Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.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: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{73}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.77200 | 1.74032 | 0.870162 | − | 0.492766i | \(-0.164014\pi\) | ||||
0.870162 | + | 0.492766i | \(0.164014\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.77200 | −1.04617 | −0.523083 | − | 0.852282i | \(-0.675218\pi\) | ||||
−0.523083 | + | 0.852282i | \(0.675218\pi\) | |||||||
\(14\) | 3.00000 | 0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.772002 | 0.187238 | 0.0936190 | − | 0.995608i | \(-0.470156\pi\) | ||||
0.0936190 | + | 0.995608i | \(0.470156\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 7.77200 | 1.78302 | 0.891510 | − | 0.453001i | \(-0.149647\pi\) | ||||
0.891510 | + | 0.453001i | \(0.149647\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | −5.77200 | −1.23059 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.77200 | 0.739750 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.00000 | −0.566947 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.54400 | −1.71415 | −0.857077 | − | 0.515189i | \(-0.827722\pi\) | ||||
−0.857077 | + | 0.515189i | \(0.827722\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.77200 | 1.00478 | ||||||||
\(34\) | −0.772002 | −0.132397 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.77200 | 1.11331 | 0.556655 | − | 0.830744i | \(-0.312084\pi\) | ||||
0.556655 | + | 0.830744i | \(0.312084\pi\) | |||||||
\(38\) | −7.77200 | −1.26079 | ||||||||
\(39\) | −3.77200 | −0.604004 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.77200 | −0.901435 | −0.450718 | − | 0.892667i | \(-0.648832\pi\) | ||||
−0.450718 | + | 0.892667i | \(0.648832\pi\) | |||||||
\(42\) | 3.00000 | 0.462910 | ||||||||
\(43\) | 7.77200 | 1.18522 | 0.592610 | − | 0.805490i | \(-0.298098\pi\) | ||||
0.592610 | + | 0.805490i | \(0.298098\pi\) | |||||||
\(44\) | 5.77200 | 0.870162 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −8.77200 | −1.27953 | −0.639764 | − | 0.768571i | \(-0.720968\pi\) | ||||
−0.639764 | + | 0.768571i | \(0.720968\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.772002 | 0.108102 | ||||||||
\(52\) | −3.77200 | −0.523083 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 7.77200 | 1.02943 | ||||||||
\(58\) | −3.00000 | −0.393919 | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.54400 | −1.22198 | −0.610992 | − | 0.791637i | \(-0.709229\pi\) | ||||
−0.610992 | + | 0.791637i | \(0.709229\pi\) | |||||||
\(62\) | 9.54400 | 1.21209 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.77200 | −0.710484 | ||||||||
\(67\) | −9.54400 | −1.16599 | −0.582993 | − | 0.812477i | \(-0.698118\pi\) | ||||
−0.582993 | + | 0.812477i | \(0.698118\pi\) | |||||||
\(68\) | 0.772002 | 0.0936190 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.77200 | −0.566332 | −0.283166 | − | 0.959071i | \(-0.591385\pi\) | ||||
−0.283166 | + | 0.959071i | \(0.591385\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 6.54400 | 0.765918 | 0.382959 | − | 0.923765i | \(-0.374905\pi\) | ||||
0.382959 | + | 0.923765i | \(0.374905\pi\) | |||||||
\(74\) | −6.77200 | −0.787229 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.77200 | 0.891510 | ||||||||
\(77\) | −17.3160 | −1.97334 | ||||||||
\(78\) | 3.77200 | 0.427095 | ||||||||
\(79\) | 2.22800 | 0.250669 | 0.125335 | − | 0.992115i | \(-0.460000\pi\) | ||||
0.125335 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.77200 | 0.637411 | ||||||||
\(83\) | −1.00000 | −0.109764 | −0.0548821 | − | 0.998493i | \(-0.517478\pi\) | ||||
−0.0548821 | + | 0.998493i | \(0.517478\pi\) | |||||||
\(84\) | −3.00000 | −0.327327 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.77200 | −0.838077 | ||||||||
\(87\) | 3.00000 | 0.321634 | ||||||||
\(88\) | −5.77200 | −0.615297 | ||||||||
\(89\) | 16.7720 | 1.77783 | 0.888914 | − | 0.458073i | \(-0.151460\pi\) | ||||
0.888914 | + | 0.458073i | \(0.151460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.3160 | 1.18624 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −9.54400 | −0.989667 | ||||||||
\(94\) | 8.77200 | 0.904763 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 17.5440 | 1.78132 | 0.890662 | − | 0.454666i | \(-0.150241\pi\) | ||||
0.890662 | + | 0.454666i | \(0.150241\pi\) | |||||||
\(98\) | −2.00000 | −0.202031 | ||||||||
\(99\) | 5.77200 | 0.580108 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.3160 | 1.42450 | 0.712248 | − | 0.701928i | \(-0.247677\pi\) | ||||
0.712248 | + | 0.701928i | \(0.247677\pi\) | |||||||
\(102\) | −0.772002 | −0.0764396 | ||||||||
\(103\) | 11.0000 | 1.08386 | 0.541931 | − | 0.840423i | \(-0.317693\pi\) | ||||
0.541931 | + | 0.840423i | \(0.317693\pi\) | |||||||
\(104\) | 3.77200 | 0.369875 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 14.7720 | 1.41490 | 0.707451 | − | 0.706763i | \(-0.249845\pi\) | ||||
0.707451 | + | 0.706763i | \(0.249845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.77200 | 0.642770 | ||||||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | 4.77200 | 0.448912 | 0.224456 | − | 0.974484i | \(-0.427939\pi\) | ||||
0.224456 | + | 0.974484i | \(0.427939\pi\) | |||||||
\(114\) | −7.77200 | −0.727915 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | −3.77200 | −0.348722 | ||||||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | −2.31601 | −0.212308 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.3160 | 2.02873 | ||||||||
\(122\) | 9.54400 | 0.864073 | ||||||||
\(123\) | −5.77200 | −0.520444 | ||||||||
\(124\) | −9.54400 | −0.857077 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.00000 | 0.267261 | ||||||||
\(127\) | 4.45600 | 0.395406 | 0.197703 | − | 0.980262i | \(-0.436652\pi\) | ||||
0.197703 | + | 0.980262i | \(0.436652\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.77200 | 0.684287 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.0880 | −1.66773 | −0.833863 | − | 0.551971i | \(-0.813876\pi\) | ||||
−0.833863 | + | 0.551971i | \(0.813876\pi\) | |||||||
\(132\) | 5.77200 | 0.502388 | ||||||||
\(133\) | −23.3160 | −2.02175 | ||||||||
\(134\) | 9.54400 | 0.824476 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.772002 | −0.0661986 | ||||||||
\(137\) | 14.7720 | 1.26206 | 0.631029 | − | 0.775760i | \(-0.282633\pi\) | ||||
