Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7440,2,Mod(1,7440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("7440.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7440.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(59.4086991038\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 465) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.08613\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7440.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.08613 | −1.92238 | −0.961188 | − | 0.275893i | \(-0.911026\pi\) | ||||
−0.961188 | + | 0.275893i | \(0.911026\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.17226 | 1.25798 | 0.628992 | − | 0.777412i | \(-0.283468\pi\) | ||||
0.628992 | + | 0.777412i | \(0.283468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.08613 | −0.301238 | −0.150619 | − | 0.988592i | \(-0.548127\pi\) | ||||
−0.150619 | + | 0.988592i | \(0.548127\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.648061 | 0.157178 | 0.0785889 | − | 0.996907i | \(-0.474959\pi\) | ||||
0.0785889 | + | 0.996907i | \(0.474959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.70388 | 0.620312 | 0.310156 | − | 0.950686i | \(-0.399619\pi\) | ||||
0.310156 | + | 0.950686i | \(0.399619\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.08613 | −1.10988 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.52420 | −1.56890 | −0.784452 | − | 0.620189i | \(-0.787056\pi\) | ||||
−0.784452 | + | 0.620189i | \(0.787056\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.90645 | 1.09680 | 0.548400 | − | 0.836216i | \(-0.315237\pi\) | ||||
0.548400 | + | 0.836216i | \(0.315237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.17226 | 0.726297 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.08613 | 0.859713 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.913870 | 0.150239 | 0.0751196 | − | 0.997175i | \(-0.476066\pi\) | ||||
0.0751196 | + | 0.997175i | \(0.476066\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.08613 | −0.173920 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.17226 | 0.339250 | 0.169625 | − | 0.985509i | \(-0.445744\pi\) | ||||
0.169625 | + | 0.985509i | \(0.445744\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.17226 | −1.24626 | −0.623129 | − | 0.782119i | \(-0.714139\pi\) | ||||
−0.623129 | + | 0.782119i | \(0.714139\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.2281 | 1.49192 | 0.745959 | − | 0.665992i | \(-0.231991\pi\) | ||||
0.745959 | + | 0.665992i | \(0.231991\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.8687 | 2.69553 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.648061 | 0.0907467 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.52420 | 0.758807 | 0.379404 | − | 0.925231i | \(-0.376129\pi\) | ||||
0.379404 | + | 0.925231i | \(0.376129\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.17226 | −0.562587 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.70388 | 0.358137 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.438069 | −0.0570318 | −0.0285159 | − | 0.999593i | \(-0.509078\pi\) | ||||
−0.0285159 | + | 0.999593i | \(0.509078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.08613 | −0.640792 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.08613 | 0.134718 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.79001 | −1.19604 | −0.598020 | − | 0.801481i | \(-0.704046\pi\) | ||||
−0.598020 | + | 0.801481i | \(0.704046\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.52420 | −0.905807 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.96969 | −0.352437 | −0.176219 | − | 0.984351i | \(-0.556387\pi\) | ||||
−0.176219 | + | 0.984351i | \(0.556387\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.25839 | −0.147283 | −0.0736417 | − | 0.997285i | \(-0.523462\pi\) | ||||
−0.0736417 | + | 0.997285i | \(0.523462\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.2207 | −2.41832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8203 | −1.21738 | −0.608691 | − | 0.793408i | \(-0.708305\pi\) | ||||
−0.608691 | + | 0.793408i | \(0.708305\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.2281 | −1.56173 | −0.780867 | − | 0.624697i | \(-0.785222\pi\) | ||||
−0.780867 | + | 0.624697i | \(0.785222\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.648061 | −0.0702921 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.90645 | 0.633238 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.1903 | 1.92817 | 0.964086 | − | 0.265589i | \(-0.0855663\pi\) | ||||
0.964086 | + | 0.265589i | \(0.0855663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.52420 | 0.579093 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.70388 | −0.277412 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2207 | −1.34235 | −0.671177 | − | 0.741297i | \(-0.734211\pi\) | ||||
−0.671177 | + | 0.741297i | \(0.734211\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.17226 | 0.419328 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.8761 | −1.67924 | −0.839619 | − | 0.543175i | \(-0.817222\pi\) | ||||
−0.839619 | + | 0.543175i | \(0.817222\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.493887 | 0.0486641 | 0.0243321 | − | 0.999704i | \(-0.492254\pi\) | ||||
0.0243321 | + | 0.999704i | \(0.492254\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.08613 | 0.496355 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.69646 | −0.937392 | −0.468696 | − | 0.883359i | \(-0.655276\pi\) | ||||
−0.468696 | + | 0.883359i | \(0.655276\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.4003 | −1.57087 | −0.785434 | − | 0.618946i | \(-0.787560\pi\) | ||||
−0.785434 | + | 0.618946i | \(0.787560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.913870 | 0.0867407 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.5168 | 1.17748 | 0.588740 | − | 0.808323i | \(-0.299624\pi\) | ||||
0.588740 | + | 0.808323i | \(0.299624\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.52420 | 0.701635 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.08613 | −0.100413 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.29612 | −0.302155 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.40776 | 0.582523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.17226 | 0.195866 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.58002 | 0.672618 | 0.336309 | − | 0.941752i | \(-0.390821\pi\) | ||||
