Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,2,Mod(1,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, 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("2025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.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: | \(16.1697064093\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.51414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51414 | −1.77776 | −0.888882 | − | 0.458137i | \(-0.848517\pi\) | ||||
−0.888882 | + | 0.458137i | \(0.848517\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.32088 | 2.16044 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.514137 | 0.194325 | 0.0971627 | − | 0.995269i | \(-0.469023\pi\) | ||||
0.0971627 | + | 0.995269i | \(0.469023\pi\) | |||||||
\(8\) | −5.83502 | −2.06299 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.32088 | −1.00128 | −0.500642 | − | 0.865654i | \(-0.666903\pi\) | ||||
−0.500642 | + | 0.865654i | \(0.666903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.32088 | 0.366347 | 0.183174 | − | 0.983081i | \(-0.441363\pi\) | ||||
0.183174 | + | 0.983081i | \(0.441363\pi\) | |||||||
\(14\) | −1.29261 | −0.345465 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.02827 | 1.50707 | ||||||||
\(17\) | 3.32088 | 0.805433 | 0.402716 | − | 0.915325i | \(-0.368066\pi\) | ||||
0.402716 | + | 0.915325i | \(0.368066\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.32088 | −0.303032 | −0.151516 | − | 0.988455i | \(-0.548415\pi\) | ||||
−0.151516 | + | 0.988455i | \(0.548415\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.34916 | 1.78005 | ||||||||
\(23\) | −4.12763 | −0.860671 | −0.430335 | − | 0.902669i | \(-0.641605\pi\) | ||||
−0.430335 | + | 0.902669i | \(0.641605\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.32088 | −0.651279 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.22153 | 0.419829 | ||||||||
\(29\) | −1.38650 | −0.257467 | −0.128734 | − | 0.991679i | \(-0.541091\pi\) | ||||
−0.128734 | + | 0.991679i | \(0.541091\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.73566 | 1.56897 | 0.784486 | − | 0.620147i | \(-0.212927\pi\) | ||||
0.784486 | + | 0.620147i | \(0.212927\pi\) | |||||||
\(32\) | −3.48586 | −0.616219 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.34916 | −1.43187 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.292611 | −0.0481049 | −0.0240524 | − | 0.999711i | \(-0.507657\pi\) | ||||
−0.0240524 | + | 0.999711i | \(0.507657\pi\) | |||||||
\(38\) | 3.32088 | 0.538719 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.3492 | −1.77244 | −0.886220 | − | 0.463264i | \(-0.846678\pi\) | ||||
−0.886220 | + | 0.463264i | \(0.846678\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3492 | −1.57823 | −0.789116 | − | 0.614244i | \(-0.789461\pi\) | ||||
−0.789116 | + | 0.614244i | \(0.789461\pi\) | |||||||
\(44\) | −14.3492 | −2.16322 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.3774 | 1.53007 | ||||||||
\(47\) | 4.86330 | 0.709385 | 0.354692 | − | 0.934983i | \(-0.384586\pi\) | ||||
0.354692 | + | 0.934983i | \(0.384586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.73566 | −0.962238 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.70739 | 0.791472 | ||||||||
\(53\) | 5.02827 | 0.690687 | 0.345343 | − | 0.938476i | \(-0.387762\pi\) | ||||
0.345343 | + | 0.938476i | \(0.387762\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.48586 | 0.457716 | ||||||||
\(59\) | −5.02827 | −0.654625 | −0.327313 | − | 0.944916i | \(-0.606143\pi\) | ||||
−0.327313 | + | 0.944916i | \(0.606143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.34916 | 0.940963 | 0.470482 | − | 0.882410i | \(-0.344080\pi\) | ||||
0.470482 | + | 0.882410i | \(0.344080\pi\) | |||||||
\(62\) | −21.9627 | −2.78926 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.29261 | −0.411576 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.44852 | −1.15432 | −0.577160 | − | 0.816631i | \(-0.695839\pi\) | ||||
−0.577160 | + | 0.816631i | \(0.695839\pi\) | |||||||
\(68\) | 14.3492 | 1.74009 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.99093 | 1.06703 | 0.533513 | − | 0.845792i | \(-0.320871\pi\) | ||||
0.533513 | + | 0.845792i | \(0.320871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.05655 | −0.708865 | −0.354433 | − | 0.935082i | \(-0.615326\pi\) | ||||
−0.354433 | + | 0.935082i | \(0.615326\pi\) | |||||||
\(74\) | 0.735663 | 0.0855191 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.70739 | −0.654682 | ||||||||
\(77\) | −1.70739 | −0.194575 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.05655 | −0.906432 | −0.453216 | − | 0.891401i | \(-0.649723\pi\) | ||||
−0.453216 | + | 0.891401i | \(0.649723\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 28.5333 | 3.15098 | ||||||||
\(83\) | −1.54241 | −0.169302 | −0.0846508 | − | 0.996411i | \(-0.526977\pi\) | ||||
−0.0846508 | + | 0.996411i | \(0.526977\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 26.0192 | 2.80572 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 19.3774 | 2.06564 | ||||||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.679116 | 0.0711906 | ||||||||
\(92\) | −17.8350 | −1.85943 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.2270 | −1.26112 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2553 | 1.24433 | 0.622167 | − | 0.782885i | \(-0.286253\pi\) | ||||
0.622167 | + | 0.782885i | \(0.286253\pi\) | |||||||
\(98\) | 16.9344 | 1.71063 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6700 | 1.16121 | 0.580606 | − | 0.814184i | \(-0.302816\pi\) | ||||
0.580606 | + | 0.814184i | \(0.302816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.292611 | −0.0288318 | −0.0144159 | − | 0.999896i | \(-0.504589\pi\) | ||||
−0.0144159 | + | 0.999896i | \(0.504589\pi\) | |||||||
\(104\) | −7.70739 | −0.755772 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.6418 | −1.22788 | ||||||||
\(107\) | −1.87237 | −0.181009 | −0.0905043 | − | 0.995896i | \(-0.528848\pi\) | ||||
−0.0905043 | + | 0.995896i | \(0.528848\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.54787 | 0.531390 | 0.265695 | − | 0.964057i | \(-0.414399\pi\) | ||||
0.265695 | + | 0.964057i | \(0.414399\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.09936 | 0.292862 | ||||||||