0.631029 | + | 0.775760i | \(0.282633\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −0.772002 | −0.0654803 | −0.0327402 | − | 0.999464i | \(-0.510423\pi\) | ||||
−0.0327402 | + | 0.999464i | \(0.510423\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.77200 | −0.738736 | ||||||||
\(142\) | 4.77200 | 0.400458 | ||||||||
\(143\) | −21.7720 | −1.82067 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.54400 | −0.541586 | ||||||||
\(147\) | 2.00000 | 0.164957 | ||||||||
\(148\) | 6.77200 | 0.556655 | ||||||||
\(149\) | −11.0880 | −0.908365 | −0.454182 | − | 0.890909i | \(-0.650069\pi\) | ||||
−0.454182 | + | 0.890909i | \(0.650069\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.5440 | 1.91598 | 0.957992 | − | 0.286795i | \(-0.0925899\pi\) | ||||
0.957992 | + | 0.286795i | \(0.0925899\pi\) | |||||||
\(152\) | −7.77200 | −0.630393 | ||||||||
\(153\) | 0.772002 | 0.0624127 | ||||||||
\(154\) | 17.3160 | 1.39536 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.77200 | −0.302002 | ||||||||
\(157\) | 13.5440 | 1.08093 | 0.540465 | − | 0.841367i | \(-0.318248\pi\) | ||||
0.540465 | + | 0.841367i | \(0.318248\pi\) | |||||||
\(158\) | −2.22800 | −0.177250 | ||||||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | −0.236433 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 16.0000 | 1.25322 | 0.626608 | − | 0.779334i | \(-0.284443\pi\) | ||||
0.626608 | + | 0.779334i | \(0.284443\pi\) | |||||||
\(164\) | −5.77200 | −0.450718 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.00000 | 0.0776151 | ||||||||
\(167\) | 16.3160 | 1.26257 | 0.631285 | − | 0.775551i | \(-0.282528\pi\) | ||||
0.631285 | + | 0.775551i | \(0.282528\pi\) | |||||||
\(168\) | 3.00000 | 0.231455 | ||||||||
\(169\) | 1.22800 | 0.0944614 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.77200 | 0.594340 | ||||||||
\(172\) | 7.77200 | 0.592610 | ||||||||
\(173\) | −15.7720 | −1.19912 | −0.599562 | − | 0.800329i | \(-0.704658\pi\) | ||||
−0.599562 | + | 0.800329i | \(0.704658\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.77200 | 0.435081 | ||||||||
\(177\) | 6.00000 | 0.450988 | ||||||||
\(178\) | −16.7720 | −1.25711 | ||||||||
\(179\) | 7.54400 | 0.563865 | 0.281933 | − | 0.959434i | \(-0.409025\pi\) | ||||
0.281933 | + | 0.959434i | \(0.409025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.3160 | 1.06410 | 0.532050 | − | 0.846713i | \(-0.321422\pi\) | ||||
0.532050 | + | 0.846713i | \(0.321422\pi\) | |||||||
\(182\) | −11.3160 | −0.838798 | ||||||||
\(183\) | −9.54400 | −0.705513 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.54400 | 0.699800 | ||||||||
\(187\) | 4.45600 | 0.325855 | ||||||||
\(188\) | −8.77200 | −0.639764 | ||||||||
\(189\) | −3.00000 | −0.218218 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.31601 | −0.529368 | −0.264684 | − | 0.964335i | \(-0.585268\pi\) | ||||
−0.264684 | + | 0.964335i | \(0.585268\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 4.77200 | 0.343496 | 0.171748 | − | 0.985141i | \(-0.445058\pi\) | ||||
0.171748 | + | 0.985141i | \(0.445058\pi\) | |||||||
\(194\) | −17.5440 | −1.25959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | −13.0000 | −0.926212 | −0.463106 | − | 0.886303i | \(-0.653265\pi\) | ||||
−0.463106 | + | 0.886303i | \(0.653265\pi\) | |||||||
\(198\) | −5.77200 | −0.410198 | ||||||||
\(199\) | 12.0880 | 0.856896 | 0.428448 | − | 0.903566i | \(-0.359060\pi\) | ||||
0.428448 | + | 0.903566i | \(0.359060\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.54400 | −0.673182 | ||||||||
\(202\) | −14.3160 | −1.00727 | ||||||||
\(203\) | −9.00000 | −0.631676 | ||||||||
\(204\) | 0.772002 | 0.0540509 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.0000 | −0.766406 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −3.77200 | −0.261541 | ||||||||
\(209\) | 44.8600 | 3.10303 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3160 | −0.710183 | −0.355092 | − | 0.934832i | \(-0.615550\pi\) | ||||
−0.355092 | + | 0.934832i | \(0.615550\pi\) | |||||||
\(212\) | 4.00000 | 0.274721 | ||||||||
\(213\) | −4.77200 | −0.326972 | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 28.6320 | 1.94367 | ||||||||
\(218\) | −14.7720 | −1.00049 | ||||||||
\(219\) | 6.54400 | 0.442203 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.91199 | −0.195882 | ||||||||
\(222\) | −6.77200 | −0.454507 | ||||||||
\(223\) | 10.0000 | 0.669650 | 0.334825 | − | 0.942280i | \(-0.391323\pi\) | ||||
0.334825 | + | 0.942280i | \(0.391323\pi\) | |||||||
\(224\) | 3.00000 | 0.200446 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.77200 | −0.317429 | ||||||||
\(227\) | −10.7720 | −0.714963 | −0.357481 | − | 0.933920i | \(-0.616364\pi\) | ||||
−0.357481 | + | 0.933920i | \(0.616364\pi\) | |||||||
\(228\) | 7.77200 | 0.514713 | ||||||||
\(229\) | −6.45600 | −0.426624 | −0.213312 | − | 0.976984i | \(-0.568425\pi\) | ||||
−0.213312 | + | 0.976984i | \(0.568425\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.3160 | −1.13931 | ||||||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | −2.68399 | −0.175834 | −0.0879172 | − | 0.996128i | \(-0.528021\pi\) | ||||
−0.0879172 | + | 0.996128i | \(0.528021\pi\) | |||||||
\(234\) | 3.77200 | 0.246583 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.00000 | 0.390567 | ||||||||
\(237\) | 2.22800 | 0.144724 | ||||||||
\(238\) | 2.31601 | 0.150124 | ||||||||
\(239\) | 22.7720 | 1.47300 | 0.736499 | − | 0.676438i | \(-0.236478\pi\) | ||||
0.736499 | + | 0.676438i | \(0.236478\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.6320 | −1.71552 | −0.857759 | − | 0.514051i | \(-0.828144\pi\) | ||||
−0.857759 | + | 0.514051i | \(0.828144\pi\) | |||||||
\(242\) | −22.3160 | −1.43453 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.54400 | −0.610992 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.77200 | 0.368009 | ||||||||
\(247\) | −29.3160 | −1.86533 | ||||||||
\(248\) | 9.54400 | 0.606045 | ||||||||
\(249\) | −1.00000 | −0.0633724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.68399 | −0.232532 | −0.116266 | − | 0.993218i | \(-0.537092\pi\) | ||||
−0.116266 | + | 0.993218i | \(0.537092\pi\) | |||||||
\(252\) | −3.00000 | −0.188982 | ||||||||
\(253\) | 5.77200 | 0.362883 | ||||||||
\(254\) | −4.45600 | −0.279594 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.08801 | −0.566894 | −0.283447 | − | 0.958988i | \(-0.591478\pi\) | ||||