0.336309 | + | 0.941752i | \(0.390821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.17226 | −0.719527 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.67357 | 0.670443 | 0.335221 | − | 0.942139i | \(-0.391189\pi\) | ||||
0.335221 | + | 0.942139i | \(0.391189\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.7523 | −1.19247 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.75970 | −0.406648 | −0.203324 | − | 0.979111i | \(-0.565175\pi\) | ||||
−0.203324 | + | 0.979111i | \(0.565175\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.2839 | −0.872269 | −0.436134 | − | 0.899882i | \(-0.643653\pi\) | ||||
−0.436134 | + | 0.899882i | \(0.643653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2281 | 0.861360 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.53162 | −0.378953 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.90645 | −0.490504 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18.8687 | 1.55627 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.764504 | −0.0626306 | −0.0313153 | − | 0.999510i | \(-0.509970\pi\) | ||||
−0.0313153 | + | 0.999510i | \(0.509970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.992582 | 0.0807751 | 0.0403876 | − | 0.999184i | \(-0.487141\pi\) | ||||
0.0403876 | + | 0.999184i | \(0.487141\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.648061 | 0.0523926 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.9245 | 1.27092 | 0.635458 | − | 0.772135i | \(-0.280811\pi\) | ||||
0.635458 | + | 0.772135i | \(0.280811\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.52420 | 0.438098 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 38.2691 | 3.01602 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.25839 | 0.0985648 | 0.0492824 | − | 0.998785i | \(-0.484307\pi\) | ||||
0.0492824 | + | 0.998785i | \(0.484307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.17226 | −0.324810 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.5800 | −1.82468 | −0.912338 | − | 0.409437i | \(-0.865725\pi\) | ||||
−0.912338 | + | 0.409437i | \(0.865725\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8203 | −0.909255 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.70388 | 0.206771 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.1723 | −1.53367 | −0.766834 | − | 0.641845i | \(-0.778169\pi\) | ||||
−0.766834 | + | 0.641845i | \(0.778169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.08613 | −0.384475 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.438069 | −0.0329273 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.11164 | 0.307318 | 0.153659 | − | 0.988124i | \(-0.450894\pi\) | ||||
0.153659 | + | 0.988124i | \(0.450894\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3445 | 0.768902 | 0.384451 | − | 0.923145i | \(-0.374391\pi\) | ||||
0.384451 | + | 0.923145i | \(0.374391\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.913870 | −0.0671890 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.70388 | 0.197727 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.08613 | −0.369962 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.56193 | −0.257732 | −0.128866 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128866 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.58002 | −0.257695 | −0.128848 | − | 0.991664i | \(-0.541128\pi\) | ||||
−0.128848 | + | 0.991664i | \(0.541128\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.08613 | 0.0777794 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.35194 | 0.523804 | 0.261902 | − | 0.965094i | \(-0.415650\pi\) | ||||
0.261902 | + | 0.965094i | \(0.415650\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.1042 | −1.77959 | −0.889795 | − | 0.456360i | \(-0.849153\pi\) | ||||
−0.889795 | + | 0.456360i | \(0.849153\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.79001 | −0.690534 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −30.0410 | −2.10846 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.17226 | −0.151717 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.52420 | −0.522968 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.2813 | 0.780343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4051 | 0.991691 | 0.495846 | − | 0.868411i | \(-0.334858\pi\) | ||||
0.495846 | + | 0.868411i | \(0.334858\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.96969 | −0.203480 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.17226 | 0.557344 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.08613 | 0.345269 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.25839 | −0.0850342 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.703878 | −0.0473480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.4078 | −0.763920 | −0.381960 | − | 0.924179i | \(-0.624751\pi\) | ||||
−0.381960 | + | 0.924179i | \(0.624751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.3371 | 1.01796 | 0.508980 | − | 0.860779i | \(-0.330023\pi\) | ||||
0.508980 | + | 0.860779i | \(0.330023\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8277 | −1.04593 | −0.522963 | − | 0.852355i | \(-0.675174\pi\) | ||||
−0.522963 | + | 0.852355i | \(0.675174\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.2207 | −1.39622 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.9293 | −1.82971 | −0.914856 | − | 0.403780i | \(-0.867696\pi\) | ||||
−0.914856 | + | 0.403780i | \(0.867696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2281 | −0.667206 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.8203 | −0.702855 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.4562 | 0.676353 | 0.338176 | − | 0.941083i | \(-0.390190\pi\) | ||||
0.338176 | + | 0.941083i | \(0.390190\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.87614 | −0.442931 | −0.221466 | − | 0.975168i | \(-0.571084\pi\) | ||||
−0.221466 | + | 0.975168i | \(0.571084\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.8687 | −1.20548 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.93676 | −0.186862 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.2281 | −0.901668 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.39292 | −0.466637 | −0.233318 | − | 0.972400i | \(-0.574958\pi\) | ||||
