Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1725,2,Mod(1,1725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1725, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1725.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1725 = 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1725.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: | \(13.7741943487\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 345) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1725.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949 | 1.73205 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 2.00000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.44949 | −1.00000 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 4.89898 | 1.73205 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949 | 0.738549 | 0.369274 | − | 0.929320i | \(-0.379606\pi\) | ||||
0.369274 | + | 0.929320i | \(0.379606\pi\) | |||||||
\(12\) | −4.00000 | −1.15470 | ||||||||
\(13\) | −4.44949 | −1.23407 | −0.617033 | − | 0.786937i | \(-0.711666\pi\) | ||||
−0.617033 | + | 0.786937i | \(0.711666\pi\) | |||||||
\(14\) | 2.44949 | 0.654654 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 5.44949 | 1.32170 | 0.660848 | − | 0.750520i | \(-0.270197\pi\) | ||||
0.660848 | + | 0.750520i | \(0.270197\pi\) | |||||||
\(18\) | 2.44949 | 0.577350 | ||||||||
\(19\) | 4.44949 | 1.02078 | 0.510391 | − | 0.859942i | \(-0.329501\pi\) | ||||
0.510391 | + | 0.859942i | \(0.329501\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 6.00000 | 1.27920 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −4.89898 | −1.00000 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −10.8990 | −2.13747 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | 10.3485 | 1.92166 | 0.960831 | − | 0.277134i | \(-0.0893846\pi\) | ||||
0.960831 | + | 0.277134i | \(0.0893846\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.101021 | 0.0181438 | 0.00907191 | − | 0.999959i | \(-0.497112\pi\) | ||||
0.00907191 | + | 0.999959i | \(0.497112\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.44949 | −0.426401 | ||||||||
\(34\) | 13.3485 | 2.28924 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.00000 | 0.666667 | ||||||||
\(37\) | −3.89898 | −0.640988 | −0.320494 | − | 0.947250i | \(-0.603849\pi\) | ||||
−0.320494 | + | 0.947250i | \(0.603849\pi\) | |||||||
\(38\) | 10.8990 | 1.76805 | ||||||||
\(39\) | 4.44949 | 0.712489 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.44949 | 0.851067 | 0.425534 | − | 0.904943i | \(-0.360086\pi\) | ||||
0.425534 | + | 0.904943i | \(0.360086\pi\) | |||||||
\(42\) | −2.44949 | −0.377964 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 9.79796 | 1.47710 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.44949 | 0.361158 | ||||||||
\(47\) | −8.44949 | −1.23248 | −0.616242 | − | 0.787557i | \(-0.711346\pi\) | ||||
−0.616242 | + | 0.787557i | \(0.711346\pi\) | |||||||
\(48\) | −4.00000 | −0.577350 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.44949 | −0.763081 | ||||||||
\(52\) | −17.7980 | −2.46813 | ||||||||
\(53\) | −0.550510 | −0.0756184 | −0.0378092 | − | 0.999285i | \(-0.512038\pi\) | ||||
−0.0378092 | + | 0.999285i | \(0.512038\pi\) | |||||||
\(54\) | −2.44949 | −0.333333 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.89898 | 0.654654 | ||||||||
\(57\) | −4.44949 | −0.589349 | ||||||||
\(58\) | 25.3485 | 3.32842 | ||||||||
\(59\) | 10.3485 | 1.34726 | 0.673628 | − | 0.739071i | \(-0.264735\pi\) | ||||
0.673628 | + | 0.739071i | \(0.264735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.651531 | 0.0834200 | 0.0417100 | − | 0.999130i | \(-0.486719\pi\) | ||||
0.0417100 | + | 0.999130i | \(0.486719\pi\) | |||||||
\(62\) | 0.247449 | 0.0314260 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | −0.738549 | ||||||||
\(67\) | 7.00000 | 0.855186 | 0.427593 | − | 0.903971i | \(-0.359362\pi\) | ||||
0.427593 | + | 0.903971i | \(0.359362\pi\) | |||||||
\(68\) | 21.7980 | 2.64339 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.34847 | −0.516068 | −0.258034 | − | 0.966136i | \(-0.583075\pi\) | ||||
−0.258034 | + | 0.966136i | \(0.583075\pi\) | |||||||
\(72\) | 4.89898 | 0.577350 | ||||||||
\(73\) | 5.34847 | 0.625991 | 0.312995 | − | 0.949755i | \(-0.398668\pi\) | ||||
0.312995 | + | 0.949755i | \(0.398668\pi\) | |||||||
\(74\) | −9.55051 | −1.11022 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17.7980 | 2.04157 | ||||||||
\(77\) | 2.44949 | 0.279145 | ||||||||
\(78\) | 10.8990 | 1.23407 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.3485 | 1.47409 | ||||||||
\(83\) | −15.2474 | −1.67362 | −0.836812 | − | 0.547490i | \(-0.815584\pi\) | ||||
−0.836812 | + | 0.547490i | \(0.815584\pi\) | |||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.89898 | −0.528271 | ||||||||
\(87\) | −10.3485 | −1.10947 | ||||||||
\(88\) | 12.0000 | 1.27920 | ||||||||
\(89\) | −16.8990 | −1.79129 | −0.895644 | − | 0.444771i | \(-0.853285\pi\) | ||||
−0.895644 | + | 0.444771i | \(0.853285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.44949 | −0.466433 | ||||||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | −0.101021 | −0.0104753 | ||||||||
\(94\) | −20.6969 | −2.13473 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.10102 | −0.314861 | −0.157430 | − | 0.987530i | \(-0.550321\pi\) | ||||
−0.157430 | + | 0.987530i | \(0.550321\pi\) | |||||||
\(98\) | −14.6969 | −1.48461 | ||||||||
\(99\) | 2.44949 | 0.246183 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.5505 | −1.24882 | −0.624411 | − | 0.781096i | \(-0.714661\pi\) | ||||
−0.624411 | + | 0.781096i | \(0.714661\pi\) | |||||||
\(102\) | −13.3485 | −1.32170 | ||||||||
\(103\) | 12.6969 | 1.25107 | 0.625533 | − | 0.780198i | \(-0.284881\pi\) | ||||
0.625533 | + | 0.780198i | \(0.284881\pi\) | |||||||
\(104\) | −21.7980 | −2.13747 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.34847 | −0.130975 | ||||||||
\(107\) | 5.44949 | 0.526822 | 0.263411 | − | 0.964684i | \(-0.415152\pi\) | ||||
0.263411 | + | 0.964684i | \(0.415152\pi\) | |||||||
\(108\) | −4.00000 | −0.384900 | ||||||||
\(109\) | 11.5505 | 1.10634 | 0.553169 | − | 0.833069i | \(-0.313418\pi\) | ||||
0.553169 | + | 0.833069i | \(0.313418\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.89898 | 0.370075 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 1.65153 | 0.155363 | 0.0776815 | − | 0.996978i | \(-0.475248\pi\) | ||||
0.0776815 | + | 0.996978i | \(0.475248\pi\) | |||||||
\(114\) | −10.8990 | −1.02078 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 41.3939 | 3.84332 | ||||||||
\(117\) | −4.44949 | −0.411355 | ||||||||
\(118\) | 25.3485 | 2.33352 | ||||||||