−0.283447 | + | 0.958988i | \(0.591478\pi\) | |||||||
\(258\) | −7.77200 | −0.483864 | ||||||||
\(259\) | −20.3160 | −1.26238 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | 0.185695 | ||||||||
\(262\) | 19.0880 | 1.17926 | ||||||||
\(263\) | −6.45600 | −0.398094 | −0.199047 | − | 0.979990i | \(-0.563785\pi\) | ||||
−0.199047 | + | 0.979990i | \(0.563785\pi\) | |||||||
\(264\) | −5.77200 | −0.355242 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 23.3160 | 1.42960 | ||||||||
\(267\) | 16.7720 | 1.02643 | ||||||||
\(268\) | −9.54400 | −0.582993 | ||||||||
\(269\) | −26.8600 | −1.63768 | −0.818842 | − | 0.574019i | \(-0.805383\pi\) | ||||
−0.818842 | + | 0.574019i | \(0.805383\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0.772002 | 0.0468095 | ||||||||
\(273\) | 11.3160 | 0.684876 | ||||||||
\(274\) | −14.7720 | −0.892409 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −8.22800 | −0.494372 | −0.247186 | − | 0.968968i | \(-0.579506\pi\) | ||||
−0.247186 | + | 0.968968i | \(0.579506\pi\) | |||||||
\(278\) | 0.772002 | 0.0463016 | ||||||||
\(279\) | −9.54400 | −0.571385 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8600 | 0.946129 | 0.473064 | − | 0.881028i | \(-0.343148\pi\) | ||||
0.473064 | + | 0.881028i | \(0.343148\pi\) | |||||||
\(282\) | 8.77200 | 0.522365 | ||||||||
\(283\) | 28.0000 | 1.66443 | 0.832214 | − | 0.554455i | \(-0.187073\pi\) | ||||
0.832214 | + | 0.554455i | \(0.187073\pi\) | |||||||
\(284\) | −4.77200 | −0.283166 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.7720 | 1.28741 | ||||||||
\(287\) | 17.3160 | 1.02213 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.4040 | −0.964942 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.5440 | 1.02845 | ||||||||
\(292\) | 6.54400 | 0.382959 | ||||||||
\(293\) | −9.54400 | −0.557567 | −0.278783 | − | 0.960354i | \(-0.589931\pi\) | ||||
−0.278783 | + | 0.960354i | \(0.589931\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.77200 | −0.393615 | ||||||||
\(297\) | 5.77200 | 0.334926 | ||||||||
\(298\) | 11.0880 | 0.642311 | ||||||||
\(299\) | −3.77200 | −0.218141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.3160 | −1.34391 | ||||||||
\(302\) | −23.5440 | −1.35481 | ||||||||
\(303\) | 14.3160 | 0.822433 | ||||||||
\(304\) | 7.77200 | 0.445755 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.772002 | −0.0441324 | ||||||||
\(307\) | −20.3160 | −1.15950 | −0.579748 | − | 0.814796i | \(-0.696849\pi\) | ||||
−0.579748 | + | 0.814796i | \(0.696849\pi\) | |||||||
\(308\) | −17.3160 | −0.986671 | ||||||||
\(309\) | 11.0000 | 0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.8600 | −1.01275 | −0.506374 | − | 0.862314i | \(-0.669015\pi\) | ||||
−0.506374 | + | 0.862314i | \(0.669015\pi\) | |||||||
\(312\) | 3.77200 | 0.213548 | ||||||||
\(313\) | −8.00000 | −0.452187 | −0.226093 | − | 0.974106i | \(-0.572595\pi\) | ||||
−0.226093 | + | 0.974106i | \(0.572595\pi\) | |||||||
\(314\) | −13.5440 | −0.764332 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.22800 | 0.125335 | ||||||||
\(317\) | −9.00000 | −0.505490 | −0.252745 | − | 0.967533i | \(-0.581333\pi\) | ||||
−0.252745 | + | 0.967533i | \(0.581333\pi\) | |||||||
\(318\) | −4.00000 | −0.224309 | ||||||||
\(319\) | 17.3160 | 0.969510 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 3.00000 | 0.167183 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.0000 | −0.886158 | ||||||||
\(327\) | 14.7720 | 0.816894 | ||||||||
\(328\) | 5.77200 | 0.318705 | ||||||||
\(329\) | 26.3160 | 1.45085 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.7720 | 1.91124 | 0.955621 | − | 0.294599i | \(-0.0951860\pi\) | ||||
0.955621 | + | 0.294599i | \(0.0951860\pi\) | |||||||
\(332\) | −1.00000 | −0.0548821 | ||||||||
\(333\) | 6.77200 | 0.371103 | ||||||||
\(334\) | −16.3160 | −0.892772 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.00000 | −0.163663 | ||||||||
\(337\) | 4.00000 | 0.217894 | 0.108947 | − | 0.994048i | \(-0.465252\pi\) | ||||
0.108947 | + | 0.994048i | \(0.465252\pi\) | |||||||
\(338\) | −1.22800 | −0.0667943 | ||||||||
\(339\) | 4.77200 | 0.259180 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −55.0880 | −2.98318 | ||||||||
\(342\) | −7.77200 | −0.420262 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −7.77200 | −0.419038 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.7720 | 0.847908 | ||||||||
\(347\) | 9.54400 | 0.512349 | 0.256174 | − | 0.966631i | \(-0.417538\pi\) | ||||
0.256174 | + | 0.966631i | \(0.417538\pi\) | |||||||
\(348\) | 3.00000 | 0.160817 | ||||||||
\(349\) | −0.227998 | −0.0122045 | −0.00610223 | − | 0.999981i | \(-0.501942\pi\) | ||||
−0.00610223 | + | 0.999981i | \(0.501942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.77200 | −0.201335 | ||||||||
\(352\) | −5.77200 | −0.307649 | ||||||||
\(353\) | −18.8600 | −1.00382 | −0.501909 | − | 0.864921i | \(-0.667369\pi\) | ||||
−0.501909 | + | 0.864921i | \(0.667369\pi\) | |||||||
\(354\) | −6.00000 | −0.318896 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 16.7720 | 0.888914 | ||||||||
\(357\) | −2.31601 | −0.122576 | ||||||||
\(358\) | −7.54400 | −0.398713 | ||||||||
\(359\) | −10.2280 | −0.539813 | −0.269907 | − | 0.962887i | \(-0.586993\pi\) | ||||
−0.269907 | + | 0.962887i | \(0.586993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.4040 | 2.17916 | ||||||||
\(362\) | −14.3160 | −0.752433 | ||||||||
\(363\) | 22.3160 | 1.17129 | ||||||||
\(364\) | 11.3160 | 0.593120 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.54400 | 0.498873 | ||||||||
\(367\) | 33.3160 | 1.73908 | 0.869541 | − | 0.493861i | \(-0.164415\pi\) | ||||
0.869541 | + | 0.493861i | \(0.164415\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −5.77200 | −0.300478 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | −0.623009 | ||||||||
\(372\) | −9.54400 | −0.494834 | ||||||||
\(373\) | −12.7720 | −0.661309 | −0.330655 | − | 0.943752i | \(-0.607270\pi\) | ||||
−0.330655 | + | 0.943752i | \(0.607270\pi\) | |||||||
\(374\) | −4.45600 | −0.230414 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.77200 | 0.452381 | ||||||||
\(377\) | −11.3160 | −0.582804 | ||||||||
\(378\) | 3.00000 | 0.154303 | ||||||||
\(379\) | −23.0880 | −1.18595 | −0.592976 | − | 0.805220i | \(-0.702047\pi\) | ||||