−0.233318 | + | 0.972400i | \(0.574958\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.3929 | −1.97366 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.648061 | −0.0405831 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.28870 | −0.392279 | −0.196139 | − | 0.980576i | \(-0.562840\pi\) | ||||
−0.196139 | + | 0.980576i | \(0.562840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.64806 | −0.288816 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.90645 | 0.365600 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.6284 | 0.902027 | 0.451013 | − | 0.892517i | \(-0.351063\pi\) | ||||
0.451013 | + | 0.892517i | \(0.351063\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.52420 | −0.339349 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.1903 | 1.11323 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.4381 | −0.636420 | −0.318210 | − | 0.948020i | \(-0.603082\pi\) | ||||
−0.318210 | + | 0.948020i | \(0.603082\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.1574 | 1.95342 | 0.976712 | − | 0.214554i | \(-0.0688297\pi\) | ||||
0.976712 | + | 0.214554i | \(0.0688297\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.52420 | 0.334340 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.17226 | 0.251597 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.5397 | −1.95512 | −0.977560 | − | 0.210658i | \(-0.932439\pi\) | ||||
−0.977560 | + | 0.210658i | \(0.932439\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.82774 | −0.228344 | −0.114172 | − | 0.993461i | \(-0.536421\pi\) | ||||
−0.114172 | + | 0.993461i | \(0.536421\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.03773 | −0.358906 | −0.179453 | − | 0.983767i | \(-0.557433\pi\) | ||||
−0.179453 | + | 0.983767i | \(0.557433\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.70388 | −0.160164 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.0484 | −0.652166 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5800 | −0.975295 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.2207 | −0.775009 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.33710 | 0.545479 | 0.272740 | − | 0.962088i | \(-0.412070\pi\) | ||||
0.272740 | + | 0.962088i | \(0.412070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.438069 | 0.0255054 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.17226 | 0.242099 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.17226 | 0.472614 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.5652 | 2.39578 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.8761 | −0.969509 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.4184 | −1.50778 | −0.753890 | − | 0.657001i | \(-0.771825\pi\) | ||||
−0.753890 | + | 0.657001i | \(0.771825\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.493887 | 0.0280962 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.36261 | 0.360790 | 0.180395 | − | 0.983594i | \(-0.442262\pi\) | ||||
0.180395 | + | 0.983594i | \(0.442262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.02289 | 0.453481 | 0.226740 | − | 0.973955i | \(-0.427193\pi\) | ||||
0.226740 | + | 0.973955i | \(0.427193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.08613 | 0.286571 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.75970 | 0.267331 | 0.133666 | − | 0.991026i | \(-0.457325\pi\) | ||||
0.133666 | + | 0.991026i | \(0.457325\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.6433 | 1.37976 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.69646 | −0.541204 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.75228 | 0.0974993 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.08613 | −0.0602477 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.4003 | −0.906941 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −52.0213 | −2.86803 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.9804 | 1.20815 | 0.604075 | − | 0.796928i | \(-0.293543\pi\) | ||||
0.604075 | + | 0.796928i | \(0.293543\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.913870 | 0.0500798 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.79001 | 0.534885 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.1952 | 1.53589 | 0.767944 | − | 0.640517i | \(-0.221280\pi\) | ||||
0.767944 | + | 0.640517i | \(0.221280\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.5168 | 0.679818 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.17226 | −0.225941 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −60.3659 | −3.25945 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.52420 | 0.405089 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.1090 | −0.918461 | −0.459230 | − | 0.888317i | \(-0.651875\pi\) | ||||
−0.459230 | + | 0.888317i | \(0.651875\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.53643 | −0.135772 | −0.0678859 | − | 0.997693i | \(-0.521625\pi\) | ||||
−0.0678859 | + | 0.997693i | \(0.521625\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.08613 | −0.0579733 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.2255 | −1.34262 | −0.671308 | − | 0.741178i | \(-0.734267\pi\) | ||||
−0.671308 | + | 0.741178i | \(0.734267\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.96969 | 0.157615 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.29612 | −0.174449 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.7704 | −1.57122 | −0.785610 | − | 0.618722i | \(-0.787651\pi\) | ||||
−0.785610 | + | 0.618722i | \(0.787651\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.6890 | −0.615213 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.40776 | 0.336320 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.25839 | 0.0658672 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.3445 | 0.644379 | 0.322189 | − | 0.946675i | \(-0.395581\pi\) | ||||
0.322189 | + | 0.946675i | \(0.395581\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.17226 | 0.113083 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.0968 | −1.45871 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.3807 | 1.78016 | 0.890082 | − | 0.455800i | \(-0.150647\pi\) | ||||