\(119\) | 5.44949 | 0.499554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 1.59592 | 0.144488 | ||||||||
\(123\) | −5.44949 | −0.491364 | ||||||||
\(124\) | 0.404082 | 0.0362876 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.44949 | 0.218218 | ||||||||
\(127\) | 1.55051 | 0.137586 | 0.0687928 | − | 0.997631i | \(-0.478085\pi\) | ||||
0.0687928 | + | 0.997631i | \(0.478085\pi\) | |||||||
\(128\) | −19.5959 | −1.73205 | ||||||||
\(129\) | 2.00000 | 0.176090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.5959 | −1.71210 | −0.856052 | − | 0.516890i | \(-0.827090\pi\) | ||||
−0.856052 | + | 0.516890i | \(0.827090\pi\) | |||||||
\(132\) | −9.79796 | −0.852803 | ||||||||
\(133\) | 4.44949 | 0.385820 | ||||||||
\(134\) | 17.1464 | 1.48123 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 26.6969 | 2.28924 | ||||||||
\(137\) | 16.8990 | 1.44378 | 0.721889 | − | 0.692009i | \(-0.243274\pi\) | ||||
0.721889 | + | 0.692009i | \(0.243274\pi\) | |||||||
\(138\) | −2.44949 | −0.208514 | ||||||||
\(139\) | −4.79796 | −0.406958 | −0.203479 | − | 0.979079i | \(-0.565225\pi\) | ||||
−0.203479 | + | 0.979079i | \(0.565225\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.44949 | 0.711575 | ||||||||
\(142\) | −10.6515 | −0.893857 | ||||||||
\(143\) | −10.8990 | −0.911418 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.1010 | 1.08425 | ||||||||
\(147\) | 6.00000 | 0.494872 | ||||||||
\(148\) | −15.5959 | −1.28198 | ||||||||
\(149\) | −1.34847 | −0.110471 | −0.0552355 | − | 0.998473i | \(-0.517591\pi\) | ||||
−0.0552355 | + | 0.998473i | \(0.517591\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0000 | 1.13930 | 0.569652 | − | 0.821886i | \(-0.307078\pi\) | ||||
0.569652 | + | 0.821886i | \(0.307078\pi\) | |||||||
\(152\) | 21.7980 | 1.76805 | ||||||||
\(153\) | 5.44949 | 0.440565 | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 17.7980 | 1.42498 | ||||||||
\(157\) | −18.5959 | −1.48412 | −0.742058 | − | 0.670336i | \(-0.766150\pi\) | ||||
−0.742058 | + | 0.670336i | \(0.766150\pi\) | |||||||
\(158\) | −9.79796 | −0.779484 | ||||||||
\(159\) | 0.550510 | 0.0436583 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 2.44949 | 0.192450 | ||||||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | 21.7980 | 1.70213 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −37.3485 | −2.89880 | ||||||||
\(167\) | −13.3485 | −1.03294 | −0.516468 | − | 0.856307i | \(-0.672753\pi\) | ||||
−0.516468 | + | 0.856307i | \(0.672753\pi\) | |||||||
\(168\) | −4.89898 | −0.377964 | ||||||||
\(169\) | 6.79796 | 0.522920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.44949 | 0.340261 | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | −19.5959 | −1.48985 | −0.744925 | − | 0.667148i | \(-0.767515\pi\) | ||||
−0.744925 | + | 0.667148i | \(0.767515\pi\) | |||||||
\(174\) | −25.3485 | −1.92166 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.79796 | 0.738549 | ||||||||
\(177\) | −10.3485 | −0.777839 | ||||||||
\(178\) | −41.3939 | −3.10260 | ||||||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.89898 | −0.661456 | −0.330728 | − | 0.943726i | \(-0.607294\pi\) | ||||
−0.330728 | + | 0.943726i | \(0.607294\pi\) | |||||||
\(182\) | −10.8990 | −0.807886 | ||||||||
\(183\) | −0.651531 | −0.0481625 | ||||||||
\(184\) | 4.89898 | 0.361158 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.247449 | −0.0181438 | ||||||||
\(187\) | 13.3485 | 0.976137 | ||||||||
\(188\) | −33.7980 | −2.46497 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.2474 | −1.32034 | −0.660170 | − | 0.751117i | \(-0.729516\pi\) | ||||
−0.660170 | + | 0.751117i | \(0.729516\pi\) | |||||||
\(192\) | 8.00000 | 0.577350 | ||||||||
\(193\) | 6.69694 | 0.482056 | 0.241028 | − | 0.970518i | \(-0.422515\pi\) | ||||
0.241028 | + | 0.970518i | \(0.422515\pi\) | |||||||
\(194\) | −7.59592 | −0.545355 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.0000 | −1.71429 | ||||||||
\(197\) | 22.8990 | 1.63148 | 0.815742 | − | 0.578415i | \(-0.196329\pi\) | ||||
0.815742 | + | 0.578415i | \(0.196329\pi\) | |||||||
\(198\) | 6.00000 | 0.426401 | ||||||||
\(199\) | −2.89898 | −0.205503 | −0.102752 | − | 0.994707i | \(-0.532765\pi\) | ||||
−0.102752 | + | 0.994707i | \(0.532765\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.00000 | −0.493742 | ||||||||
\(202\) | −30.7423 | −2.16302 | ||||||||
\(203\) | 10.3485 | 0.726320 | ||||||||
\(204\) | −21.7980 | −1.52616 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 31.1010 | 2.16691 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −17.7980 | −1.23407 | ||||||||
\(209\) | 10.8990 | 0.753898 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0000 | 0.757271 | 0.378636 | − | 0.925546i | \(-0.376393\pi\) | ||||
0.378636 | + | 0.925546i | \(0.376393\pi\) | |||||||
\(212\) | −2.20204 | −0.151237 | ||||||||
\(213\) | 4.34847 | 0.297952 | ||||||||
\(214\) | 13.3485 | 0.912483 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.89898 | −0.333333 | ||||||||
\(217\) | 0.101021 | 0.00685772 | ||||||||
\(218\) | 28.2929 | 1.91623 | ||||||||
\(219\) | −5.34847 | −0.361416 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.2474 | −1.63106 | ||||||||
\(222\) | 9.55051 | 0.640988 | ||||||||
\(223\) | −21.5959 | −1.44617 | −0.723085 | − | 0.690759i | \(-0.757276\pi\) | ||||
−0.723085 | + | 0.690759i | \(0.757276\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.04541 | 0.269097 | ||||||||
\(227\) | −21.7980 | −1.44678 | −0.723391 | − | 0.690439i | \(-0.757417\pi\) | ||||
−0.723391 | + | 0.690439i | \(0.757417\pi\) | |||||||
\(228\) | −17.7980 | −1.17870 | ||||||||
\(229\) | −28.4949 | −1.88300 | −0.941498 | − | 0.337019i | \(-0.890581\pi\) | ||||
−0.941498 | + | 0.337019i | \(0.890581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.44949 | −0.161165 | ||||||||
\(232\) | 50.6969 | 3.32842 | ||||||||
\(233\) | −21.7980 | −1.42803 | −0.714016 | − | 0.700129i | \(-0.753126\pi\) | ||||
−0.714016 | + | 0.700129i | \(0.753126\pi\) | |||||||
\(234\) | −10.8990 | −0.712489 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 41.3939 | 2.69451 | ||||||||
\(237\) | 4.00000 | 0.259828 | ||||||||
\(238\) | 13.3485 | 0.865253 | ||||||||
\(239\) | 6.55051 | 0.423717 | 0.211859 | − | 0.977300i | \(-0.432048\pi\) | ||||
0.211859 | + | 0.977300i | \(0.432048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.3485 | −1.89050 | −0.945251 | − | 0.326346i | \(-0.894183\pi\) | ||||
−0.945251 | + | 0.326346i | \(0.894183\pi\) | |||||||
\(242\) | −12.2474 | −0.787296 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.60612 | 0.166840 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.3485 | −0.851067 | ||||||||
