Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, 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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 133) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214 | 0.292893 | 0.146447 | − | 0.989219i | \(-0.453216\pi\) | ||||
0.146447 | + | 0.989219i | \(0.453216\pi\) | |||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | −0.585786 | −0.239146 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.58579 | −0.560660 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.414214 | 0.130986 | ||||||||
\(11\) | 2.41421 | 0.727913 | 0.363956 | − | 0.931416i | \(-0.381426\pi\) | ||||
0.363956 | + | 0.931416i | \(0.381426\pi\) | |||||||
\(12\) | 2.58579 | 0.746452 | ||||||||
\(13\) | 6.24264 | 1.73140 | 0.865699 | − | 0.500566i | \(-0.166875\pi\) | ||||
0.865699 | + | 0.500566i | \(0.166875\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | −0.414214 | −0.0976311 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −1.82843 | −0.408849 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −8.41421 | −1.75448 | −0.877242 | − | 0.480048i | \(-0.840619\pi\) | ||||
−0.877242 | + | 0.480048i | \(0.840619\pi\) | |||||||
\(24\) | 2.24264 | 0.457777 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 2.58579 | 0.507114 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.41421 | −1.74818 | −0.874088 | − | 0.485768i | \(-0.838540\pi\) | ||||
−0.874088 | + | 0.485768i | \(0.838540\pi\) | |||||||
\(30\) | −0.585786 | −0.106949 | ||||||||
\(31\) | 2.24264 | 0.402790 | 0.201395 | − | 0.979510i | \(-0.435452\pi\) | ||||
0.201395 | + | 0.979510i | \(0.435452\pi\) | |||||||
\(32\) | 4.41421 | 0.780330 | ||||||||
\(33\) | −3.41421 | −0.594338 | ||||||||
\(34\) | −1.65685 | −0.284148 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.82843 | 0.304738 | ||||||||
\(37\) | −5.07107 | −0.833678 | −0.416839 | − | 0.908980i | \(-0.636862\pi\) | ||||
−0.416839 | + | 0.908980i | \(0.636862\pi\) | |||||||
\(38\) | −0.414214 | −0.0671943 | ||||||||
\(39\) | −8.82843 | −1.41368 | ||||||||
\(40\) | −1.58579 | −0.250735 | ||||||||
\(41\) | −8.82843 | −1.37877 | −0.689384 | − | 0.724396i | \(-0.742119\pi\) | ||||
−0.689384 | + | 0.724396i | \(0.742119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.07107 | −0.925829 | −0.462915 | − | 0.886403i | \(-0.653196\pi\) | ||||
−0.462915 | + | 0.886403i | \(0.653196\pi\) | |||||||
\(44\) | −4.41421 | −0.665468 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −3.48528 | −0.513877 | ||||||||
\(47\) | −1.58579 | −0.231311 | −0.115655 | − | 0.993289i | \(-0.536897\pi\) | ||||
−0.115655 | + | 0.993289i | \(0.536897\pi\) | |||||||
\(48\) | −4.24264 | −0.612372 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.65685 | −0.234315 | ||||||||
\(51\) | 5.65685 | 0.792118 | ||||||||
\(52\) | −11.4142 | −1.58287 | ||||||||
\(53\) | 4.24264 | 0.582772 | 0.291386 | − | 0.956606i | \(-0.405884\pi\) | ||||
0.291386 | + | 0.956606i | \(0.405884\pi\) | |||||||
\(54\) | 2.34315 | 0.318862 | ||||||||
\(55\) | 2.41421 | 0.325532 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.41421 | 0.187317 | ||||||||
\(58\) | −3.89949 | −0.512029 | ||||||||
\(59\) | 1.17157 | 0.152526 | 0.0762629 | − | 0.997088i | \(-0.475701\pi\) | ||||
0.0762629 | + | 0.997088i | \(0.475701\pi\) | |||||||
\(60\) | 2.58579 | 0.333824 | ||||||||
\(61\) | 6.17157 | 0.790189 | 0.395094 | − | 0.918640i | \(-0.370712\pi\) | ||||
0.395094 | + | 0.918640i | \(0.370712\pi\) | |||||||
\(62\) | 0.928932 | 0.117975 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 6.24264 | 0.774304 | ||||||||
\(66\) | −1.41421 | −0.174078 | ||||||||
\(67\) | 6.82843 | 0.834225 | 0.417113 | − | 0.908855i | \(-0.363042\pi\) | ||||
0.417113 | + | 0.908855i | \(0.363042\pi\) | |||||||
\(68\) | 7.31371 | 0.886917 | ||||||||
\(69\) | 11.8995 | 1.43253 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.75736 | −0.683273 | −0.341636 | − | 0.939832i | \(-0.610981\pi\) | ||||
−0.341636 | + | 0.939832i | \(0.610981\pi\) | |||||||
\(72\) | 1.58579 | 0.186887 | ||||||||
\(73\) | −13.1421 | −1.53817 | −0.769085 | − | 0.639146i | \(-0.779288\pi\) | ||||
−0.769085 | + | 0.639146i | \(0.779288\pi\) | |||||||
\(74\) | −2.10051 | −0.244179 | ||||||||
\(75\) | 5.65685 | 0.653197 | ||||||||
\(76\) | 1.82843 | 0.209735 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.65685 | −0.414057 | ||||||||
\(79\) | −1.41421 | −0.159111 | −0.0795557 | − | 0.996830i | \(-0.525350\pi\) | ||||
−0.0795557 | + | 0.996830i | \(0.525350\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −3.65685 | −0.403832 | ||||||||
\(83\) | 0.757359 | 0.0831310 | 0.0415655 | − | 0.999136i | \(-0.486765\pi\) | ||||
0.0415655 | + | 0.999136i | \(0.486765\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | −2.51472 | −0.271169 | ||||||||
\(87\) | 13.3137 | 1.42738 | ||||||||
\(88\) | −3.82843 | −0.408112 | ||||||||
\(89\) | −8.58579 | −0.910092 | −0.455046 | − | 0.890468i | \(-0.650377\pi\) | ||||
−0.455046 | + | 0.890468i | \(0.650377\pi\) | |||||||
\(90\) | −0.414214 | −0.0436619 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 15.3848 | 1.60397 | ||||||||
\(93\) | −3.17157 | −0.328877 | ||||||||
\(94\) | −0.656854 | −0.0677493 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | −6.24264 | −0.637137 | ||||||||
\(97\) | −8.82843 | −0.896391 | −0.448195 | − | 0.893936i | \(-0.647933\pi\) | ||||
−0.448195 | + | 0.893936i | \(0.647933\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.41421 | −0.242638 | ||||||||
\(100\) | 7.31371 | 0.731371 | ||||||||
\(101\) | −4.31371 | −0.429230 | −0.214615 | − | 0.976699i | \(-0.568850\pi\) | ||||
−0.214615 | + | 0.976699i | \(0.568850\pi\) | |||||||
\(102\) | 2.34315 | 0.232006 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | −9.89949 | −0.970725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.75736 | 0.170690 | ||||||||
\(107\) | 5.89949 | 0.570326 | 0.285163 | − | 0.958479i | \(-0.407952\pi\) | ||||
0.285163 | + | 0.958479i | \(0.407952\pi\) | |||||||
\(108\) | −10.3431 | −0.995270 | ||||||||
\(109\) | 1.65685 | 0.158698 | 0.0793489 | − | 0.996847i | \(-0.474716\pi\) | ||||
0.0793489 | + | 0.996847i | \(0.474716\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 7.17157 | 0.680696 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.24264 | 0.775402 | 0.387701 | − | 0.921785i | \(-0.373269\pi\) | ||||
0.387701 | + | 0.921785i | \(0.373269\pi\) | |||||||
\(114\) | 0.585786 | 0.0548639 | ||||||||
\(115\) | −8.41421 | −0.784629 | ||||||||
\(116\) | 17.2132 | 1.59821 | ||||||||
\(117\) | −6.24264 | −0.577132 | ||||||||
\(118\) | 0.485281 | 0.0446738 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.24264 | 0.204724 | ||||||||
\(121\) | −5.17157 | −0.470143 | ||||||||
\(122\) | 2.55635 | 0.231441 | ||||||||
\(123\) | 12.4853 | 1.12576 | ||||||||