\(113\) | −7.80128 | −0.733883 | −0.366942 | − | 0.930244i | \(-0.619595\pi\) | ||||
−0.366942 | + | 0.930244i | \(0.619595\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.99093 | −0.556244 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.6418 | 1.16377 | ||||||||
\(119\) | 1.70739 | 0.156516 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0282739 | 0.00257035 | ||||||||
\(122\) | −18.4768 | −1.67281 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 37.7458 | 3.38967 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8916 | −1.58762 | −0.793810 | − | 0.608166i | \(-0.791906\pi\) | ||||
−0.793810 | + | 0.608166i | \(0.791906\pi\) | |||||||
\(128\) | 15.2498 | 1.34790 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.679116 | −0.0588868 | ||||||||
\(134\) | 23.7549 | 2.05211 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19.3774 | −1.66160 | ||||||||
\(137\) | −5.67004 | −0.484424 | −0.242212 | − | 0.970223i | \(-0.577873\pi\) | ||||
−0.242212 | + | 0.970223i | \(0.577873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −22.6044 | −1.89692 | ||||||||
\(143\) | −4.38650 | −0.366818 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 15.2270 | 1.26019 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.26434 | −0.103928 | ||||||||
\(149\) | 17.6610 | 1.44684 | 0.723422 | − | 0.690407i | \(-0.242568\pi\) | ||||
0.723422 | + | 0.690407i | \(0.242568\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.26434 | 0.102890 | 0.0514451 | − | 0.998676i | \(-0.483617\pi\) | ||||
0.0514451 | + | 0.998676i | \(0.483617\pi\) | |||||||
\(152\) | 7.70739 | 0.625152 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.29261 | 0.345908 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.6700 | 1.25061 | 0.625303 | − | 0.780382i | \(-0.284975\pi\) | ||||
0.625303 | + | 0.780382i | \(0.284975\pi\) | |||||||
\(158\) | 20.2553 | 1.61142 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.12217 | −0.167250 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.7074 | −1.23030 | −0.615149 | − | 0.788411i | \(-0.710904\pi\) | ||||
−0.615149 | + | 0.788411i | \(0.710904\pi\) | |||||||
\(164\) | −49.0384 | −3.82926 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.87783 | 0.300978 | ||||||||
\(167\) | −6.16498 | −0.477060 | −0.238530 | − | 0.971135i | \(-0.576666\pi\) | ||||
−0.238530 | + | 0.971135i | \(0.576666\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2553 | −0.865790 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −44.7175 | −3.40968 | ||||||||
\(173\) | −8.58522 | −0.652722 | −0.326361 | − | 0.945245i | \(-0.605823\pi\) | ||||
−0.326361 | + | 0.945245i | \(0.605823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.0192 | −1.50900 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.54241 | 0.565328 | ||||||||
\(179\) | −1.06562 | −0.0796482 | −0.0398241 | − | 0.999207i | \(-0.512680\pi\) | ||||
−0.0398241 | + | 0.999207i | \(0.512680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6700 | −0.941757 | −0.470878 | − | 0.882198i | \(-0.656063\pi\) | ||||
−0.470878 | + | 0.882198i | \(0.656063\pi\) | |||||||
\(182\) | −1.70739 | −0.126560 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24.0848 | 1.77556 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.0283 | −0.806467 | ||||||||
\(188\) | 21.0137 | 1.53258 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9344 | −1.22533 | −0.612664 | − | 0.790343i | \(-0.709902\pi\) | ||||
−0.612664 | + | 0.790343i | \(0.709902\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.7175 | −1.92317 | −0.961585 | − | 0.274509i | \(-0.911485\pi\) | ||||
−0.961585 | + | 0.274509i | \(0.911485\pi\) | |||||||
\(194\) | −30.8114 | −2.21213 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.1040 | −2.07886 | ||||||||
\(197\) | 14.2553 | 1.01565 | 0.507823 | − | 0.861462i | \(-0.330450\pi\) | ||||
0.507823 | + | 0.861462i | \(0.330450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.6610 | −1.74817 | −0.874085 | − | 0.485773i | \(-0.838538\pi\) | ||||
−0.874085 | + | 0.485773i | \(0.838538\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −29.3401 | −2.06436 | ||||||||
\(203\) | −0.712853 | −0.0500325 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.735663 | 0.0512561 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.96265 | 0.552111 | ||||||||
\(209\) | 4.38650 | 0.303421 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.37743 | −0.370198 | −0.185099 | − | 0.982720i | \(-0.559261\pi\) | ||||
−0.185099 | + | 0.982720i | \(0.559261\pi\) | |||||||
\(212\) | 21.7266 | 1.49219 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.70739 | 0.321791 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.49133 | 0.304891 | ||||||||
\(218\) | −13.9481 | −0.944686 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.38650 | 0.295068 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.66458 | −0.580223 | −0.290112 | − | 0.956993i | \(-0.593692\pi\) | ||||
−0.290112 | + | 0.956993i | \(0.593692\pi\) | |||||||
\(224\) | −1.79221 | −0.119747 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.6135 | 1.30467 | ||||||||
\(227\) | −3.32088 | −0.220415 | −0.110207 | − | 0.993909i | \(-0.535152\pi\) | ||||
−0.110207 | + | 0.993909i | \(0.535152\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.3118 | −1.67265 | −0.836326 | − | 0.548233i | \(-0.815301\pi\) | ||||
−0.836326 | + | 0.548233i | \(0.815301\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.09029 | 0.531153 | ||||||||
\(233\) | −27.6327 | −1.81028 | −0.905139 | − | 0.425116i | \(-0.860233\pi\) | ||||
−0.905139 | + | 0.425116i | \(0.860233\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −21.7266 | −1.41428 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.29261 | −0.278249 | ||||||||
\(239\) | −4.19872 | −0.271592 | −0.135796 | − | 0.990737i | \(-0.543359\pi\) | ||||
−0.135796 | + | 0.990737i | \(0.543359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.60442 | 0.232181 | 0.116091 | − | 0.993239i | \(-0.462964\pi\) | ||||
0.116091 | + | 0.993239i | \(0.462964\pi\) | |||||||
\(242\) | −0.0710844 | −0.00456948 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 31.7549 | 2.03290 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.74474 | −0.111015 | ||||||||