\(247\) | −19.7980 | −1.25971 | ||||||||
\(248\) | 0.494897 | 0.0314260 | ||||||||
\(249\) | 15.2474 | 0.966268 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 4.00000 | 0.251976 | ||||||||
\(253\) | 2.44949 | 0.153998 | ||||||||
\(254\) | 3.79796 | 0.238305 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0000 | −2.00000 | ||||||||
\(257\) | 25.3485 | 1.58119 | 0.790597 | − | 0.612337i | \(-0.209770\pi\) | ||||
0.790597 | + | 0.612337i | \(0.209770\pi\) | |||||||
\(258\) | 4.89898 | 0.304997 | ||||||||
\(259\) | −3.89898 | −0.242271 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.3485 | 0.640554 | ||||||||
\(262\) | −48.0000 | −2.96545 | ||||||||
\(263\) | −27.2474 | −1.68015 | −0.840075 | − | 0.542471i | \(-0.817489\pi\) | ||||
−0.840075 | + | 0.542471i | \(0.817489\pi\) | |||||||
\(264\) | −12.0000 | −0.738549 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.8990 | 0.668259 | ||||||||
\(267\) | 16.8990 | 1.03420 | ||||||||
\(268\) | 28.0000 | 1.71037 | ||||||||
\(269\) | −5.44949 | −0.332261 | −0.166131 | − | 0.986104i | \(-0.553127\pi\) | ||||
−0.166131 | + | 0.986104i | \(0.553127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.6969 | 1.92545 | 0.962726 | − | 0.270479i | \(-0.0871820\pi\) | ||||
0.962726 | + | 0.270479i | \(0.0871820\pi\) | |||||||
\(272\) | 21.7980 | 1.32170 | ||||||||
\(273\) | 4.44949 | 0.269295 | ||||||||
\(274\) | 41.3939 | 2.50070 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.00000 | −0.240772 | ||||||||
\(277\) | 10.0000 | 0.600842 | 0.300421 | − | 0.953807i | \(-0.402873\pi\) | ||||
0.300421 | + | 0.953807i | \(0.402873\pi\) | |||||||
\(278\) | −11.7526 | −0.704871 | ||||||||
\(279\) | 0.101021 | 0.00604794 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.3485 | −1.15423 | −0.577116 | − | 0.816662i | \(-0.695822\pi\) | ||||
−0.577116 | + | 0.816662i | \(0.695822\pi\) | |||||||
\(282\) | 20.6969 | 1.23248 | ||||||||
\(283\) | 2.10102 | 0.124893 | 0.0624464 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624464 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(284\) | −17.3939 | −1.03214 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.6969 | −1.57862 | ||||||||
\(287\) | 5.44949 | 0.321673 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6969 | 0.746879 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.10102 | 0.181785 | ||||||||
\(292\) | 21.3939 | 1.25198 | ||||||||
\(293\) | 21.2474 | 1.24129 | 0.620645 | − | 0.784092i | \(-0.286871\pi\) | ||||
0.620645 | + | 0.784092i | \(0.286871\pi\) | |||||||
\(294\) | 14.6969 | 0.857143 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −19.1010 | −1.11022 | ||||||||
\(297\) | −2.44949 | −0.142134 | ||||||||
\(298\) | −3.30306 | −0.191341 | ||||||||
\(299\) | −4.44949 | −0.257321 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | 34.2929 | 1.97333 | ||||||||
\(303\) | 12.5505 | 0.721008 | ||||||||
\(304\) | 17.7980 | 1.02078 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.3485 | 0.763081 | ||||||||
\(307\) | 2.65153 | 0.151331 | 0.0756654 | − | 0.997133i | \(-0.475892\pi\) | ||||
0.0756654 | + | 0.997133i | \(0.475892\pi\) | |||||||
\(308\) | 9.79796 | 0.558291 | ||||||||
\(309\) | −12.6969 | −0.722304 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 21.7980 | 1.23407 | ||||||||
\(313\) | −19.6969 | −1.11334 | −0.556668 | − | 0.830735i | \(-0.687921\pi\) | ||||
−0.556668 | + | 0.830735i | \(0.687921\pi\) | |||||||
\(314\) | −45.5505 | −2.57056 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.0000 | −0.900070 | ||||||||
\(317\) | −6.24745 | −0.350892 | −0.175446 | − | 0.984489i | \(-0.556137\pi\) | ||||
−0.175446 | + | 0.984489i | \(0.556137\pi\) | |||||||
\(318\) | 1.34847 | 0.0756184 | ||||||||
\(319\) | 25.3485 | 1.41924 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.44949 | −0.304161 | ||||||||
\(322\) | 2.44949 | 0.136505 | ||||||||
\(323\) | 24.2474 | 1.34916 | ||||||||
\(324\) | 4.00000 | 0.222222 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.4949 | 1.35665 | ||||||||
\(327\) | −11.5505 | −0.638745 | ||||||||
\(328\) | 26.6969 | 1.47409 | ||||||||
\(329\) | −8.44949 | −0.465835 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5959 | 1.35191 | 0.675957 | − | 0.736941i | \(-0.263731\pi\) | ||||
0.675957 | + | 0.736941i | \(0.263731\pi\) | |||||||
\(332\) | −60.9898 | −3.34725 | ||||||||
\(333\) | −3.89898 | −0.213663 | ||||||||
\(334\) | −32.6969 | −1.78910 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.00000 | −0.218218 | ||||||||
\(337\) | 19.7980 | 1.07846 | 0.539232 | − | 0.842157i | \(-0.318715\pi\) | ||||
0.539232 | + | 0.842157i | \(0.318715\pi\) | |||||||
\(338\) | 16.6515 | 0.905724 | ||||||||
\(339\) | −1.65153 | −0.0896988 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.247449 | 0.0134001 | ||||||||
\(342\) | 10.8990 | 0.589349 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −9.79796 | −0.528271 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −48.0000 | −2.58050 | ||||||||
\(347\) | 28.8990 | 1.55138 | 0.775689 | − | 0.631115i | \(-0.217402\pi\) | ||||
0.775689 | + | 0.631115i | \(0.217402\pi\) | |||||||
\(348\) | −41.3939 | −2.21894 | ||||||||
\(349\) | 23.4949 | 1.25765 | 0.628827 | − | 0.777546i | \(-0.283536\pi\) | ||||
0.628827 | + | 0.777546i | \(0.283536\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.44949 | 0.237496 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5505 | 0.827670 | 0.413835 | − | 0.910352i | \(-0.364189\pi\) | ||||
0.413835 | + | 0.910352i | \(0.364189\pi\) | |||||||
\(354\) | −25.3485 | −1.34726 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −67.5959 | −3.58258 | ||||||||
\(357\) | −5.44949 | −0.288418 | ||||||||
\(358\) | −14.6969 | −0.776757 | ||||||||
\(359\) | −3.55051 | −0.187389 | −0.0936944 | − | 0.995601i | \(-0.529868\pi\) | ||||
−0.0936944 | + | 0.995601i | \(0.529868\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.797959 | 0.0419978 | ||||||||
\(362\) | −21.7980 | −1.14568 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | −17.7980 | −0.932867 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.59592 | −0.0834200 | ||||||||
\(367\) | −13.6969 | −0.714974 | −0.357487 | − | 0.933918i | \(-0.616366\pi\) | ||||
−0.357487 | + | 0.933918i | \(0.616366\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 5.44949 | 0.283689 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.550510 | −0.0285811 | ||||||||
\(372\) | −0.404082 | −0.0209507 | ||||||||
\(373\) | −27.5959 | −1.42886 | −0.714431 | − | 0.699706i | \(-0.753314\pi\) | ||||
−0.714431 | + | 0.699706i | \(0.753314\pi\) | |||||||
\(374\) | 32.6969 | 1.69072 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −41.3939 | −2.13473 | ||||||||
