Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9680,2,Mod(1,9680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9680.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: | \(77.2951891566\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.45753625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - x^{5} - 13x^{4} + 11x^{3} + 41x^{2} - 30x - 20 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.87511\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9680.1 |
$q$-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 | ||||||||
\(3\) | 3.03399 | 1.75168 | 0.875838 | − | 0.482605i | \(-0.160309\pi\) | ||||
0.875838 | + | 0.482605i | \(0.160309\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.865927 | 0.327290 | 0.163645 | − | 0.986519i | \(-0.447675\pi\) | ||||
0.163645 | + | 0.986519i | \(0.447675\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.20511 | 2.06837 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.43509 | 1.23007 | 0.615037 | − | 0.788499i | \(-0.289141\pi\) | ||||
0.615037 | + | 0.788499i | \(0.289141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.03399 | −0.783373 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.550031 | 0.133402 | 0.0667010 | − | 0.997773i | \(-0.478753\pi\) | ||||
0.0667010 | + | 0.997773i | \(0.478753\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.258962 | −0.0594100 | −0.0297050 | − | 0.999559i | \(-0.509457\pi\) | ||||
−0.0297050 | + | 0.999559i | \(0.509457\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.62722 | 0.573306 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.92701 | −1.65290 | −0.826448 | − | 0.563013i | \(-0.809642\pi\) | ||||
−0.826448 | + | 0.563013i | \(0.809642\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.72427 | 1.87144 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.36210 | 1.73850 | 0.869250 | − | 0.494374i | \(-0.164602\pi\) | ||||
0.869250 | + | 0.494374i | \(0.164602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.31588 | 0.954760 | 0.477380 | − | 0.878697i | \(-0.341587\pi\) | ||||
0.477380 | + | 0.878697i | \(0.341587\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.865927 | −0.146368 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.38739 | 1.05008 | 0.525040 | − | 0.851077i | \(-0.324050\pi\) | ||||
0.525040 | + | 0.851077i | \(0.324050\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.4560 | 2.15469 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.74218 | −1.36530 | −0.682650 | − | 0.730746i | \(-0.739173\pi\) | ||||
−0.682650 | + | 0.730746i | \(0.739173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.38622 | 0.973890 | 0.486945 | − | 0.873433i | \(-0.338111\pi\) | ||||
0.486945 | + | 0.873433i | \(0.338111\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.20511 | −0.925003 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.823208 | −0.120077 | −0.0600386 | − | 0.998196i | \(-0.519122\pi\) | ||||
−0.0600386 | + | 0.998196i | \(0.519122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.25017 | −0.892881 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.66879 | 0.233677 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.40110 | 0.329816 | 0.164908 | − | 0.986309i | \(-0.447267\pi\) | ||||
0.164908 | + | 0.986309i | \(0.447267\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.785690 | −0.104067 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.5148 | 1.75948 | 0.879741 | − | 0.475453i | \(-0.157716\pi\) | ||||
0.879741 | + | 0.475453i | \(0.157716\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.60761 | 0.846018 | 0.423009 | − | 0.906126i | \(-0.360974\pi\) | ||||
0.423009 | + | 0.906126i | \(0.360974\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.37317 | 0.676956 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.43509 | −0.550105 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.17725 | −0.876840 | −0.438420 | − | 0.898770i | \(-0.644462\pi\) | ||||
−0.438420 | + | 0.898770i | \(0.644462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −24.0505 | −2.89534 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.79910 | −0.332192 | −0.166096 | − | 0.986110i | \(-0.553116\pi\) | ||||
−0.166096 | + | 0.986110i | \(0.553116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.89074 | 0.338335 | 0.169168 | − | 0.985587i | \(-0.445892\pi\) | ||||
0.169168 | + | 0.985587i | \(0.445892\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.03399 | 0.350335 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.91452 | −0.665436 | −0.332718 | − | 0.943026i | \(-0.607966\pi\) | ||||
−0.332718 | + | 0.943026i | \(0.607966\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.8880 | 1.20978 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.09821 | −0.779129 | −0.389565 | − | 0.920999i | \(-0.627375\pi\) | ||||
−0.389565 | + | 0.920999i | \(0.627375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.550031 | −0.0596592 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28.4046 | 3.04529 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.6470 | −1.76458 | −0.882291 | − | 0.470704i | \(-0.844000\pi\) | ||||
−0.882291 | + | 0.470704i | \(0.844000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.84047 | 0.402590 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.1283 | 1.67243 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.258962 | 0.0265690 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.83395 | −0.795417 | −0.397708 | − | 0.917512i | \(-0.630194\pi\) | ||||
−0.397708 | + | 0.917512i | \(0.630194\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.1989 | 1.81086 | 0.905431 | − | 0.424493i | \(-0.139548\pi\) | ||||
0.905431 | + | 0.424493i | \(0.139548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8025 | −1.16294 | −0.581469 | − | 0.813569i | \(-0.697522\pi\) | ||||