\(248\) | −50.9728 | −3.23677 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.87783 | −0.434125 | −0.217062 | − | 0.976158i | \(-0.569648\pi\) | ||||
−0.217062 | + | 0.976158i | \(0.569648\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.7074 | 0.861776 | ||||||||
\(254\) | 44.9819 | 2.82241 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.7549 | −1.98468 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.150442 | −0.00934801 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.0848 | 0.931943 | ||||||||
\(263\) | −6.23606 | −0.384532 | −0.192266 | − | 0.981343i | \(-0.561584\pi\) | ||||
−0.192266 | + | 0.981343i | \(0.561584\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.70739 | 0.104687 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −40.8259 | −2.49384 | ||||||||
\(269\) | 9.92345 | 0.605044 | 0.302522 | − | 0.953142i | \(-0.402172\pi\) | ||||
0.302522 | + | 0.953142i | \(0.402172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.60442 | 0.401190 | 0.200595 | − | 0.979674i | \(-0.435712\pi\) | ||||
0.200595 | + | 0.979674i | \(0.435712\pi\) | |||||||
\(272\) | 20.0192 | 1.21384 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.2553 | 0.861192 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.6610 | −1.36157 | −0.680783 | − | 0.732485i | \(-0.738360\pi\) | ||||
−0.680783 | + | 0.732485i | \(0.738360\pi\) | |||||||
\(278\) | −20.1131 | −1.20630 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.5479 | −0.927508 | −0.463754 | − | 0.885964i | \(-0.653498\pi\) | ||||
−0.463754 | + | 0.885964i | \(0.653498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.645378 | −0.0383637 | −0.0191819 | − | 0.999816i | \(-0.506106\pi\) | ||||
−0.0191819 | + | 0.999816i | \(0.506106\pi\) | |||||||
\(284\) | 38.8488 | 2.30525 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.0283 | 0.652116 | ||||||||
\(287\) | −5.83502 | −0.344430 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.97173 | −0.351278 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −26.1696 | −1.53146 | ||||||||
\(293\) | 1.37743 | 0.0804704 | 0.0402352 | − | 0.999190i | \(-0.487189\pi\) | ||||
0.0402352 | + | 0.999190i | \(0.487189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.70739 | 0.0992400 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −44.4021 | −2.57214 | ||||||||
\(299\) | −5.45213 | −0.315305 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.32088 | −0.306691 | ||||||||
\(302\) | −3.17872 | −0.182915 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.96265 | −0.456689 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.98546 | 0.455754 | 0.227877 | − | 0.973690i | \(-0.426822\pi\) | ||||
0.227877 | + | 0.973690i | \(0.426822\pi\) | |||||||
\(308\) | −7.37743 | −0.420368 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.63270 | 0.546220 | 0.273110 | − | 0.961983i | \(-0.411948\pi\) | ||||
0.273110 | + | 0.961983i | \(0.411948\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.5369 | 1.38691 | 0.693455 | − | 0.720500i | \(-0.256088\pi\) | ||||
0.693455 | + | 0.720500i | \(0.256088\pi\) | |||||||
\(314\) | −39.3966 | −2.22328 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −34.8114 | −1.95829 | ||||||||
\(317\) | 20.3492 | 1.14292 | 0.571461 | − | 0.820629i | \(-0.306377\pi\) | ||||
0.571461 | + | 0.820629i | \(0.306377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.60442 | 0.257798 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.33542 | 0.297331 | ||||||||
\(323\) | −4.38650 | −0.244072 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 39.4905 | 2.18718 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 66.2226 | 3.65653 | ||||||||
\(329\) | 2.50040 | 0.137851 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.4431 | 0.903792 | 0.451896 | − | 0.892071i | \(-0.350748\pi\) | ||||
0.451896 | + | 0.892071i | \(0.350748\pi\) | |||||||
\(332\) | −6.66458 | −0.365766 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.4996 | 0.848100 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.89703 | −0.266758 | −0.133379 | − | 0.991065i | \(-0.542583\pi\) | ||||
−0.133379 | + | 0.991065i | \(0.542583\pi\) | |||||||
\(338\) | 28.2973 | 1.53917 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.0101 | −1.57099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.06201 | −0.381313 | ||||||||
\(344\) | 60.3876 | 3.25588 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.5844 | 1.16039 | ||||||||
\(347\) | −22.2745 | −1.19576 | −0.597878 | − | 0.801587i | \(-0.703989\pi\) | ||||
−0.597878 | + | 0.801587i | \(0.703989\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.94345 | −0.157559 | −0.0787797 | − | 0.996892i | \(-0.525102\pi\) | ||||
−0.0787797 | + | 0.996892i | \(0.525102\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.5761 | 0.617011 | ||||||||
\(353\) | −18.8296 | −1.00220 | −0.501098 | − | 0.865390i | \(-0.667070\pi\) | ||||
−0.501098 | + | 0.865390i | \(0.667070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.9627 | −0.687019 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.67912 | 0.141596 | ||||||||
\(359\) | −31.8770 | −1.68241 | −0.841203 | − | 0.540720i | \(-0.818152\pi\) | ||||
−0.841203 | + | 0.540720i | \(0.818152\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2553 | −0.908172 | ||||||||
\(362\) | 31.8542 | 1.67422 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.93438 | 0.153803 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3492 | 0.957818 | 0.478909 | − | 0.877864i | \(-0.341032\pi\) | ||||
0.478909 | + | 0.877864i | \(0.341032\pi\) | |||||||
\(368\) | −24.8825 | −1.29709 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.58522 | 0.134218 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.19872 | 0.113845 | 0.0569226 | − | 0.998379i | \(-0.481871\pi\) | ||||
0.0569226 | + | 0.998379i | \(0.481871\pi\) | |||||||
\(374\) | 27.7266 | 1.43371 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −28.3774 | −1.46345 | ||||||||
\(377\) | −1.83141 | −0.0943226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.4713 | 0.794709 | 0.397354 | − | 0.917665i | \(-0.369928\pi\) | ||||