\(124\) | −4.10051 | −0.368236 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.24264 | −0.376473 | −0.188237 | − | 0.982124i | \(-0.560277\pi\) | ||||
−0.188237 | + | 0.982124i | \(0.560277\pi\) | |||||||
\(128\) | −10.5563 | −0.933058 | ||||||||
\(129\) | 8.58579 | 0.755936 | ||||||||
\(130\) | 2.58579 | 0.226788 | ||||||||
\(131\) | 20.4853 | 1.78981 | 0.894904 | − | 0.446259i | \(-0.147244\pi\) | ||||
0.894904 | + | 0.446259i | \(0.147244\pi\) | |||||||
\(132\) | 6.24264 | 0.543352 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.82843 | 0.244339 | ||||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | 6.34315 | 0.543920 | ||||||||
\(137\) | −14.1716 | −1.21076 | −0.605380 | − | 0.795937i | \(-0.706979\pi\) | ||||
−0.605380 | + | 0.795937i | \(0.706979\pi\) | |||||||
\(138\) | 4.92893 | 0.419579 | ||||||||
\(139\) | 8.07107 | 0.684579 | 0.342290 | − | 0.939595i | \(-0.388798\pi\) | ||||
0.342290 | + | 0.939595i | \(0.388798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.24264 | 0.188864 | ||||||||
\(142\) | −2.38478 | −0.200126 | ||||||||
\(143\) | 15.0711 | 1.26031 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −9.41421 | −0.781808 | ||||||||
\(146\) | −5.44365 | −0.450520 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.27208 | 0.762160 | ||||||||
\(149\) | −5.82843 | −0.477483 | −0.238742 | − | 0.971083i | \(-0.576735\pi\) | ||||
−0.238742 | + | 0.971083i | \(0.576735\pi\) | |||||||
\(150\) | 2.34315 | 0.191317 | ||||||||
\(151\) | 5.31371 | 0.432423 | 0.216212 | − | 0.976346i | \(-0.430630\pi\) | ||||
0.216212 | + | 0.976346i | \(0.430630\pi\) | |||||||
\(152\) | 1.58579 | 0.128624 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.24264 | 0.180133 | ||||||||
\(156\) | 16.1421 | 1.29241 | ||||||||
\(157\) | 11.8284 | 0.944011 | 0.472006 | − | 0.881596i | \(-0.343530\pi\) | ||||
0.472006 | + | 0.881596i | \(0.343530\pi\) | |||||||
\(158\) | −0.585786 | −0.0466027 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 4.41421 | 0.348974 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.07107 | −0.162718 | ||||||||
\(163\) | 18.0711 | 1.41544 | 0.707718 | − | 0.706495i | \(-0.249725\pi\) | ||||
0.707718 | + | 0.706495i | \(0.249725\pi\) | |||||||
\(164\) | 16.1421 | 1.26049 | ||||||||
\(165\) | −3.41421 | −0.265796 | ||||||||
\(166\) | 0.313708 | 0.0243485 | ||||||||
\(167\) | −1.07107 | −0.0828817 | −0.0414409 | − | 0.999141i | \(-0.513195\pi\) | ||||
−0.0414409 | + | 0.999141i | \(0.513195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.9706 | 1.99774 | ||||||||
\(170\) | −1.65685 | −0.127075 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 11.1005 | 0.846406 | ||||||||
\(173\) | 15.3137 | 1.16428 | 0.582140 | − | 0.813089i | \(-0.302216\pi\) | ||||
0.582140 | + | 0.813089i | \(0.302216\pi\) | |||||||
\(174\) | 5.51472 | 0.418070 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.24264 | 0.545935 | ||||||||
\(177\) | −1.65685 | −0.124537 | ||||||||
\(178\) | −3.55635 | −0.266560 | ||||||||
\(179\) | −21.7990 | −1.62933 | −0.814667 | − | 0.579930i | \(-0.803080\pi\) | ||||
−0.814667 | + | 0.579930i | \(0.803080\pi\) | |||||||
\(180\) | 1.82843 | 0.136283 | ||||||||
\(181\) | −9.89949 | −0.735824 | −0.367912 | − | 0.929861i | \(-0.619927\pi\) | ||||
−0.367912 | + | 0.929861i | \(0.619927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.72792 | −0.645187 | ||||||||
\(184\) | 13.3431 | 0.983670 | ||||||||
\(185\) | −5.07107 | −0.372832 | ||||||||
\(186\) | −1.31371 | −0.0963258 | ||||||||
\(187\) | −9.65685 | −0.706179 | ||||||||
\(188\) | 2.89949 | 0.211467 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.414214 | −0.0300502 | ||||||||
\(191\) | 5.58579 | 0.404173 | 0.202087 | − | 0.979368i | \(-0.435228\pi\) | ||||
0.202087 | + | 0.979368i | \(0.435228\pi\) | |||||||
\(192\) | 5.89949 | 0.425759 | ||||||||
\(193\) | −11.8995 | −0.856544 | −0.428272 | − | 0.903650i | \(-0.640878\pi\) | ||||
−0.428272 | + | 0.903650i | \(0.640878\pi\) | |||||||
\(194\) | −3.65685 | −0.262547 | ||||||||
\(195\) | −8.82843 | −0.632217 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.4853 | 1.53076 | 0.765381 | − | 0.643577i | \(-0.222550\pi\) | ||||
0.765381 | + | 0.643577i | \(0.222550\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | 1.92893 | 0.136738 | 0.0683692 | − | 0.997660i | \(-0.478220\pi\) | ||||
0.0683692 | + | 0.997660i | \(0.478220\pi\) | |||||||
\(200\) | 6.34315 | 0.448528 | ||||||||
\(201\) | −9.65685 | −0.681142 | ||||||||
\(202\) | −1.78680 | −0.125719 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.3431 | −0.724165 | ||||||||
\(205\) | −8.82843 | −0.616604 | ||||||||
\(206\) | −2.48528 | −0.173158 | ||||||||
\(207\) | 8.41421 | 0.584828 | ||||||||
\(208\) | 18.7279 | 1.29855 | ||||||||
\(209\) | −2.41421 | −0.166995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.82843 | −0.470088 | −0.235044 | − | 0.971985i | \(-0.575523\pi\) | ||||
−0.235044 | + | 0.971985i | \(0.575523\pi\) | |||||||
\(212\) | −7.75736 | −0.532778 | ||||||||
\(213\) | 8.14214 | 0.557890 | ||||||||
\(214\) | 2.44365 | 0.167045 | ||||||||
\(215\) | −6.07107 | −0.414043 | ||||||||
\(216\) | −8.97056 | −0.610369 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.686292 | 0.0464815 | ||||||||
\(219\) | 18.5858 | 1.25591 | ||||||||
\(220\) | −4.41421 | −0.297606 | ||||||||
\(221\) | −24.9706 | −1.67970 | ||||||||
\(222\) | 2.97056 | 0.199371 | ||||||||
\(223\) | −6.24264 | −0.418038 | −0.209019 | − | 0.977912i | \(-0.567027\pi\) | ||||
−0.209019 | + | 0.977912i | \(0.567027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 3.41421 | 0.227110 | ||||||||
\(227\) | −11.7574 | −0.780363 | −0.390182 | − | 0.920738i | \(-0.627588\pi\) | ||||
−0.390182 | + | 0.920738i | \(0.627588\pi\) | |||||||
\(228\) | −2.58579 | −0.171248 | ||||||||
\(229\) | −4.48528 | −0.296396 | −0.148198 | − | 0.988958i | \(-0.547347\pi\) | ||||
−0.148198 | + | 0.988958i | \(0.547347\pi\) | |||||||
\(230\) | −3.48528 | −0.229813 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.9289 | 0.980132 | ||||||||
\(233\) | −16.4853 | −1.07999 | −0.539993 | − | 0.841669i | \(-0.681573\pi\) | ||||
−0.539993 | + | 0.841669i | \(0.681573\pi\) | |||||||
\(234\) | −2.58579 | −0.169038 | ||||||||
\(235\) | −1.58579 | −0.103445 | ||||||||
\(236\) | −2.14214 | −0.139441 | ||||||||
\(237\) | 2.00000 | 0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | −4.24264 | −0.273861 | ||||||||
\(241\) | 22.0416 | 1.41983 | 0.709913 | − | 0.704289i | \(-0.248734\pi\) | ||||
0.709913 | + | 0.704289i | \(0.248734\pi\) | |||||||
\(242\) | −2.14214 | −0.137702 | ||||||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | −11.2843 | −0.722401 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.17157 | 0.329727 | ||||||||
\(247\) | −6.24264 | −0.397210 | ||||||||
\(248\) | −3.55635 | −0.225828 | ||||||||
\(249\) | −1.07107 | −0.0678762 | ||||||||
\(250\) | −3.72792 | −0.235774 | ||||||||