−0.581469 | + | 0.813569i | \(0.697522\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.62722 | −0.256390 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.520965 | −0.0503636 | −0.0251818 | − | 0.999683i | \(-0.508016\pi\) | ||||
−0.0251818 | + | 0.999683i | \(0.508016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.22545 | 0.596290 | 0.298145 | − | 0.954521i | \(-0.403632\pi\) | ||||
0.298145 | + | 0.954521i | \(0.403632\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.3793 | 1.83940 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.87578 | −0.929035 | −0.464518 | − | 0.885564i | \(-0.653772\pi\) | ||||
−0.464518 | + | 0.885564i | \(0.653772\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.92701 | 0.739198 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 27.5202 | 2.54425 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.476287 | 0.0436611 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.5237 | −2.39156 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.71934 | 0.330038 | 0.165019 | − | 0.986290i | \(-0.447231\pi\) | ||||
0.165019 | + | 0.986290i | \(0.447231\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.3758 | 1.70594 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.4259 | 1.78462 | 0.892308 | − | 0.451426i | \(-0.149085\pi\) | ||||
0.892308 | + | 0.451426i | \(0.149085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.224243 | −0.0194443 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.72427 | −0.836932 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.4216 | 1.14669 | 0.573344 | − | 0.819315i | \(-0.305646\pi\) | ||||
0.573344 | + | 0.819315i | \(0.305646\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0856 | 1.19473 | 0.597364 | − | 0.801970i | \(-0.296215\pi\) | ||||
0.597364 | + | 0.801970i | \(0.296215\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.49761 | −0.210336 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.36210 | −0.777480 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.9630 | −1.56404 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.79173 | −0.146784 | −0.0733920 | − | 0.997303i | \(-0.523382\pi\) | ||||
−0.0733920 | + | 0.997303i | \(0.523382\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0871 | 1.55328 | 0.776641 | − | 0.629943i | \(-0.216922\pi\) | ||||
0.776641 | + | 0.629943i | \(0.216922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.41300 | 0.275925 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.31588 | −0.426982 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.78753 | 0.781130 | 0.390565 | − | 0.920575i | \(-0.372280\pi\) | ||||
0.390565 | + | 0.920575i | \(0.372280\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.28492 | 0.577732 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.86422 | −0.540976 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.396843 | −0.0310831 | −0.0155416 | − | 0.999879i | \(-0.504947\pi\) | ||||
−0.0155416 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.9140 | 1.07670 | 0.538349 | − | 0.842722i | \(-0.319048\pi\) | ||||
0.538349 | + | 0.842722i | \(0.319048\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.67004 | 0.513080 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.60689 | −0.122882 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.33390 | −0.405529 | −0.202765 | − | 0.979228i | \(-0.564993\pi\) | ||||
−0.202765 | + | 0.979228i | \(0.564993\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.865927 | 0.0654580 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 41.0039 | 3.08204 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.63478 | −0.570650 | −0.285325 | − | 0.958431i | \(-0.592102\pi\) | ||||
−0.285325 | + | 0.958431i | \(0.592102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.30453 | 0.0969647 | 0.0484824 | − | 0.998824i | \(-0.484562\pi\) | ||||
0.0484824 | + | 0.998824i | \(0.484562\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.0474 | 1.48195 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.38739 | −0.469610 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.42052 | 0.612502 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.0833 | −1.81497 | −0.907483 | − | 0.420088i | \(-0.861999\pi\) | ||||
−0.907483 | + | 0.420088i | \(0.861999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.9561 | 1.43647 | 0.718235 | − | 0.695801i | \(-0.244950\pi\) | ||||
0.718235 | + | 0.695801i | \(0.244950\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.4560 | −0.963607 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.31088 | 0.0933960 | 0.0466980 | − | 0.998909i | \(-0.485130\pi\) | ||||
0.0466980 | + | 0.998909i | \(0.485130\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.99115 | 0.353813 | 0.176907 | − | 0.984228i | \(-0.443391\pi\) | ||||
0.176907 | + | 0.984228i | \(0.443391\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.7757 | −1.53594 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.10690 | 0.568993 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.74218 | 0.610581 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −49.1880 | −3.41880 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.41108 | −0.441357 | −0.220678 | − | 0.975347i | \(-0.570827\pi\) | ||||
−0.220678 | + | 0.975347i | \(0.570827\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.49245 | −0.581893 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.38622 | −0.435537 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.60316 | 0.312483 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.77047 | 0.592654 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.43944 | 0.164094 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.8484 | 0.994321 | 0.497160 | − | 0.867659i | \(-0.334376\pi\) | ||||
0.497160 | + | 0.867659i | \(0.334376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.20511 | 0.413674 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.4761 | −1.55816 | −0.779081 | − | 0.626923i | \(-0.784314\pi\) | ||||