\(377\) | −46.0454 | −2.37146 | ||||||||
\(378\) | −2.44949 | −0.125988 | ||||||||
\(379\) | 25.3939 | 1.30440 | 0.652198 | − | 0.758049i | \(-0.273847\pi\) | ||||
0.652198 | + | 0.758049i | \(0.273847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.55051 | −0.0794350 | ||||||||
\(382\) | −44.6969 | −2.28689 | ||||||||
\(383\) | −1.65153 | −0.0843893 | −0.0421946 | − | 0.999109i | \(-0.513435\pi\) | ||||
−0.0421946 | + | 0.999109i | \(0.513435\pi\) | |||||||
\(384\) | 19.5959 | 1.00000 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.4041 | 0.834946 | ||||||||
\(387\) | −2.00000 | −0.101666 | ||||||||
\(388\) | −12.4041 | −0.629722 | ||||||||
\(389\) | −3.30306 | −0.167472 | −0.0837359 | − | 0.996488i | \(-0.526685\pi\) | ||||
−0.0837359 | + | 0.996488i | \(0.526685\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.44949 | 0.275593 | ||||||||
\(392\) | −29.3939 | −1.48461 | ||||||||
\(393\) | 19.5959 | 0.988483 | ||||||||
\(394\) | 56.0908 | 2.82581 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.79796 | 0.492366 | ||||||||
\(397\) | 13.7980 | 0.692500 | 0.346250 | − | 0.938142i | \(-0.387455\pi\) | ||||
0.346250 | + | 0.938142i | \(0.387455\pi\) | |||||||
\(398\) | −7.10102 | −0.355942 | ||||||||
\(399\) | −4.44949 | −0.222753 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1010 | −0.654234 | −0.327117 | − | 0.944984i | \(-0.606077\pi\) | ||||
−0.327117 | + | 0.944984i | \(0.606077\pi\) | |||||||
\(402\) | −17.1464 | −0.855186 | ||||||||
\(403\) | −0.449490 | −0.0223907 | ||||||||
\(404\) | −50.2020 | −2.49764 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 25.3485 | 1.25802 | ||||||||
\(407\) | −9.55051 | −0.473401 | ||||||||
\(408\) | −26.6969 | −1.32170 | ||||||||
\(409\) | 21.8990 | 1.08283 | 0.541417 | − | 0.840754i | \(-0.317888\pi\) | ||||
0.541417 | + | 0.840754i | \(0.317888\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.8990 | −0.833565 | ||||||||
\(412\) | 50.7878 | 2.50213 | ||||||||
\(413\) | 10.3485 | 0.509215 | ||||||||
\(414\) | 2.44949 | 0.120386 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.79796 | 0.234957 | ||||||||
\(418\) | 26.6969 | 1.30579 | ||||||||
\(419\) | 33.5505 | 1.63905 | 0.819525 | − | 0.573044i | \(-0.194237\pi\) | ||||
0.819525 | + | 0.573044i | \(0.194237\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.2474 | −1.08427 | −0.542137 | − | 0.840290i | \(-0.682385\pi\) | ||||
−0.542137 | + | 0.840290i | \(0.682385\pi\) | |||||||
\(422\) | 26.9444 | 1.31163 | ||||||||
\(423\) | −8.44949 | −0.410828 | ||||||||
\(424\) | −2.69694 | −0.130975 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.6515 | 0.516068 | ||||||||
\(427\) | 0.651531 | 0.0315298 | ||||||||
\(428\) | 21.7980 | 1.05364 | ||||||||
\(429\) | 10.8990 | 0.526208 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.4949 | −1.17988 | −0.589939 | − | 0.807448i | \(-0.700848\pi\) | ||||
−0.589939 | + | 0.807448i | \(0.700848\pi\) | |||||||
\(432\) | −4.00000 | −0.192450 | ||||||||
\(433\) | −2.79796 | −0.134461 | −0.0672307 | − | 0.997737i | \(-0.521416\pi\) | ||||
−0.0672307 | + | 0.997737i | \(0.521416\pi\) | |||||||
\(434\) | 0.247449 | 0.0118779 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 46.2020 | 2.21268 | ||||||||
\(437\) | 4.44949 | 0.212848 | ||||||||
\(438\) | −13.1010 | −0.625991 | ||||||||
\(439\) | −36.6969 | −1.75145 | −0.875725 | − | 0.482811i | \(-0.839616\pi\) | ||||
−0.875725 | + | 0.482811i | \(0.839616\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | −59.3939 | −2.82508 | ||||||||
\(443\) | 20.4495 | 0.971585 | 0.485792 | − | 0.874074i | \(-0.338531\pi\) | ||||
0.485792 | + | 0.874074i | \(0.338531\pi\) | |||||||
\(444\) | 15.5959 | 0.740150 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −52.8990 | −2.50484 | ||||||||
\(447\) | 1.34847 | 0.0637804 | ||||||||
\(448\) | −8.00000 | −0.377964 | ||||||||
\(449\) | −21.2474 | −1.00273 | −0.501365 | − | 0.865236i | \(-0.667168\pi\) | ||||
−0.501365 | + | 0.865236i | \(0.667168\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.3485 | 0.628555 | ||||||||
\(452\) | 6.60612 | 0.310726 | ||||||||
\(453\) | −14.0000 | −0.657777 | ||||||||
\(454\) | −53.3939 | −2.50590 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −21.7980 | −1.02078 | ||||||||
\(457\) | −0.101021 | −0.00472554 | −0.00236277 | − | 0.999997i | \(-0.500752\pi\) | ||||
−0.00236277 | + | 0.999997i | \(0.500752\pi\) | |||||||
\(458\) | −69.7980 | −3.26144 | ||||||||
\(459\) | −5.44949 | −0.254360 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.4949 | −0.861393 | −0.430697 | − | 0.902497i | \(-0.641732\pi\) | ||||
−0.430697 | + | 0.902497i | \(0.641732\pi\) | |||||||
\(462\) | −6.00000 | −0.279145 | ||||||||
\(463\) | 24.9444 | 1.15926 | 0.579632 | − | 0.814878i | \(-0.303196\pi\) | ||||
0.579632 | + | 0.814878i | \(0.303196\pi\) | |||||||
\(464\) | 41.3939 | 1.92166 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −53.3939 | −2.47342 | ||||||||
\(467\) | 34.8434 | 1.61236 | 0.806179 | − | 0.591671i | \(-0.201532\pi\) | ||||
0.806179 | + | 0.591671i | \(0.201532\pi\) | |||||||
\(468\) | −17.7980 | −0.822711 | ||||||||
\(469\) | 7.00000 | 0.323230 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.5959 | 0.856855 | ||||||||
\(472\) | 50.6969 | 2.33352 | ||||||||
\(473\) | −4.89898 | −0.225255 | ||||||||
\(474\) | 9.79796 | 0.450035 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.7980 | 0.999108 | ||||||||
\(477\) | −0.550510 | −0.0252061 | ||||||||
\(478\) | 16.0454 | 0.733900 | ||||||||
\(479\) | 32.9444 | 1.50527 | 0.752634 | − | 0.658439i | \(-0.228783\pi\) | ||||
0.752634 | + | 0.658439i | \(0.228783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.3485 | 0.791022 | ||||||||
\(482\) | −71.8888 | −3.27444 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | −20.0000 | −0.909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.44949 | −0.111111 | ||||||||
\(487\) | 18.9444 | 0.858452 | 0.429226 | − | 0.903197i | \(-0.358786\pi\) | ||||
0.429226 | + | 0.903197i | \(0.358786\pi\) | |||||||
\(488\) | 3.19184 | 0.144488 | ||||||||
\(489\) | −10.0000 | −0.452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.5505 | 0.566397 | 0.283198 | − | 0.959061i | \(-0.408605\pi\) | ||||
0.283198 | + | 0.959061i | \(0.408605\pi\) | |||||||
\(492\) | −21.7980 | −0.982728 | ||||||||
\(493\) | 56.3939 | 2.53985 | ||||||||
\(494\) | −48.4949 | −2.18189 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.404082 | 0.0181438 | ||||||||
\(497\) | −4.34847 | −0.195056 | ||||||||
\(498\) | 37.3485 | 1.67362 | ||||||||
\(499\) | −1.00000 | −0.0447661 | −0.0223831 | − | 0.999749i | \(-0.507125\pi\) | ||||