0.397354 | + | 0.917665i | \(0.369928\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 42.5753 | 2.17834 | ||||||||
\(383\) | −7.70739 | −0.393829 | −0.196915 | − | 0.980421i | \(-0.563092\pi\) | ||||
−0.196915 | + | 0.980421i | \(0.563092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 67.1715 | 3.41894 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 52.9536 | 2.68831 | ||||||||
\(389\) | −24.6327 | −1.24893 | −0.624464 | − | 0.781054i | \(-0.714682\pi\) | ||||
−0.624464 | + | 0.781054i | \(0.714682\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.7074 | −0.693212 | ||||||||
\(392\) | 39.3027 | 1.98509 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −35.8397 | −1.80558 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.77301 | 0.339928 | 0.169964 | − | 0.985450i | \(-0.445635\pi\) | ||||
0.169964 | + | 0.985450i | \(0.445635\pi\) | |||||||
\(398\) | 62.0011 | 3.10783 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.4996 | −0.923826 | −0.461913 | − | 0.886925i | \(-0.652837\pi\) | ||||
−0.461913 | + | 0.886925i | \(0.652837\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.5388 | 0.574789 | ||||||||
\(404\) | 50.4249 | 2.50873 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.79221 | 0.0889459 | ||||||||
\(407\) | 0.971726 | 0.0481667 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.4148 | −0.663318 | −0.331659 | − | 0.943399i | \(-0.607608\pi\) | ||||
−0.331659 | + | 0.943399i | \(0.607608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.26434 | −0.0622894 | ||||||||
\(413\) | −2.58522 | −0.127210 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.60442 | −0.225750 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.0283 | −0.539411 | ||||||||
\(419\) | −33.1150 | −1.61777 | −0.808886 | − | 0.587966i | \(-0.799929\pi\) | ||||
−0.808886 | + | 0.587966i | \(0.799929\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.6983 | −0.716352 | −0.358176 | − | 0.933654i | \(-0.616601\pi\) | ||||
−0.358176 | + | 0.933654i | \(0.616601\pi\) | |||||||
\(422\) | 13.5196 | 0.658124 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −29.3401 | −1.42488 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.77847 | 0.182853 | ||||||||
\(428\) | −8.09029 | −0.391059 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.7549 | −1.57775 | −0.788873 | − | 0.614556i | \(-0.789335\pi\) | ||||
−0.788873 | + | 0.614556i | \(0.789335\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8314 | 0.568581 | 0.284291 | − | 0.958738i | \(-0.408242\pi\) | ||||
0.284291 | + | 0.958738i | \(0.408242\pi\) | |||||||
\(434\) | −11.2918 | −0.542024 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 23.9717 | 1.14804 | ||||||||
\(437\) | 5.45213 | 0.260811 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.31181 | 0.396701 | 0.198351 | − | 0.980131i | \(-0.436442\pi\) | ||||
0.198351 | + | 0.980131i | \(0.436442\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.0283 | −0.524561 | ||||||||
\(443\) | 29.1751 | 1.38615 | 0.693076 | − | 0.720865i | \(-0.256255\pi\) | ||||
0.693076 | + | 0.720865i | \(0.256255\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.7839 | 1.03150 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.69285 | −0.0799798 | ||||||||
\(449\) | 18.9717 | 0.895331 | 0.447666 | − | 0.894201i | \(-0.352256\pi\) | ||||
0.447666 | + | 0.894201i | \(0.352256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.6892 | 1.77472 | ||||||||
\(452\) | −33.7084 | −1.58551 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.34916 | 0.391845 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.2353 | 1.08690 | 0.543450 | − | 0.839442i | \(-0.317118\pi\) | ||||
0.543450 | + | 0.839442i | \(0.317118\pi\) | |||||||
\(458\) | 63.6374 | 2.97358 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.42571 | 0.206126 | 0.103063 | − | 0.994675i | \(-0.467136\pi\) | ||||
0.103063 | + | 0.994675i | \(0.467136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.5087 | 0.906645 | 0.453322 | − | 0.891347i | \(-0.350239\pi\) | ||||
0.453322 | + | 0.891347i | \(0.350239\pi\) | |||||||
\(464\) | −8.35823 | −0.388021 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 69.4724 | 3.21825 | ||||||||
\(467\) | 24.5935 | 1.13805 | 0.569026 | − | 0.822320i | \(-0.307321\pi\) | ||||
0.569026 | + | 0.822320i | \(0.307321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.85783 | −0.224314 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 29.3401 | 1.35049 | ||||||||
\(473\) | 34.3684 | 1.58026 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.37743 | 0.338144 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.5561 | 0.482827 | ||||||||
\(479\) | 32.7549 | 1.49661 | 0.748304 | − | 0.663356i | \(-0.230868\pi\) | ||||
0.748304 | + | 0.663356i | \(0.230868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.386505 | −0.0176231 | ||||||||
\(482\) | −9.06201 | −0.412763 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.122168 | 0.00555309 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.03735 | 0.273578 | 0.136789 | − | 0.990600i | \(-0.456322\pi\) | ||||
0.136789 | + | 0.990600i | \(0.456322\pi\) | |||||||
\(488\) | −42.8825 | −1.94120 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4431 | 0.651806 | 0.325903 | − | 0.945403i | \(-0.394332\pi\) | ||||
0.325903 | + | 0.945403i | \(0.394332\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.60442 | −0.207373 | ||||||||
\(494\) | 4.38650 | 0.197358 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 52.6610 | 2.36455 | ||||||||
\(497\) | 4.62257 | 0.207351 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.9717 | 0.938823 | 0.469412 | − | 0.882979i | \(-0.344466\pi\) | ||||
0.469412 | + | 0.882979i | \(0.344466\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.2918 | 0.771771 | ||||||||
\(503\) | 5.31728 | 0.237086 | 0.118543 | − | 0.992949i | \(-0.462178\pi\) | ||||
0.118543 | + | 0.992949i | \(0.462178\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −34.4623 | −1.53203 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −77.3074 | −3.42996 | ||||||||
\(509\) | 18.2270 | 0.807897 | 0.403949 | − | 0.914782i | \(-0.367637\pi\) | ||||