−0.779081 | + | 0.626923i | \(0.784314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6330 | 1.29739 | 0.648693 | − | 0.761050i | \(-0.275316\pi\) | ||||
0.648693 | + | 0.761050i | \(0.275316\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.9946 | −1.37541 | −0.687703 | − | 0.725993i | \(-0.741381\pi\) | ||||
−0.687703 | + | 0.725993i | \(0.741381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.823208 | 0.0537002 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.9446 | −1.16563 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.8533 | −1.21952 | −0.609761 | − | 0.792586i | \(-0.708734\pi\) | ||||
−0.609761 | + | 0.792586i | \(0.708734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8318 | 0.890987 | 0.445494 | − | 0.895285i | \(-0.353028\pi\) | ||||
0.445494 | + | 0.895285i | \(0.353028\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.86143 | 0.247711 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.25017 | 0.399309 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.14852 | −0.0730787 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.5359 | −1.36478 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2719 | −0.963956 | −0.481978 | − | 0.876183i | \(-0.660081\pi\) | ||||
−0.481978 | + | 0.876183i | \(0.660081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.66879 | −0.104504 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.7880 | 1.79575 | 0.897873 | − | 0.440254i | \(-0.145112\pi\) | ||||
0.897873 | + | 0.440254i | \(0.145112\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.53101 | 0.343681 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 58.0929 | 3.59586 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.23218 | −0.569281 | −0.284640 | − | 0.958634i | \(-0.591874\pi\) | ||||
−0.284640 | + | 0.958634i | \(0.591874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.40110 | −0.147498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −50.5070 | −3.09098 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.8324 | 1.63600 | 0.817999 | − | 0.575220i | \(-0.195084\pi\) | ||||
0.817999 | + | 0.575220i | \(0.195084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.5612 | 1.43124 | 0.715620 | − | 0.698490i | \(-0.246144\pi\) | ||||
0.715620 | + | 0.698490i | \(0.246144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.6519 | 0.705208 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.99241 | −0.600386 | −0.300193 | − | 0.953879i | \(-0.597051\pi\) | ||||
−0.300193 | + | 0.953879i | \(0.597051\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 32.9856 | 1.97480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.09042 | −0.244014 | −0.122007 | − | 0.992529i | \(-0.538933\pi\) | ||||
−0.122007 | + | 0.992529i | \(0.538933\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.77268 | 0.283706 | 0.141853 | − | 0.989888i | \(-0.454694\pi\) | ||||
0.141853 | + | 0.989888i | \(0.454694\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.785690 | 0.0465402 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.57010 | −0.446849 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6975 | −0.982204 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.7681 | −1.39331 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.144012 | −0.00841327 | −0.00420664 | − | 0.999991i | \(-0.501339\pi\) | ||||
−0.00420664 | + | 0.999991i | \(0.501339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.5148 | −0.786864 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −35.1570 | −2.03318 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.53001 | 0.318744 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 55.2154 | 3.17204 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.60761 | −0.378351 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.7576 | −1.47006 | −0.735031 | − | 0.678034i | \(-0.762832\pi\) | ||||
−0.735031 | + | 0.678034i | \(0.762832\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −35.8088 | −2.03709 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3915 | −0.929475 | −0.464738 | − | 0.885448i | \(-0.653851\pi\) | ||||
−0.464738 | + | 0.885448i | \(0.653851\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.5238 | 1.49921 | 0.749606 | − | 0.661885i | \(-0.230243\pi\) | ||||
0.749606 | + | 0.661885i | \(0.230243\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.37317 | −0.302744 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.7158 | 0.938852 | 0.469426 | − | 0.882972i | \(-0.344461\pi\) | ||||
0.469426 | + | 0.882972i | \(0.344461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.58060 | −0.0882206 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.142437 | −0.00792542 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.43509 | 0.246015 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.8880 | 1.04451 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.712839 | −0.0393001 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.39584 | −0.241617 | −0.120809 | − | 0.992676i | \(-0.538549\pi\) | ||||
−0.120809 | + | 0.992676i | \(0.538549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 39.6344 | 2.17195 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.17725 | 0.392135 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.6035 | −0.686558 | −0.343279 | − | 0.939233i | \(-0.611538\pi\) | ||||
−0.343279 | + | 0.939233i | \(0.611538\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −29.9630 | −1.62737 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4737 | −0.619521 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.0505 | 1.29484 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.9827 | −1.28746 | −0.643731 | − | 0.765252i | \(-0.722614\pi\) | ||||