−0.0223831 | + | 0.999749i | \(0.507125\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.3485 | 0.596366 | ||||||||
\(502\) | 44.0908 | 1.96787 | ||||||||
\(503\) | −7.04541 | −0.314139 | −0.157070 | − | 0.987588i | \(-0.550205\pi\) | ||||
−0.157070 | + | 0.987588i | \(0.550205\pi\) | |||||||
\(504\) | 4.89898 | 0.218218 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.00000 | 0.266733 | ||||||||
\(507\) | −6.79796 | −0.301908 | ||||||||
\(508\) | 6.20204 | 0.275171 | ||||||||
\(509\) | 28.8990 | 1.28092 | 0.640462 | − | 0.767990i | \(-0.278743\pi\) | ||||
0.640462 | + | 0.767990i | \(0.278743\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.34847 | 0.236602 | ||||||||
\(512\) | −39.1918 | −1.73205 | ||||||||
\(513\) | −4.44949 | −0.196450 | ||||||||
\(514\) | 62.0908 | 2.73871 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | −20.6969 | −0.910250 | ||||||||
\(518\) | −9.55051 | −0.419625 | ||||||||
\(519\) | 19.5959 | 0.860165 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.8434 | −1.92081 | −0.960406 | − | 0.278603i | \(-0.910129\pi\) | ||||
−0.960406 | + | 0.278603i | \(0.910129\pi\) | |||||||
\(522\) | 25.3485 | 1.10947 | ||||||||
\(523\) | 33.3939 | 1.46021 | 0.730106 | − | 0.683334i | \(-0.239471\pi\) | ||||
0.730106 | + | 0.683334i | \(0.239471\pi\) | |||||||
\(524\) | −78.3837 | −3.42421 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −66.7423 | −2.91010 | ||||||||
\(527\) | 0.550510 | 0.0239806 | ||||||||
\(528\) | −9.79796 | −0.426401 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3485 | 0.449085 | ||||||||
\(532\) | 17.7980 | 0.771639 | ||||||||
\(533\) | −24.2474 | −1.05027 | ||||||||
\(534\) | 41.3939 | 1.79129 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 34.2929 | 1.48123 | ||||||||
\(537\) | 6.00000 | 0.258919 | ||||||||
\(538\) | −13.3485 | −0.575493 | ||||||||
\(539\) | −14.6969 | −0.633042 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.8990 | 0.554570 | 0.277285 | − | 0.960788i | \(-0.410565\pi\) | ||||
0.277285 | + | 0.960788i | \(0.410565\pi\) | |||||||
\(542\) | 77.6413 | 3.33498 | ||||||||
\(543\) | 8.89898 | 0.381892 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.8990 | 0.466433 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 67.5959 | 2.88755 | ||||||||
\(549\) | 0.651531 | 0.0278067 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 46.0454 | 1.96160 | ||||||||
\(552\) | −4.89898 | −0.208514 | ||||||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 24.4949 | 1.04069 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.1918 | −0.813915 | ||||||||
\(557\) | 19.0454 | 0.806980 | 0.403490 | − | 0.914984i | \(-0.367797\pi\) | ||||
0.403490 | + | 0.914984i | \(0.367797\pi\) | |||||||
\(558\) | 0.247449 | 0.0104753 | ||||||||
\(559\) | 8.89898 | 0.376387 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.3485 | −0.563573 | ||||||||
\(562\) | −47.3939 | −1.99919 | ||||||||
\(563\) | −5.44949 | −0.229669 | −0.114834 | − | 0.993385i | \(-0.536634\pi\) | ||||
−0.114834 | + | 0.993385i | \(0.536634\pi\) | |||||||
\(564\) | 33.7980 | 1.42315 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.14643 | 0.216321 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −21.3031 | −0.893857 | ||||||||
\(569\) | −28.2929 | −1.18610 | −0.593049 | − | 0.805166i | \(-0.702076\pi\) | ||||
−0.593049 | + | 0.805166i | \(0.702076\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.1464 | 0.550161 | 0.275080 | − | 0.961421i | \(-0.411296\pi\) | ||||
0.275080 | + | 0.961421i | \(0.411296\pi\) | |||||||
\(572\) | −43.5959 | −1.82284 | ||||||||
\(573\) | 18.2474 | 0.762298 | ||||||||
\(574\) | 13.3485 | 0.557154 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | 28.0000 | 1.16566 | 0.582828 | − | 0.812596i | \(-0.301946\pi\) | ||||
0.582828 | + | 0.812596i | \(0.301946\pi\) | |||||||
\(578\) | 31.1010 | 1.29363 | ||||||||
\(579\) | −6.69694 | −0.278315 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.2474 | −0.632571 | ||||||||
\(582\) | 7.59592 | 0.314861 | ||||||||
\(583\) | −1.34847 | −0.0558479 | ||||||||
\(584\) | 26.2020 | 1.08425 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 52.0454 | 2.14998 | ||||||||
\(587\) | 6.00000 | 0.247647 | 0.123823 | − | 0.992304i | \(-0.460484\pi\) | ||||
0.123823 | + | 0.992304i | \(0.460484\pi\) | |||||||
\(588\) | 24.0000 | 0.989743 | ||||||||
\(589\) | 0.449490 | 0.0185209 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.8990 | −0.941938 | ||||||||
\(592\) | −15.5959 | −0.640988 | ||||||||
\(593\) | −27.5505 | −1.13136 | −0.565682 | − | 0.824624i | \(-0.691387\pi\) | ||||
−0.565682 | + | 0.824624i | \(0.691387\pi\) | |||||||
\(594\) | −6.00000 | −0.246183 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.39388 | −0.220942 | ||||||||
\(597\) | 2.89898 | 0.118647 | ||||||||
\(598\) | −10.8990 | −0.445692 | ||||||||
\(599\) | −2.69694 | −0.110194 | −0.0550970 | − | 0.998481i | \(-0.517547\pi\) | ||||
−0.0550970 | + | 0.998481i | \(0.517547\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.00000 | 0.203954 | 0.101977 | − | 0.994787i | \(-0.467483\pi\) | ||||
0.101977 | + | 0.994787i | \(0.467483\pi\) | |||||||
\(602\) | −4.89898 | −0.199667 | ||||||||
\(603\) | 7.00000 | 0.285062 | ||||||||
\(604\) | 56.0000 | 2.27861 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 30.7423 | 1.24882 | ||||||||
\(607\) | 16.2474 | 0.659464 | 0.329732 | − | 0.944075i | \(-0.393042\pi\) | ||||
0.329732 | + | 0.944075i | \(0.393042\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.3485 | −0.419341 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.5959 | 1.52097 | ||||||||
\(612\) | 21.7980 | 0.881130 | ||||||||
\(613\) | −14.0000 | −0.565455 | −0.282727 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282727 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(614\) | 6.49490 | 0.262113 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.0000 | 0.483494 | ||||||||
\(617\) | −12.5505 | −0.505265 | −0.252632 | − | 0.967562i | \(-0.581296\pi\) | ||||
−0.252632 | + | 0.967562i | \(0.581296\pi\) | |||||||
\(618\) | −31.1010 | −1.25107 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 29.3939 | 1.17859 | ||||||||
\(623\) | −16.8990 | −0.677043 | ||||||||
\(624\) | 17.7980 | 0.712489 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −48.2474 | −1.92836 | ||||||||
\(627\) | −10.8990 | −0.435263 | ||||||||
\(628\) | −74.3837 | −2.96823 | ||||||||
\(629\) | −21.2474 | −0.847191 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.5505 | 1.17639 | 0.588194 | − | 0.808720i | \(-0.299839\pi\) | ||||
0.588194 | + | 0.808720i | \(0.299839\pi\) | |||||||
