720 | + | 0.864449i | \(0.332333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4752 | −0.972381 | ||||||||
\(362\) | −30.2421 | −1.58949 | ||||||||
\(363\) | 11.6539 | 0.611671 | ||||||||
\(364\) | −0.219617 | −0.0115110 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.0601 | 0.734935 | ||||||||
\(367\) | −16.7694 | −0.875357 | −0.437679 | − | 0.899131i | \(-0.644199\pi\) | ||||
−0.437679 | + | 0.899131i | \(0.644199\pi\) | |||||||
\(368\) | −34.8580 | −1.81710 | ||||||||
\(369\) | 7.20977 | 0.375326 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.44960 | −0.231012 | ||||||||
\(372\) | 2.21414 | 0.114798 | ||||||||
\(373\) | 17.0520 | 0.882920 | 0.441460 | − | 0.897281i | \(-0.354461\pi\) | ||||
0.441460 | + | 0.897281i | \(0.354461\pi\) | |||||||
\(374\) | 56.0953 | 2.90062 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.25516 | 0.0647298 | ||||||||
\(377\) | −0.414152 | −0.0213299 | ||||||||
\(378\) | −2.05697 | −0.105799 | ||||||||
\(379\) | 1.66611 | 0.0855825 | 0.0427913 | − | 0.999084i | \(-0.486375\pi\) | ||||
0.0427913 | + | 0.999084i | \(0.486375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.29144 | 0.373552 | ||||||||
\(382\) | −25.7212 | −1.31601 | ||||||||
\(383\) | −3.05361 | −0.156032 | −0.0780162 | − | 0.996952i | \(-0.524859\pi\) | ||||
−0.0780162 | + | 0.996952i | \(0.524859\pi\) | |||||||
\(384\) | −1.22397 | −0.0624603 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.85045 | 0.450476 | ||||||||
\(387\) | −8.62791 | −0.438581 | ||||||||
\(388\) | −13.9055 | −0.705947 | ||||||||
\(389\) | 28.2725 | 1.43347 | 0.716737 | − | 0.697343i | \(-0.245635\pi\) | ||||
0.716737 | + | 0.697343i | \(0.245635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.9574 | 2.67817 | ||||||||
\(392\) | −0.912802 | −0.0461035 | ||||||||
\(393\) | −9.55386 | −0.481928 | ||||||||
\(394\) | −6.50410 | −0.327672 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.88018 | 0.496498 | ||||||||
\(397\) | 20.4783 | 1.02778 | 0.513888 | − | 0.857858i | \(-0.328205\pi\) | ||||
0.513888 | + | 0.857858i | \(0.328205\pi\) | |||||||
\(398\) | −5.46140 | −0.273755 | ||||||||
\(399\) | 0.738074 | 0.0369499 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.5952 | 1.27816 | 0.639081 | − | 0.769139i | \(-0.279315\pi\) | ||||
0.639081 | + | 0.769139i | \(0.279315\pi\) | |||||||
\(402\) | 20.0271 | 0.998863 | ||||||||
\(403\) | 0.110755 | 0.00551711 | ||||||||
\(404\) | 11.7523 | 0.584698 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.20416 | 0.407165 | ||||||||
\(407\) | −19.1632 | −0.949885 | ||||||||
\(408\) | 0.893796 | 0.0442495 | ||||||||
\(409\) | −12.0402 | −0.595349 | −0.297675 | − | 0.954667i | \(-0.596211\pi\) | ||||
−0.297675 | + | 0.954667i | \(0.596211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.19984 | 0.305816 | ||||||||
\(412\) | −1.23406 | −0.0607979 | ||||||||
\(413\) | 5.00556 | 0.246307 | ||||||||
\(414\) | 18.3142 | 0.900095 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.837329 | −0.0410534 | ||||||||
\(417\) | −0.906531 | −0.0443930 | ||||||||
\(418\) | −6.96083 | −0.340465 | ||||||||
\(419\) | −34.6045 | −1.69054 | −0.845270 | − | 0.534340i | \(-0.820560\pi\) | ||||
−0.845270 | + | 0.534340i | \(0.820560\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.9525 | −0.728738 | −0.364369 | − | 0.931255i | \(-0.618715\pi\) | ||||
−0.364369 | + | 0.931255i | \(0.618715\pi\) | |||||||
\(422\) | 53.3859 | 2.59879 | ||||||||
\(423\) | 8.19797 | 0.398599 | ||||||||
\(424\) | 0.668643 | 0.0324722 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −21.7767 | −1.05508 | ||||||||
\(427\) | −7.09577 | −0.343389 | ||||||||
\(428\) | −2.87816 | −0.139121 | ||||||||
\(429\) | 0.494225 | 0.0238614 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.81107 | 0.231741 | 0.115871 | − | 0.993264i | \(-0.463034\pi\) | ||||
0.115871 | + | 0.993264i | \(0.463034\pi\) | |||||||
\(432\) | −3.84257 | −0.184876 | ||||||||
\(433\) | −10.3435 | −0.497077 | −0.248538 | − | 0.968622i | \(-0.579950\pi\) | ||||
−0.248538 | + | 0.968622i | \(0.579950\pi\) | |||||||
\(434\) | −2.19401 | −0.105316 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.3852 | −0.880492 | ||||||||
\(437\) | −6.57145 | −0.314355 | ||||||||
\(438\) | −17.4252 | −0.832607 | ||||||||
\(439\) | 30.7640 | 1.46829 | 0.734143 | − | 0.678995i | \(-0.237584\pi\) | ||||
0.734143 | + | 0.678995i | \(0.237584\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.96190 | −0.283900 | ||||||||