−0.643731 | + | 0.765252i | \(0.722614\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.5901 | −1.26275 | −0.631376 | − | 0.775477i | \(-0.717509\pi\) | ||||
−0.631376 | + | 0.775477i | \(0.717509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 43.1281 | 2.30201 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.46751 | 0.344231 | 0.172115 | − | 0.985077i | \(-0.444940\pi\) | ||||
0.172115 | + | 0.985077i | \(0.444940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.79910 | 0.148561 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.44505 | 0.0764802 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.8241 | 0.624053 | 0.312026 | − | 0.950073i | \(-0.398992\pi\) | ||||
0.312026 | + | 0.950073i | \(0.398992\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9329 | −0.996470 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.89074 | −0.151308 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.38713 | −0.437805 | −0.218902 | − | 0.975747i | \(-0.570248\pi\) | ||||
−0.218902 | + | 0.975747i | \(0.570248\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −54.2462 | −2.82394 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.07918 | 0.107946 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.6263 | −1.79288 | −0.896441 | − | 0.443163i | \(-0.853856\pi\) | ||||
−0.896441 | + | 0.443163i | \(0.853856\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.03399 | −0.156675 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.5218 | 2.13848 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0726 | −0.825592 | −0.412796 | − | 0.910823i | \(-0.635448\pi\) | ||||
−0.412796 | + | 0.910823i | \(0.635448\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.2844 | 0.578120 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.41569 | −0.430022 | −0.215011 | − | 0.976612i | \(-0.568979\pi\) | ||||
−0.215011 | + | 0.976612i | \(0.568979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 39.6272 | 2.01436 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.5917 | 0.942636 | 0.471318 | − | 0.881963i | \(-0.343778\pi\) | ||||
0.471318 | + | 0.881963i | \(0.343778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.36010 | −0.220500 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 61.9719 | 3.12607 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.91452 | 0.297592 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.9897 | −0.601743 | −0.300872 | − | 0.953665i | \(-0.597278\pi\) | ||||
−0.300872 | + | 0.953665i | \(0.597278\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.680350 | −0.0340601 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.7991 | 0.938781 | 0.469391 | − | 0.882991i | \(-0.344474\pi\) | ||||
0.469391 | + | 0.882991i | \(0.344474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.5764 | 1.17442 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.8880 | −0.541031 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.50429 | 0.469957 | 0.234978 | − | 0.972001i | \(-0.424498\pi\) | ||||
0.234978 | + | 0.972001i | \(0.424498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 40.7211 | 2.00863 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.7029 | 0.575860 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.09821 | 0.348437 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 42.7357 | 2.09278 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.9152 | −1.60801 | −0.804007 | − | 0.594620i | \(-0.797302\pi\) | ||||
−0.804007 | + | 0.594620i | \(0.797302\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.03559 | −0.0504717 | −0.0252359 | − | 0.999682i | \(-0.508034\pi\) | ||||
−0.0252359 | + | 0.999682i | \(0.508034\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.10810 | −0.248364 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.550031 | 0.0266804 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.72171 | 0.276893 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.7613 | 1.24088 | 0.620439 | − | 0.784255i | \(-0.286954\pi\) | ||||
0.620439 | + | 0.784255i | \(0.286954\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4406 | −0.886201 | −0.443100 | − | 0.896472i | \(-0.646121\pi\) | ||||
−0.443100 | + | 0.896472i | \(0.646121\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −28.4046 | −1.36189 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.05280 | 0.0981986 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.44724 | −0.212255 | −0.106128 | − | 0.994353i | \(-0.533845\pi\) | ||||
−0.106128 | + | 0.994353i | \(0.533845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −38.7830 | −1.84681 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.0738 | 1.19129 | 0.595646 | − | 0.803247i | \(-0.296896\pi\) | ||||
0.595646 | + | 0.803247i | \(0.296896\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.6470 | 0.789145 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.43609 | −0.257118 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.6745 | −0.881306 | −0.440653 | − | 0.897678i | \(-0.645253\pi\) | ||||
−0.440653 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 57.9100 | 2.72085 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.84047 | −0.180044 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5569 | 0.680941 | 0.340471 | − | 0.940255i | \(-0.389414\pi\) | ||||
0.340471 | + | 0.940255i | \(0.389414\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.34865 | 0.249654 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.6525 | −0.961884 | −0.480942 | − | 0.876752i | \(-0.659705\pi\) | ||||
−0.480942 | + | 0.876752i | \(0.659705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.8605 | 1.01594 | 0.507971 | − | 0.861374i | \(-0.330396\pi\) | ||||
0.507971 | + | 0.861374i | \(0.330396\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.1283 | −0.747933 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.2984 | −0.939296 | −0.469648 | − | 0.882854i | \(-0.655619\pi\) | ||||