\(632\) | −19.5959 | −0.779484 | ||||||||
\(633\) | −11.0000 | −0.437211 | ||||||||
\(634\) | −15.3031 | −0.607762 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.20204 | 0.0873166 | ||||||||
\(637\) | 26.6969 | 1.05777 | ||||||||
\(638\) | 62.0908 | 2.45820 | ||||||||
\(639\) | −4.34847 | −0.172023 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.9444 | 1.06424 | 0.532120 | − | 0.846669i | \(-0.321396\pi\) | ||||
0.532120 | + | 0.846669i | \(0.321396\pi\) | |||||||
\(642\) | −13.3485 | −0.526822 | ||||||||
\(643\) | 9.69694 | 0.382410 | 0.191205 | − | 0.981550i | \(-0.438760\pi\) | ||||
0.191205 | + | 0.981550i | \(0.438760\pi\) | |||||||
\(644\) | 4.00000 | 0.157622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 59.3939 | 2.33682 | ||||||||
\(647\) | −1.95459 | −0.0768430 | −0.0384215 | − | 0.999262i | \(-0.512233\pi\) | ||||
−0.0384215 | + | 0.999262i | \(0.512233\pi\) | |||||||
\(648\) | 4.89898 | 0.192450 | ||||||||
\(649\) | 25.3485 | 0.995014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.101021 | −0.00395931 | ||||||||
\(652\) | 40.0000 | 1.56652 | ||||||||
\(653\) | −43.8434 | −1.71572 | −0.857862 | − | 0.513881i | \(-0.828207\pi\) | ||||
−0.857862 | + | 0.513881i | \(0.828207\pi\) | |||||||
\(654\) | −28.2929 | −1.10634 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 21.7980 | 0.851067 | ||||||||
\(657\) | 5.34847 | 0.208664 | ||||||||
\(658\) | −20.6969 | −0.806851 | ||||||||
\(659\) | −5.14643 | −0.200476 | −0.100238 | − | 0.994963i | \(-0.531960\pi\) | ||||
−0.100238 | + | 0.994963i | \(0.531960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.0908 | 1.79272 | 0.896362 | − | 0.443322i | \(-0.146200\pi\) | ||||
0.896362 | + | 0.443322i | \(0.146200\pi\) | |||||||
\(662\) | 60.2474 | 2.34158 | ||||||||
\(663\) | 24.2474 | 0.941693 | ||||||||
\(664\) | −74.6969 | −2.89880 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.55051 | −0.370075 | ||||||||
\(667\) | 10.3485 | 0.400694 | ||||||||
\(668\) | −53.3939 | −2.06587 | ||||||||
\(669\) | 21.5959 | 0.834946 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.59592 | 0.0616097 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.4495 | −0.865364 | −0.432682 | − | 0.901547i | \(-0.642433\pi\) | ||||
−0.432682 | + | 0.901547i | \(0.642433\pi\) | |||||||
\(674\) | 48.4949 | 1.86795 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 27.1918 | 1.04584 | ||||||||
\(677\) | 12.5505 | 0.482355 | 0.241178 | − | 0.970481i | \(-0.422466\pi\) | ||||
0.241178 | + | 0.970481i | \(0.422466\pi\) | |||||||
\(678\) | −4.04541 | −0.155363 | ||||||||
\(679\) | −3.10102 | −0.119006 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.7980 | 0.835300 | ||||||||
\(682\) | 0.606123 | 0.0232097 | ||||||||
\(683\) | −18.2474 | −0.698219 | −0.349110 | − | 0.937082i | \(-0.613516\pi\) | ||||
−0.349110 | + | 0.937082i | \(0.613516\pi\) | |||||||
\(684\) | 17.7980 | 0.680522 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −31.8434 | −1.21579 | ||||||||
\(687\) | 28.4949 | 1.08715 | ||||||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | 2.44949 | 0.0933181 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2020 | 0.616355 | 0.308177 | − | 0.951329i | \(-0.400281\pi\) | ||||
0.308177 | + | 0.951329i | \(0.400281\pi\) | |||||||
\(692\) | −78.3837 | −2.97970 | ||||||||
\(693\) | 2.44949 | 0.0930484 | ||||||||
\(694\) | 70.7878 | 2.68707 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −50.6969 | −1.92166 | ||||||||
\(697\) | 29.6969 | 1.12485 | ||||||||
\(698\) | 57.5505 | 2.17832 | ||||||||
\(699\) | 21.7980 | 0.824475 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −52.0454 | −1.96573 | −0.982864 | − | 0.184332i | \(-0.940988\pi\) | ||||
−0.982864 | + | 0.184332i | \(0.940988\pi\) | |||||||
\(702\) | 10.8990 | 0.411355 | ||||||||
\(703\) | −17.3485 | −0.654310 | ||||||||
\(704\) | −19.5959 | −0.738549 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 38.0908 | 1.43357 | ||||||||
\(707\) | −12.5505 | −0.472011 | ||||||||
\(708\) | −41.3939 | −1.55568 | ||||||||
\(709\) | −28.7423 | −1.07944 | −0.539721 | − | 0.841844i | \(-0.681470\pi\) | ||||
−0.539721 | + | 0.841844i | \(0.681470\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | −0.150012 | ||||||||
\(712\) | −82.7878 | −3.10260 | ||||||||
\(713\) | 0.101021 | 0.00378325 | ||||||||
\(714\) | −13.3485 | −0.499554 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.0000 | −0.896922 | ||||||||
\(717\) | −6.55051 | −0.244633 | ||||||||
\(718\) | −8.69694 | −0.324567 | ||||||||
\(719\) | −11.9444 | −0.445450 | −0.222725 | − | 0.974881i | \(-0.571495\pi\) | ||||
−0.222725 | + | 0.974881i | \(0.571495\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.6969 | 0.472859 | ||||||||
\(722\) | 1.95459 | 0.0727424 | ||||||||
\(723\) | 29.3485 | 1.09148 | ||||||||
\(724\) | −35.5959 | −1.32291 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.2474 | 0.454545 | ||||||||
\(727\) | 16.3031 | 0.604647 | 0.302324 | − | 0.953205i | \(-0.402238\pi\) | ||||
0.302324 | + | 0.953205i | \(0.402238\pi\) | |||||||
\(728\) | −21.7980 | −0.807886 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.8990 | −0.403113 | ||||||||
\(732\) | −2.60612 | −0.0963251 | ||||||||
\(733\) | 8.59592 | 0.317497 | 0.158749 | − | 0.987319i | \(-0.449254\pi\) | ||||
0.158749 | + | 0.987319i | \(0.449254\pi\) | |||||||
\(734\) | −33.5505 | −1.23837 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.1464 | 0.631597 | ||||||||
\(738\) | 13.3485 | 0.491364 | ||||||||
\(739\) | −9.20204 | −0.338503 | −0.169251 | − | 0.985573i | \(-0.554135\pi\) | ||||
−0.169251 | + | 0.985573i | \(0.554135\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.7980 | 0.727296 | ||||||||
\(742\) | −1.34847 | −0.0495039 | ||||||||
\(743\) | 21.7980 | 0.799690 | 0.399845 | − | 0.916583i | \(-0.369064\pi\) | ||||
0.399845 | + | 0.916583i | \(0.369064\pi\) | |||||||
\(744\) | −0.494897 | −0.0181438 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −67.5959 | −2.47486 | ||||||||
\(747\) | −15.2474 | −0.557875 | ||||||||
\(748\) | 53.3939 | 1.95227 | ||||||||
\(749\) | 5.44949 | 0.199120 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.6515 | 1.11849 | 0.559245 | − | 0.829002i | \(-0.311091\pi\) | ||||
0.559245 | + | 0.829002i | \(0.311091\pi\) | |||||||
\(752\) | −33.7980 | −1.23248 | ||||||||
\(753\) | −18.0000 | −0.655956 | ||||||||
\(754\) | −112.788 | −4.10749 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.00000 | −0.145479 | ||||||||
\(757\) | 3.69694 | 0.134368 | 0.0671838 | − | 0.997741i | \(-0.478599\pi\) | ||||
0.0671838 | + | 0.997741i | \(0.478599\pi\) | |||||||
\(758\) | 62.2020 | 2.25928 | ||||||||