\(251\) | 11.7279 | 0.740260 | 0.370130 | − | 0.928980i | \(-0.379313\pi\) | ||||
0.370130 | + | 0.928980i | \(0.379313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.3137 | −1.27711 | ||||||||
\(254\) | −1.75736 | −0.110267 | ||||||||
\(255\) | 5.65685 | 0.354246 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | −13.3137 | −0.830486 | −0.415243 | − | 0.909710i | \(-0.636304\pi\) | ||||
−0.415243 | + | 0.909710i | \(0.636304\pi\) | |||||||
\(258\) | 3.55635 | 0.221409 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −11.4142 | −0.707879 | ||||||||
\(261\) | 9.41421 | 0.582725 | ||||||||
\(262\) | 8.48528 | 0.524222 | ||||||||
\(263\) | −0.485281 | −0.0299237 | −0.0149619 | − | 0.999888i | \(-0.504763\pi\) | ||||
−0.0149619 | + | 0.999888i | \(0.504763\pi\) | |||||||
\(264\) | 5.41421 | 0.333222 | ||||||||
\(265\) | 4.24264 | 0.260623 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1421 | 0.743087 | ||||||||
\(268\) | −12.4853 | −0.762660 | ||||||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 2.34315 | 0.142599 | ||||||||
\(271\) | −6.75736 | −0.410480 | −0.205240 | − | 0.978712i | \(-0.565798\pi\) | ||||
−0.205240 | + | 0.978712i | \(0.565798\pi\) | |||||||
\(272\) | −12.0000 | −0.727607 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.87006 | −0.354623 | ||||||||
\(275\) | −9.65685 | −0.582330 | ||||||||
\(276\) | −21.7574 | −1.30964 | ||||||||
\(277\) | 28.4558 | 1.70975 | 0.854873 | − | 0.518837i | \(-0.173635\pi\) | ||||
0.854873 | + | 0.518837i | \(0.173635\pi\) | |||||||
\(278\) | 3.34315 | 0.200509 | ||||||||
\(279\) | −2.24264 | −0.134263 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.7574 | −1.17863 | −0.589313 | − | 0.807905i | \(-0.700601\pi\) | ||||
−0.589313 | + | 0.807905i | \(0.700601\pi\) | |||||||
\(282\) | 0.928932 | 0.0553171 | ||||||||
\(283\) | 15.9289 | 0.946877 | 0.473438 | − | 0.880827i | \(-0.343013\pi\) | ||||
0.473438 | + | 0.880827i | \(0.343013\pi\) | |||||||
\(284\) | 10.5269 | 0.624657 | ||||||||
\(285\) | 1.41421 | 0.0837708 | ||||||||
\(286\) | 6.24264 | 0.369135 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.41421 | −0.260110 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −3.89949 | −0.228986 | ||||||||
\(291\) | 12.4853 | 0.731900 | ||||||||
\(292\) | 24.0294 | 1.40622 | ||||||||
\(293\) | 8.82843 | 0.515762 | 0.257881 | − | 0.966177i | \(-0.416976\pi\) | ||||
0.257881 | + | 0.966177i | \(0.416976\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.17157 | 0.0682116 | ||||||||
\(296\) | 8.04163 | 0.467410 | ||||||||
\(297\) | 13.6569 | 0.792451 | ||||||||
\(298\) | −2.41421 | −0.139852 | ||||||||
\(299\) | −52.5269 | −3.03771 | ||||||||
\(300\) | −10.3431 | −0.597162 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.20101 | 0.126654 | ||||||||
\(303\) | 6.10051 | 0.350465 | ||||||||
\(304\) | −3.00000 | −0.172062 | ||||||||
\(305\) | 6.17157 | 0.353383 | ||||||||
\(306\) | 1.65685 | 0.0947161 | ||||||||
\(307\) | 6.68629 | 0.381607 | 0.190803 | − | 0.981628i | \(-0.438891\pi\) | ||||
0.190803 | + | 0.981628i | \(0.438891\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.48528 | 0.482711 | ||||||||
\(310\) | 0.928932 | 0.0527598 | ||||||||
\(311\) | 15.7990 | 0.895879 | 0.447939 | − | 0.894064i | \(-0.352158\pi\) | ||||
0.447939 | + | 0.894064i | \(0.352158\pi\) | |||||||
\(312\) | 14.0000 | 0.792594 | ||||||||
\(313\) | 4.65685 | 0.263221 | 0.131610 | − | 0.991302i | \(-0.457985\pi\) | ||||
0.131610 | + | 0.991302i | \(0.457985\pi\) | |||||||
\(314\) | 4.89949 | 0.276494 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.58579 | 0.145462 | ||||||||
\(317\) | −11.7574 | −0.660359 | −0.330180 | − | 0.943918i | \(-0.607109\pi\) | ||||
−0.330180 | + | 0.943918i | \(0.607109\pi\) | |||||||
\(318\) | −2.48528 | −0.139368 | ||||||||
\(319\) | −22.7279 | −1.27252 | ||||||||
\(320\) | −4.17157 | −0.233198 | ||||||||
\(321\) | −8.34315 | −0.465669 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | 9.14214 | 0.507896 | ||||||||
\(325\) | −24.9706 | −1.38512 | ||||||||
\(326\) | 7.48528 | 0.414571 | ||||||||
\(327\) | −2.34315 | −0.129576 | ||||||||
\(328\) | 14.0000 | 0.773021 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.41421 | −0.0778499 | ||||||||
\(331\) | 19.4558 | 1.06939 | 0.534695 | − | 0.845045i | \(-0.320427\pi\) | ||||
0.534695 | + | 0.845045i | \(0.320427\pi\) | |||||||
\(332\) | −1.38478 | −0.0759995 | ||||||||
\(333\) | 5.07107 | 0.277893 | ||||||||
\(334\) | −0.443651 | −0.0242755 | ||||||||
\(335\) | 6.82843 | 0.373077 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5563 | −0.629514 | −0.314757 | − | 0.949172i | \(-0.601923\pi\) | ||||
−0.314757 | + | 0.949172i | \(0.601923\pi\) | |||||||
\(338\) | 10.7574 | 0.585123 | ||||||||
\(339\) | −11.6569 | −0.633113 | ||||||||
\(340\) | 7.31371 | 0.396642 | ||||||||
\(341\) | 5.41421 | 0.293196 | ||||||||
\(342\) | 0.414214 | 0.0223981 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.62742 | 0.519076 | ||||||||
\(345\) | 11.8995 | 0.640647 | ||||||||
\(346\) | 6.34315 | 0.341010 | ||||||||
\(347\) | −21.0416 | −1.12957 | −0.564787 | − | 0.825237i | \(-0.691042\pi\) | ||||
−0.564787 | + | 0.825237i | \(0.691042\pi\) | |||||||
\(348\) | −24.3431 | −1.30493 | ||||||||
\(349\) | −12.4853 | −0.668322 | −0.334161 | − | 0.942516i | \(-0.608453\pi\) | ||||
−0.334161 | + | 0.942516i | \(0.608453\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 35.3137 | 1.88491 | ||||||||
\(352\) | 10.6569 | 0.568012 | ||||||||
\(353\) | −16.4853 | −0.877423 | −0.438711 | − | 0.898628i | \(-0.644565\pi\) | ||||
−0.438711 | + | 0.898628i | \(0.644565\pi\) | |||||||
\(354\) | −0.686292 | −0.0364760 | ||||||||
\(355\) | −5.75736 | −0.305569 | ||||||||
\(356\) | 15.6985 | 0.832018 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.02944 | −0.477221 | ||||||||
\(359\) | −3.24264 | −0.171140 | −0.0855700 | − | 0.996332i | \(-0.527271\pi\) | ||||
−0.0855700 | + | 0.996332i | \(0.527271\pi\) | |||||||
\(360\) | 1.58579 | 0.0835783 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −4.10051 | −0.215518 | ||||||||
\(363\) | 7.31371 | 0.383870 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.1421 | −0.687891 | ||||||||
\(366\) | −3.61522 | −0.188971 | ||||||||
\(367\) | −35.6569 | −1.86127 | −0.930636 | − | 0.365945i | \(-0.880746\pi\) | ||||
−0.930636 | + | 0.365945i | \(0.880746\pi\) | |||||||
\(368\) | −25.2426 | −1.31586 | ||||||||
\(369\) | 8.82843 | 0.459590 | ||||||||
\(370\) | −2.10051 | −0.109200 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.79899 | 0.300664 | ||||||||
\(373\) | −11.3137 | −0.585802 | −0.292901 | − | 0.956143i | \(-0.594621\pi\) | ||||
−0.292901 | + | 0.956143i | \(0.594621\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | 12.7279 | 0.657267 | ||||||||
\(376\) | 2.51472 | 0.129687 | ||||||||