−0.469648 | + | 0.882854i | \(0.655619\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.21498 | −0.286981 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.6953 | 1.36829 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.258962 | −0.0118820 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.8991 | 0.682182 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.89152 | −0.451955 | −0.225978 | − | 0.974132i | \(-0.572558\pi\) | ||||
−0.225978 | + | 0.974132i | \(0.572558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.3287 | 1.29168 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.8260 | −0.947615 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.83395 | 0.355721 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.93879 | −0.269112 | −0.134556 | − | 0.990906i | \(-0.542961\pi\) | ||||
−0.134556 | + | 0.990906i | \(0.542961\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.20402 | −0.0544476 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.3348 | 1.23360 | 0.616801 | − | 0.787119i | \(-0.288428\pi\) | ||||
0.616801 | + | 0.787119i | \(0.288428\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.14945 | 0.231919 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.42382 | −0.108723 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.1678 | 0.544705 | 0.272353 | − | 0.962198i | \(-0.412198\pi\) | ||||
0.272353 | + | 0.962198i | \(0.412198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.2150 | 1.88603 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.49180 | −0.423218 | −0.211609 | − | 0.977354i | \(-0.567870\pi\) | ||||
−0.211609 | + | 0.977354i | \(0.567870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.1989 | −0.809842 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.2369 | 0.898750 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.957696 | −0.0424491 | −0.0212246 | − | 0.999775i | \(-0.506756\pi\) | ||||
−0.0212246 | + | 0.999775i | \(0.506756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.50317 | 0.110734 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.51822 | −0.111182 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.8025 | 0.520082 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.1830 | −0.710356 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.2415 | −0.799176 | −0.399588 | − | 0.916695i | \(-0.630847\pi\) | ||||
−0.399588 | + | 0.916695i | \(0.630847\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.3274 | 1.23867 | 0.619335 | − | 0.785127i | \(-0.287402\pi\) | ||||
0.619335 | + | 0.785127i | \(0.287402\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.62722 | 0.114661 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.92390 | 0.127367 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.8375 | 1.73207 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 83.8610 | 3.63926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.7724 | −1.67942 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.520965 | 0.0225233 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.1639 | −0.999594 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7569 | 1.36534 | 0.682668 | − | 0.730729i | \(-0.260819\pi\) | ||||
0.682668 | + | 0.730729i | \(0.260819\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.95792 | 0.169851 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.22545 | −0.266669 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.58429 | 0.153253 | 0.0766265 | − | 0.997060i | \(-0.475585\pi\) | ||||
0.0766265 | + | 0.997060i | \(0.475585\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 41.0009 | 1.74988 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.42443 | −0.103284 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.12155 | −0.217790 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.3793 | −0.822605 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.6556 | 0.705719 | 0.352860 | − | 0.935676i | \(-0.385209\pi\) | ||||
0.352860 | + | 0.935676i | \(0.385209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.3235 | 1.19796 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.8978 | 1.68149 | 0.840745 | − | 0.541431i | \(-0.182117\pi\) | ||||
0.840745 | + | 0.541431i | \(0.182117\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.87578 | 0.415477 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.42826 | 0.395950 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −45.4644 | −1.90597 | −0.952983 | − | 0.303024i | \(-0.902004\pi\) | ||||
−0.952983 | + | 0.303024i | \(0.902004\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8877 | −0.664880 | −0.332440 | − | 0.943124i | \(-0.607872\pi\) | ||||
−0.332440 | + | 0.943124i | \(0.607872\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −76.1027 | −3.17923 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.92701 | −0.330579 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.1413 | −0.547078 | −0.273539 | − | 0.961861i | \(-0.588194\pi\) | ||||
−0.273539 | + | 0.961861i | \(0.588194\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 60.5466 | 2.51623 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.14653 | −0.255001 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.5202 | −1.13782 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.9640 | −0.617629 | −0.308814 | − | 0.951122i | \(-0.599932\pi\) | ||||
−0.308814 | + | 0.951122i | \(0.599932\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.37661 | −0.0567223 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.97719 | 0.163600 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.7967 | 0.566564 | 0.283282 | − | 0.959037i | \(-0.408577\pi\) | ||||
0.283282 | + | 0.959037i | \(0.408577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.476287 | −0.0195259 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.1431 | 0.619766 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.3893 | −1.28253 | −0.641267 | − | 0.767318i | \(-0.721591\pi\) | ||||