\(442\) | 1.22379 | 0.0582099 | ||||||||
\(443\) | 17.7545 | 0.843543 | 0.421772 | − | 0.906702i | \(-0.361408\pi\) | ||||
0.421772 | + | 0.906702i | \(0.361408\pi\) | |||||||
\(444\) | −8.35776 | −0.396642 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.2165 | 0.767873 | ||||||||
\(447\) | −4.89808 | −0.231671 | ||||||||
\(448\) | 8.75695 | 0.413727 | ||||||||
\(449\) | −37.2184 | −1.75645 | −0.878223 | − | 0.478251i | \(-0.841271\pi\) | ||||
−0.878223 | + | 0.478251i | \(0.841271\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.3157 | 1.61586 | ||||||||
\(452\) | −13.6806 | −0.643480 | ||||||||
\(453\) | −10.2626 | −0.482181 | ||||||||
\(454\) | −33.2258 | −1.55937 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.110911 | −0.00519386 | ||||||||
\(457\) | 27.6987 | 1.29569 | 0.647846 | − | 0.761772i | \(-0.275670\pi\) | ||||
0.647846 | + | 0.761772i | \(0.275670\pi\) | |||||||
\(458\) | 0.826293 | 0.0386101 | ||||||||
\(459\) | 5.83776 | 0.272484 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.81742 | 0.457243 | 0.228621 | − | 0.973515i | \(-0.426578\pi\) | ||||
0.228621 | + | 0.973515i | \(0.426578\pi\) | |||||||
\(462\) | −9.79036 | −0.455489 | ||||||||
\(463\) | 3.72732 | 0.173223 | 0.0866115 | − | 0.996242i | \(-0.472396\pi\) | ||||
0.0866115 | + | 0.996242i | \(0.472396\pi\) | |||||||
\(464\) | 15.3260 | 0.711492 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 37.2766 | 1.72680 | ||||||||
\(467\) | 7.09925 | 0.328514 | 0.164257 | − | 0.986418i | \(-0.447477\pi\) | ||||
0.164257 | + | 0.986418i | \(0.447477\pi\) | |||||||
\(468\) | 0.215549 | 0.00996376 | ||||||||
\(469\) | −10.1072 | −0.466706 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.89537 | 0.409877 | ||||||||
\(472\) | −0.752186 | −0.0346222 | ||||||||
\(473\) | −41.0655 | −1.88819 | ||||||||
\(474\) | 5.01268 | 0.230240 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.3469 | −0.565920 | ||||||||
\(477\) | 4.36719 | 0.199960 | ||||||||
\(478\) | −9.32076 | −0.426322 | ||||||||
\(479\) | −28.4451 | −1.29969 | −0.649845 | − | 0.760066i | \(-0.725166\pi\) | ||||
−0.649845 | + | 0.760066i | \(0.725166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.418070 | −0.0190624 | ||||||||
\(482\) | −58.9555 | −2.68535 | ||||||||
\(483\) | −9.24270 | −0.420557 | ||||||||
\(484\) | 24.1916 | 1.09962 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.01887 | 0.0915778 | ||||||||
\(487\) | 14.7384 | 0.667860 | 0.333930 | − | 0.942598i | \(-0.391625\pi\) | ||||
0.333930 | + | 0.942598i | \(0.391625\pi\) | |||||||
\(488\) | 1.06628 | 0.0482684 | ||||||||
\(489\) | −11.7791 | −0.532668 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.4014 | −1.28174 | −0.640869 | − | 0.767650i | \(-0.721426\pi\) | ||||
−0.640869 | + | 0.767650i | \(0.721426\pi\) | |||||||
\(492\) | 14.9663 | 0.674733 | ||||||||
\(493\) | −23.2838 | −1.04865 | ||||||||
\(494\) | −0.151860 | −0.00683248 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.09858 | −0.184032 | ||||||||
\(497\) | 10.9901 | 0.492974 | ||||||||
\(498\) | −8.56778 | −0.383931 | ||||||||
\(499\) | 26.3842 | 1.18112 | 0.590559 | − | 0.806995i | \(-0.298907\pi\) | ||||
0.590559 | + | 0.806995i | \(0.298907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3762 | −0.776312 | ||||||||
\(502\) | 0.786682 | 0.0351113 | ||||||||
\(503\) | −16.6592 | −0.742795 | −0.371398 | − | 0.928474i | \(-0.621121\pi\) | ||||
−0.371398 | + | 0.928474i | \(0.621121\pi\) | |||||||
\(504\) | −0.155995 | −0.00694857 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 87.1686 | 3.87512 | ||||||||
\(507\) | −12.9892 | −0.576871 | ||||||||
\(508\) | 15.1358 | 0.671544 | ||||||||
\(509\) | −31.7760 | −1.40845 | −0.704223 | − | 0.709979i | \(-0.748704\pi\) | ||||
−0.704223 | + | 0.709979i | \(0.748704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.79403 | 0.389025 | ||||||||
\(512\) | 32.1627 | 1.42140 | ||||||||
\(513\) | −0.724404 | −0.0319832 | ||||||||
\(514\) | −16.2181 | −0.715349 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −17.9101 | −0.788450 | ||||||||
\(517\) | 39.0192 | 1.71606 | ||||||||
\(518\) | 8.28179 | 0.363881 | ||||||||
\(519\) | 12.9596 | 0.568862 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.592363 | −0.0259519 | −0.0129759 | − | 0.999916i | \(-0.504130\pi\) | ||||
−0.0129759 | + | 0.999916i | \(0.504130\pi\) | |||||||
\(522\) | −8.05221 | −0.352436 | ||||||||