\(377\) | −58.7696 | −3.02679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.24264 | −0.217930 | −0.108965 | − | 0.994046i | \(-0.534754\pi\) | ||||
−0.108965 | + | 0.994046i | \(0.534754\pi\) | |||||||
\(380\) | 1.82843 | 0.0937963 | ||||||||
\(381\) | 6.00000 | 0.307389 | ||||||||
\(382\) | 2.31371 | 0.118380 | ||||||||
\(383\) | 28.2426 | 1.44313 | 0.721566 | − | 0.692346i | \(-0.243423\pi\) | ||||
0.721566 | + | 0.692346i | \(0.243423\pi\) | |||||||
\(384\) | 14.9289 | 0.761839 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.92893 | −0.250876 | ||||||||
\(387\) | 6.07107 | 0.308610 | ||||||||
\(388\) | 16.1421 | 0.819493 | ||||||||
\(389\) | −28.4853 | −1.44426 | −0.722131 | − | 0.691757i | \(-0.756837\pi\) | ||||
−0.722131 | + | 0.691757i | \(0.756837\pi\) | |||||||
\(390\) | −3.65685 | −0.185172 | ||||||||
\(391\) | 33.6569 | 1.70210 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.9706 | −1.46137 | ||||||||
\(394\) | 8.89949 | 0.448350 | ||||||||
\(395\) | −1.41421 | −0.0711568 | ||||||||
\(396\) | 4.41421 | 0.221823 | ||||||||
\(397\) | 36.6274 | 1.83828 | 0.919139 | − | 0.393934i | \(-0.128886\pi\) | ||||
0.919139 | + | 0.393934i | \(0.128886\pi\) | |||||||
\(398\) | 0.798990 | 0.0400497 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | −0.600000 | ||||||||
\(401\) | −16.4853 | −0.823236 | −0.411618 | − | 0.911357i | \(-0.635036\pi\) | ||||
−0.411618 | + | 0.911357i | \(0.635036\pi\) | |||||||
\(402\) | −4.00000 | −0.199502 | ||||||||
\(403\) | 14.0000 | 0.697390 | ||||||||
\(404\) | 7.88730 | 0.392408 | ||||||||
\(405\) | −5.00000 | −0.248452 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.2426 | −0.606845 | ||||||||
\(408\) | −8.97056 | −0.444109 | ||||||||
\(409\) | −25.3137 | −1.25168 | −0.625841 | − | 0.779951i | \(-0.715244\pi\) | ||||
−0.625841 | + | 0.779951i | \(0.715244\pi\) | |||||||
\(410\) | −3.65685 | −0.180599 | ||||||||
\(411\) | 20.0416 | 0.988581 | ||||||||
\(412\) | 10.9706 | 0.540481 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.48528 | 0.171292 | ||||||||
\(415\) | 0.757359 | 0.0371773 | ||||||||
\(416\) | 27.5563 | 1.35106 | ||||||||
\(417\) | −11.4142 | −0.558956 | ||||||||
\(418\) | −1.00000 | −0.0489116 | ||||||||
\(419\) | −8.07107 | −0.394297 | −0.197149 | − | 0.980374i | \(-0.563168\pi\) | ||||
−0.197149 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.21320 | 0.254076 | 0.127038 | − | 0.991898i | \(-0.459453\pi\) | ||||
0.127038 | + | 0.991898i | \(0.459453\pi\) | |||||||
\(422\) | −2.82843 | −0.137686 | ||||||||
\(423\) | 1.58579 | 0.0771036 | ||||||||
\(424\) | −6.72792 | −0.326737 | ||||||||
\(425\) | 16.0000 | 0.776114 | ||||||||
\(426\) | 3.37258 | 0.163402 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.7868 | −0.521399 | ||||||||
\(429\) | −21.3137 | −1.02904 | ||||||||
\(430\) | −2.51472 | −0.121271 | ||||||||
\(431\) | 38.0416 | 1.83240 | 0.916200 | − | 0.400720i | \(-0.131240\pi\) | ||||
0.916200 | + | 0.400720i | \(0.131240\pi\) | |||||||
\(432\) | 16.9706 | 0.816497 | ||||||||
\(433\) | 28.0000 | 1.34559 | 0.672797 | − | 0.739827i | \(-0.265093\pi\) | ||||
0.672797 | + | 0.739827i | \(0.265093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.3137 | 0.638343 | ||||||||
\(436\) | −3.02944 | −0.145084 | ||||||||
\(437\) | 8.41421 | 0.402506 | ||||||||
\(438\) | 7.69848 | 0.367848 | ||||||||
\(439\) | −7.51472 | −0.358658 | −0.179329 | − | 0.983789i | \(-0.557393\pi\) | ||||
−0.179329 | + | 0.983789i | \(0.557393\pi\) | |||||||
\(440\) | −3.82843 | −0.182513 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.3431 | −0.491973 | ||||||||
\(443\) | 6.34315 | 0.301372 | 0.150686 | − | 0.988582i | \(-0.451852\pi\) | ||||
0.150686 | + | 0.988582i | \(0.451852\pi\) | |||||||
\(444\) | −13.1127 | −0.622301 | ||||||||
\(445\) | −8.58579 | −0.407005 | ||||||||
\(446\) | −2.58579 | −0.122441 | ||||||||
\(447\) | 8.24264 | 0.389864 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.65685 | −0.0781918 | −0.0390959 | − | 0.999235i | \(-0.512448\pi\) | ||||
−0.0390959 | + | 0.999235i | \(0.512448\pi\) | |||||||
\(450\) | 1.65685 | 0.0781049 | ||||||||
\(451\) | −21.3137 | −1.00362 | ||||||||
\(452\) | −15.0711 | −0.708883 | ||||||||
\(453\) | −7.51472 | −0.353072 | ||||||||
\(454\) | −4.87006 | −0.228563 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.24264 | −0.105021 | ||||||||
\(457\) | −2.17157 | −0.101582 | −0.0507909 | − | 0.998709i | \(-0.516174\pi\) | ||||
−0.0507909 | + | 0.998709i | \(0.516174\pi\) | |||||||
\(458\) | −1.85786 | −0.0868123 | ||||||||
\(459\) | −22.6274 | −1.05616 | ||||||||
\(460\) | 15.3848 | 0.717319 | ||||||||
\(461\) | −3.97056 | −0.184928 | −0.0924638 | − | 0.995716i | \(-0.529474\pi\) | ||||
−0.0924638 | + | 0.995716i | \(0.529474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0711 | 0.468042 | 0.234021 | − | 0.972232i | \(-0.424812\pi\) | ||||
0.234021 | + | 0.972232i | \(0.424812\pi\) | |||||||
\(464\) | −28.2426 | −1.31113 | ||||||||
\(465\) | −3.17157 | −0.147078 | ||||||||
\(466\) | −6.82843 | −0.316321 | ||||||||
\(467\) | 38.8995 | 1.80005 | 0.900027 | − | 0.435834i | \(-0.143547\pi\) | ||||
0.900027 | + | 0.435834i | \(0.143547\pi\) | |||||||
\(468\) | 11.4142 | 0.527622 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.656854 | −0.0302984 | ||||||||
\(471\) | −16.7279 | −0.770782 | ||||||||
\(472\) | −1.85786 | −0.0855151 | ||||||||
\(473\) | −14.6569 | −0.673923 | ||||||||
\(474\) | 0.828427 | 0.0380509 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.24264 | −0.194257 | ||||||||
\(478\) | 0.828427 | 0.0378914 | ||||||||
\(479\) | 11.3848 | 0.520184 | 0.260092 | − | 0.965584i | \(-0.416247\pi\) | ||||
0.260092 | + | 0.965584i | \(0.416247\pi\) | |||||||
\(480\) | −6.24264 | −0.284936 | ||||||||
\(481\) | −31.6569 | −1.44343 | ||||||||
\(482\) | 9.12994 | 0.415857 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.45584 | 0.429811 | ||||||||
\(485\) | −8.82843 | −0.400878 | ||||||||
\(486\) | −4.10051 | −0.186003 | ||||||||
\(487\) | 20.8284 | 0.943826 | 0.471913 | − | 0.881645i | \(-0.343564\pi\) | ||||
0.471913 | + | 0.881645i | \(0.343564\pi\) | |||||||
\(488\) | −9.78680 | −0.443027 | ||||||||
\(489\) | −25.5563 | −1.15570 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.5563 | −1.46925 | −0.734624 | − | 0.678475i | \(-0.762641\pi\) | ||||
−0.734624 | + | 0.678475i | \(0.762641\pi\) | |||||||
\(492\) | −22.8284 | −1.02918 | ||||||||
\(493\) | 37.6569 | 1.69598 | ||||||||
\(494\) | −2.58579 | −0.116340 | ||||||||
\(495\) | −2.41421 | −0.108511 | ||||||||
\(496\) | 6.72792 | 0.302093 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.443651 | −0.0198805 | ||||||||
\(499\) | 3.44365 | 0.154159 | 0.0770795 | − | 0.997025i | \(-0.475440\pi\) | ||||
0.0770795 | + | 0.997025i | \(0.475440\pi\) | |||||||
\(500\) | 16.4558 | 0.735928 | ||||||||
\(501\) | 1.51472 | 0.0676726 | ||||||||