−0.641267 | + | 0.767318i | \(0.721591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.55635 | 0.104276 | 0.0521379 | − | 0.998640i | \(-0.483396\pi\) | ||||
0.0521379 | + | 0.998640i | \(0.483396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −44.5356 | −1.81363 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.8289 | −1.53543 | −0.767713 | − | 0.640794i | \(-0.778605\pi\) | ||||
−0.767713 | + | 0.640794i | \(0.778605\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.5963 | 0.996692 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.65100 | −0.147704 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6599 | −0.470940 | −0.235470 | − | 0.971882i | \(-0.575663\pi\) | ||||
−0.235470 | + | 0.971882i | \(0.575663\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.5237 | 1.06954 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.5910 | 1.55361 | 0.776807 | − | 0.629739i | \(-0.216838\pi\) | ||||
0.776807 | + | 0.629739i | \(0.216838\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.16365 | 0.328125 | 0.164062 | − | 0.986450i | \(-0.447540\pi\) | ||||
0.164062 | + | 0.986450i | \(0.447540\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −77.0844 | −3.09329 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.4151 | −0.577530 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.51326 | 0.140083 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.0813 | 0.520759 | 0.260379 | − | 0.965506i | \(-0.416152\pi\) | ||||
0.260379 | + | 0.965506i | \(0.416152\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.4512 | −0.773114 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.71934 | −0.147597 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.7201 | −1.09831 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.3687 | −0.687096 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.6499 | 1.40809 | 0.704044 | − | 0.710156i | \(-0.251376\pi\) | ||||
0.704044 | + | 0.710156i | \(0.251376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.65614 | 0.301929 | 0.150964 | − | 0.988539i | \(-0.451762\pi\) | ||||
0.150964 | + | 0.988539i | \(0.451762\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.3758 | −0.762919 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.18246 | −0.361000 | −0.180500 | − | 0.983575i | \(-0.557772\pi\) | ||||
−0.180500 | + | 0.983575i | \(0.557772\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.9660 | 0.547369 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.85282 | −0.229039 | −0.114519 | − | 0.993421i | \(-0.536533\pi\) | ||||
−0.114519 | + | 0.993421i | \(0.536533\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.4259 | −0.798105 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.9373 | 0.699802 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.6530 | −0.882434 | −0.441217 | − | 0.897400i | \(-0.645453\pi\) | ||||
−0.441217 | + | 0.897400i | \(0.645453\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.68482 | 0.0655320 | 0.0327660 | − | 0.999463i | \(-0.489568\pi\) | ||||
0.0327660 | + | 0.999463i | \(0.489568\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.40123 | 0.287440 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.224243 | 0.00869575 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −74.2135 | −2.87356 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 45.0499 | 1.74173 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.48493 | 0.365617 | 0.182809 | − | 0.983149i | \(-0.441481\pi\) | ||||
0.182809 | + | 0.983149i | \(0.441481\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.72427 | 0.374288 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.11952 | 0.158326 | 0.0791631 | − | 0.996862i | \(-0.474775\pi\) | ||||
0.0791631 | + | 0.996862i | \(0.474775\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.78363 | −0.260332 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −71.2262 | −2.72940 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.0594 | −1.11193 | −0.555963 | − | 0.831207i | \(-0.687651\pi\) | ||||
−0.555963 | + | 0.831207i | \(0.687651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.4216 | −0.512814 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 59.5664 | 2.27260 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.6491 | 0.405698 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.4633 | −0.740418 | −0.370209 | − | 0.928949i | \(-0.620714\pi\) | ||||
−0.370209 | + | 0.928949i | \(0.620714\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.0856 | −0.534298 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.80847 | −0.182134 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −63.6976 | −2.40926 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.1359 | 0.571675 | 0.285838 | − | 0.958278i | \(-0.407728\pi\) | ||||
0.285838 | + | 0.958278i | \(0.407728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.65409 | −0.0623853 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.49761 | 0.0940653 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.7590 | 0.592677 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.0377 | −1.01542 | −0.507712 | − | 0.861527i | \(-0.669508\pi\) | ||||
−0.507712 | + | 0.861527i | \(0.669508\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.7003 | −1.37637 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −42.1390 | −1.57812 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −57.2009 | −2.13621 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.74967 | −0.139839 | −0.0699195 | − | 0.997553i | \(-0.522274\pi\) | ||||
−0.0699195 | + | 0.997553i | \(0.522274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2201 | −0.380618 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 41.9657 | 1.56072 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.36210 | 0.347700 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.5685 | −1.69004 | −0.845022 | − | 0.534732i | \(-0.820413\pi\) | ||||