0.403949 | + | 0.914782i | \(0.367637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.11389 | −0.137751 | ||||||||
\(512\) | 49.3365 | 2.18038 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −45.2545 | −1.99609 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.1504 | −0.710296 | ||||||||
\(518\) | 0.378232 | 0.0166185 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.1232 | 1.75783 | 0.878915 | − | 0.476978i | \(-0.158268\pi\) | ||||
0.878915 | + | 0.476978i | \(0.158268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.9873 | −0.830257 | −0.415129 | − | 0.909763i | \(-0.636263\pi\) | ||||
−0.415129 | + | 0.909763i | \(0.636263\pi\) | |||||||
\(524\) | −25.9253 | −1.13255 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.6783 | 0.683607 | ||||||||
\(527\) | 29.0101 | 1.26370 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.96265 | −0.259246 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.93438 | −0.127221 | ||||||||
\(533\) | −14.9909 | −0.649329 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 55.1323 | 2.38135 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.9489 | −1.07562 | ||||||||
\(539\) | 22.3684 | 0.963473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5279 | 0.710589 | 0.355294 | − | 0.934754i | \(-0.384381\pi\) | ||||
0.355294 | + | 0.934754i | \(0.384381\pi\) | |||||||
\(542\) | −16.6044 | −0.713221 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.5761 | −0.496323 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6737 | −0.755671 | −0.377835 | − | 0.925873i | \(-0.623331\pi\) | ||||
−0.377835 | + | 0.925873i | \(0.623331\pi\) | |||||||
\(548\) | −24.4996 | −1.04657 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.83141 | 0.0780208 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.14217 | −0.176143 | ||||||||
\(554\) | 56.9728 | 2.42054 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 34.5671 | 1.46597 | ||||||||
\(557\) | −17.3401 | −0.734723 | −0.367362 | − | 0.930078i | \(-0.619739\pi\) | ||||
−0.367362 | + | 0.930078i | \(0.619739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6700 | −0.578181 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 39.0895 | 1.64889 | ||||||||
\(563\) | −12.9945 | −0.547654 | −0.273827 | − | 0.961779i | \(-0.588290\pi\) | ||||
−0.273827 | + | 0.961779i | \(0.588290\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.62257 | 0.0682016 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −52.4623 | −2.20127 | ||||||||
\(569\) | −16.6802 | −0.699269 | −0.349635 | − | 0.936886i | \(-0.613694\pi\) | ||||
−0.349635 | + | 0.936886i | \(0.613694\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | −18.9536 | −0.792489 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.6700 | 0.612316 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5953 | 0.982287 | 0.491144 | − | 0.871079i | \(-0.336579\pi\) | ||||
0.491144 | + | 0.871079i | \(0.336579\pi\) | |||||||
\(578\) | 15.0137 | 0.624489 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.793010 | −0.0328996 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.6983 | −0.691574 | ||||||||
\(584\) | 35.3401 | 1.46238 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.46305 | −0.143057 | ||||||||
\(587\) | −28.1276 | −1.16095 | −0.580476 | − | 0.814277i | \(-0.697133\pi\) | ||||
−0.580476 | + | 0.814277i | \(0.697133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.5388 | −0.475448 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.76394 | −0.0724974 | ||||||||
\(593\) | 9.17872 | 0.376925 | 0.188462 | − | 0.982080i | \(-0.439650\pi\) | ||||
0.188462 | + | 0.982080i | \(0.439650\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 76.3110 | 3.12582 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.7074 | 0.560537 | ||||||||
\(599\) | −31.4713 | −1.28588 | −0.642942 | − | 0.765915i | \(-0.722286\pi\) | ||||
−0.642942 | + | 0.765915i | \(0.722286\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.2654 | −1.19376 | −0.596880 | − | 0.802330i | \(-0.703593\pi\) | ||||
−0.596880 | + | 0.802330i | \(0.703593\pi\) | |||||||
\(602\) | 13.3774 | 0.545223 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.46305 | 0.222288 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.2034 | 1.79416 | 0.897080 | − | 0.441868i | \(-0.145684\pi\) | ||||
0.897080 | + | 0.441868i | \(0.145684\pi\) | |||||||
\(608\) | 4.60442 | 0.186734 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.42385 | 0.259881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.1715 | 1.42056 | 0.710282 | − | 0.703918i | \(-0.248568\pi\) | ||||
0.710282 | + | 0.703918i | \(0.248568\pi\) | |||||||
\(614\) | −20.0765 | −0.810224 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.96265 | 0.401407 | ||||||||
\(617\) | 7.42571 | 0.298948 | 0.149474 | − | 0.988766i | \(-0.452242\pi\) | ||||
0.149474 | + | 0.988766i | \(0.452242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.54787 | 0.343568 | 0.171784 | − | 0.985135i | \(-0.445047\pi\) | ||||
0.171784 | + | 0.985135i | \(0.445047\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.2179 | −0.971050 | ||||||||
\(623\) | −1.54241 | −0.0617954 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −61.6892 | −2.46560 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 67.7084 | 2.70186 | ||||||||
\(629\) | −0.971726 | −0.0387453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.36836 | −0.0942829 | −0.0471415 | − | 0.998888i | \(-0.515011\pi\) | ||||
−0.0471415 | + | 0.998888i | \(0.515011\pi\) | |||||||
\(632\) | 47.0101 | 1.86996 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −51.1606 | −2.03185 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.89703 | −0.352513 | ||||||||
\(638\) | −11.5761 | −0.458304 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.133096 | −0.00525698 | −0.00262849 | − | 0.999997i | \(-0.500837\pi\) | ||||
−0.00262849 | + | 0.999997i | \(0.500837\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.6464 | 0.893088 | 0.446544 | − | 0.894762i | \(-0.352655\pi\) | ||||
0.446544 | + | 0.894762i | \(0.352655\pi\) | |||||||
\(644\) | −9.16964 | −0.361335 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.0283 | 0.433902 | ||||||||
\(647\) | −46.3912 | −1.82383 | −0.911913 | − | 0.410385i | \(-0.865394\pi\) | ||||