\(523\) | 17.2298 | 0.753405 | 0.376703 | − | 0.926334i | \(-0.377058\pi\) | ||||
0.376703 | + | 0.926334i | \(0.377058\pi\) | |||||||
\(524\) | −19.8323 | −0.866376 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 48.8832 | 2.13141 | ||||||||
\(527\) | 6.22670 | 0.271240 | ||||||||
\(528\) | −18.2892 | −0.795934 | ||||||||
\(529\) | 59.2924 | 2.57793 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.91285 | −0.213200 | ||||||||
\(532\) | 1.53212 | 0.0664259 | ||||||||
\(533\) | 0.748642 | 0.0324273 | ||||||||
\(534\) | −37.0971 | −1.60535 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.51881 | 0.0656025 | ||||||||
\(537\) | 1.09897 | 0.0474241 | ||||||||
\(538\) | 53.3108 | 2.29839 | ||||||||
\(539\) | −28.3763 | −1.22226 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7990 | 0.636258 | 0.318129 | − | 0.948047i | \(-0.396945\pi\) | ||||
0.318129 | + | 0.948047i | \(0.396945\pi\) | |||||||
\(542\) | −21.0139 | −0.902626 | ||||||||
\(543\) | −14.9797 | −0.642840 | ||||||||
\(544\) | −47.0750 | −2.01832 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.213590 | −0.00914079 | ||||||||
\(547\) | −6.50806 | −0.278264 | −0.139132 | − | 0.990274i | \(-0.544431\pi\) | ||||
−0.139132 | + | 0.990274i | \(0.544431\pi\) | |||||||
\(548\) | 12.8699 | 0.549773 | ||||||||
\(549\) | 6.96435 | 0.297231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.88927 | 0.123087 | ||||||||
\(552\) | 1.38890 | 0.0591156 | ||||||||
\(553\) | −2.52977 | −0.107577 | ||||||||
\(554\) | 49.5041 | 2.10323 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.88181 | −0.0798066 | ||||||||
\(557\) | 6.67224 | 0.282712 | 0.141356 | − | 0.989959i | \(-0.454854\pi\) | ||||
0.141356 | + | 0.989959i | \(0.454854\pi\) | |||||||
\(558\) | 2.15338 | 0.0911597 | ||||||||
\(559\) | −0.895898 | −0.0378924 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.7855 | 1.17310 | ||||||||
\(562\) | −29.1178 | −1.22826 | ||||||||
\(563\) | −20.0663 | −0.845694 | −0.422847 | − | 0.906201i | \(-0.638969\pi\) | ||||
−0.422847 | + | 0.906201i | \(0.638969\pi\) | |||||||
\(564\) | 17.0177 | 0.716573 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.33906 | −0.182384 | ||||||||
\(567\) | −1.01887 | −0.0427885 | ||||||||
\(568\) | −1.65149 | −0.0692949 | ||||||||
\(569\) | −21.5938 | −0.905261 | −0.452631 | − | 0.891698i | \(-0.649514\pi\) | ||||
−0.452631 | + | 0.891698i | \(0.649514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.3338 | −1.10203 | −0.551017 | − | 0.834494i | \(-0.685760\pi\) | ||||
−0.551017 | + | 0.834494i | \(0.685760\pi\) | |||||||
\(572\) | 1.02593 | 0.0428963 | ||||||||
\(573\) | −12.7404 | −0.532237 | ||||||||
\(574\) | −14.8303 | −0.619003 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.59476 | −0.358115 | ||||||||
\(577\) | 9.18240 | 0.382268 | 0.191134 | − | 0.981564i | \(-0.438783\pi\) | ||||
0.191134 | + | 0.981564i | \(0.438783\pi\) | |||||||
\(578\) | 34.4813 | 1.43423 | ||||||||
\(579\) | 4.38386 | 0.182187 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.32393 | 0.179387 | ||||||||
\(582\) | −13.5239 | −0.560585 | ||||||||
\(583\) | 20.7861 | 0.860874 | ||||||||
\(584\) | −1.32148 | −0.0546832 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.2298 | 0.753066 | ||||||||
\(587\) | −39.9771 | −1.65003 | −0.825017 | − | 0.565108i | \(-0.808834\pi\) | ||||
−0.825017 | + | 0.565108i | \(0.808834\pi\) | |||||||
\(588\) | −12.3759 | −0.510375 | ||||||||
\(589\) | −0.772668 | −0.0318372 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.22165 | −0.132521 | ||||||||
\(592\) | 15.4710 | 0.635855 | ||||||||
\(593\) | 41.6331 | 1.70967 | 0.854834 | − | 0.518902i | \(-0.173659\pi\) | ||||
0.854834 | + | 0.518902i | \(0.173659\pi\) | |||||||
\(594\) | 9.60904 | 0.394264 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.1676 | −0.416482 | ||||||||
\(597\) | −2.70518 | −0.110716 | ||||||||
\(598\) | 1.90170 | 0.0777661 | ||||||||
\(599\) | 39.0726 | 1.59646 | 0.798232 | − | 0.602350i | \(-0.205769\pi\) | ||||
0.798232 | + | 0.602350i | \(0.205769\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.46965 | 0.223112 | 0.111556 | − | 0.993758i | \(-0.464417\pi\) | ||||
0.111556 | + | 0.993758i | \(0.464417\pi\) | |||||||
\(602\) | 17.7473 | 0.723327 | ||||||||
\(603\) | 9.91998 | 0.403973 | ||||||||
\(604\) | −21.3036 | −0.866829 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.4298 | 0.464303 | ||||||||
\(607\) | −42.3108 | −1.71734 | −0.858671 | − | 0.512527i | \(-0.828709\pi\) | ||||