−0.845022 | + | 0.534732i | \(0.820413\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.9486 | −0.775874 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.51262 | 0.129919 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.1793 | 1.37325 | 0.686625 | − | 0.727012i | \(-0.259091\pi\) | ||||
0.686625 | + | 0.727012i | \(0.259091\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.9630 | 0.699460 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.86380 | −0.142132 | −0.0710661 | − | 0.997472i | \(-0.522640\pi\) | ||||
−0.0710661 | + | 0.997472i | \(0.522640\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.48461 | −0.128010 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.73510 | −0.283773 | −0.141887 | − | 0.989883i | \(-0.545317\pi\) | ||||
−0.141887 | + | 0.989883i | \(0.545317\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.79173 | 0.0656438 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −44.0451 | −1.61153 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.451118 | −0.0164835 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.7386 | 0.720271 | 0.360135 | − | 0.932900i | \(-0.382731\pi\) | ||||
0.360135 | + | 0.932900i | \(0.382731\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −46.3349 | −1.68854 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.0871 | −0.694649 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.5828 | 0.384637 | 0.192319 | − | 0.981333i | \(-0.438399\pi\) | ||||
0.192319 | + | 0.981333i | \(0.438399\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.6698 | −1.83678 | −0.918390 | − | 0.395677i | \(-0.870510\pi\) | ||||
−0.918390 | + | 0.395677i | \(0.870510\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.39079 | 0.195160 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.41300 | −0.123397 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 59.9395 | 2.16429 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.2588 | 0.586306 | 0.293153 | − | 0.956066i | \(-0.405295\pi\) | ||||
0.293153 | + | 0.956066i | \(0.405295\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 87.3426 | 3.14557 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.4897 | 0.593095 | 0.296547 | − | 0.955018i | \(-0.404165\pi\) | ||||
0.296547 | + | 0.955018i | \(0.404165\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.31588 | 0.190952 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.7811 | 0.602017 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.26390 | 0.0811125 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 91.0397 | 3.25349 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.78753 | −0.349332 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.7184 | 0.916762 | 0.458381 | − | 0.888756i | \(-0.348430\pi\) | ||||
0.458381 | + | 0.888756i | \(0.348430\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.0104 | −0.997196 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.55171 | −0.304064 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.3054 | 1.04066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.28492 | −0.258369 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.59752 | 0.198274 | 0.0991372 | − | 0.995074i | \(-0.468392\pi\) | ||||
0.0991372 | + | 0.995074i | \(0.468392\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.452790 | −0.0160186 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −103.297 | −3.64981 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.86422 | 0.241932 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 81.4092 | 2.86574 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.6788 | −0.691871 | −0.345936 | − | 0.938258i | \(-0.612438\pi\) | ||||
−0.345936 | + | 0.938258i | \(0.612438\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.41499 | −0.260375 | −0.130188 | − | 0.991489i | \(-0.541558\pi\) | ||||
−0.130188 | + | 0.991489i | \(0.541558\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 71.4844 | 2.50707 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.396843 | 0.0139008 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.65379 | −0.0578588 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 23.8305 | 0.832706 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.30773 | 0.185241 | 0.0926205 | − | 0.995701i | \(-0.470476\pi\) | ||||
0.0926205 | + | 0.995701i | \(0.470476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.1952 | 0.564528 | 0.282264 | − | 0.959337i | \(-0.408915\pi\) | ||||
0.282264 | + | 0.959337i | \(0.408915\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.97372 | −0.346820 | −0.173410 | − | 0.984850i | \(-0.555479\pi\) | ||||
−0.173410 | + | 0.984850i | \(0.555479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.4859 | −0.919893 | −0.459947 | − | 0.887947i | \(-0.652131\pi\) | ||||
−0.459947 | + | 0.887947i | \(0.652131\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.3169 | −1.05168 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.43779 | −0.119112 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.9140 | −0.481514 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 51.6931 | 1.78677 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0591 | −0.830613 | −0.415307 | − | 0.909681i | \(-0.636326\pi\) | ||||
−0.415307 | + | 0.909681i | \(0.636326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.6490 | 2.02238 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.4103 | −0.427433 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.67004 | −0.229456 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.4803 | 0.496962 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.6329 | −1.73567 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.5471 | −0.771997 | −0.385999 | − | 0.922499i | \(-0.626143\pi\) | ||||