0.890082 | + | 0.455800i | \(0.150647\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.41518 | −0.330398 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3297 | −1.14700 | −0.573499 | − | 0.819206i | \(-0.694415\pi\) | ||||
−0.573499 | + | 0.819206i | \(0.694415\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.58002 | 0.388336 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.4126 | −0.787545 | −0.393773 | − | 0.919208i | \(-0.628830\pi\) | ||||
−0.393773 | + | 0.919208i | \(0.628830\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.2207 | 1.08150 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.17226 | −0.415419 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.9549 | −0.758241 | −0.379121 | − | 0.925347i | \(-0.623773\pi\) | ||||
−0.379121 | + | 0.925347i | \(0.623773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.87614 | −0.246597 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.67357 | 0.387080 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.8203 | 0.544429 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.0484 | −1.65865 | −0.829326 | − | 0.558765i | \(-0.811275\pi\) | ||||
−0.829326 | + | 0.558765i | \(0.811275\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.7523 | −0.688475 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.56193 | 0.177874 | 0.0889372 | − | 0.996037i | \(-0.471653\pi\) | ||||
0.0889372 | + | 0.996037i | \(0.471653\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.08613 | 0.0541040 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.81290 | 0.188999 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6555 | −0.675220 | −0.337610 | − | 0.941286i | \(-0.609618\pi\) | ||||
−0.337610 | + | 0.941286i | \(0.609618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.75970 | −0.234778 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.22808 | 0.109637 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.2281 | 0.698429 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.2839 | −0.503605 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.7948 | 0.869334 | 0.434667 | − | 0.900591i | \(-0.356866\pi\) | ||||
0.434667 | + | 0.900591i | \(0.356866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.70869 | 0.424435 | 0.212218 | − | 0.977222i | \(-0.431931\pi\) | ||||
0.212218 | + | 0.977222i | \(0.431931\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.2281 | 0.497306 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.648061 | 0.0314356 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.1723 | 0.492270 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.53162 | −0.218789 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.2658 | 0.783496 | 0.391748 | − | 0.920072i | \(-0.371870\pi\) | ||||
0.391748 | + | 0.920072i | \(0.371870\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.85063 | −0.377277 | −0.188639 | − | 0.982047i | \(-0.560408\pi\) | ||||
−0.188639 | + | 0.982047i | \(0.560408\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.90645 | −0.283193 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.3445 | −0.973210 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2233 | −0.774294 | −0.387147 | − | 0.922018i | \(-0.626539\pi\) | ||||
−0.387147 | + | 0.922018i | \(0.626539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.8687 | 0.898510 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.7449 | −0.985618 | −0.492809 | − | 0.870138i | \(-0.664030\pi\) | ||||
−0.492809 | + | 0.870138i | \(0.664030\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.1903 | −0.862305 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.764504 | −0.0361598 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.7826 | −1.16956 | −0.584781 | − | 0.811191i | \(-0.698820\pi\) | ||||
−0.584781 | + | 0.811191i | \(0.698820\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.06324 | 0.426771 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.992582 | 0.0466356 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.52420 | −0.258978 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.8868 | 1.30449 | 0.652245 | − | 0.758008i | \(-0.273827\pi\) | ||||
0.652245 | + | 0.758008i | \(0.273827\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.648061 | 0.0302489 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.4110 | −1.36981 | −0.684904 | − | 0.728634i | \(-0.740156\pi\) | ||||
−0.684904 | + | 0.728634i | \(0.740156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.1239 | 1.16760 | 0.583802 | − | 0.811896i | \(-0.301564\pi\) | ||||
0.583802 | + | 0.811896i | \(0.301564\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.8055 | 1.61061 | 0.805303 | − | 0.592864i | \(-0.202003\pi\) | ||||
0.805303 | + | 0.592864i | \(0.202003\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 49.7933 | 2.29924 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.9245 | 0.733764 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.0968 | −1.56777 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.70388 | 0.124062 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.52420 | 0.252936 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.7704 | −1.63439 | −0.817195 | − | 0.576362i | \(-0.804472\pi\) | ||||
−0.817195 | + | 0.576362i | \(0.804472\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.992582 | −0.0452578 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 38.2691 | 1.74130 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.2207 | 0.600319 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.5652 | 0.977212 | 0.488606 | − | 0.872505i | \(-0.337506\pi\) | ||||
0.488606 | + | 0.872505i | \(0.337506\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.25839 | 0.0569064 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.7497 | −1.20720 | −0.603598 | − | 0.797289i | \(-0.706267\pi\) | ||||
−0.603598 | + | 0.797289i | \(0.706267\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.82774 | 0.172393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.17226 | −0.187529 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.1042 | 0.677517 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.9368 | 0.489597 | 0.244798 | − | 0.969574i | \(-0.421278\pi\) | ||||