−0.858671 | + | 0.512527i | \(0.828709\pi\) | |||||||
\(608\) | 5.84150 | 0.236904 | ||||||||
\(609\) | 4.06374 | 0.164671 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.851254 | 0.0344380 | ||||||||
\(612\) | 12.1183 | 0.489851 | ||||||||
\(613\) | 34.0064 | 1.37351 | 0.686753 | − | 0.726891i | \(-0.259035\pi\) | ||||
0.686753 | + | 0.726891i | \(0.259035\pi\) | |||||||
\(614\) | −10.1641 | −0.410189 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.742476 | −0.0299152 | ||||||||
\(617\) | −23.3173 | −0.938717 | −0.469359 | − | 0.883008i | \(-0.655515\pi\) | ||||
−0.469359 | + | 0.883008i | \(0.655515\pi\) | |||||||
\(618\) | −1.20020 | −0.0482790 | ||||||||
\(619\) | 35.2998 | 1.41882 | 0.709409 | − | 0.704797i | \(-0.248962\pi\) | ||||
0.709409 | + | 0.704797i | \(0.248962\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.07152 | 0.364027 | ||||||||
\(622\) | −9.87547 | −0.395970 | ||||||||
\(623\) | 18.7219 | 0.750079 | ||||||||
\(624\) | −0.399002 | −0.0159729 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.40551 | 0.256016 | ||||||||
\(627\) | −3.44788 | −0.137695 | ||||||||
\(628\) | 18.4653 | 0.736847 | ||||||||
\(629\) | −23.5041 | −0.937169 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.50433 | −0.139505 | −0.0697526 | − | 0.997564i | \(-0.522221\pi\) | ||||
−0.0697526 | + | 0.997564i | \(0.522221\pi\) | |||||||
\(632\) | 0.380149 | 0.0151215 | ||||||||
\(633\) | 26.4435 | 1.05103 | ||||||||
\(634\) | 40.3679 | 1.60321 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.06559 | 0.359474 | ||||||||
\(637\) | −0.619067 | −0.0245283 | ||||||||
\(638\) | −38.3254 | −1.51732 | ||||||||
\(639\) | −10.7866 | −0.426710 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.28841 | −0.366870 | −0.183435 | − | 0.983032i | \(-0.558722\pi\) | ||||
−0.183435 | + | 0.983032i | \(0.558722\pi\) | |||||||
\(642\) | −2.79918 | −0.110475 | ||||||||
\(643\) | 0.0291680 | 0.00115028 | 0.000575138 | − | 1.00000i | \(-0.499817\pi\) | ||||
0.000575138 | 1.00000i | \(0.499817\pi\) | ||||||||
\(644\) | −19.1863 | −0.756048 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.53760 | −0.335908 | ||||||||
\(647\) | 0.844100 | 0.0331850 | 0.0165925 | − | 0.999862i | \(-0.494718\pi\) | ||||
0.0165925 | + | 0.999862i | \(0.494718\pi\) | |||||||
\(648\) | 0.153106 | 0.00601457 | ||||||||
\(649\) | −23.3833 | −0.917874 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.08675 | −0.0425932 | ||||||||
\(652\) | −24.4514 | −0.957591 | ||||||||
\(653\) | −38.0711 | −1.48984 | −0.744918 | − | 0.667156i | \(-0.767511\pi\) | ||||
−0.744918 | + | 0.667156i | \(0.767511\pi\) | |||||||
\(654\) | −17.8807 | −0.699189 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27.7041 | −1.08166 | ||||||||
\(657\) | −8.63115 | −0.336733 | ||||||||
\(658\) | −16.8630 | −0.657387 | ||||||||
\(659\) | 37.8343 | 1.47382 | 0.736908 | − | 0.675993i | \(-0.236285\pi\) | ||||
0.736908 | + | 0.675993i | \(0.236285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.5614 | −0.721956 | −0.360978 | − | 0.932574i | \(-0.617557\pi\) | ||||
−0.360978 | + | 0.932574i | \(0.617557\pi\) | |||||||
\(662\) | 12.1480 | 0.472147 | ||||||||
\(663\) | 0.606177 | 0.0235420 | ||||||||
\(664\) | −0.649758 | −0.0252155 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.12840 | −0.314969 | ||||||||
\(667\) | −36.1815 | −1.40095 | ||||||||
\(668\) | −36.0702 | −1.39560 | ||||||||
\(669\) | 8.03245 | 0.310553 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.1476 | 1.27965 | ||||||||
\(672\) | 8.21604 | 0.316941 | ||||||||
\(673\) | −18.1607 | −0.700044 | −0.350022 | − | 0.936742i | \(-0.613826\pi\) | ||||
−0.350022 | + | 0.936742i | \(0.613826\pi\) | |||||||
\(674\) | −46.0578 | −1.77408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.9635 | −1.03706 | ||||||||
\(677\) | 5.64312 | 0.216883 | 0.108441 | − | 0.994103i | \(-0.465414\pi\) | ||||
0.108441 | + | 0.994103i | \(0.465414\pi\) | |||||||
\(678\) | −13.3051 | −0.510981 | ||||||||
\(679\) | 6.82517 | 0.261926 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.4576 | −0.630658 | ||||||||
\(682\) | 10.2492 | 0.392464 | ||||||||
\(683\) | −30.4468 | −1.16502 | −0.582508 | − | 0.812825i | \(-0.697929\pi\) | ||||
−0.582508 | + | 0.812825i | \(0.697929\pi\) | |||||||
\(684\) | −1.50375 | −0.0574971 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.6622 | 1.01797 | ||||||||
\(687\) | 0.409285 | 0.0156152 | ||||||||