−0.911913 | + | 0.410385i | \(0.865394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.6983 | 0.655466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −67.8698 | −2.65799 | ||||||||
\(653\) | −36.4057 | −1.42467 | −0.712333 | − | 0.701842i | \(-0.752361\pi\) | ||||
−0.712333 | + | 0.701842i | \(0.752361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −68.4158 | −2.67119 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.28635 | −0.245067 | ||||||||
\(659\) | 19.1414 | 0.745642 | 0.372821 | − | 0.927903i | \(-0.378391\pi\) | ||||
0.372821 | + | 0.927903i | \(0.378391\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.9072 | 1.55221 | 0.776104 | − | 0.630605i | \(-0.217193\pi\) | ||||
0.776104 | + | 0.630605i | \(0.217193\pi\) | |||||||
\(662\) | −41.3401 | −1.60673 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.00000 | 0.349268 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.72298 | 0.221595 | ||||||||
\(668\) | −26.6382 | −1.03066 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.4057 | −0.942172 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.6508 | −0.911673 | −0.455836 | − | 0.890064i | \(-0.650660\pi\) | ||||
−0.455836 | + | 0.890064i | \(0.650660\pi\) | |||||||
\(674\) | 12.3118 | 0.474233 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −48.6327 | −1.87049 | ||||||||
\(677\) | 14.8031 | 0.568931 | 0.284465 | − | 0.958686i | \(-0.408184\pi\) | ||||
0.284465 | + | 0.958686i | \(0.408184\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.30088 | 0.241806 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 72.9354 | 2.79284 | ||||||||
\(683\) | 4.95252 | 0.189503 | 0.0947515 | − | 0.995501i | \(-0.469794\pi\) | ||||
0.0947515 | + | 0.995501i | \(0.469794\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.7549 | 0.677884 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −62.3876 | −2.37850 | ||||||||
\(689\) | 6.64177 | 0.253031 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.2088 | −0.730739 | −0.365369 | − | 0.930863i | \(-0.619057\pi\) | ||||
−0.365369 | + | 0.930863i | \(0.619057\pi\) | |||||||
\(692\) | −37.0957 | −1.41017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 56.0011 | 2.12577 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.6892 | −1.42758 | ||||||||
\(698\) | 7.40024 | 0.280103 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.3492 | −1.10850 | −0.554251 | − | 0.832349i | \(-0.686995\pi\) | ||||
−0.554251 | + | 0.832349i | \(0.686995\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.386505 | 0.0145773 | ||||||||
\(704\) | 10.9344 | 0.412105 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 47.3401 | 1.78167 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.7266 | 1.45441 | 0.727204 | − | 0.686422i | \(-0.240820\pi\) | ||||
0.727204 | + | 0.686422i | \(0.240820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.5051 | 0.656030 | ||||||||
\(713\) | −36.0576 | −1.35037 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.60442 | −0.172075 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 80.1432 | 2.99092 | ||||||||
\(719\) | −15.0848 | −0.562569 | −0.281284 | − | 0.959624i | \(-0.590760\pi\) | ||||
−0.281284 | + | 0.959624i | \(0.590760\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.150442 | −0.00560275 | ||||||||
\(722\) | 43.3821 | 1.61451 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −54.7458 | −2.03461 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.3455 | −0.457871 | −0.228936 | − | 0.973442i | \(-0.573525\pi\) | ||||
−0.228936 | + | 0.973442i | \(0.573525\pi\) | |||||||
\(728\) | −3.96265 | −0.146866 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.3684 | −1.27116 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0000 | 0.812589 | 0.406294 | − | 0.913742i | \(-0.366821\pi\) | ||||
0.406294 | + | 0.913742i | \(0.366821\pi\) | |||||||
\(734\) | −46.1323 | −1.70277 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.3884 | 0.530362 | ||||||||
\(737\) | 31.3774 | 1.15580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.7266 | 1.09351 | 0.546755 | − | 0.837293i | \(-0.315863\pi\) | ||||
0.546755 | + | 0.837293i | \(0.315863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.49960 | −0.238608 | ||||||||
\(743\) | −48.3648 | −1.77433 | −0.887165 | − | 0.461452i | \(-0.847329\pi\) | ||||
−0.887165 | + | 0.461452i | \(0.847329\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.52787 | −0.202390 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −47.6519 | −1.74233 | ||||||||
\(749\) | −0.962653 | −0.0351746 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.8205 | −1.16115 | −0.580573 | − | 0.814208i | \(-0.697171\pi\) | ||||
−0.580573 | + | 0.814208i | \(0.697171\pi\) | |||||||
\(752\) | 29.3173 | 1.06909 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.60442 | 0.167683 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.94531 | −0.179740 | −0.0898701 | − | 0.995953i | \(-0.528645\pi\) | ||||
−0.0898701 | + | 0.995953i | \(0.528645\pi\) | |||||||
\(758\) | −38.8970 | −1.41280 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.4249 | 1.28415 | 0.642076 | − | 0.766641i | \(-0.278073\pi\) | ||||
0.642076 | + | 0.766641i | \(0.278073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.85237 | 0.103263 | ||||||||
\(764\) | −73.1715 | −2.64725 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.3774 | 0.700135 | ||||||||
\(767\) | −6.64177 | −0.239820 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.4249 | 1.78231 | 0.891154 | − | 0.453701i | \(-0.149897\pi\) | ||||
0.891154 | + | 0.453701i | \(0.149897\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −115.443 | −4.15490 | ||||||||
\(773\) | −12.6599 | −0.455345 | −0.227673 | − | 0.973738i | \(-0.573112\pi\) | ||||
−0.227673 | + | 0.973738i | \(0.573112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −71.5097 | −2.56705 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 61.9300 | 2.22030 | ||||||||
\(779\) | 14.9909 | 0.537106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.8578 | −1.06840 | ||||||||
\(782\) | 34.4623 | 1.23237 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −40.6044 | −1.45016 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.9344 | −1.10269 | −0.551346 | − | 0.834277i | \(-0.685885\pi\) | ||||