−0.592976 | + | 0.805220i | \(0.702047\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.45600 | 0.228288 | ||||||||
\(382\) | 7.31601 | 0.374319 | ||||||||
\(383\) | 13.7720 | 0.703716 | 0.351858 | − | 0.936053i | \(-0.385550\pi\) | ||||
0.351858 | + | 0.936053i | \(0.385550\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.77200 | −0.242889 | ||||||||
\(387\) | 7.77200 | 0.395073 | ||||||||
\(388\) | 17.5440 | 0.890662 | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.772002 | 0.0390418 | ||||||||
\(392\) | −2.00000 | −0.101015 | ||||||||
\(393\) | −19.0880 | −0.962863 | ||||||||
\(394\) | 13.0000 | 0.654931 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.77200 | 0.290054 | ||||||||
\(397\) | −14.6320 | −0.734360 | −0.367180 | − | 0.930150i | \(-0.619677\pi\) | ||||
−0.367180 | + | 0.930150i | \(0.619677\pi\) | |||||||
\(398\) | −12.0880 | −0.605917 | ||||||||
\(399\) | −23.3160 | −1.16726 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.6320 | −1.42981 | −0.714907 | − | 0.699219i | \(-0.753531\pi\) | ||||
−0.714907 | + | 0.699219i | \(0.753531\pi\) | |||||||
\(402\) | 9.54400 | 0.476012 | ||||||||
\(403\) | 36.0000 | 1.79329 | ||||||||
\(404\) | 14.3160 | 0.712248 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.00000 | 0.446663 | ||||||||
\(407\) | 39.0880 | 1.93752 | ||||||||
\(408\) | −0.772002 | −0.0382198 | ||||||||
\(409\) | −23.0000 | −1.13728 | −0.568638 | − | 0.822588i | \(-0.692530\pi\) | ||||
−0.568638 | + | 0.822588i | \(0.692530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.7720 | 0.728649 | ||||||||
\(412\) | 11.0000 | 0.541931 | ||||||||
\(413\) | −18.0000 | −0.885722 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.77200 | 0.184938 | ||||||||
\(417\) | −0.772002 | −0.0378051 | ||||||||
\(418\) | −44.8600 | −2.19417 | ||||||||
\(419\) | 25.6320 | 1.25221 | 0.626103 | − | 0.779740i | \(-0.284649\pi\) | ||||
0.626103 | + | 0.779740i | \(0.284649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 10.3160 | 0.502175 | ||||||||
\(423\) | −8.77200 | −0.426509 | ||||||||
\(424\) | −4.00000 | −0.194257 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.77200 | 0.231204 | ||||||||
\(427\) | 28.6320 | 1.38560 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | −21.7720 | −1.05116 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.6320 | 1.18648 | 0.593241 | − | 0.805025i | \(-0.297848\pi\) | ||||
0.593241 | + | 0.805025i | \(0.297848\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 6.45600 | 0.310255 | 0.155128 | − | 0.987894i | \(-0.450421\pi\) | ||||
0.155128 | + | 0.987894i | \(0.450421\pi\) | |||||||
\(434\) | −28.6320 | −1.37438 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.7720 | 0.707451 | ||||||||
\(437\) | 7.77200 | 0.371785 | ||||||||
\(438\) | −6.54400 | −0.312685 | ||||||||
\(439\) | −12.0000 | −0.572729 | −0.286364 | − | 0.958121i | \(-0.592447\pi\) | ||||
−0.286364 | + | 0.958121i | \(0.592447\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | 2.91199 | 0.138509 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 6.77200 | 0.321385 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.0000 | −0.473514 | ||||||||
\(447\) | −11.0880 | −0.524445 | ||||||||
\(448\) | −3.00000 | −0.141737 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.3160 | −1.56879 | ||||||||
\(452\) | 4.77200 | 0.224456 | ||||||||
\(453\) | 23.5440 | 1.10619 | ||||||||
\(454\) | 10.7720 | 0.505555 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.77200 | −0.363957 | ||||||||
\(457\) | −30.6320 | −1.43291 | −0.716453 | − | 0.697636i | \(-0.754235\pi\) | ||||
−0.716453 | + | 0.697636i | \(0.754235\pi\) | |||||||
\(458\) | 6.45600 | 0.301669 | ||||||||
\(459\) | 0.772002 | 0.0360340 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.5440 | 0.584232 | 0.292116 | − | 0.956383i | \(-0.405641\pi\) | ||||
0.292116 | + | 0.956383i | \(0.405641\pi\) | |||||||
\(462\) | 17.3160 | 0.805613 | ||||||||
\(463\) | 0.911993 | 0.0423839 | 0.0211919 | − | 0.999775i | \(-0.493254\pi\) | ||||
0.0211919 | + | 0.999775i | \(0.493254\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.68399 | 0.124334 | ||||||||
\(467\) | 18.5440 | 0.858114 | 0.429057 | − | 0.903277i | \(-0.358846\pi\) | ||||
0.429057 | + | 0.903277i | \(0.358846\pi\) | |||||||
\(468\) | −3.77200 | −0.174361 | ||||||||
\(469\) | 28.6320 | 1.32210 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.5440 | 0.624075 | ||||||||
\(472\) | −6.00000 | −0.276172 | ||||||||
\(473\) | 44.8600 | 2.06267 | ||||||||
\(474\) | −2.22800 | −0.102335 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.31601 | −0.106154 | ||||||||
\(477\) | 4.00000 | 0.183147 | ||||||||
\(478\) | −22.7720 | −1.04157 | ||||||||
\(479\) | −35.3160 | −1.61363 | −0.806815 | − | 0.590805i | \(-0.798810\pi\) | ||||
−0.806815 | + | 0.590805i | \(0.798810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.5440 | −1.16471 | ||||||||
\(482\) | 26.6320 | 1.21305 | ||||||||
\(483\) | −3.00000 | −0.136505 | ||||||||
\(484\) | 22.3160 | 1.01436 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 12.4560 | 0.564435 | 0.282218 | − | 0.959350i | \(-0.408930\pi\) | ||||
0.282218 | + | 0.959350i | \(0.408930\pi\) | |||||||
\(488\) | 9.54400 | 0.432037 | ||||||||
\(489\) | 16.0000 | 0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.4560 | −0.471873 | −0.235936 | − | 0.971769i | \(-0.575816\pi\) | ||||
−0.235936 | + | 0.971769i | \(0.575816\pi\) | |||||||
\(492\) | −5.77200 | −0.260222 | ||||||||
\(493\) | 2.31601 | 0.104308 | ||||||||
\(494\) | 29.3160 | 1.31899 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.54400 | −0.428538 | ||||||||
\(497\) | 14.3160 | 0.642161 | ||||||||
\(498\) | 1.00000 | 0.0448111 | ||||||||
\(499\) | −9.68399 | −0.433515 | −0.216758 | − | 0.976225i | \(-0.569548\pi\) | ||||
−0.216758 | + | 0.976225i | \(0.569548\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.3160 | 0.728945 | ||||||||
\(502\) | 3.68399 | 0.164425 | ||||||||
\(503\) | −39.9480 | −1.78119 | −0.890597 | − | 0.454793i | \(-0.849713\pi\) | ||||
−0.890597 | + | 0.454793i | \(0.849713\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.77200 | −0.256597 | ||||||||
\(507\) | 1.22800 | 0.0545373 | ||||||||
\(508\) | 4.45600 | 0.197703 | ||||||||
\(509\) | 27.8600 | 1.23487 | 0.617437 | − | 0.786621i | \(-0.288171\pi\) | ||||