\(688\) | 33.1534 | 1.26396 | ||||||||
\(689\) | 0.453477 | 0.0172761 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.22470 | −0.350924 | −0.175462 | − | 0.984486i | \(-0.556142\pi\) | ||||
−0.175462 | + | 0.984486i | \(0.556142\pi\) | |||||||
\(692\) | 26.9020 | 1.02266 | ||||||||
\(693\) | −4.84943 | −0.184215 | ||||||||
\(694\) | −19.7661 | −0.750311 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.610658 | −0.0231469 | ||||||||
\(697\) | 42.0889 | 1.59423 | ||||||||
\(698\) | −2.59724 | −0.0983071 | ||||||||
\(699\) | 18.4641 | 0.698375 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9822 | −0.754717 | −0.377358 | − | 0.926067i | \(-0.623168\pi\) | ||||
−0.377358 | + | 0.926067i | \(0.623168\pi\) | |||||||
\(702\) | 0.209634 | 0.00791212 | ||||||||
\(703\) | 2.91661 | 0.110002 | ||||||||
\(704\) | −40.9077 | −1.54177 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.35042 | −0.0884591 | ||||||||
\(707\) | −5.76830 | −0.216939 | ||||||||
\(708\) | −10.1983 | −0.383275 | ||||||||
\(709\) | −26.8259 | −1.00747 | −0.503734 | − | 0.863859i | \(-0.668041\pi\) | ||||
−0.503734 | + | 0.863859i | \(0.668041\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.48291 | 0.0931166 | ||||||||
\(712\) | −2.81335 | −0.105435 | ||||||||
\(713\) | 9.67591 | 0.362366 | ||||||||
\(714\) | −12.0081 | −0.449391 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.28128 | 0.0852556 | ||||||||
\(717\) | −4.61682 | −0.172418 | ||||||||
\(718\) | 38.4602 | 1.43532 | ||||||||
\(719\) | 38.8224 | 1.44783 | 0.723915 | − | 0.689889i | \(-0.242341\pi\) | ||||
0.723915 | + | 0.689889i | \(0.242341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.605707 | 0.0225577 | ||||||||
\(722\) | −37.2991 | −1.38813 | ||||||||
\(723\) | −29.2022 | −1.08604 | ||||||||
\(724\) | −31.0954 | −1.15565 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 23.5277 | 0.873196 | ||||||||
\(727\) | −29.5764 | −1.09693 | −0.548465 | − | 0.836174i | \(-0.684787\pi\) | ||||
−0.548465 | + | 0.836174i | \(0.684787\pi\) | |||||||
\(728\) | −0.0161981 | −0.000600341 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −50.3677 | −1.86292 | ||||||||
\(732\) | 14.4569 | 0.534341 | ||||||||
\(733\) | 48.8782 | 1.80536 | 0.902679 | − | 0.430315i | \(-0.141598\pi\) | ||||
0.902679 | + | 0.430315i | \(0.141598\pi\) | |||||||
\(734\) | −33.8553 | −1.24962 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −73.1515 | −2.69640 | ||||||||
\(737\) | 47.2152 | 1.73920 | ||||||||
\(738\) | 14.5556 | 0.535799 | ||||||||
\(739\) | 21.7603 | 0.800466 | 0.400233 | − | 0.916413i | \(-0.368929\pi\) | ||||
0.400233 | + | 0.916413i | \(0.368929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0752201 | −0.00276328 | ||||||||
\(742\) | −8.98317 | −0.329783 | ||||||||
\(743\) | 9.75724 | 0.357959 | 0.178979 | − | 0.983853i | \(-0.442720\pi\) | ||||
0.178979 | + | 0.983853i | \(0.442720\pi\) | |||||||
\(744\) | 0.163307 | 0.00598711 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 34.4258 | 1.26042 | ||||||||
\(747\) | −4.24385 | −0.155274 | ||||||||
\(748\) | 57.6782 | 2.10892 | ||||||||
\(749\) | 1.41267 | 0.0516178 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.6413 | −0.643741 | −0.321871 | − | 0.946784i | \(-0.604312\pi\) | ||||
−0.321871 | + | 0.946784i | \(0.604312\pi\) | |||||||
\(752\) | −31.5013 | −1.14873 | ||||||||
\(753\) | 0.389664 | 0.0142002 | ||||||||
\(754\) | −0.836118 | −0.0304496 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.11501 | −0.0769221 | ||||||||
\(757\) | 44.2551 | 1.60848 | 0.804240 | − | 0.594305i | \(-0.202573\pi\) | ||||
0.804240 | + | 0.594305i | \(0.202573\pi\) | |||||||
\(758\) | 3.36367 | 0.122174 | ||||||||
\(759\) | 43.1769 | 1.56722 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.8755 | 1.44549 | 0.722743 | − | 0.691117i | \(-0.242881\pi\) | ||||
0.722743 | + | 0.691117i | \(0.242881\pi\) | |||||||
\(762\) | 14.7205 | 0.533266 | ||||||||
\(763\) | 9.02390 | 0.326687 | ||||||||
\(764\) | −26.4470 | −0.956818 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.16485 | −0.222745 | ||||||||
\(767\) | −0.510137 | −0.0184200 | ||||||||
\(768\) | 14.7185 | 0.531108 | ||||||||
\(769\) | 35.2667 | 1.27175 | 0.635876 | − | 0.771792i | \(-0.280639\pi\) | ||||
0.635876 | + | 0.771792i | \(0.280639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.03324 | −0.289310 | ||||||||
\(772\) | 9.10018 | 0.327523 | ||||||||
\(773\) | 23.2417 | 0.835946 | 0.417973 | − | 0.908459i | \(-0.362741\pi\) | ||||