\(759\) | −2.44949 | −0.0889108 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1464 | 0.512808 | 0.256404 | − | 0.966570i | \(-0.417462\pi\) | ||||
0.256404 | + | 0.966570i | \(0.417462\pi\) | |||||||
\(762\) | −3.79796 | −0.137586 | ||||||||
\(763\) | 11.5505 | 0.418157 | ||||||||
\(764\) | −72.9898 | −2.64068 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.04541 | −0.146167 | ||||||||
\(767\) | −46.0454 | −1.66260 | ||||||||
\(768\) | 32.0000 | 1.15470 | ||||||||
\(769\) | 10.4495 | 0.376818 | 0.188409 | − | 0.982091i | \(-0.439667\pi\) | ||||
0.188409 | + | 0.982091i | \(0.439667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.3485 | −0.912903 | ||||||||
\(772\) | 26.7878 | 0.964112 | ||||||||
\(773\) | 16.2929 | 0.586013 | 0.293007 | − | 0.956110i | \(-0.405344\pi\) | ||||
0.293007 | + | 0.956110i | \(0.405344\pi\) | |||||||
\(774\) | −4.89898 | −0.176090 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15.1918 | −0.545355 | ||||||||
\(777\) | 3.89898 | 0.139875 | ||||||||
\(778\) | −8.09082 | −0.290070 | ||||||||
\(779\) | 24.2474 | 0.868755 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.6515 | −0.381142 | ||||||||
\(782\) | 13.3485 | 0.477340 | ||||||||
\(783\) | −10.3485 | −0.369824 | ||||||||
\(784\) | −24.0000 | −0.857143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 48.0000 | 1.71210 | ||||||||
\(787\) | 21.6969 | 0.773412 | 0.386706 | − | 0.922203i | \(-0.373613\pi\) | ||||
0.386706 | + | 0.922203i | \(0.373613\pi\) | |||||||
\(788\) | 91.5959 | 3.26297 | ||||||||
\(789\) | 27.2474 | 0.970035 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.65153 | 0.0587217 | ||||||||
\(792\) | 12.0000 | 0.426401 | ||||||||
\(793\) | −2.89898 | −0.102946 | ||||||||
\(794\) | 33.7980 | 1.19944 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.5959 | −0.411006 | ||||||||
\(797\) | −9.24745 | −0.327561 | −0.163781 | − | 0.986497i | \(-0.552369\pi\) | ||||
−0.163781 | + | 0.986497i | \(0.552369\pi\) | |||||||
\(798\) | −10.8990 | −0.385820 | ||||||||
\(799\) | −46.0454 | −1.62897 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.8990 | −0.597096 | ||||||||
\(802\) | −32.0908 | −1.13317 | ||||||||
\(803\) | 13.1010 | 0.462325 | ||||||||
\(804\) | −28.0000 | −0.987484 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.10102 | −0.0387818 | ||||||||
\(807\) | 5.44949 | 0.191831 | ||||||||
\(808\) | −61.4847 | −2.16302 | ||||||||
\(809\) | 6.55051 | 0.230304 | 0.115152 | − | 0.993348i | \(-0.463265\pi\) | ||||
0.115152 | + | 0.993348i | \(0.463265\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.3939 | −1.48865 | −0.744325 | − | 0.667817i | \(-0.767229\pi\) | ||||
−0.744325 | + | 0.667817i | \(0.767229\pi\) | |||||||
\(812\) | 41.3939 | 1.45264 | ||||||||
\(813\) | −31.6969 | −1.11166 | ||||||||
\(814\) | −23.3939 | −0.819955 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −21.7980 | −0.763081 | ||||||||
\(817\) | −8.89898 | −0.311336 | ||||||||
\(818\) | 53.6413 | 1.87552 | ||||||||
\(819\) | −4.44949 | −0.155478 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.3031 | 0.743482 | 0.371741 | − | 0.928336i | \(-0.378761\pi\) | ||||
0.371741 | + | 0.928336i | \(0.378761\pi\) | |||||||
\(822\) | −41.3939 | −1.44378 | ||||||||
\(823\) | −3.59592 | −0.125346 | −0.0626729 | − | 0.998034i | \(-0.519962\pi\) | ||||
−0.0626729 | + | 0.998034i | \(0.519962\pi\) | |||||||
\(824\) | 62.2020 | 2.16691 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.3485 | 0.881986 | ||||||||
\(827\) | −32.1464 | −1.11784 | −0.558920 | − | 0.829221i | \(-0.688784\pi\) | ||||
−0.558920 | + | 0.829221i | \(0.688784\pi\) | |||||||
\(828\) | 4.00000 | 0.139010 | ||||||||
\(829\) | −27.6969 | −0.961954 | −0.480977 | − | 0.876733i | \(-0.659718\pi\) | ||||
−0.480977 | + | 0.876733i | \(0.659718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | −0.346896 | ||||||||
\(832\) | 35.5959 | 1.23407 | ||||||||
\(833\) | −32.6969 | −1.13288 | ||||||||
\(834\) | 11.7526 | 0.406958 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 43.5959 | 1.50780 | ||||||||
\(837\) | −0.101021 | −0.00349178 | ||||||||
\(838\) | 82.1816 | 2.83892 | ||||||||
\(839\) | −45.1918 | −1.56020 | −0.780098 | − | 0.625658i | \(-0.784831\pi\) | ||||
−0.780098 | + | 0.625658i | \(0.784831\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 78.0908 | 2.69279 | ||||||||
\(842\) | −54.4949 | −1.87802 | ||||||||
\(843\) | 19.3485 | 0.666397 | ||||||||
\(844\) | 44.0000 | 1.51454 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −20.6969 | −0.711575 | ||||||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | −2.20204 | −0.0756184 | ||||||||
\(849\) | −2.10102 | −0.0721068 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.89898 | −0.133655 | ||||||||
\(852\) | 17.3939 | 0.595904 | ||||||||
\(853\) | −46.0908 | −1.57812 | −0.789060 | − | 0.614316i | \(-0.789432\pi\) | ||||
−0.789060 | + | 0.614316i | \(0.789432\pi\) | |||||||
\(854\) | 1.59592 | 0.0546112 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.6969 | 0.912483 | ||||||||
\(857\) | 13.5959 | 0.464428 | 0.232214 | − | 0.972665i | \(-0.425403\pi\) | ||||
0.232214 | + | 0.972665i | \(0.425403\pi\) | |||||||
\(858\) | 26.6969 | 0.911418 | ||||||||
\(859\) | 38.1918 | 1.30309 | 0.651544 | − | 0.758611i | \(-0.274121\pi\) | ||||
0.651544 | + | 0.758611i | \(0.274121\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.44949 | −0.185718 | ||||||||
\(862\) | −60.0000 | −2.04361 | ||||||||
\(863\) | −6.49490 | −0.221089 | −0.110544 | − | 0.993871i | \(-0.535259\pi\) | ||||
−0.110544 | + | 0.993871i | \(0.535259\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.85357 | −0.232894 | ||||||||
\(867\) | −12.6969 | −0.431211 | ||||||||
\(868\) | 0.404082 | 0.0137154 | ||||||||
\(869\) | −9.79796 | −0.332373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.1464 | −1.05536 | ||||||||
\(872\) | 56.5857 | 1.91623 | ||||||||
\(873\) | −3.10102 | −0.104954 | ||||||||
\(874\) | 10.8990 | 0.368663 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.3939 | −0.722832 | ||||||||
\(877\) | 10.4949 | 0.354388 | 0.177194 | − | 0.984176i | \(-0.443298\pi\) | ||||
0.177194 | + | 0.984176i | \(0.443298\pi\) | |||||||
\(878\) | −89.8888 | −3.03360 | ||||||||
\(879\) | −21.2474 | −0.716659 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.44949 | 0.284671 | 0.142335 | − | 0.989819i | \(-0.454539\pi\) | ||||
0.142335 | + | 0.989819i | \(0.454539\pi\) | |||||||
\(882\) | −14.6969 | −0.494872 | ||||||||
\(883\) | 37.5505 | 1.26368 | 0.631838 | − | 0.775101i | \(-0.282301\pi\) | ||||
0.631838 | + | 0.775101i | \(0.282301\pi\) | |||||||
\(884\) | −96.9898 | −3.26212 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 50.0908 | 1.68283 | ||||||||