0.617437 | + | 0.786621i | \(0.288171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.6320 | −0.868469 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.77200 | 0.343142 | ||||||||
\(514\) | 9.08801 | 0.400855 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.77200 | 0.342143 | ||||||||
\(517\) | −50.6320 | −2.22679 | ||||||||
\(518\) | 20.3160 | 0.892634 | ||||||||
\(519\) | −15.7720 | −0.692314 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.77200 | 0.296687 | 0.148343 | − | 0.988936i | \(-0.452606\pi\) | ||||
0.148343 | + | 0.988936i | \(0.452606\pi\) | |||||||
\(522\) | −3.00000 | −0.131306 | ||||||||
\(523\) | −13.3160 | −0.582268 | −0.291134 | − | 0.956682i | \(-0.594033\pi\) | ||||
−0.291134 | + | 0.956682i | \(0.594033\pi\) | |||||||
\(524\) | −19.0880 | −0.833863 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.45600 | 0.281495 | ||||||||
\(527\) | −7.36799 | −0.320955 | ||||||||
\(528\) | 5.77200 | 0.251194 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | −23.3160 | −1.01088 | ||||||||
\(533\) | 21.7720 | 0.943050 | ||||||||
\(534\) | −16.7720 | −0.725796 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.54400 | 0.412238 | ||||||||
\(537\) | 7.54400 | 0.325548 | ||||||||
\(538\) | 26.8600 | 1.15802 | ||||||||
\(539\) | 11.5440 | 0.497235 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6840 | −0.459341 | −0.229670 | − | 0.973268i | \(-0.573765\pi\) | ||||
−0.229670 | + | 0.973268i | \(0.573765\pi\) | |||||||
\(542\) | −16.0000 | −0.687259 | ||||||||
\(543\) | 14.3160 | 0.614359 | ||||||||
\(544\) | −0.772002 | −0.0330993 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.3160 | −0.484280 | ||||||||
\(547\) | 11.8600 | 0.507097 | 0.253549 | − | 0.967323i | \(-0.418402\pi\) | ||||
0.253549 | + | 0.967323i | \(0.418402\pi\) | |||||||
\(548\) | 14.7720 | 0.631029 | ||||||||
\(549\) | −9.54400 | −0.407328 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.3160 | 0.993295 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −6.68399 | −0.284232 | ||||||||
\(554\) | 8.22800 | 0.349574 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.772002 | −0.0327402 | ||||||||
\(557\) | −21.0880 | −0.893528 | −0.446764 | − | 0.894652i | \(-0.647424\pi\) | ||||
−0.446764 | + | 0.894652i | \(0.647424\pi\) | |||||||
\(558\) | 9.54400 | 0.404030 | ||||||||
\(559\) | −29.3160 | −1.23993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.45600 | 0.188132 | ||||||||
\(562\) | −15.8600 | −0.669014 | ||||||||
\(563\) | 43.9480 | 1.85219 | 0.926094 | − | 0.377293i | \(-0.123145\pi\) | ||||
0.926094 | + | 0.377293i | \(0.123145\pi\) | |||||||
\(564\) | −8.77200 | −0.369368 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −28.0000 | −1.17693 | ||||||||
\(567\) | −3.00000 | −0.125988 | ||||||||
\(568\) | 4.77200 | 0.200229 | ||||||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.6320 | 0.528633 | 0.264317 | − | 0.964436i | \(-0.414854\pi\) | ||||
0.264317 | + | 0.964436i | \(0.414854\pi\) | |||||||
\(572\) | −21.7720 | −0.910333 | ||||||||
\(573\) | −7.31601 | −0.305631 | ||||||||
\(574\) | −17.3160 | −0.722756 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −31.3160 | −1.30370 | −0.651851 | − | 0.758347i | \(-0.726007\pi\) | ||||
−0.651851 | + | 0.758347i | \(0.726007\pi\) | |||||||
\(578\) | 16.4040 | 0.682317 | ||||||||
\(579\) | 4.77200 | 0.198318 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.00000 | 0.124461 | ||||||||
\(582\) | −17.5440 | −0.727222 | ||||||||
\(583\) | 23.0880 | 0.956208 | ||||||||
\(584\) | −6.54400 | −0.270793 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.54400 | 0.394259 | ||||||||
\(587\) | 24.4560 | 1.00941 | 0.504703 | − | 0.863293i | \(-0.331602\pi\) | ||||
0.504703 | + | 0.863293i | \(0.331602\pi\) | |||||||
\(588\) | 2.00000 | 0.0824786 | ||||||||
\(589\) | −74.1760 | −3.05637 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.0000 | −0.534749 | ||||||||
\(592\) | 6.77200 | 0.278328 | ||||||||
\(593\) | 41.3160 | 1.69664 | 0.848322 | − | 0.529480i | \(-0.177613\pi\) | ||||
0.848322 | + | 0.529480i | \(0.177613\pi\) | |||||||
\(594\) | −5.77200 | −0.236828 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.0880 | −0.454182 | ||||||||
\(597\) | 12.0880 | 0.494729 | ||||||||
\(598\) | 3.77200 | 0.154249 | ||||||||
\(599\) | 8.00000 | 0.326871 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.7720 | −1.33680 | −0.668399 | − | 0.743803i | \(-0.733020\pi\) | ||||
−0.668399 | + | 0.743803i | \(0.733020\pi\) | |||||||
\(602\) | 23.3160 | 0.950289 | ||||||||
\(603\) | −9.54400 | −0.388662 | ||||||||
\(604\) | 23.5440 | 0.957992 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.3160 | −0.581548 | ||||||||
\(607\) | 5.08801 | 0.206516 | 0.103258 | − | 0.994655i | \(-0.467073\pi\) | ||||
0.103258 | + | 0.994655i | \(0.467073\pi\) | |||||||
\(608\) | −7.77200 | −0.315196 | ||||||||
\(609\) | −9.00000 | −0.364698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.0880 | 1.33860 | ||||||||
\(612\) | 0.772002 | 0.0312063 | ||||||||
\(613\) | 20.7720 | 0.838973 | 0.419487 | − | 0.907762i | \(-0.362210\pi\) | ||||
0.419487 | + | 0.907762i | \(0.362210\pi\) | |||||||
\(614\) | 20.3160 | 0.819887 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.3160 | 0.697682 | ||||||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | −11.0000 | −0.442485 | ||||||||
\(619\) | −0.911993 | −0.0366561 | −0.0183280 | − | 0.999832i | \(-0.505834\pi\) | ||||
−0.0183280 | + | 0.999832i | \(0.505834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 17.8600 | 0.716121 | ||||||||
\(623\) | −50.3160 | −2.01587 | ||||||||
\(624\) | −3.77200 | −0.151001 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.00000 | 0.319744 | ||||||||
\(627\) | 44.8600 | 1.79154 | ||||||||
\(628\) | 13.5440 | 0.540465 | ||||||||
\(629\) | 5.22800 | 0.208454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0880 | 0.560835 | 0.280417 | − | 0.959878i | \(-0.409527\pi\) | ||||
0.280417 | + | 0.959878i | \(0.409527\pi\) | |||||||
\(632\) | −2.22800 | −0.0886250 | ||||||||
\(633\) | −10.3160 | −0.410024 | ||||||||
\(634\) | 9.00000 | 0.357436 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.00000 | 0.158610 | ||||||||
\(637\) | −7.54400 | −0.298904 | ||||||||
\(638\) | −17.3160 | −0.685547 | ||||||||