\(502\) | 4.85786 | 0.216817 | ||||||||
\(503\) | 19.0416 | 0.849024 | 0.424512 | − | 0.905422i | \(-0.360446\pi\) | ||||
0.424512 | + | 0.905422i | \(0.360446\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.31371 | −0.191958 | ||||||||
\(506\) | −8.41421 | −0.374057 | ||||||||
\(507\) | −36.7279 | −1.63114 | ||||||||
\(508\) | 7.75736 | 0.344177 | ||||||||
\(509\) | 18.9706 | 0.840855 | 0.420428 | − | 0.907326i | \(-0.361880\pi\) | ||||
0.420428 | + | 0.907326i | \(0.361880\pi\) | |||||||
\(510\) | 2.34315 | 0.103756 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.7574 | 1.00574 | ||||||||
\(513\) | −5.65685 | −0.249756 | ||||||||
\(514\) | −5.51472 | −0.243244 | ||||||||
\(515\) | −6.00000 | −0.264392 | ||||||||
\(516\) | −15.6985 | −0.691087 | ||||||||
\(517\) | −3.82843 | −0.168374 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.6569 | −0.950630 | ||||||||
\(520\) | −9.89949 | −0.434122 | ||||||||
\(521\) | 10.4437 | 0.457545 | 0.228772 | − | 0.973480i | \(-0.426529\pi\) | ||||
0.228772 | + | 0.973480i | \(0.426529\pi\) | |||||||
\(522\) | 3.89949 | 0.170676 | ||||||||
\(523\) | −23.6569 | −1.03444 | −0.517221 | − | 0.855852i | \(-0.673033\pi\) | ||||
−0.517221 | + | 0.855852i | \(0.673033\pi\) | |||||||
\(524\) | −37.4558 | −1.63627 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.201010 | −0.00876446 | ||||||||
\(527\) | −8.97056 | −0.390764 | ||||||||
\(528\) | −10.2426 | −0.445754 | ||||||||
\(529\) | 47.7990 | 2.07822 | ||||||||
\(530\) | 1.75736 | 0.0763348 | ||||||||
\(531\) | −1.17157 | −0.0508419 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −55.1127 | −2.38720 | ||||||||
\(534\) | 5.02944 | 0.217645 | ||||||||
\(535\) | 5.89949 | 0.255057 | ||||||||
\(536\) | −10.8284 | −0.467717 | ||||||||
\(537\) | 30.8284 | 1.33034 | ||||||||
\(538\) | −1.65685 | −0.0714321 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.3431 | −0.445098 | ||||||||
\(541\) | 5.14214 | 0.221078 | 0.110539 | − | 0.993872i | \(-0.464742\pi\) | ||||
0.110539 | + | 0.993872i | \(0.464742\pi\) | |||||||
\(542\) | −2.79899 | −0.120227 | ||||||||
\(543\) | 14.0000 | 0.600798 | ||||||||
\(544\) | −17.6569 | −0.757031 | ||||||||
\(545\) | 1.65685 | 0.0709718 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.5563 | 1.26374 | 0.631869 | − | 0.775075i | \(-0.282288\pi\) | ||||
0.631869 | + | 0.775075i | \(0.282288\pi\) | |||||||
\(548\) | 25.9117 | 1.10689 | ||||||||
\(549\) | −6.17157 | −0.263396 | ||||||||
\(550\) | −4.00000 | −0.170561 | ||||||||
\(551\) | 9.41421 | 0.401059 | ||||||||
\(552\) | −18.8701 | −0.803163 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 11.7868 | 0.500773 | ||||||||
\(555\) | 7.17157 | 0.304416 | ||||||||
\(556\) | −14.7574 | −0.625851 | ||||||||
\(557\) | 10.1716 | 0.430983 | 0.215492 | − | 0.976506i | \(-0.430865\pi\) | ||||
0.215492 | + | 0.976506i | \(0.430865\pi\) | |||||||
\(558\) | −0.928932 | −0.0393248 | ||||||||
\(559\) | −37.8995 | −1.60298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.6569 | 0.576593 | ||||||||
\(562\) | −8.18377 | −0.345211 | ||||||||
\(563\) | −13.8995 | −0.585794 | −0.292897 | − | 0.956144i | \(-0.594619\pi\) | ||||
−0.292897 | + | 0.956144i | \(0.594619\pi\) | |||||||
\(564\) | −4.10051 | −0.172662 | ||||||||
\(565\) | 8.24264 | 0.346770 | ||||||||
\(566\) | 6.59798 | 0.277334 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.12994 | 0.383084 | ||||||||
\(569\) | −42.9706 | −1.80142 | −0.900710 | − | 0.434421i | \(-0.856953\pi\) | ||||
−0.900710 | + | 0.434421i | \(0.856953\pi\) | |||||||
\(570\) | 0.585786 | 0.0245359 | ||||||||
\(571\) | −18.8995 | −0.790919 | −0.395460 | − | 0.918483i | \(-0.629415\pi\) | ||||
−0.395460 | + | 0.918483i | \(0.629415\pi\) | |||||||
\(572\) | −27.5563 | −1.15219 | ||||||||
\(573\) | −7.89949 | −0.330006 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.6569 | 1.40359 | ||||||||
\(576\) | 4.17157 | 0.173816 | ||||||||
\(577\) | 27.9706 | 1.16443 | 0.582215 | − | 0.813035i | \(-0.302186\pi\) | ||||
0.582215 | + | 0.813035i | \(0.302186\pi\) | |||||||
\(578\) | −0.414214 | −0.0172290 | ||||||||
\(579\) | 16.8284 | 0.699366 | ||||||||
\(580\) | 17.2132 | 0.714739 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.17157 | 0.214369 | ||||||||
\(583\) | 10.2426 | 0.424207 | ||||||||
\(584\) | 20.8406 | 0.862391 | ||||||||
\(585\) | −6.24264 | −0.258101 | ||||||||
\(586\) | 3.65685 | 0.151063 | ||||||||
\(587\) | 14.0000 | 0.577842 | 0.288921 | − | 0.957353i | \(-0.406704\pi\) | ||||
0.288921 | + | 0.957353i | \(0.406704\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.24264 | −0.0924064 | ||||||||
\(590\) | 0.485281 | 0.0199787 | ||||||||
\(591\) | −30.3848 | −1.24986 | ||||||||
\(592\) | −15.2132 | −0.625259 | ||||||||
\(593\) | 6.17157 | 0.253436 | 0.126718 | − | 0.991939i | \(-0.459556\pi\) | ||||
0.126718 | + | 0.991939i | \(0.459556\pi\) | |||||||
\(594\) | 5.65685 | 0.232104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.6569 | 0.436522 | ||||||||
\(597\) | −2.72792 | −0.111646 | ||||||||
\(598\) | −21.7574 | −0.889725 | ||||||||
\(599\) | −31.6985 | −1.29516 | −0.647582 | − | 0.761995i | \(-0.724220\pi\) | ||||
−0.647582 | + | 0.761995i | \(0.724220\pi\) | |||||||
\(600\) | −8.97056 | −0.366222 | ||||||||
\(601\) | −9.27208 | −0.378216 | −0.189108 | − | 0.981956i | \(-0.560560\pi\) | ||||
−0.189108 | + | 0.981956i | \(0.560560\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.82843 | −0.278075 | ||||||||
\(604\) | −9.71573 | −0.395327 | ||||||||
\(605\) | −5.17157 | −0.210254 | ||||||||
\(606\) | 2.52691 | 0.102649 | ||||||||
\(607\) | 32.5269 | 1.32023 | 0.660113 | − | 0.751166i | \(-0.270508\pi\) | ||||
0.660113 | + | 0.751166i | \(0.270508\pi\) | |||||||
\(608\) | −4.41421 | −0.179020 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.55635 | 0.103504 | ||||||||
\(611\) | −9.89949 | −0.400491 | ||||||||
\(612\) | −7.31371 | −0.295639 | ||||||||
\(613\) | −8.68629 | −0.350836 | −0.175418 | − | 0.984494i | \(-0.556128\pi\) | ||||
−0.175418 | + | 0.984494i | \(0.556128\pi\) | |||||||
\(614\) | 2.76955 | 0.111770 | ||||||||
\(615\) | 12.4853 | 0.503455 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.4558 | −1.70921 | −0.854604 | − | 0.519280i | \(-0.826200\pi\) | ||||
−0.854604 | + | 0.519280i | \(0.826200\pi\) | |||||||
\(618\) | 3.51472 | 0.141383 | ||||||||
\(619\) | 3.44365 | 0.138412 | 0.0692060 | − | 0.997602i | \(-0.477953\pi\) | ||||
0.0692060 | + | 0.997602i | \(0.477953\pi\) | |||||||
\(620\) | −4.10051 | −0.164680 | ||||||||
\(621\) | −47.5980 | −1.91004 | ||||||||
\(622\) | 6.54416 | 0.262397 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −26.4853 | −1.06026 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 1.92893 | 0.0770956 | ||||||||
\(627\) | 3.41421 | 0.136351 | ||||||||
\(628\) | −21.6274 | −0.863028 | ||||||||