0.244798 | + | 0.969574i | \(0.421278\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.5800 | −1.05348 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.2281 | 0.812750 | 0.406375 | − | 0.913706i | \(-0.366793\pi\) | ||||
0.406375 | + | 0.913706i | \(0.366793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.8761 | 0.750978 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.8203 | −0.524959 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.6103 | 0.470295 | 0.235147 | − | 0.971960i | \(-0.424443\pi\) | ||||
0.235147 | + | 0.971960i | \(0.424443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.40034 | 0.283134 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.70388 | 0.119379 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.493887 | −0.0217633 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42.6742 | 1.87681 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.1723 | −0.885464 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.6768 | −1.12492 | −0.562461 | − | 0.826824i | \(-0.690145\pi\) | ||||
−0.562461 | + | 0.826824i | \(0.690145\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.1574 | −0.881423 | −0.440711 | − | 0.897649i | \(-0.645274\pi\) | ||||
−0.440711 | + | 0.897649i | \(0.645274\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.08613 | −0.221977 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.648061 | −0.0282300 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.6136 | 1.46146 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.438069 | −0.0190106 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.35936 | −0.102195 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.69646 | 0.419215 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.11164 | 0.177430 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 78.7252 | 3.39094 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.4610 | 1.30962 | 0.654810 | − | 0.755794i | \(-0.272749\pi\) | ||||
0.654810 | + | 0.755794i | \(0.272749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3445 | 0.443926 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.4003 | 0.702513 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.8506 | 0.506697 | 0.253348 | − | 0.967375i | \(-0.418468\pi\) | ||||
0.253348 | + | 0.967375i | \(0.418468\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.9703 | 0.680359 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.0336 | 2.34027 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.913870 | −0.0387916 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.95902 | −0.167749 | −0.0838745 | − | 0.996476i | \(-0.526729\pi\) | ||||
−0.0838745 | + | 0.996476i | \(0.526729\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.87614 | 0.375421 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.70388 | 0.114158 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.6965 | 0.577237 | 0.288618 | − | 0.957444i | \(-0.406804\pi\) | ||||
0.288618 | + | 0.957444i | \(0.406804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.5168 | −0.526585 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.08613 | −0.213597 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.4865 | 0.900760 | 0.450380 | − | 0.892837i | \(-0.351289\pi\) | ||||
0.450380 | + | 0.892837i | \(0.351289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.46838 | 0.145147 | 0.0725736 | − | 0.997363i | \(-0.476879\pi\) | ||||
0.0725736 | + | 0.997363i | \(0.476879\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.56193 | −0.148802 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.52420 | −0.313781 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.9516 | 0.705704 | 0.352852 | − | 0.935679i | \(-0.385212\pi\) | ||||
0.352852 | + | 0.935679i | \(0.385212\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.58002 | −0.148780 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 72.3659 | 3.00224 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.0484 | 0.954567 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.08613 | 0.0449060 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.97294 | −0.287804 | −0.143902 | − | 0.989592i | \(-0.545965\pi\) | ||||
−0.143902 | + | 0.989592i | \(0.545965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.70388 | −0.111411 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.35194 | 0.302418 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.9097 | −1.14611 | −0.573057 | − | 0.819515i | \(-0.694243\pi\) | ||||
−0.573057 | + | 0.819515i | \(0.694243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.29612 | 0.135128 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.1042 | −1.02745 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.4381 | −1.24367 | −0.621833 | − | 0.783150i | \(-0.713612\pi\) | ||||
−0.621833 | + | 0.783150i | \(0.713612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.7013 | −1.04838 | −0.524188 | − | 0.851602i | \(-0.675631\pi\) | ||||
−0.524188 | + | 0.851602i | \(0.675631\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.79001 | −0.398680 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.40776 | −0.260512 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.7119 | 0.921849 | 0.460925 | − | 0.887439i | \(-0.347518\pi\) | ||||
0.460925 | + | 0.887439i | \(0.347518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.0410 | −1.21732 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.1090 | −0.449423 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.4939 | 1.23164 | 0.615818 | − | 0.787888i | \(-0.288826\pi\) | ||||
0.615818 | + | 0.787888i | \(0.288826\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.17226 | −0.0875940 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.6890 | 0.430325 | 0.215162 | − | 0.976578i | \(-0.430972\pi\) | ||||
0.215162 | + | 0.976578i | \(0.430972\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.3397 | 0.495975 | 0.247987 | − | 0.968763i | \(-0.420231\pi\) | ||||