0.417973 | + | 0.908459i | \(0.362741\pi\) | |||||||
\(774\) | −17.4186 | −0.626100 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.02562 | −0.0368176 | ||||||||
\(777\) | 4.10219 | 0.147165 | ||||||||
\(778\) | 57.0786 | 2.04637 | ||||||||
\(779\) | −5.22279 | −0.187126 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −51.3399 | −1.83709 | ||||||||
\(782\) | 106.914 | 3.82324 | ||||||||
\(783\) | −3.98847 | −0.142536 | ||||||||
\(784\) | 22.9091 | 0.818180 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −19.2880 | −0.687980 | ||||||||
\(787\) | −6.83095 | −0.243497 | −0.121749 | − | 0.992561i | \(-0.538850\pi\) | ||||
−0.121749 | + | 0.992561i | \(0.538850\pi\) | |||||||
\(788\) | −6.68762 | −0.238237 | ||||||||
\(789\) | 24.2131 | 0.862010 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.71475 | 0.238749 | ||||||||
\(792\) | 0.728724 | 0.0258941 | ||||||||
\(793\) | 0.723159 | 0.0256801 | ||||||||
\(794\) | 41.3430 | 1.46721 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.61551 | −0.199036 | ||||||||
\(797\) | −53.9287 | −1.91025 | −0.955126 | − | 0.296198i | \(-0.904281\pi\) | ||||
−0.955126 | + | 0.296198i | \(0.904281\pi\) | |||||||
\(798\) | 1.49008 | 0.0527481 | ||||||||
\(799\) | 47.8578 | 1.69309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.3752 | −0.649256 | ||||||||
\(802\) | 51.6734 | 1.82465 | ||||||||
\(803\) | −41.0809 | −1.44971 | ||||||||
\(804\) | 20.5923 | 0.726233 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.223601 | 0.00787599 | ||||||||
\(807\) | 26.4063 | 0.929544 | ||||||||
\(808\) | 0.866804 | 0.0304941 | ||||||||
\(809\) | −18.4104 | −0.647275 | −0.323637 | − | 0.946181i | \(-0.604906\pi\) | ||||
−0.323637 | + | 0.946181i | \(0.604906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.7910 | −0.414040 | −0.207020 | − | 0.978337i | \(-0.566376\pi\) | ||||
−0.207020 | + | 0.978337i | \(0.566376\pi\) | |||||||
\(812\) | 8.43565 | 0.296033 | ||||||||
\(813\) | −10.4088 | −0.365051 | ||||||||
\(814\) | −38.6880 | −1.35601 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −22.4320 | −0.785279 | ||||||||
\(817\) | 6.25009 | 0.218663 | ||||||||
\(818\) | −24.3076 | −0.849895 | ||||||||
\(819\) | −0.105797 | −0.00369683 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.3261 | −0.430185 | −0.215093 | − | 0.976594i | \(-0.569005\pi\) | ||||
−0.215093 | + | 0.976594i | \(0.569005\pi\) | |||||||
\(822\) | 12.5167 | 0.436569 | ||||||||
\(823\) | −2.81852 | −0.0982475 | −0.0491237 | − | 0.998793i | \(-0.515643\pi\) | ||||
−0.0491237 | + | 0.998793i | \(0.515643\pi\) | |||||||
\(824\) | −0.0910197 | −0.00317082 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.1056 | 0.351618 | ||||||||
\(827\) | 37.4251 | 1.30140 | 0.650700 | − | 0.759335i | \(-0.274476\pi\) | ||||
0.650700 | + | 0.759335i | \(0.274476\pi\) | |||||||
\(828\) | 18.8310 | 0.654422 | ||||||||
\(829\) | 30.9434 | 1.07471 | 0.537355 | − | 0.843356i | \(-0.319424\pi\) | ||||
0.537355 | + | 0.843356i | \(0.319424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.5207 | 0.850613 | ||||||||
\(832\) | −0.892455 | −0.0309403 | ||||||||
\(833\) | −34.8042 | −1.20589 | ||||||||
\(834\) | −1.83017 | −0.0633736 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.15724 | −0.247538 | ||||||||
\(837\) | 1.06662 | 0.0368679 | ||||||||
\(838\) | −69.8620 | −2.41334 | ||||||||
\(839\) | −26.6975 | −0.921701 | −0.460851 | − | 0.887478i | \(-0.652456\pi\) | ||||
−0.460851 | + | 0.887478i | \(0.652456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0921 | −0.451451 | ||||||||
\(842\) | −30.1871 | −1.04032 | ||||||||
\(843\) | −14.4228 | −0.496748 | ||||||||
\(844\) | 54.8923 | 1.88947 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16.5506 | 0.569023 | ||||||||
\(847\) | −11.8738 | −0.407989 | ||||||||
\(848\) | −16.7813 | −0.576271 | ||||||||
\(849\) | −2.14925 | −0.0737620 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.5239 | −1.25202 | ||||||||
\(852\) | −22.3912 | −0.767109 | ||||||||
\(853\) | −29.2600 | −1.00184 | −0.500921 | − | 0.865493i | \(-0.667005\pi\) | ||||
−0.500921 | + | 0.865493i | \(0.667005\pi\) | |||||||
\(854\) | −14.3254 | −0.490207 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.212282 | −0.00725566 | ||||||||
\(857\) | 33.5284 | 1.14531 | 0.572654 | − | 0.819797i | \(-0.305914\pi\) | ||||
0.572654 | + | 0.819797i | \(0.305914\pi\) | |||||||
\(858\) | 0.997775 | 0.0340635 | ||||||||