\(629\) | 20.2843 | 0.808787 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.44365 | −0.216708 | −0.108354 | − | 0.994112i | \(-0.534558\pi\) | ||||
−0.108354 | + | 0.994112i | \(0.534558\pi\) | |||||||
\(632\) | 2.24264 | 0.0892075 | ||||||||
\(633\) | 9.65685 | 0.383825 | ||||||||
\(634\) | −4.87006 | −0.193415 | ||||||||
\(635\) | −4.24264 | −0.168364 | ||||||||
\(636\) | 10.9706 | 0.435011 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.41421 | −0.372712 | ||||||||
\(639\) | 5.75736 | 0.227758 | ||||||||
\(640\) | −10.5563 | −0.417276 | ||||||||
\(641\) | 3.79899 | 0.150051 | 0.0750255 | − | 0.997182i | \(-0.476096\pi\) | ||||
0.0750255 | + | 0.997182i | \(0.476096\pi\) | |||||||
\(642\) | −3.45584 | −0.136391 | ||||||||
\(643\) | 30.1421 | 1.18869 | 0.594345 | − | 0.804210i | \(-0.297411\pi\) | ||||
0.594345 | + | 0.804210i | \(0.297411\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.58579 | 0.338065 | ||||||||
\(646\) | 1.65685 | 0.0651881 | ||||||||
\(647\) | 6.21320 | 0.244266 | 0.122133 | − | 0.992514i | \(-0.461027\pi\) | ||||
0.122133 | + | 0.992514i | \(0.461027\pi\) | |||||||
\(648\) | 7.92893 | 0.311478 | ||||||||
\(649\) | 2.82843 | 0.111025 | ||||||||
\(650\) | −10.3431 | −0.405692 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33.0416 | −1.29401 | ||||||||
\(653\) | −1.85786 | −0.0727039 | −0.0363519 | − | 0.999339i | \(-0.511574\pi\) | ||||
−0.0363519 | + | 0.999339i | \(0.511574\pi\) | |||||||
\(654\) | −0.970563 | −0.0379520 | ||||||||
\(655\) | 20.4853 | 0.800426 | ||||||||
\(656\) | −26.4853 | −1.03408 | ||||||||
\(657\) | 13.1421 | 0.512724 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.0416 | −1.48189 | −0.740946 | − | 0.671565i | \(-0.765622\pi\) | ||||
−0.740946 | + | 0.671565i | \(0.765622\pi\) | |||||||
\(660\) | 6.24264 | 0.242994 | ||||||||
\(661\) | −22.7279 | −0.884014 | −0.442007 | − | 0.897012i | \(-0.645733\pi\) | ||||
−0.442007 | + | 0.897012i | \(0.645733\pi\) | |||||||
\(662\) | 8.05887 | 0.313217 | ||||||||
\(663\) | 35.3137 | 1.37147 | ||||||||
\(664\) | −1.20101 | −0.0466082 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.10051 | 0.0813929 | ||||||||
\(667\) | 79.2132 | 3.06715 | ||||||||
\(668\) | 1.95837 | 0.0757716 | ||||||||
\(669\) | 8.82843 | 0.341327 | ||||||||
\(670\) | 2.82843 | 0.109272 | ||||||||
\(671\) | 14.8995 | 0.575189 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.7990 | 1.37995 | 0.689975 | − | 0.723833i | \(-0.257622\pi\) | ||||
0.689975 | + | 0.723833i | \(0.257622\pi\) | |||||||
\(674\) | −4.78680 | −0.184381 | ||||||||
\(675\) | −22.6274 | −0.870930 | ||||||||
\(676\) | −47.4853 | −1.82636 | ||||||||
\(677\) | 0.686292 | 0.0263763 | 0.0131882 | − | 0.999913i | \(-0.495802\pi\) | ||||
0.0131882 | + | 0.999913i | \(0.495802\pi\) | |||||||
\(678\) | −4.82843 | −0.185435 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.34315 | 0.243249 | ||||||||
\(681\) | 16.6274 | 0.637164 | ||||||||
\(682\) | 2.24264 | 0.0858752 | ||||||||
\(683\) | 10.4853 | 0.401208 | 0.200604 | − | 0.979672i | \(-0.435710\pi\) | ||||
0.200604 | + | 0.979672i | \(0.435710\pi\) | |||||||
\(684\) | −1.82843 | −0.0699117 | ||||||||
\(685\) | −14.1716 | −0.541468 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.34315 | 0.242006 | ||||||||
\(688\) | −18.2132 | −0.694372 | ||||||||
\(689\) | 26.4853 | 1.00901 | ||||||||
\(690\) | 4.92893 | 0.187641 | ||||||||
\(691\) | −2.97056 | −0.113006 | −0.0565028 | − | 0.998402i | \(-0.517995\pi\) | ||||
−0.0565028 | + | 0.998402i | \(0.517995\pi\) | |||||||
\(692\) | −28.0000 | −1.06440 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.71573 | −0.330845 | ||||||||
\(695\) | 8.07107 | 0.306153 | ||||||||
\(696\) | −21.1127 | −0.800275 | ||||||||
\(697\) | 35.3137 | 1.33760 | ||||||||
\(698\) | −5.17157 | −0.195747 | ||||||||
\(699\) | 23.3137 | 0.881805 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.82843 | 0.144598 | 0.0722988 | − | 0.997383i | \(-0.476966\pi\) | ||||
0.0722988 | + | 0.997383i | \(0.476966\pi\) | |||||||
\(702\) | 14.6274 | 0.552076 | ||||||||
\(703\) | 5.07107 | 0.191259 | ||||||||
\(704\) | −10.0711 | −0.379568 | ||||||||
\(705\) | 2.24264 | 0.0844627 | ||||||||
\(706\) | −6.82843 | −0.256991 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.02944 | 0.113853 | ||||||||
\(709\) | 24.9411 | 0.936684 | 0.468342 | − | 0.883547i | \(-0.344852\pi\) | ||||
0.468342 | + | 0.883547i | \(0.344852\pi\) | |||||||
\(710\) | −2.38478 | −0.0894991 | ||||||||
\(711\) | 1.41421 | 0.0530372 | ||||||||
\(712\) | 13.6152 | 0.510252 | ||||||||
\(713\) | −18.8701 | −0.706689 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0711 | 0.563626 | ||||||||
\(716\) | 39.8579 | 1.48956 | ||||||||
\(717\) | −2.82843 | −0.105630 | ||||||||
\(718\) | −1.34315 | −0.0501258 | ||||||||
\(719\) | −44.0833 | −1.64403 | −0.822014 | − | 0.569467i | \(-0.807150\pi\) | ||||
−0.822014 | + | 0.569467i | \(0.807150\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.414214 | 0.0154154 | ||||||||
\(723\) | −31.1716 | −1.15928 | ||||||||
\(724\) | 18.1005 | 0.672700 | ||||||||
\(725\) | 37.6569 | 1.39854 | ||||||||
\(726\) | 3.02944 | 0.112433 | ||||||||
\(727\) | 5.92893 | 0.219892 | 0.109946 | − | 0.993938i | \(-0.464932\pi\) | ||||
0.109946 | + | 0.993938i | \(0.464932\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −5.44365 | −0.201479 | ||||||||
\(731\) | 24.2843 | 0.898186 | ||||||||
\(732\) | 15.9584 | 0.589838 | ||||||||
\(733\) | −29.4558 | −1.08798 | −0.543988 | − | 0.839093i | \(-0.683086\pi\) | ||||
−0.543988 | + | 0.839093i | \(0.683086\pi\) | |||||||
\(734\) | −14.7696 | −0.545154 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.1421 | −1.36908 | ||||||||
\(737\) | 16.4853 | 0.607243 | ||||||||
\(738\) | 3.65685 | 0.134611 | ||||||||
\(739\) | −19.6569 | −0.723089 | −0.361545 | − | 0.932355i | \(-0.617750\pi\) | ||||
−0.361545 | + | 0.932355i | \(0.617750\pi\) | |||||||
\(740\) | 9.27208 | 0.340848 | ||||||||
\(741\) | 8.82843 | 0.324320 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.8701 | 1.86624 | 0.933121 | − | 0.359563i | \(-0.117074\pi\) | ||||
0.933121 | + | 0.359563i | \(0.117074\pi\) | |||||||
\(744\) | 5.02944 | 0.184388 | ||||||||
\(745\) | −5.82843 | −0.213537 | ||||||||
\(746\) | −4.68629 | −0.171577 | ||||||||
\(747\) | −0.757359 | −0.0277103 | ||||||||
\(748\) | 17.6569 | 0.645599 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.27208 | 0.192509 | ||||||||
\(751\) | −41.4558 | −1.51275 | −0.756373 | − | 0.654141i | \(-0.773030\pi\) | ||||
−0.756373 | + | 0.654141i | \(0.773030\pi\) | |||||||
\(752\) | −4.75736 | −0.173483 | ||||||||
\(753\) | −16.5858 | −0.604420 | ||||||||
\(754\) | −24.3431 | −0.886525 | ||||||||
\(755\) | 5.31371 | 0.193386 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.00000 | −0.181728 | −0.0908640 | − | 0.995863i | \(-0.528963\pi\) | ||||
−0.0908640 | + | 0.995863i | \(0.528963\pi\) | |||||||