0.247987 | + | 0.968763i | \(0.420231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.52420 | −0.301936 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −92.5185 | −3.70667 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.2813 | 0.450531 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.592243 | 0.0236143 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1600 | 0.921986 | 0.460993 | − | 0.887404i | \(-0.347493\pi\) | ||||
0.460993 | + | 0.887404i | \(0.347493\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.4051 | 0.572553 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.58002 | −0.300804 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.4939 | −0.811997 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.96969 | −0.117479 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.63739 | 0.0646731 | 0.0323366 | − | 0.999477i | \(-0.489705\pi\) | ||||
0.0323366 | + | 0.999477i | \(0.489705\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.531618 | 0.0209650 | 0.0104825 | − | 0.999945i | \(-0.496663\pi\) | ||||
0.0104825 | + | 0.999945i | \(0.496663\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.17226 | 0.321782 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.86391 | 0.387790 | 0.193895 | − | 0.981022i | \(-0.437888\pi\) | ||||
0.193895 | + | 0.981022i | \(0.437888\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.82774 | −0.0717451 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.08613 | 0.199341 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.8081 | −1.71434 | −0.857172 | − | 0.515031i | \(-0.827780\pi\) | ||||
−0.857172 | + | 0.515031i | \(0.827780\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.67357 | −0.299831 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.25839 | −0.0490945 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.0639 | −1.32694 | −0.663470 | − | 0.748203i | \(-0.730917\pi\) | ||||
−0.663470 | + | 0.748203i | \(0.730917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.3567 | 0.830681 | 0.415341 | − | 0.909666i | \(-0.363662\pi\) | ||||
0.415341 | + | 0.909666i | \(0.363662\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.703878 | −0.0273364 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.7523 | 0.533290 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.4413 | −1.72077 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.4078 | −0.441049 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.34452 | −0.322137 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.8990 | 1.11398 | 0.556988 | − | 0.830521i | \(-0.311957\pi\) | ||||
0.556988 | + | 0.830521i | \(0.311957\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.8539 | −1.07051 | −0.535256 | − | 0.844690i | \(-0.679785\pi\) | ||||
−0.535256 | + | 0.844690i | \(0.679785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 67.2420 | 2.58051 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.3371 | 0.587719 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.7113 | −0.601176 | −0.300588 | − | 0.953754i | \(-0.597183\pi\) | ||||
−0.300588 | + | 0.953754i | \(0.597183\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.75970 | 0.181859 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.8277 | −0.603866 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | −0.228582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.92454 | −0.301464 | −0.150732 | − | 0.988575i | \(-0.548163\pi\) | ||||
−0.150732 | + | 0.988575i | \(0.548163\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21.2207 | −0.806106 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.2839 | 0.390090 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.40776 | 0.0533226 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.9293 | −1.05638 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.0968 | 1.28782 | 0.643909 | − | 0.765102i | \(-0.277311\pi\) | ||||
0.643909 | + | 0.765102i | \(0.277311\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.47099 | 0.0931953 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.2281 | −0.385212 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 85.8342 | 3.22813 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.8826 | −1.76071 | −0.880357 | − | 0.474311i | \(-0.842697\pi\) | ||||
−0.880357 | + | 0.474311i | \(0.842697\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.8203 | −0.405794 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.52420 | 0.281783 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.53162 | 0.169473 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.4562 | 0.390492 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.51678 | 0.168448 | 0.0842238 | − | 0.996447i | \(-0.473159\pi\) | ||||
0.0842238 | + | 0.996447i | \(0.473159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.51197 | −0.0935508 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.87614 | −0.255726 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.90645 | 0.219360 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.72677 | −0.175306 | −0.0876531 | − | 0.996151i | \(-0.527937\pi\) | ||||
−0.0876531 | + | 0.996151i | \(0.527937\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.29612 | −0.195884 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.87875 | −0.0693932 | −0.0346966 | − | 0.999398i | \(-0.511046\pi\) | ||||
−0.0346966 | + | 0.999398i | \(0.511046\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.8687 | −0.695983 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40.8465 | −1.50460 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.1526 | 0.594184 | 0.297092 | − | 0.954849i | \(-0.403983\pi\) | ||||
0.297092 | + | 0.954849i | \(0.403983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.93676 | −0.107885 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.3175 | 0.855435 | 0.427717 | − | 0.903913i | \(-0.359318\pi\) | ||||
0.427717 | + | 0.903913i | \(0.359318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.764504 | 0.0280092 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.2281 | −0.520578 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.3175 | 1.80202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.46838 | 0.126563 | 0.0632815 | − | 0.997996i | \(-0.479843\pi\) | ||||