\(859\) | −25.8243 | −0.881115 | −0.440557 | − | 0.897725i | \(-0.645219\pi\) | ||||
−0.440557 | + | 0.897725i | \(0.645219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.34582 | −0.250345 | ||||||||
\(862\) | 9.71293 | 0.330824 | ||||||||
\(863\) | 28.8886 | 0.983378 | 0.491689 | − | 0.870771i | \(-0.336380\pi\) | ||||
0.491689 | + | 0.870771i | \(0.336380\pi\) | |||||||
\(864\) | −8.06387 | −0.274338 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.8822 | −0.709605 | ||||||||
\(867\) | 17.0795 | 0.580050 | ||||||||
\(868\) | −2.25592 | −0.0765710 | ||||||||
\(869\) | 11.8177 | 0.400888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.03006 | 0.0349023 | ||||||||
\(872\) | −1.35602 | −0.0459207 | ||||||||
\(873\) | −6.69876 | −0.226719 | ||||||||
\(874\) | −13.2669 | −0.448759 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.9169 | −0.605355 | ||||||||
\(877\) | 15.1004 | 0.509905 | 0.254953 | − | 0.966954i | \(-0.417940\pi\) | ||||
0.254953 | + | 0.966954i | \(0.417940\pi\) | |||||||
\(878\) | 62.1086 | 2.09606 | ||||||||
\(879\) | 9.02970 | 0.304564 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.6216 | 1.23381 | 0.616906 | − | 0.787037i | \(-0.288386\pi\) | ||||
0.616906 | + | 0.787037i | \(0.288386\pi\) | |||||||
\(882\) | −12.0363 | −0.405284 | ||||||||
\(883\) | 34.5459 | 1.16256 | 0.581281 | − | 0.813703i | \(-0.302552\pi\) | ||||
0.581281 | + | 0.813703i | \(0.302552\pi\) | |||||||
\(884\) | 1.25832 | 0.0423220 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.8441 | 1.20421 | ||||||||
\(887\) | −33.0360 | −1.10924 | −0.554620 | − | 0.832104i | \(-0.687136\pi\) | ||||
−0.554620 | + | 0.832104i | \(0.687136\pi\) | |||||||
\(888\) | −0.616437 | −0.0206863 | ||||||||
\(889\) | −7.42903 | −0.249162 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.75961 | 0.159453 | ||||||||
\(892\) | 16.6741 | 0.558289 | ||||||||
\(893\) | −5.93864 | −0.198729 | ||||||||
\(894\) | −9.88860 | −0.330724 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.24706 | 0.0416614 | ||||||||
\(897\) | 0.941960 | 0.0314511 | ||||||||
\(898\) | −75.1392 | −2.50743 | ||||||||
\(899\) | −4.25420 | −0.141886 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.4947 | 0.849350 | ||||||||
\(902\) | 69.2789 | 2.30674 | ||||||||
\(903\) | 8.79072 | 0.292537 | ||||||||
\(904\) | −1.00903 | −0.0335597 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −20.7189 | −0.688340 | ||||||||
\(907\) | 44.2708 | 1.46999 | 0.734994 | − | 0.678074i | \(-0.237185\pi\) | ||||
0.734994 | + | 0.678074i | \(0.237185\pi\) | |||||||
\(908\) | −34.1634 | −1.13375 | ||||||||
\(909\) | 5.66147 | 0.187779 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.8844 | −1.28830 | −0.644148 | − | 0.764901i | \(-0.722788\pi\) | ||||
−0.644148 | + | 0.764901i | \(0.722788\pi\) | |||||||
\(912\) | 2.78358 | 0.0921734 | ||||||||
\(913\) | −20.1991 | −0.668492 | ||||||||
\(914\) | 55.9201 | 1.84967 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.849608 | 0.0280719 | ||||||||
\(917\) | 9.73414 | 0.321450 | ||||||||
\(918\) | 11.7857 | 0.388986 | ||||||||
\(919\) | −28.5303 | −0.941127 | −0.470563 | − | 0.882366i | \(-0.655949\pi\) | ||||
−0.470563 | + | 0.882366i | \(0.655949\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.03454 | −0.165894 | ||||||||
\(922\) | 19.8201 | 0.652740 | ||||||||
\(923\) | −1.12005 | −0.0368668 | ||||||||
\(924\) | −10.0666 | −0.331168 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.52497 | 0.247286 | ||||||||
\(927\) | −0.594489 | −0.0195256 | ||||||||
\(928\) | 32.1625 | 1.05579 | ||||||||
\(929\) | 36.3886 | 1.19387 | 0.596936 | − | 0.802289i | \(-0.296385\pi\) | ||||
0.596936 | + | 0.802289i | \(0.296385\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.31883 | 0.141544 | ||||||||
\(932\) | 38.3284 | 1.25549 | ||||||||
\(933\) | −4.89158 | −0.160143 | ||||||||
\(934\) | 14.3325 | 0.468973 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.0158981 | 0.000519645 0 | ||||||||
\(937\) | 47.3354 | 1.54638 | 0.773189 | − | 0.634175i | \(-0.218660\pi\) | ||||
0.773189 | + | 0.634175i | \(0.218660\pi\) | |||||||
\(938\) | −20.4051 | −0.666249 | ||||||||
\(939\) | 3.17282 | 0.103541 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.9254 | 1.72532 | 0.862659 | − | 0.505787i | \(-0.168798\pi\) | ||||
0.862659 | + | 0.505787i | \(0.168798\pi\) | |||||||
\(942\) | 17.9586 | 0.585123 | ||||||||
\(943\) | 65.4035 | 2.12983 | ||||||||