\(639\) | −4.77200 | −0.188777 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.8600 | −0.705428 | −0.352714 | − | 0.935731i | \(-0.614741\pi\) | ||||
−0.352714 | + | 0.935731i | \(0.614741\pi\) | |||||||
\(642\) | 4.00000 | 0.157867 | ||||||||
\(643\) | −19.3160 | −0.761749 | −0.380874 | − | 0.924627i | \(-0.624377\pi\) | ||||
−0.380874 | + | 0.924627i | \(0.624377\pi\) | |||||||
\(644\) | −3.00000 | −0.118217 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | −0.236067 | ||||||||
\(647\) | −30.7720 | −1.20977 | −0.604886 | − | 0.796312i | \(-0.706781\pi\) | ||||
−0.604886 | + | 0.796312i | \(0.706781\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 34.6320 | 1.35943 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.6320 | 1.12218 | ||||||||
\(652\) | 16.0000 | 0.626608 | ||||||||
\(653\) | 23.4560 | 0.917904 | 0.458952 | − | 0.888461i | \(-0.348225\pi\) | ||||
0.458952 | + | 0.888461i | \(0.348225\pi\) | |||||||
\(654\) | −14.7720 | −0.577631 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.77200 | −0.225359 | ||||||||
\(657\) | 6.54400 | 0.255306 | ||||||||
\(658\) | −26.3160 | −1.02590 | ||||||||
\(659\) | −43.6320 | −1.69966 | −0.849831 | − | 0.527055i | \(-0.823296\pi\) | ||||
−0.849831 | + | 0.527055i | \(0.823296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.8600 | −0.694674 | −0.347337 | − | 0.937740i | \(-0.612914\pi\) | ||||
−0.347337 | + | 0.937740i | \(0.612914\pi\) | |||||||
\(662\) | −34.7720 | −1.35145 | ||||||||
\(663\) | −2.91199 | −0.113092 | ||||||||
\(664\) | 1.00000 | 0.0388075 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.77200 | −0.262410 | ||||||||
\(667\) | 3.00000 | 0.116160 | ||||||||
\(668\) | 16.3160 | 0.631285 | ||||||||
\(669\) | 10.0000 | 0.386622 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −55.0880 | −2.12665 | ||||||||
\(672\) | 3.00000 | 0.115728 | ||||||||
\(673\) | −26.5440 | −1.02320 | −0.511598 | − | 0.859225i | \(-0.670946\pi\) | ||||
−0.511598 | + | 0.859225i | \(0.670946\pi\) | |||||||
\(674\) | −4.00000 | −0.154074 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.22800 | 0.0472307 | ||||||||
\(677\) | −48.0000 | −1.84479 | −0.922395 | − | 0.386248i | \(-0.873771\pi\) | ||||
−0.922395 | + | 0.386248i | \(0.873771\pi\) | |||||||
\(678\) | −4.77200 | −0.183268 | ||||||||
\(679\) | −52.6320 | −2.01983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.7720 | −0.412784 | ||||||||
\(682\) | 55.0880 | 2.10943 | ||||||||
\(683\) | −26.6320 | −1.01905 | −0.509523 | − | 0.860457i | \(-0.670178\pi\) | ||||
−0.509523 | + | 0.860457i | \(0.670178\pi\) | |||||||
\(684\) | 7.77200 | 0.297170 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.0000 | −0.572703 | ||||||||
\(687\) | −6.45600 | −0.246312 | ||||||||
\(688\) | 7.77200 | 0.296305 | ||||||||
\(689\) | −15.0880 | −0.574807 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.2280 | −1.49230 | −0.746152 | − | 0.665776i | \(-0.768101\pi\) | ||||
−0.746152 | + | 0.665776i | \(0.768101\pi\) | |||||||
\(692\) | −15.7720 | −0.599562 | ||||||||
\(693\) | −17.3160 | −0.657781 | ||||||||
\(694\) | −9.54400 | −0.362285 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.00000 | −0.113715 | ||||||||
\(697\) | −4.45600 | −0.168783 | ||||||||
\(698\) | 0.227998 | 0.00862986 | ||||||||
\(699\) | −2.68399 | −0.101518 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.54400 | 0.0583162 | 0.0291581 | − | 0.999575i | \(-0.490717\pi\) | ||||
0.0291581 | + | 0.999575i | \(0.490717\pi\) | |||||||
\(702\) | 3.77200 | 0.142365 | ||||||||
\(703\) | 52.6320 | 1.98505 | ||||||||
\(704\) | 5.77200 | 0.217541 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.8600 | 0.709806 | ||||||||
\(707\) | −42.9480 | −1.61523 | ||||||||
\(708\) | 6.00000 | 0.225494 | ||||||||
\(709\) | 24.3160 | 0.913207 | 0.456603 | − | 0.889670i | \(-0.349066\pi\) | ||||
0.456603 | + | 0.889670i | \(0.349066\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.22800 | 0.0835565 | ||||||||
\(712\) | −16.7720 | −0.628557 | ||||||||
\(713\) | −9.54400 | −0.357426 | ||||||||
\(714\) | 2.31601 | 0.0866743 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.54400 | 0.281933 | ||||||||
\(717\) | 22.7720 | 0.850436 | ||||||||
\(718\) | 10.2280 | 0.381705 | ||||||||
\(719\) | −30.3160 | −1.13060 | −0.565298 | − | 0.824887i | \(-0.691239\pi\) | ||||
−0.565298 | + | 0.824887i | \(0.691239\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.0000 | −1.22898 | ||||||||
\(722\) | −41.4040 | −1.54090 | ||||||||
\(723\) | −26.6320 | −0.990455 | ||||||||
\(724\) | 14.3160 | 0.532050 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.3160 | −0.828225 | ||||||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | −11.3160 | −0.419399 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | 0.221918 | ||||||||
\(732\) | −9.54400 | −0.352757 | ||||||||
\(733\) | 17.2280 | 0.636331 | 0.318165 | − | 0.948035i | \(-0.396933\pi\) | ||||
0.318165 | + | 0.948035i | \(0.396933\pi\) | |||||||
\(734\) | −33.3160 | −1.22972 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −55.0880 | −2.02919 | ||||||||
\(738\) | 5.77200 | 0.212470 | ||||||||
\(739\) | 17.2280 | 0.633742 | 0.316871 | − | 0.948469i | \(-0.397368\pi\) | ||||
0.316871 | + | 0.948469i | \(0.397368\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29.3160 | −1.07695 | ||||||||
\(742\) | 12.0000 | 0.440534 | ||||||||
\(743\) | 20.2280 | 0.742093 | 0.371047 | − | 0.928614i | \(-0.378999\pi\) | ||||
0.371047 | + | 0.928614i | \(0.378999\pi\) | |||||||
\(744\) | 9.54400 | 0.349900 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.7720 | 0.467616 | ||||||||
\(747\) | −1.00000 | −0.0365881 | ||||||||
\(748\) | 4.45600 | 0.162927 | ||||||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.5440 | −0.968604 | −0.484302 | − | 0.874901i | \(-0.660926\pi\) | ||||
−0.484302 | + | 0.874901i | \(0.660926\pi\) | |||||||
\(752\) | −8.77200 | −0.319882 | ||||||||
\(753\) | −3.68399 | −0.134252 | ||||||||
\(754\) | 11.3160 | 0.412105 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.00000 | −0.109109 | ||||||||
\(757\) | −41.2280 | −1.49846 | −0.749229 | − | 0.662312i | \(-0.769576\pi\) | ||||
−0.749229 | + | 0.662312i | \(0.769576\pi\) | |||||||
\(758\) | 23.0880 | 0.838594 | ||||||||
\(759\) | 5.77200 | 0.209510 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.8600 | −0.538675 | −0.269337 | − | 0.963046i | \(-0.586805\pi\) | ||||