0.0632815 | + | 0.997996i | \(0.479843\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.39292 | −0.269413 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.992582 | −0.0361237 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.9326 | 1.52407 | 0.762033 | − | 0.647538i | \(-0.224201\pi\) | ||||
0.762033 | + | 0.647538i | \(0.224201\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.3929 | −1.13949 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.1877 | −0.478055 | −0.239028 | − | 0.971013i | \(-0.576829\pi\) | ||||
−0.239028 | + | 0.971013i | \(0.576829\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 83.4143 | 3.01980 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.648061 | −0.0234307 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.475800 | 0.0171802 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.6816 | −1.71944 | −0.859722 | − | 0.510763i | \(-0.829363\pi\) | ||||
−0.859722 | + | 0.510763i | \(0.829363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.28870 | −0.226482 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.6236 | 1.10145 | 0.550727 | − | 0.834685i | \(-0.314350\pi\) | ||||
0.550727 | + | 0.834685i | \(0.314350\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.64806 | −0.166748 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.87353 | 0.210441 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3903 | −0.443360 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.90645 | 0.211079 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.9245 | −0.568371 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.9219 | −0.959663 | −0.479832 | − | 0.877361i | \(-0.659302\pi\) | ||||
−0.479832 | + | 0.877361i | \(0.659302\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.6284 | 0.520785 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −63.6620 | −2.26356 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.17226 | 0.0771392 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.52420 | −0.195923 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.9197 | −0.847280 | −0.423640 | − | 0.905831i | \(-0.639248\pi\) | ||||
−0.423640 | + | 0.905831i | \(0.639248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.62842 | 0.234497 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.1903 | 0.642724 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.25033 | −0.185280 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −38.2691 | −1.34881 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.4381 | −0.367437 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.8336 | 1.22468 | 0.612342 | − | 0.790593i | \(-0.290228\pi\) | ||||
0.612342 | + | 0.790593i | \(0.290228\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.8277 | 1.32831 | 0.664156 | − | 0.747594i | \(-0.268791\pi\) | ||||
0.664156 | + | 0.747594i | \(0.268791\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.1574 | 1.12781 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.25839 | −0.0440795 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.0968 | −0.773069 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.52420 | 0.193031 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.6439 | −1.10438 | −0.552190 | − | 0.833718i | \(-0.686208\pi\) | ||||
−0.552190 | + | 0.833718i | \(0.686208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.9729 | −0.591639 | −0.295820 | − | 0.955244i | \(-0.595593\pi\) | ||||
−0.295820 | + | 0.955244i | \(0.595593\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.17226 | 0.145259 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.0532 | 0.871185 | 0.435593 | − | 0.900144i | \(-0.356539\pi\) | ||||
0.435593 | + | 0.900144i | \(0.356539\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.7497 | 0.998517 | 0.499259 | − | 0.866453i | \(-0.333606\pi\) | ||||
0.499259 | + | 0.866453i | \(0.333606\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.5397 | −1.12879 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.2281 | 0.423678 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.5800 | 0.816020 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.83099 | 0.270356 | 0.135178 | − | 0.990821i | \(-0.456839\pi\) | ||||
0.135178 | + | 0.990821i | \(0.456839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.88617 | 0.202971 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.82774 | −0.131834 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.8203 | 0.406631 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.5907 | −1.11983 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.03773 | −0.207214 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.87614 | −0.235711 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.1600 | 1.20386 | 0.601928 | − | 0.798550i | \(-0.294399\pi\) | ||||
0.601928 | + | 0.798550i | \(0.294399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.70388 | −0.0924707 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.6136 | 0.362553 | 0.181276 | − | 0.983432i | \(-0.441977\pi\) | ||||
0.181276 | + | 0.983432i | \(0.441977\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.8491 | −0.677242 | −0.338621 | − | 0.940923i | \(-0.609960\pi\) | ||||
−0.338621 | + | 0.940923i | \(0.609960\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.0484 | −0.376528 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.03356 | 0.307506 | 0.153753 | − | 0.988109i | \(-0.450864\pi\) | ||||
0.153753 | + | 0.988109i | \(0.450864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.1723 | 0.685877 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.5800 | −0.563087 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.1452 | −1.53145 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.6332 | 0.360293 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.2207 | −0.447452 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.08613 | 0.171943 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.6406 | 1.13596 | 0.567982 | − | 0.823041i | \(-0.307724\pi\) | ||||
0.567982 | + | 0.823041i | \(0.307724\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.33710 | 0.314933 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.48647 | 0.252226 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.7374 | −0.596912 | −0.298456 | − | 0.954423i | \(-0.596472\pi\) | ||||