\(758\) | −1.75736 | −0.0638302 | ||||||||
\(759\) | 28.7279 | 1.04276 | ||||||||
\(760\) | 1.58579 | 0.0575225 | ||||||||
\(761\) | 28.1127 | 1.01908 | 0.509542 | − | 0.860446i | \(-0.329815\pi\) | ||||
0.509542 | + | 0.860446i | \(0.329815\pi\) | |||||||
\(762\) | 2.48528 | 0.0900322 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.2132 | −0.369501 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | 11.6985 | 0.422683 | ||||||||
\(767\) | 7.31371 | 0.264083 | ||||||||
\(768\) | −5.61522 | −0.202622 | ||||||||
\(769\) | 41.4264 | 1.49387 | 0.746937 | − | 0.664895i | \(-0.231524\pi\) | ||||
0.746937 | + | 0.664895i | \(0.231524\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.8284 | 0.678089 | ||||||||
\(772\) | 21.7574 | 0.783064 | ||||||||
\(773\) | −25.7574 | −0.926428 | −0.463214 | − | 0.886247i | \(-0.653304\pi\) | ||||
−0.463214 | + | 0.886247i | \(0.653304\pi\) | |||||||
\(774\) | 2.51472 | 0.0903897 | ||||||||
\(775\) | −8.97056 | −0.322232 | ||||||||
\(776\) | 14.0000 | 0.502571 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.7990 | −0.423014 | ||||||||
\(779\) | 8.82843 | 0.316311 | ||||||||
\(780\) | 16.1421 | 0.577981 | ||||||||
\(781\) | −13.8995 | −0.497363 | ||||||||
\(782\) | 13.9411 | 0.498534 | ||||||||
\(783\) | −53.2548 | −1.90317 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.8284 | 0.422175 | ||||||||
\(786\) | −12.0000 | −0.428026 | ||||||||
\(787\) | −41.0122 | −1.46193 | −0.730963 | − | 0.682417i | \(-0.760929\pi\) | ||||
−0.730963 | + | 0.682417i | \(0.760929\pi\) | |||||||
\(788\) | −39.2843 | −1.39944 | ||||||||
\(789\) | 0.686292 | 0.0244326 | ||||||||
\(790\) | −0.585786 | −0.0208413 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.82843 | 0.136037 | ||||||||
\(793\) | 38.5269 | 1.36813 | ||||||||
\(794\) | 15.1716 | 0.538419 | ||||||||
\(795\) | −6.00000 | −0.212798 | ||||||||
\(796\) | −3.52691 | −0.125008 | ||||||||
\(797\) | −21.7574 | −0.770685 | −0.385343 | − | 0.922774i | \(-0.625917\pi\) | ||||
−0.385343 | + | 0.922774i | \(0.625917\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.34315 | 0.224404 | ||||||||
\(800\) | −17.6569 | −0.624264 | ||||||||
\(801\) | 8.58579 | 0.303364 | ||||||||
\(802\) | −6.82843 | −0.241120 | ||||||||
\(803\) | −31.7279 | −1.11965 | ||||||||
\(804\) | 17.6569 | 0.622709 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.79899 | 0.204261 | ||||||||
\(807\) | 5.65685 | 0.199131 | ||||||||
\(808\) | 6.84062 | 0.240652 | ||||||||
\(809\) | 2.85786 | 0.100477 | 0.0502386 | − | 0.998737i | \(-0.484002\pi\) | ||||
0.0502386 | + | 0.998737i | \(0.484002\pi\) | |||||||
\(810\) | −2.07107 | −0.0727699 | ||||||||
\(811\) | −51.4558 | −1.80686 | −0.903430 | − | 0.428737i | \(-0.858959\pi\) | ||||
−0.903430 | + | 0.428737i | \(0.858959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.55635 | 0.335156 | ||||||||
\(814\) | −5.07107 | −0.177741 | ||||||||
\(815\) | 18.0711 | 0.633002 | ||||||||
\(816\) | 16.9706 | 0.594089 | ||||||||
\(817\) | 6.07107 | 0.212400 | ||||||||
\(818\) | −10.4853 | −0.366609 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.1421 | 0.563708 | ||||||||
\(821\) | −52.1127 | −1.81875 | −0.909373 | − | 0.415982i | \(-0.863438\pi\) | ||||
−0.909373 | + | 0.415982i | \(0.863438\pi\) | |||||||
\(822\) | 8.30152 | 0.289549 | ||||||||
\(823\) | 36.2132 | 1.26231 | 0.631156 | − | 0.775656i | \(-0.282581\pi\) | ||||
0.631156 | + | 0.775656i | \(0.282581\pi\) | |||||||
\(824\) | 9.51472 | 0.331461 | ||||||||
\(825\) | 13.6569 | 0.475471 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.2843 | −1.53991 | −0.769957 | − | 0.638095i | \(-0.779723\pi\) | ||||
−0.769957 | + | 0.638095i | \(0.779723\pi\) | |||||||
\(828\) | −15.3848 | −0.534658 | ||||||||
\(829\) | 28.2843 | 0.982353 | 0.491177 | − | 0.871060i | \(-0.336567\pi\) | ||||
0.491177 | + | 0.871060i | \(0.336567\pi\) | |||||||
\(830\) | 0.313708 | 0.0108890 | ||||||||
\(831\) | −40.2426 | −1.39600 | ||||||||
\(832\) | −26.0416 | −0.902831 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.72792 | −0.163715 | ||||||||
\(835\) | −1.07107 | −0.0370658 | ||||||||
\(836\) | 4.41421 | 0.152669 | ||||||||
\(837\) | 12.6863 | 0.438502 | ||||||||
\(838\) | −3.34315 | −0.115487 | ||||||||
\(839\) | 19.7990 | 0.683537 | 0.341769 | − | 0.939784i | \(-0.388974\pi\) | ||||
0.341769 | + | 0.939784i | \(0.388974\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.6274 | 2.05612 | ||||||||
\(842\) | 2.15938 | 0.0744171 | ||||||||
\(843\) | 27.9411 | 0.962343 | ||||||||
\(844\) | 12.4853 | 0.429761 | ||||||||
\(845\) | 25.9706 | 0.893415 | ||||||||
\(846\) | 0.656854 | 0.0225831 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.7279 | 0.437079 | ||||||||
\(849\) | −22.5269 | −0.773122 | ||||||||
\(850\) | 6.62742 | 0.227319 | ||||||||
\(851\) | 42.6690 | 1.46268 | ||||||||
\(852\) | −14.8873 | −0.510031 | ||||||||
\(853\) | 10.0294 | 0.343401 | 0.171701 | − | 0.985149i | \(-0.445074\pi\) | ||||
0.171701 | + | 0.985149i | \(0.445074\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | −9.35534 | −0.319759 | ||||||||
\(857\) | 20.9706 | 0.716341 | 0.358170 | − | 0.933656i | \(-0.383401\pi\) | ||||
0.358170 | + | 0.933656i | \(0.383401\pi\) | |||||||
\(858\) | −8.82843 | −0.301398 | ||||||||
\(859\) | 2.07107 | 0.0706639 | 0.0353320 | − | 0.999376i | \(-0.488751\pi\) | ||||
0.0353320 | + | 0.999376i | \(0.488751\pi\) | |||||||
\(860\) | 11.1005 | 0.378524 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.7574 | 0.536698 | ||||||||
\(863\) | 7.41421 | 0.252383 | 0.126191 | − | 0.992006i | \(-0.459725\pi\) | ||||
0.126191 | + | 0.992006i | \(0.459725\pi\) | |||||||
\(864\) | 24.9706 | 0.849516 | ||||||||
\(865\) | 15.3137 | 0.520682 | ||||||||
\(866\) | 11.5980 | 0.394115 | ||||||||
\(867\) | 1.41421 | 0.0480292 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.41421 | −0.115819 | ||||||||
\(870\) | 5.51472 | 0.186966 | ||||||||
\(871\) | 42.6274 | 1.44437 | ||||||||
\(872\) | −2.62742 | −0.0889756 | ||||||||
\(873\) | 8.82843 | 0.298797 | ||||||||
\(874\) | 3.48528 | 0.117891 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −33.9828 | −1.14817 | ||||||||
\(877\) | −8.10051 | −0.273535 | −0.136767 | − | 0.990603i | \(-0.543671\pi\) | ||||
−0.136767 | + | 0.990603i | \(0.543671\pi\) | |||||||
\(878\) | −3.11270 | −0.105048 | ||||||||
\(879\) | −12.4853 | −0.421118 | ||||||||
\(880\) | 7.24264 | 0.244149 | ||||||||
\(881\) | 4.28427 | 0.144341 | 0.0721704 | − | 0.997392i | \(-0.477007\pi\) | ||||
0.0721704 | + | 0.997392i | \(0.477007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.65685 | 0.190368 | 0.0951842 | − | 0.995460i | \(-0.469656\pi\) | ||||
0.0951842 | + | 0.995460i | \(0.469656\pi\) | |||||||
\(884\) | 45.6569 | 1.53561 | ||||||||
\(885\) | −1.65685 | −0.0556945 | ||||||||
\(886\) | 2.62742 | 0.0882698 | ||||||||