−0.269337 | + | 0.963046i | \(0.586805\pi\) | |||||||
\(762\) | −4.45600 | −0.161424 | ||||||||
\(763\) | −44.3160 | −1.60435 | ||||||||
\(764\) | −7.31601 | −0.264684 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.7720 | −0.497603 | ||||||||
\(767\) | −22.6320 | −0.817195 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −9.08801 | −0.327722 | −0.163861 | − | 0.986483i | \(-0.552395\pi\) | ||||
−0.163861 | + | 0.986483i | \(0.552395\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.08801 | −0.327297 | ||||||||
\(772\) | 4.77200 | 0.171748 | ||||||||
\(773\) | −14.4560 | −0.519946 | −0.259973 | − | 0.965616i | \(-0.583714\pi\) | ||||
−0.259973 | + | 0.965616i | \(0.583714\pi\) | |||||||
\(774\) | −7.77200 | −0.279359 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.5440 | −0.629793 | ||||||||
\(777\) | −20.3160 | −0.728833 | ||||||||
\(778\) | −18.0000 | −0.645331 | ||||||||
\(779\) | −44.8600 | −1.60728 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.5440 | −0.985602 | ||||||||
\(782\) | −0.772002 | −0.0276067 | ||||||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 2.00000 | 0.0714286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.0880 | 0.680847 | ||||||||
\(787\) | 21.7720 | 0.776088 | 0.388044 | − | 0.921641i | \(-0.373151\pi\) | ||||
0.388044 | + | 0.921641i | \(0.373151\pi\) | |||||||
\(788\) | −13.0000 | −0.463106 | ||||||||
\(789\) | −6.45600 | −0.229840 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.3160 | −0.509019 | ||||||||
\(792\) | −5.77200 | −0.205099 | ||||||||
\(793\) | 36.0000 | 1.27840 | ||||||||
\(794\) | 14.6320 | 0.519271 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.0880 | 0.428448 | ||||||||
\(797\) | −2.91199 | −0.103148 | −0.0515740 | − | 0.998669i | \(-0.516424\pi\) | ||||
−0.0515740 | + | 0.998669i | \(0.516424\pi\) | |||||||
\(798\) | 23.3160 | 0.825378 | ||||||||
\(799\) | −6.77200 | −0.239576 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.7720 | 0.592610 | ||||||||
\(802\) | 28.6320 | 1.01103 | ||||||||
\(803\) | 37.7720 | 1.33294 | ||||||||
\(804\) | −9.54400 | −0.336591 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.0000 | −1.26805 | ||||||||
\(807\) | −26.8600 | −0.945517 | ||||||||
\(808\) | −14.3160 | −0.503635 | ||||||||
\(809\) | 47.3160 | 1.66354 | 0.831771 | − | 0.555119i | \(-0.187327\pi\) | ||||
0.831771 | + | 0.555119i | \(0.187327\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.6320 | −1.35655 | −0.678277 | − | 0.734807i | \(-0.737273\pi\) | ||||
−0.678277 | + | 0.734807i | \(0.737273\pi\) | |||||||
\(812\) | −9.00000 | −0.315838 | ||||||||
\(813\) | 16.0000 | 0.561144 | ||||||||
\(814\) | −39.0880 | −1.37003 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.772002 | 0.0270255 | ||||||||
\(817\) | 60.4040 | 2.11327 | ||||||||
\(818\) | 23.0000 | 0.804176 | ||||||||
\(819\) | 11.3160 | 0.395413 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.2280 | −0.426760 | −0.213380 | − | 0.976969i | \(-0.568447\pi\) | ||||
−0.213380 | + | 0.976969i | \(0.568447\pi\) | |||||||
\(822\) | −14.7720 | −0.515233 | ||||||||
\(823\) | −23.5440 | −0.820692 | −0.410346 | − | 0.911930i | \(-0.634592\pi\) | ||||
−0.410346 | + | 0.911930i | \(0.634592\pi\) | |||||||
\(824\) | −11.0000 | −0.383203 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0000 | 0.626300 | ||||||||
\(827\) | −51.6320 | −1.79542 | −0.897710 | − | 0.440586i | \(-0.854771\pi\) | ||||
−0.897710 | + | 0.440586i | \(0.854771\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −38.4040 | −1.33383 | −0.666913 | − | 0.745135i | \(-0.732385\pi\) | ||||
−0.666913 | + | 0.745135i | \(0.732385\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.22800 | −0.285426 | ||||||||
\(832\) | −3.77200 | −0.130771 | ||||||||
\(833\) | 1.54400 | 0.0534966 | ||||||||
\(834\) | 0.772002 | 0.0267322 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 44.8600 | 1.55152 | ||||||||
\(837\) | −9.54400 | −0.329889 | ||||||||
\(838\) | −25.6320 | −0.885443 | ||||||||
\(839\) | 32.4040 | 1.11871 | 0.559355 | − | 0.828928i | \(-0.311049\pi\) | ||||
0.559355 | + | 0.828928i | \(0.311049\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −22.0000 | −0.758170 | ||||||||
\(843\) | 15.8600 | 0.546248 | ||||||||
\(844\) | −10.3160 | −0.355092 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.77200 | 0.301588 | ||||||||
\(847\) | −66.9480 | −2.30036 | ||||||||
\(848\) | 4.00000 | 0.137361 | ||||||||
\(849\) | 28.0000 | 0.960958 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.77200 | 0.232141 | ||||||||
\(852\) | −4.77200 | −0.163486 | ||||||||
\(853\) | 8.86001 | 0.303361 | 0.151680 | − | 0.988430i | \(-0.451532\pi\) | ||||
0.151680 | + | 0.988430i | \(0.451532\pi\) | |||||||
\(854\) | −28.6320 | −0.979767 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.00000 | 0.136717 | ||||||||
\(857\) | 6.00000 | 0.204956 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(858\) | 21.7720 | 0.743284 | ||||||||
\(859\) | −24.4560 | −0.834428 | −0.417214 | − | 0.908808i | \(-0.636993\pi\) | ||||
−0.417214 | + | 0.908808i | \(0.636993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.3160 | 0.590128 | ||||||||
\(862\) | −24.6320 | −0.838970 | ||||||||
\(863\) | 2.31601 | 0.0788377 | 0.0394189 | − | 0.999223i | \(-0.487449\pi\) | ||||
0.0394189 | + | 0.999223i | \(0.487449\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.45600 | −0.219384 | ||||||||
\(867\) | −16.4040 | −0.557109 | ||||||||
\(868\) | 28.6320 | 0.971834 | ||||||||
\(869\) | 12.8600 | 0.436246 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.0000 | 1.21981 | ||||||||
\(872\) | −14.7720 | −0.500243 | ||||||||
\(873\) | 17.5440 | 0.593775 | ||||||||
\(874\) | −7.77200 | −0.262892 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.54400 | 0.221101 | ||||||||
\(877\) | 47.2640 | 1.59599 | 0.797996 | − | 0.602662i | \(-0.205893\pi\) | ||||
0.797996 | + | 0.602662i | \(0.205893\pi\) | |||||||
\(878\) | 12.0000 | 0.404980 | ||||||||
\(879\) | −9.54400 | −0.321911 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.4560 | 0.352271 | 0.176136 | − | 0.984366i | \(-0.443640\pi\) | ||||
0.176136 | + | 0.984366i | \(0.443640\pi\) | |||||||
\(882\) | −2.00000 | −0.0673435 | ||||||||
\(883\) | −10.7720 | −0.362507 | −0.181253 | − | 0.983436i | \(-0.558015\pi\) | ||||