−0.298456 | + | 0.954423i | \(0.596472\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.438069 | 0.0147255 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.8687 | −0.532819 | −0.266410 | − | 0.963860i | \(-0.585837\pi\) | ||||
−0.266410 | + | 0.963860i | \(0.585837\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.5530 | −1.29302 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.17226 | 0.139776 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.6555 | 0.925455 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.11164 | −0.137437 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.17226 | 0.272864 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.90645 | −0.196991 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.58002 | 0.119268 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 41.5652 | 1.38320 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.3445 | −0.343864 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.55451 | −0.284048 | −0.142024 | − | 0.989863i | \(-0.545361\pi\) | ||||
−0.142024 | + | 0.989863i | \(0.545361\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.8761 | −0.559746 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.5800 | 0.449926 | 0.224963 | − | 0.974367i | \(-0.427774\pi\) | ||||
0.224963 | + | 0.974367i | \(0.427774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −59.3632 | −1.96464 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.00000 | 0.0661180 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −39.0288 | −1.28884 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.3148 | −1.72571 | −0.862854 | − | 0.505454i | \(-0.831325\pi\) | ||||
−0.862854 | + | 0.505454i | \(0.831325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.4184 | −0.870517 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.22547 | 0.106168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.913870 | 0.0300479 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.493887 | 0.0162214 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.37483 | −0.176343 | −0.0881713 | − | 0.996105i | \(-0.528102\pi\) | ||||
−0.0881713 | + | 0.996105i | \(0.528102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.0187 | 1.67207 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.36261 | 0.208302 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.70388 | −0.0884263 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.9433 | 1.92559 | 0.962796 | − | 0.270228i | \(-0.0870992\pi\) | ||||
0.962796 | + | 0.270228i | \(0.0870992\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.02289 | 0.261817 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.62517 | −0.150776 | −0.0753881 | − | 0.997154i | \(-0.524020\pi\) | ||||
−0.0753881 | + | 0.997154i | \(0.524020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.3445 | −0.532251 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.08613 | 0.165452 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.8591 | 0.775317 | 0.387658 | − | 0.921803i | \(-0.373284\pi\) | ||||
0.387658 | + | 0.921803i | \(0.373284\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.36678 | 0.0443674 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.75970 | 0.154344 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.8081 | −0.512074 | −0.256037 | − | 0.966667i | \(-0.582417\pi\) | ||||
−0.256037 | + | 0.966667i | \(0.582417\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.56193 | 0.115261 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.6433 | 0.796603 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.2084 | 0.781731 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.69646 | −0.312464 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.58002 | 0.115245 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.90320 | −0.254150 | −0.127075 | − | 0.991893i | \(-0.540559\pi\) | ||||
−0.127075 | + | 0.991893i | \(0.540559\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.75228 | 0.0562913 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.3478 | 1.42319 | 0.711594 | − | 0.702591i | \(-0.247974\pi\) | ||||
0.711594 | + | 0.702591i | \(0.247974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.3052 | 1.67683 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.08613 | −0.0347840 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.3781 | 0.747931 | 0.373966 | − | 0.927443i | \(-0.377998\pi\) | ||||
0.373966 | + | 0.927443i | \(0.377998\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75.8949 | 2.42561 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.4003 | −0.523623 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.7374 | 1.13985 | 0.569924 | − | 0.821698i | \(-0.306973\pi\) | ||||
0.569924 | + | 0.821698i | \(0.306973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.35194 | −0.234252 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −52.0213 | −1.65586 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 61.4897 | 1.95526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.4143 | −1.95089 | −0.975444 | − | 0.220247i | \(-0.929314\pi\) | ||||
−0.975444 | + | 0.220247i | \(0.929314\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.9804 | 0.697526 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.1042 | 0.795857 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.8220 | 1.67289 | 0.836445 | − | 0.548051i | \(-0.184630\pi\) | ||||
0.836445 | + | 0.548051i | \(0.184630\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.913870 | 0.0289136 |
(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 | 7440.2.a.bs.1.1 | 3 | ||
4.3 | odd | 2 | 465.2.a.e.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 1395.2.a.j.1.3 | 3 | |||
20.3 | even | 4 | 2325.2.c.k.1024.5 | 6 | |||
20.7 | even | 4 | 2325.2.c.k.1024.2 | 6 | |||
20.19 | odd | 2 | 2325.2.a.r.1.3 | 3 | |||
60.59 | even | 2 | 6975.2.a.bf.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
465.2.a.e.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
1395.2.a.j.1.3 | 3 | 12.11 | even | 2 | |||
2325.2.a.r.1.3 | 3 | 20.19 | odd | 2 | |||
2325.2.c.k.1024.2 | 6 | 20.7 | even | 4 | |||
2325.2.c.k.1024.5 | 6 | 20.3 | even | 4 | |||
6975.2.a.bf.1.1 | 3 | 60.59 | even | 2 | |||
7440.2.a.bs.1.1 | 3 | 1.1 | even | 1 | trivial |