\(887\) | 1.31371 | 0.0441100 | 0.0220550 | − | 0.999757i | \(-0.492979\pi\) | ||||
0.0220550 | + | 0.999757i | \(0.492979\pi\) | |||||||
\(888\) | −11.3726 | −0.381639 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.55635 | −0.119209 | ||||||||
\(891\) | −12.0711 | −0.404396 | ||||||||
\(892\) | 11.4142 | 0.382176 | ||||||||
\(893\) | 1.58579 | 0.0530663 | ||||||||
\(894\) | 3.41421 | 0.114188 | ||||||||
\(895\) | −21.7990 | −0.728660 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 74.2843 | 2.48028 | ||||||||
\(898\) | −0.686292 | −0.0229018 | ||||||||
\(899\) | −21.1127 | −0.704148 | ||||||||
\(900\) | −7.31371 | −0.243790 | ||||||||
\(901\) | −16.9706 | −0.565371 | ||||||||
\(902\) | −8.82843 | −0.293954 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.0711 | −0.434737 | ||||||||
\(905\) | −9.89949 | −0.329070 | ||||||||
\(906\) | −3.11270 | −0.103412 | ||||||||
\(907\) | 28.5858 | 0.949175 | 0.474588 | − | 0.880208i | \(-0.342597\pi\) | ||||
0.474588 | + | 0.880208i | \(0.342597\pi\) | |||||||
\(908\) | 21.4975 | 0.713419 | ||||||||
\(909\) | 4.31371 | 0.143077 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.7279 | 1.15059 | 0.575294 | − | 0.817947i | \(-0.304888\pi\) | ||||
0.575294 | + | 0.817947i | \(0.304888\pi\) | |||||||
\(912\) | 4.24264 | 0.140488 | ||||||||
\(913\) | 1.82843 | 0.0605121 | ||||||||
\(914\) | −0.899495 | −0.0297526 | ||||||||
\(915\) | −8.72792 | −0.288536 | ||||||||
\(916\) | 8.20101 | 0.270969 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −9.37258 | −0.309341 | ||||||||
\(919\) | 29.0416 | 0.957995 | 0.478997 | − | 0.877816i | \(-0.341000\pi\) | ||||
0.478997 | + | 0.877816i | \(0.341000\pi\) | |||||||
\(920\) | 13.3431 | 0.439910 | ||||||||
\(921\) | −9.45584 | −0.311581 | ||||||||
\(922\) | −1.64466 | −0.0541640 | ||||||||
\(923\) | −35.9411 | −1.18302 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.2843 | 0.666943 | ||||||||
\(926\) | 4.17157 | 0.137086 | ||||||||
\(927\) | 6.00000 | 0.197066 | ||||||||
\(928\) | −41.5563 | −1.36415 | ||||||||
\(929\) | 15.0000 | 0.492134 | 0.246067 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246067 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(930\) | −1.31371 | −0.0430782 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 30.1421 | 0.987338 | ||||||||
\(933\) | −22.3431 | −0.731482 | ||||||||
\(934\) | 16.1127 | 0.527224 | ||||||||
\(935\) | −9.65685 | −0.315813 | ||||||||
\(936\) | 9.89949 | 0.323575 | ||||||||
\(937\) | −56.3137 | −1.83969 | −0.919844 | − | 0.392284i | \(-0.871685\pi\) | ||||
−0.919844 | + | 0.392284i | \(0.871685\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.58579 | −0.214919 | ||||||||
\(940\) | 2.89949 | 0.0945711 | ||||||||
\(941\) | −44.0416 | −1.43572 | −0.717858 | − | 0.696189i | \(-0.754877\pi\) | ||||
−0.717858 | + | 0.696189i | \(0.754877\pi\) | |||||||
\(942\) | −6.92893 | −0.225757 | ||||||||
\(943\) | 74.2843 | 2.41903 | ||||||||
\(944\) | 3.51472 | 0.114394 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.07107 | −0.197387 | ||||||||
\(947\) | −7.65685 | −0.248814 | −0.124407 | − | 0.992231i | \(-0.539703\pi\) | ||||
−0.124407 | + | 0.992231i | \(0.539703\pi\) | |||||||
\(948\) | −3.65685 | −0.118769 | ||||||||
\(949\) | −82.0416 | −2.66318 | ||||||||
\(950\) | 1.65685 | 0.0537555 | ||||||||
\(951\) | 16.6274 | 0.539181 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.585786 | −0.0189755 | −0.00948774 | − | 0.999955i | \(-0.503020\pi\) | ||||
−0.00948774 | + | 0.999955i | \(0.503020\pi\) | |||||||
\(954\) | −1.75736 | −0.0568966 | ||||||||
\(955\) | 5.58579 | 0.180752 | ||||||||
\(956\) | −3.65685 | −0.118271 | ||||||||
\(957\) | 32.1421 | 1.03901 | ||||||||
\(958\) | 4.71573 | 0.152358 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.89949 | 0.190405 | ||||||||
\(961\) | −25.9706 | −0.837760 | ||||||||
\(962\) | −13.1127 | −0.422770 | ||||||||
\(963\) | −5.89949 | −0.190109 | ||||||||
\(964\) | −40.3015 | −1.29802 | ||||||||
\(965\) | −11.8995 | −0.383058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.2843 | 0.652298 | 0.326149 | − | 0.945318i | \(-0.394249\pi\) | ||||
0.326149 | + | 0.945318i | \(0.394249\pi\) | |||||||
\(968\) | 8.20101 | 0.263590 | ||||||||
\(969\) | −5.65685 | −0.181724 | ||||||||
\(970\) | −3.65685 | −0.117415 | ||||||||
\(971\) | −26.8701 | −0.862301 | −0.431151 | − | 0.902280i | \(-0.641892\pi\) | ||||
−0.431151 | + | 0.902280i | \(0.641892\pi\) | |||||||
\(972\) | 18.1005 | 0.580574 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.62742 | 0.276440 | ||||||||
\(975\) | 35.3137 | 1.13094 | ||||||||
\(976\) | 18.5147 | 0.592642 | ||||||||
\(977\) | 28.7696 | 0.920420 | 0.460210 | − | 0.887810i | \(-0.347774\pi\) | ||||
0.460210 | + | 0.887810i | \(0.347774\pi\) | |||||||
\(978\) | −10.5858 | −0.338496 | ||||||||
\(979\) | −20.7279 | −0.662467 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.65685 | −0.0528993 | ||||||||
\(982\) | −13.4853 | −0.430333 | ||||||||
\(983\) | −46.0000 | −1.46717 | −0.733586 | − | 0.679597i | \(-0.762155\pi\) | ||||
−0.733586 | + | 0.679597i | \(0.762155\pi\) | |||||||
\(984\) | −19.7990 | −0.631169 | ||||||||
\(985\) | 21.4853 | 0.684578 | ||||||||
\(986\) | 15.5980 | 0.496741 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.4142 | 0.363135 | ||||||||
\(989\) | 51.0833 | 1.62435 | ||||||||
\(990\) | −1.00000 | −0.0317821 | ||||||||
\(991\) | −35.7990 | −1.13719 | −0.568596 | − | 0.822617i | \(-0.692513\pi\) | ||||
−0.568596 | + | 0.822617i | \(0.692513\pi\) | |||||||
\(992\) | 9.89949 | 0.314309 | ||||||||
\(993\) | −27.5147 | −0.873153 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.92893 | 0.0611513 | ||||||||
\(996\) | 1.95837 | 0.0620533 | ||||||||
\(997\) | 28.2843 | 0.895772 | 0.447886 | − | 0.894091i | \(-0.352177\pi\) | ||||
0.447886 | + | 0.894091i | \(0.352177\pi\) | |||||||
\(998\) | 1.42641 | 0.0451521 | ||||||||
\(999\) | −28.6863 | −0.907594 |
(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 | 931.2.a.f.1.2 | 2 | ||
3.2 | odd | 2 | 8379.2.a.bi.1.1 | 2 | |||
7.2 | even | 3 | 133.2.f.c.39.1 | ✓ | 4 | ||
7.3 | odd | 6 | 931.2.f.i.324.1 | 4 | |||
7.4 | even | 3 | 133.2.f.c.58.1 | yes | 4 | ||
7.5 | odd | 6 | 931.2.f.i.704.1 | 4 | |||
7.6 | odd | 2 | 931.2.a.e.1.2 | 2 | |||
21.2 | odd | 6 | 1197.2.j.e.172.2 | 4 | |||
21.11 | odd | 6 | 1197.2.j.e.856.2 | 4 | |||
21.20 | even | 2 | 8379.2.a.bl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
133.2.f.c.39.1 | ✓ | 4 | 7.2 | even | 3 | ||
133.2.f.c.58.1 | yes | 4 | 7.4 | even | 3 | ||
931.2.a.e.1.2 | 2 | 7.6 | odd | 2 | |||
931.2.a.f.1.2 | 2 | 1.1 | even | 1 | trivial | ||
931.2.f.i.324.1 | 4 | 7.3 | odd | 6 | |||
931.2.f.i.704.1 | 4 | 7.5 | odd | 6 | |||
1197.2.j.e.172.2 | 4 | 21.2 | odd | 6 | |||
1197.2.j.e.856.2 | 4 | 21.11 | odd | 6 | |||
8379.2.a.bi.1.1 | 2 | 3.2 | odd | 2 | |||
8379.2.a.bl.1.1 | 2 | 21.20 | even | 2 |