−0.551346 | + | 0.834277i | \(0.685885\pi\) | |||||||
\(788\) | 61.5953 | 2.19424 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.01093 | −0.142612 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.70739 | 0.344720 | ||||||||
\(794\) | −17.0283 | −0.604311 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −106.557 | −3.77682 | ||||||||
\(797\) | 30.5935 | 1.08368 | 0.541839 | − | 0.840483i | \(-0.317728\pi\) | ||||
0.541839 | + | 0.840483i | \(0.317728\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.1504 | 0.571362 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 46.5105 | 1.64234 | ||||||||
\(803\) | 20.1131 | 0.709776 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.0101 | −1.02184 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −68.0950 | −2.39557 | ||||||||
\(809\) | −2.89703 | −0.101854 | −0.0509271 | − | 0.998702i | \(-0.516218\pi\) | ||||
−0.0509271 | + | 0.998702i | \(0.516218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.8861 | −0.522722 | −0.261361 | − | 0.965241i | \(-0.584171\pi\) | ||||
−0.261361 | + | 0.965241i | \(0.584171\pi\) | |||||||
\(812\) | −3.08016 | −0.108092 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.44305 | −0.0856289 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.6700 | 0.478254 | ||||||||
\(818\) | 33.7266 | 1.17922 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.95173 | −0.312417 | −0.156209 | − | 0.987724i | \(-0.549927\pi\) | ||||
−0.156209 | + | 0.987724i | \(0.549927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.99454 | −0.104383 | −0.0521915 | − | 0.998637i | \(-0.516621\pi\) | ||||
−0.0521915 | + | 0.998637i | \(0.516621\pi\) | |||||||
\(824\) | 1.70739 | 0.0594797 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.49960 | 0.226150 | ||||||||
\(827\) | −31.9663 | −1.11158 | −0.555788 | − | 0.831324i | \(-0.687583\pi\) | ||||
−0.555788 | + | 0.831324i | \(0.687583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.7458 | 0.789994 | 0.394997 | − | 0.918682i | \(-0.370746\pi\) | ||||
0.394997 | + | 0.918682i | \(0.370746\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.34916 | −0.150780 | ||||||||
\(833\) | −22.3684 | −0.775018 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 18.9536 | 0.655523 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 83.2555 | 2.87601 | ||||||||
\(839\) | −23.2643 | −0.803174 | −0.401587 | − | 0.915821i | \(-0.631541\pi\) | ||||
−0.401587 | + | 0.915821i | \(0.631541\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0776 | −0.933710 | ||||||||
\(842\) | 36.9536 | 1.27350 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.2353 | −0.799791 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0145366 | 0.000499485 0 | ||||||||
\(848\) | 30.3118 | 1.04091 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.20779 | 0.0414025 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.9909 | −0.376322 | −0.188161 | − | 0.982138i | \(-0.560253\pi\) | ||||
−0.188161 | + | 0.982138i | \(0.560253\pi\) | |||||||
\(854\) | −9.49960 | −0.325070 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.9253 | 0.373419 | ||||||||
\(857\) | 16.1504 | 0.551689 | 0.275844 | − | 0.961202i | \(-0.411043\pi\) | ||||
0.275844 | + | 0.961202i | \(0.411043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5188 | 0.973049 | 0.486524 | − | 0.873667i | \(-0.338264\pi\) | ||||
0.486524 | + | 0.873667i | \(0.338264\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 82.3502 | 2.80486 | ||||||||
\(863\) | −12.2890 | −0.418322 | −0.209161 | − | 0.977881i | \(-0.567073\pi\) | ||||
−0.209161 | + | 0.977881i | \(0.567073\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −29.7458 | −1.01080 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 19.4065 | 0.658700 | ||||||||
\(869\) | 26.7549 | 0.907597 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.4804 | −0.422882 | ||||||||
\(872\) | −32.3720 | −1.09625 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.7074 | −0.463659 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.7002 | 1.34058 | 0.670290 | − | 0.742099i | \(-0.266170\pi\) | ||||
0.670290 | + | 0.742099i | \(0.266170\pi\) | |||||||
\(878\) | −20.8970 | −0.705241 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.1040 | 1.08161 | 0.540806 | − | 0.841147i | \(-0.318119\pi\) | ||||
0.540806 | + | 0.841147i | \(0.318119\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5051 | −0.454482 | −0.227241 | − | 0.973839i | \(-0.572970\pi\) | ||||
−0.227241 | + | 0.973839i | \(0.572970\pi\) | |||||||
\(884\) | 18.9536 | 0.637478 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −73.3502 | −2.46425 | ||||||||
\(887\) | −35.1222 | −1.17929 | −0.589643 | − | 0.807664i | \(-0.700732\pi\) | ||||
−0.589643 | + | 0.807664i | \(0.700732\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.19872 | −0.308515 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37.4386 | −1.25354 | ||||||||
\(893\) | −6.42385 | −0.214966 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.84049 | 0.261932 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −47.6975 | −1.59169 | ||||||||
\(899\) | −12.1120 | −0.403959 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.6983 | 0.556302 | ||||||||
\(902\) | −94.7559 | −3.15503 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 45.5207 | 1.51399 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.1186 | −0.502004 | −0.251002 | − | 0.967987i | \(-0.580760\pi\) | ||||
−0.251002 | + | 0.967987i | \(0.580760\pi\) | |||||||
\(908\) | −14.3492 | −0.476194 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.5561 | 1.74126 | 0.870631 | − | 0.491936i | \(-0.163711\pi\) | ||||
0.870631 | + | 0.491936i | \(0.163711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.12217 | 0.169519 | ||||||||
\(914\) | −58.4166 | −1.93225 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −109.369 | −3.61367 | ||||||||
\(917\) | −3.08482 | −0.101870 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.5489 | −1.79940 | −0.899702 | − | 0.436505i | \(-0.856216\pi\) | ||||
−0.899702 | + | 0.436505i | \(0.856216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.1268 | −0.366443 | ||||||||