\(944\) | 18.8780 | 0.614426 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −82.9059 | −2.69550 | ||||||||
\(947\) | −18.9330 | −0.615239 | −0.307619 | − | 0.951509i | \(-0.599532\pi\) | ||||
−0.307619 | + | 0.951509i | \(0.599532\pi\) | |||||||
\(948\) | 5.15413 | 0.167398 | ||||||||
\(949\) | −0.896234 | −0.0290930 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.9953 | 0.648392 | ||||||||
\(952\) | −0.910662 | −0.0295147 | ||||||||
\(953\) | 11.4499 | 0.370899 | 0.185450 | − | 0.982654i | \(-0.440626\pi\) | ||||
0.185450 | + | 0.982654i | \(0.440626\pi\) | |||||||
\(954\) | 8.81680 | 0.285454 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.58377 | −0.309961 | ||||||||
\(957\) | −18.9836 | −0.613652 | ||||||||
\(958\) | −57.4270 | −1.85538 | ||||||||
\(959\) | −6.31683 | −0.203981 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8623 | −0.963300 | ||||||||
\(962\) | −0.844030 | −0.0272126 | ||||||||
\(963\) | −1.38651 | −0.0446795 | ||||||||
\(964\) | −60.6191 | −1.95241 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −18.6598 | −0.600370 | ||||||||
\(967\) | 36.9926 | 1.18960 | 0.594801 | − | 0.803873i | \(-0.297231\pi\) | ||||
0.594801 | + | 0.803873i | \(0.297231\pi\) | |||||||
\(968\) | 1.78428 | 0.0573490 | ||||||||
\(969\) | −4.22890 | −0.135852 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.2897 | −0.972043 | −0.486022 | − | 0.873947i | \(-0.661552\pi\) | ||||
−0.486022 | + | 0.873947i | \(0.661552\pi\) | |||||||
\(972\) | 2.07584 | 0.0665825 | ||||||||
\(973\) | 0.923638 | 0.0296105 | ||||||||
\(974\) | 29.7549 | 0.953408 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.7610 | −0.856600 | ||||||||
\(977\) | −16.6410 | −0.532394 | −0.266197 | − | 0.963919i | \(-0.585767\pi\) | ||||
−0.266197 | + | 0.963919i | \(0.585767\pi\) | |||||||
\(978\) | −23.7804 | −0.760413 | ||||||||
\(979\) | −87.4588 | −2.79520 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.85677 | −0.282775 | ||||||||
\(982\) | −57.3388 | −1.82975 | ||||||||
\(983\) | −26.1897 | −0.835320 | −0.417660 | − | 0.908603i | \(-0.637150\pi\) | ||||
−0.417660 | + | 0.908603i | \(0.637150\pi\) | |||||||
\(984\) | 1.10386 | 0.0351897 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −47.0069 | −1.49700 | ||||||||
\(987\) | −8.35267 | −0.265868 | ||||||||
\(988\) | −0.156145 | −0.00496762 | ||||||||
\(989\) | −78.2682 | −2.48878 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.8373 | −0.788982 | −0.394491 | − | 0.918900i | \(-0.629079\pi\) | ||||
−0.394491 | + | 0.918900i | \(0.629079\pi\) | |||||||
\(992\) | −8.60112 | −0.273086 | ||||||||
\(993\) | 6.01724 | 0.190951 | ||||||||
\(994\) | 22.1876 | 0.703749 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.80954 | −0.279141 | ||||||||
\(997\) | −25.0863 | −0.794490 | −0.397245 | − | 0.917713i | \(-0.630034\pi\) | ||||
−0.397245 | + | 0.917713i | \(0.630034\pi\) | |||||||
\(998\) | 53.2662 | 1.68611 | ||||||||
\(999\) | −4.02621 | −0.127384 |
(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 | 1875.2.a.k.1.5 | 6 | ||
3.2 | odd | 2 | 5625.2.a.q.1.2 | 6 | |||
5.2 | odd | 4 | 1875.2.b.f.1249.9 | 12 | |||
5.3 | odd | 4 | 1875.2.b.f.1249.4 | 12 | |||
5.4 | even | 2 | 1875.2.a.j.1.2 | 6 | |||
15.14 | odd | 2 | 5625.2.a.p.1.5 | 6 | |||
25.3 | odd | 20 | 375.2.i.d.49.2 | 24 | |||
25.4 | even | 10 | 75.2.g.c.16.3 | ✓ | 12 | ||
25.6 | even | 5 | 375.2.g.c.301.1 | 12 | |||
25.8 | odd | 20 | 375.2.i.d.199.5 | 24 | |||
25.17 | odd | 20 | 375.2.i.d.199.2 | 24 | |||
25.19 | even | 10 | 75.2.g.c.61.3 | yes | 12 | ||
25.21 | even | 5 | 375.2.g.c.76.1 | 12 | |||
25.22 | odd | 20 | 375.2.i.d.49.5 | 24 | |||
75.29 | odd | 10 | 225.2.h.d.91.1 | 12 | |||
75.44 | odd | 10 | 225.2.h.d.136.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.3 | ✓ | 12 | 25.4 | even | 10 | ||
75.2.g.c.61.3 | yes | 12 | 25.19 | even | 10 | ||
225.2.h.d.91.1 | 12 | 75.29 | odd | 10 | |||
225.2.h.d.136.1 | 12 | 75.44 | odd | 10 | |||
375.2.g.c.76.1 | 12 | 25.21 | even | 5 | |||
375.2.g.c.301.1 | 12 | 25.6 | even | 5 | |||
375.2.i.d.49.2 | 24 | 25.3 | odd | 20 | |||
375.2.i.d.49.5 | 24 | 25.22 | odd | 20 | |||
375.2.i.d.199.2 | 24 | 25.17 | odd | 20 | |||
375.2.i.d.199.5 | 24 | 25.8 | odd | 20 | |||
1875.2.a.j.1.2 | 6 | 5.4 | even | 2 | |||
1875.2.a.k.1.5 | 6 | 1.1 | even | 1 | trivial | ||
1875.2.b.f.1249.4 | 12 | 5.3 | odd | 4 | |||
1875.2.b.f.1249.9 | 12 | 5.2 | odd | 4 | |||
5625.2.a.p.1.5 | 6 | 15.14 | odd | 2 | |||
5625.2.a.q.1.2 | 6 | 3.2 | odd | 2 |