\(887\) | 6.49490 | 0.218077 | 0.109039 | − | 0.994038i | \(-0.465223\pi\) | ||||
0.109039 | + | 0.994038i | \(0.465223\pi\) | |||||||
\(888\) | 19.1010 | 0.640988 | ||||||||
\(889\) | 1.55051 | 0.0520024 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.44949 | 0.0820610 | ||||||||
\(892\) | −86.3837 | −2.89234 | ||||||||
\(893\) | −37.5959 | −1.25810 | ||||||||
\(894\) | 3.30306 | 0.110471 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19.5959 | −0.654654 | ||||||||
\(897\) | 4.44949 | 0.148564 | ||||||||
\(898\) | −52.0454 | −1.73678 | ||||||||
\(899\) | 1.04541 | 0.0348663 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.00000 | −0.0999445 | ||||||||
\(902\) | 32.6969 | 1.08869 | ||||||||
\(903\) | 2.00000 | 0.0665558 | ||||||||
\(904\) | 8.09082 | 0.269097 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −34.2929 | −1.13930 | ||||||||
\(907\) | −38.7980 | −1.28827 | −0.644133 | − | 0.764914i | \(-0.722781\pi\) | ||||
−0.644133 | + | 0.764914i | \(0.722781\pi\) | |||||||
\(908\) | −87.1918 | −2.89356 | ||||||||
\(909\) | −12.5505 | −0.416274 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.2020 | −0.470535 | −0.235267 | − | 0.971931i | \(-0.575597\pi\) | ||||
−0.235267 | + | 0.971931i | \(0.575597\pi\) | |||||||
\(912\) | −17.7980 | −0.589349 | ||||||||
\(913\) | −37.3485 | −1.23605 | ||||||||
\(914\) | −0.247449 | −0.00818488 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −113.980 | −3.76599 | ||||||||
\(917\) | −19.5959 | −0.647114 | ||||||||
\(918\) | −13.3485 | −0.440565 | ||||||||
\(919\) | −45.3939 | −1.49741 | −0.748703 | − | 0.662906i | \(-0.769323\pi\) | ||||
−0.748703 | + | 0.662906i | \(0.769323\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.65153 | −0.0873709 | ||||||||
\(922\) | −45.3031 | −1.49198 | ||||||||
\(923\) | 19.3485 | 0.636863 | ||||||||
\(924\) | −9.79796 | −0.322329 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 61.1010 | 2.00790 | ||||||||
\(927\) | 12.6969 | 0.417022 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.8434 | 0.749467 | 0.374733 | − | 0.927133i | \(-0.377734\pi\) | ||||
0.374733 | + | 0.927133i | \(0.377734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.6969 | −0.874957 | ||||||||
\(932\) | −87.1918 | −2.85606 | ||||||||
\(933\) | −12.0000 | −0.392862 | ||||||||
\(934\) | 85.3485 | 2.79269 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −21.7980 | −0.712489 | ||||||||
\(937\) | 8.89898 | 0.290717 | 0.145358 | − | 0.989379i | \(-0.453566\pi\) | ||||
0.145358 | + | 0.989379i | \(0.453566\pi\) | |||||||
\(938\) | 17.1464 | 0.559851 | ||||||||
\(939\) | 19.6969 | 0.642785 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.8536 | −0.810203 | −0.405102 | − | 0.914272i | \(-0.632764\pi\) | ||||
−0.405102 | + | 0.914272i | \(0.632764\pi\) | |||||||
\(942\) | 45.5505 | 1.48412 | ||||||||
\(943\) | 5.44949 | 0.177460 | ||||||||
\(944\) | 41.3939 | 1.34726 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | 0.494897 | 0.0160820 | 0.00804100 | − | 0.999968i | \(-0.497440\pi\) | ||||
0.00804100 | + | 0.999968i | \(0.497440\pi\) | |||||||
\(948\) | 16.0000 | 0.519656 | ||||||||
\(949\) | −23.7980 | −0.772514 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.24745 | 0.202587 | ||||||||
\(952\) | 26.6969 | 0.865253 | ||||||||
\(953\) | −10.4041 | −0.337021 | −0.168511 | − | 0.985700i | \(-0.553896\pi\) | ||||
−0.168511 | + | 0.985700i | \(0.553896\pi\) | |||||||
\(954\) | −1.34847 | −0.0436583 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 26.2020 | 0.847435 | ||||||||
\(957\) | −25.3485 | −0.819400 | ||||||||
\(958\) | 80.6969 | 2.60720 | ||||||||
\(959\) | 16.8990 | 0.545697 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9898 | −0.999671 | ||||||||
\(962\) | 42.4949 | 1.37009 | ||||||||
\(963\) | 5.44949 | 0.175607 | ||||||||
\(964\) | −117.394 | −3.78100 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.44949 | −0.0788110 | ||||||||
\(967\) | −54.0454 | −1.73798 | −0.868992 | − | 0.494827i | \(-0.835231\pi\) | ||||
−0.868992 | + | 0.494827i | \(0.835231\pi\) | |||||||
\(968\) | −24.4949 | −0.787296 | ||||||||
\(969\) | −24.2474 | −0.778940 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.2929 | 0.715412 | 0.357706 | − | 0.933834i | \(-0.383559\pi\) | ||||
0.357706 | + | 0.933834i | \(0.383559\pi\) | |||||||
\(972\) | −4.00000 | −0.128300 | ||||||||
\(973\) | −4.79796 | −0.153816 | ||||||||
\(974\) | 46.4041 | 1.48688 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.60612 | 0.0834200 | ||||||||
\(977\) | −19.6515 | −0.628708 | −0.314354 | − | 0.949306i | \(-0.601788\pi\) | ||||
−0.314354 | + | 0.949306i | \(0.601788\pi\) | |||||||
\(978\) | −24.4949 | −0.783260 | ||||||||
\(979\) | −41.3939 | −1.32295 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.5505 | 0.368779 | ||||||||
\(982\) | 30.7423 | 0.981028 | ||||||||
\(983\) | 33.7423 | 1.07621 | 0.538107 | − | 0.842877i | \(-0.319140\pi\) | ||||
0.538107 | + | 0.842877i | \(0.319140\pi\) | |||||||
\(984\) | −26.6969 | −0.851067 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 138.136 | 4.39915 | ||||||||
\(987\) | 8.44949 | 0.268950 | ||||||||
\(988\) | −79.1918 | −2.51943 | ||||||||
\(989\) | −2.00000 | −0.0635963 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.7878 | 1.83569 | 0.917844 | − | 0.396941i | \(-0.129928\pi\) | ||||
0.917844 | + | 0.396941i | \(0.129928\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.5959 | −0.780528 | ||||||||
\(994\) | −10.6515 | −0.337846 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 60.9898 | 1.93254 | ||||||||
\(997\) | −40.0908 | −1.26969 | −0.634844 | − | 0.772640i | \(-0.718936\pi\) | ||||
−0.634844 | + | 0.772640i | \(0.718936\pi\) | |||||||
\(998\) | −2.44949 | −0.0775372 | ||||||||
\(999\) | 3.89898 | 0.123358 |
(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 | 1725.2.a.y.1.2 | 2 | ||
3.2 | odd | 2 | 5175.2.a.bl.1.1 | 2 | |||
5.2 | odd | 4 | 1725.2.b.m.1174.4 | 4 | |||
5.3 | odd | 4 | 1725.2.b.m.1174.1 | 4 | |||
5.4 | even | 2 | 345.2.a.i.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 1035.2.a.k.1.2 | 2 | |||
20.19 | odd | 2 | 5520.2.a.bi.1.1 | 2 | |||
115.114 | odd | 2 | 7935.2.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
345.2.a.i.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
1035.2.a.k.1.2 | 2 | 15.14 | odd | 2 | |||
1725.2.a.y.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1725.2.b.m.1174.1 | 4 | 5.3 | odd | 4 | |||
1725.2.b.m.1174.4 | 4 | 5.2 | odd | 4 | |||
5175.2.a.bl.1.1 | 2 | 3.2 | odd | 2 | |||
5520.2.a.bi.1.1 | 2 | 20.19 | odd | 2 | |||
7935.2.a.t.1.1 | 2 | 115.114 | odd | 2 |