\(923\) | 11.8760 | 0.390903 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −49.0475 | −1.61180 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.83317 | 0.158656 | ||||||||
\(929\) | 20.3793 | 0.668623 | 0.334311 | − | 0.942463i | \(-0.391496\pi\) | ||||
0.334311 | + | 0.942463i | \(0.391496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.89703 | 0.291588 | ||||||||
\(932\) | −119.398 | −3.91100 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −61.8314 | −2.02319 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.1979 | −1.60723 | −0.803613 | − | 0.595152i | \(-0.797092\pi\) | ||||
−0.803613 | + | 0.595152i | \(0.797092\pi\) | |||||||
\(938\) | 12.2133 | 0.398777 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.2371 | −0.757508 | −0.378754 | − | 0.925497i | \(-0.623647\pi\) | ||||
−0.378754 | + | 0.925497i | \(0.623647\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.8452 | 1.52549 | ||||||||
\(944\) | −30.3118 | −0.986565 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −86.4068 | −2.80933 | ||||||||
\(947\) | −37.1642 | −1.20767 | −0.603837 | − | 0.797108i | \(-0.706362\pi\) | ||||
−0.603837 | + | 0.797108i | \(0.706362\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.00000 | −0.259691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.96265 | −0.322891 | ||||||||
\(953\) | 23.5761 | 0.763706 | 0.381853 | − | 0.924223i | \(-0.375286\pi\) | ||||
0.381853 | + | 0.924223i | \(0.375286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.1422 | −0.586760 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −82.3502 | −2.66061 | ||||||||
\(959\) | −2.91518 | −0.0941360 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.3118 | 1.46167 | ||||||||
\(962\) | 0.971726 | 0.0313297 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.5743 | 0.501614 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.38290 | −0.269576 | −0.134788 | − | 0.990874i | \(-0.543035\pi\) | ||||
−0.134788 | + | 0.990874i | \(0.543035\pi\) | |||||||
\(968\) | −0.164979 | −0.00530261 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.2078 | 0.423858 | 0.211929 | − | 0.977285i | \(-0.432025\pi\) | ||||
0.211929 | + | 0.977285i | \(0.432025\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.11310 | 0.131860 | ||||||||
\(974\) | −15.1787 | −0.486357 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.3027 | 1.41810 | ||||||||
\(977\) | 14.3310 | 0.458490 | 0.229245 | − | 0.973369i | \(-0.426374\pi\) | ||||
0.229245 | + | 0.973369i | \(0.426374\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.96265 | 0.318408 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −36.3118 | −1.15876 | ||||||||
\(983\) | 32.3082 | 1.03047 | 0.515236 | − | 0.857048i | \(-0.327704\pi\) | ||||
0.515236 | + | 0.857048i | \(0.327704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.5761 | 0.368660 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.53880 | −0.239841 | ||||||||
\(989\) | 42.7175 | 1.35834 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.6700 | −1.26016 | −0.630080 | − | 0.776530i | \(-0.716978\pi\) | ||||
−0.630080 | + | 0.776530i | \(0.716978\pi\) | |||||||
\(992\) | −30.4513 | −0.966831 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.6218 | −0.368620 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.6874 | −1.22524 | −0.612621 | − | 0.790377i | \(-0.709885\pi\) | ||||
−0.612621 | + | 0.790377i | \(0.709885\pi\) | |||||||
\(998\) | −52.7258 | −1.66901 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2025.2.a.n.1.1 | 3 | ||
3.2 | odd | 2 | 2025.2.a.o.1.3 | 3 | |||
5.2 | odd | 4 | 2025.2.b.l.649.1 | 6 | |||
5.3 | odd | 4 | 2025.2.b.l.649.6 | 6 | |||
5.4 | even | 2 | 405.2.a.j.1.3 | 3 | |||
9.2 | odd | 6 | 675.2.e.b.226.1 | 6 | |||
9.4 | even | 3 | 225.2.e.b.151.3 | 6 | |||
9.5 | odd | 6 | 675.2.e.b.451.1 | 6 | |||
9.7 | even | 3 | 225.2.e.b.76.3 | 6 | |||
15.2 | even | 4 | 2025.2.b.m.649.6 | 6 | |||
15.8 | even | 4 | 2025.2.b.m.649.1 | 6 | |||
15.14 | odd | 2 | 405.2.a.i.1.1 | 3 | |||
20.19 | odd | 2 | 6480.2.a.bv.1.3 | 3 | |||
45.2 | even | 12 | 675.2.k.b.199.6 | 12 | |||
45.4 | even | 6 | 45.2.e.b.16.1 | ✓ | 6 | ||
45.7 | odd | 12 | 225.2.k.b.49.1 | 12 | |||
45.13 | odd | 12 | 225.2.k.b.124.1 | 12 | |||
45.14 | odd | 6 | 135.2.e.b.46.3 | 6 | |||
45.22 | odd | 12 | 225.2.k.b.124.6 | 12 | |||
45.23 | even | 12 | 675.2.k.b.424.6 | 12 | |||
45.29 | odd | 6 | 135.2.e.b.91.3 | 6 | |||
45.32 | even | 12 | 675.2.k.b.424.1 | 12 | |||
45.34 | even | 6 | 45.2.e.b.31.1 | yes | 6 | ||
45.38 | even | 12 | 675.2.k.b.199.1 | 12 | |||
45.43 | odd | 12 | 225.2.k.b.49.6 | 12 | |||
60.59 | even | 2 | 6480.2.a.bs.1.3 | 3 | |||
180.59 | even | 6 | 2160.2.q.k.721.1 | 6 | |||
180.79 | odd | 6 | 720.2.q.i.481.1 | 6 | |||
180.119 | even | 6 | 2160.2.q.k.1441.1 | 6 | |||
180.139 | odd | 6 | 720.2.q.i.241.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.1 | ✓ | 6 | 45.4 | even | 6 | ||
45.2.e.b.31.1 | yes | 6 | 45.34 | even | 6 | ||
135.2.e.b.46.3 | 6 | 45.14 | odd | 6 | |||
135.2.e.b.91.3 | 6 | 45.29 | odd | 6 | |||
225.2.e.b.76.3 | 6 | 9.7 | even | 3 | |||
225.2.e.b.151.3 | 6 | 9.4 | even | 3 | |||
225.2.k.b.49.1 | 12 | 45.7 | odd | 12 | |||
225.2.k.b.49.6 | 12 | 45.43 | odd | 12 | |||
225.2.k.b.124.1 | 12 | 45.13 | odd | 12 | |||
225.2.k.b.124.6 | 12 | 45.22 | odd | 12 | |||
405.2.a.i.1.1 | 3 | 15.14 | odd | 2 | |||
405.2.a.j.1.3 | 3 | 5.4 | even | 2 | |||
675.2.e.b.226.1 | 6 | 9.2 | odd | 6 | |||
675.2.e.b.451.1 | 6 | 9.5 | odd | 6 | |||
675.2.k.b.199.1 | 12 | 45.38 | even | 12 | |||
675.2.k.b.199.6 | 12 | 45.2 | even | 12 | |||
675.2.k.b.424.1 | 12 | 45.32 | even | 12 | |||
675.2.k.b.424.6 | 12 | 45.23 | even | 12 | |||
720.2.q.i.241.1 | 6 | 180.139 | odd | 6 | |||
720.2.q.i.481.1 | 6 | 180.79 | odd | 6 | |||
2025.2.a.n.1.1 | 3 | 1.1 | even | 1 | trivial | ||
2025.2.a.o.1.3 | 3 | 3.2 | odd | 2 | |||
2025.2.b.l.649.1 | 6 | 5.2 | odd | 4 | |||
2025.2.b.l.649.6 | 6 | 5.3 | odd | 4 | |||
2025.2.b.m.649.1 | 6 | 15.8 | even | 4 | |||
2025.2.b.m.649.6 | 6 | 15.2 | even | 4 | |||
2160.2.q.k.721.1 | 6 | 180.59 | even | 6 | |||
2160.2.q.k.1441.1 | 6 | 180.119 | even | 6 | |||
6480.2.a.bs.1.3 | 3 | 60.59 | even | 2 | |||
6480.2.a.bv.1.3 | 3 | 20.19 | odd | 2 |