−0.181253 | + | 0.983436i | \(0.558015\pi\) | |||||||
\(884\) | −2.91199 | −0.0979409 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0000 | −0.806296 | ||||||||
\(887\) | −46.9480 | −1.57636 | −0.788180 | − | 0.615445i | \(-0.788976\pi\) | ||||
−0.788180 | + | 0.615445i | \(0.788976\pi\) | |||||||
\(888\) | −6.77200 | −0.227254 | ||||||||
\(889\) | −13.3680 | −0.448348 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.77200 | 0.193369 | ||||||||
\(892\) | 10.0000 | 0.334825 | ||||||||
\(893\) | −68.1760 | −2.28142 | ||||||||
\(894\) | 11.0880 | 0.370838 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | −3.77200 | −0.125943 | ||||||||
\(898\) | 2.00000 | 0.0667409 | ||||||||
\(899\) | −28.6320 | −0.954931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.08801 | 0.102876 | ||||||||
\(902\) | 33.3160 | 1.10930 | ||||||||
\(903\) | −23.3160 | −0.775908 | ||||||||
\(904\) | −4.77200 | −0.158714 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −23.5440 | −0.782197 | ||||||||
\(907\) | 34.4040 | 1.14237 | 0.571183 | − | 0.820823i | \(-0.306485\pi\) | ||||
0.571183 | + | 0.820823i | \(0.306485\pi\) | |||||||
\(908\) | −10.7720 | −0.357481 | ||||||||
\(909\) | 14.3160 | 0.474832 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.77200 | 0.191235 | 0.0956175 | − | 0.995418i | \(-0.469517\pi\) | ||||
0.0956175 | + | 0.995418i | \(0.469517\pi\) | |||||||
\(912\) | 7.77200 | 0.257357 | ||||||||
\(913\) | −5.77200 | −0.191025 | ||||||||
\(914\) | 30.6320 | 1.01322 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.45600 | −0.213312 | ||||||||
\(917\) | 57.2640 | 1.89102 | ||||||||
\(918\) | −0.772002 | −0.0254799 | ||||||||
\(919\) | 20.3160 | 0.670163 | 0.335082 | − | 0.942189i | \(-0.391236\pi\) | ||||
0.335082 | + | 0.942189i | \(0.391236\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.3160 | −0.669435 | ||||||||
\(922\) | −12.5440 | −0.413115 | ||||||||
\(923\) | 18.0000 | 0.592477 | ||||||||
\(924\) | −17.3160 | −0.569655 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.911993 | −0.0299699 | ||||||||
\(927\) | 11.0000 | 0.361287 | ||||||||
\(928\) | −3.00000 | −0.0984798 | ||||||||
\(929\) | 24.6840 | 0.809856 | 0.404928 | − | 0.914349i | \(-0.367297\pi\) | ||||
0.404928 | + | 0.914349i | \(0.367297\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5440 | 0.509434 | ||||||||
\(932\) | −2.68399 | −0.0879172 | ||||||||
\(933\) | −17.8600 | −0.584710 | ||||||||
\(934\) | −18.5440 | −0.606778 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.77200 | 0.123292 | ||||||||
\(937\) | 8.63201 | 0.281996 | 0.140998 | − | 0.990010i | \(-0.454969\pi\) | ||||
0.140998 | + | 0.990010i | \(0.454969\pi\) | |||||||
\(938\) | −28.6320 | −0.934868 | ||||||||
\(939\) | −8.00000 | −0.261070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.6320 | 0.672584 | 0.336292 | − | 0.941758i | \(-0.390827\pi\) | ||||
0.336292 | + | 0.941758i | \(0.390827\pi\) | |||||||
\(942\) | −13.5440 | −0.441287 | ||||||||
\(943\) | −5.77200 | −0.187962 | ||||||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.8600 | −1.45852 | ||||||||
\(947\) | 31.0880 | 1.01022 | 0.505112 | − | 0.863054i | \(-0.331451\pi\) | ||||
0.505112 | + | 0.863054i | \(0.331451\pi\) | |||||||
\(948\) | 2.22800 | 0.0723620 | ||||||||
\(949\) | −24.6840 | −0.801276 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.00000 | −0.291845 | ||||||||
\(952\) | 2.31601 | 0.0750622 | ||||||||
\(953\) | −46.7720 | −1.51509 | −0.757547 | − | 0.652781i | \(-0.773602\pi\) | ||||
−0.757547 | + | 0.652781i | \(0.773602\pi\) | |||||||
\(954\) | −4.00000 | −0.129505 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.7720 | 0.736499 | ||||||||
\(957\) | 17.3160 | 0.559747 | ||||||||
\(958\) | 35.3160 | 1.14101 | ||||||||
\(959\) | −44.3160 | −1.43104 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.0880 | 1.93832 | ||||||||
\(962\) | 25.5440 | 0.823572 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | −26.6320 | −0.857759 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.00000 | 0.0965234 | ||||||||
\(967\) | 8.63201 | 0.277587 | 0.138793 | − | 0.990321i | \(-0.455678\pi\) | ||||
0.138793 | + | 0.990321i | \(0.455678\pi\) | |||||||
\(968\) | −22.3160 | −0.717264 | ||||||||
\(969\) | 6.00000 | 0.192748 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.6320 | −1.01512 | −0.507560 | − | 0.861617i | \(-0.669452\pi\) | ||||
−0.507560 | + | 0.861617i | \(0.669452\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 2.31601 | 0.0742477 | ||||||||
\(974\) | −12.4560 | −0.399116 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.54400 | −0.305496 | ||||||||
\(977\) | −60.3160 | −1.92968 | −0.964840 | − | 0.262838i | \(-0.915342\pi\) | ||||
−0.964840 | + | 0.262838i | \(0.915342\pi\) | |||||||
\(978\) | −16.0000 | −0.511624 | ||||||||
\(979\) | 96.8080 | 3.09400 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.7720 | 0.471634 | ||||||||
\(982\) | 10.4560 | 0.333664 | ||||||||
\(983\) | 8.40401 | 0.268046 | 0.134023 | − | 0.990978i | \(-0.457210\pi\) | ||||
0.134023 | + | 0.990978i | \(0.457210\pi\) | |||||||
\(984\) | 5.77200 | 0.184005 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.31601 | −0.0737566 | ||||||||
\(987\) | 26.3160 | 0.837648 | ||||||||
\(988\) | −29.3160 | −0.932666 | ||||||||
\(989\) | 7.77200 | 0.247135 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.1760 | 0.958573 | 0.479286 | − | 0.877659i | \(-0.340896\pi\) | ||||
0.479286 | + | 0.877659i | \(0.340896\pi\) | |||||||
\(992\) | 9.54400 | 0.303022 | ||||||||
\(993\) | 34.7720 | 1.10346 | ||||||||
\(994\) | −14.3160 | −0.454076 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.00000 | −0.0316862 | ||||||||
\(997\) | −0.227998 | −0.00722077 | −0.00361039 | − | 0.999993i | \(-0.501149\pi\) | ||||
−0.00361039 | + | 0.999993i | \(0.501149\pi\) | |||||||
\(998\) | 9.68399 | 0.306541 | ||||||||
\(999\) | 6.77200 | 0.214257 |
(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 | 3450.2.a.bh.1.2 | ✓ | 2 | |
5.2 | odd | 4 | 3450.2.d.w.2899.2 | 4 | |||
5.3 | odd | 4 | 3450.2.d.w.2899.4 | 4 | |||
5.4 | even | 2 | 3450.2.a.bj.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3450.2.a.bh.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3450.2.a.bj.1.2 | yes | 2 | 5.4 | even | 2 | ||
3450.2.d.w.2899.2 | 4 | 5.2 | odd | 4 | |||
3450.2.d.w.2899.4 | 4 | 5.3 | odd | 4 |