−0.385999 | + | 0.922499i | \(0.626143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.60689 | 0.0549545 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.0453 | −0.343143 | −0.171571 | − | 0.985172i | \(-0.554884\pi\) | ||||
−0.171571 | + | 0.985172i | \(0.554884\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.7921 | −0.538819 | −0.269409 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269409 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.9676 | −0.782734 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.6412 | 0.770717 | 0.385358 | − | 0.922767i | \(-0.374078\pi\) | ||||
0.385358 | + | 0.922767i | \(0.374078\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.33390 | 0.181358 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −50.6600 | −1.72050 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.8318 | −1.07858 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −48.6105 | −1.64522 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.865927 | −0.0292737 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.7591 | −0.802288 | −0.401144 | − | 0.916015i | \(-0.631387\pi\) | ||||
−0.401144 | + | 0.916015i | \(0.631387\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.436931 | −0.0147373 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.6772 | −0.730323 | −0.365161 | − | 0.930944i | \(-0.618986\pi\) | ||||
−0.365161 | + | 0.930944i | \(0.618986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.6198 | 1.36697 | 0.683483 | − | 0.729967i | \(-0.260465\pi\) | ||||
0.683483 | + | 0.729967i | \(0.260465\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −41.0039 | −1.37833 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.1509 | 1.14668 | 0.573338 | − | 0.819319i | \(-0.305648\pi\) | ||||
0.573338 | + | 0.819319i | \(0.305648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.22068 | 0.108018 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.213180 | 0.00713379 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.63478 | 0.255202 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −106.666 | −3.56148 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 49.7678 | 1.65985 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.32068 | 0.0439982 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.7780 | 0.558337 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.30453 | −0.0433639 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.5541 | −0.383647 | −0.191824 | − | 0.981429i | \(-0.561440\pi\) | ||||
−0.191824 | + | 0.981429i | \(0.561440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 112.926 | 3.74553 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4057 | 0.477284 | 0.238642 | − | 0.971108i | \(-0.423298\pi\) | ||||
0.238642 | + | 0.971108i | \(0.423298\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.0474 | −0.662748 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.6873 | 0.584087 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.1155 | −1.62017 | −0.810085 | − | 0.586312i | \(-0.800579\pi\) | ||||
−0.810085 | + | 0.586312i | \(0.800579\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −78.1482 | −2.57507 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.4143 | −0.408621 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.38739 | 0.210016 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −73.2360 | −2.40539 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.9888 | 0.787048 | 0.393524 | − | 0.919314i | \(-0.371256\pi\) | ||||
0.393524 | + | 0.919314i | \(0.371256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.61856 | 0.0530461 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −49.7316 | −1.62814 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.1022 | −0.428029 | −0.214014 | − | 0.976831i | \(-0.568654\pi\) | ||||
−0.214014 | + | 0.976831i | \(0.568654\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 80.4729 | 2.62613 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.6826 | 1.19582 | 0.597909 | − | 0.801564i | \(-0.295998\pi\) | ||||
0.597909 | + | 0.801564i | \(0.295998\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 69.2994 | 2.25670 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.42052 | −0.273919 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.6112 | −0.669774 | −0.334887 | − | 0.942258i | \(-0.608698\pi\) | ||||
−0.334887 | + | 0.942258i | \(0.608698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.8207 | 0.416177 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.7156 | 1.64457 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.7949 | −0.576433 | −0.288216 | − | 0.957565i | \(-0.593062\pi\) | ||||
−0.288216 | + | 0.957565i | \(0.593062\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.0833 | 0.811678 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.6222 | 0.375299 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.74144 | −0.0884337 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.23264 | −0.104170 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.9561 | −0.642409 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.828077 | −0.0266292 | −0.0133146 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133146 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.432154 | −0.0138828 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.124535 | 0.00399653 | 0.00199827 | − | 0.999998i | \(-0.499364\pi\) | ||||
0.00199827 | + | 0.999998i | \(0.499364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.1971 | 0.391022 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.4560 | 0.430938 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.4664 | −0.686770 | −0.343385 | − | 0.939195i | \(-0.611573\pi\) | ||||
−0.343385 | + | 0.939195i | \(0.611573\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.6296 | 1.23335 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.7566 | −1.01288 | −0.506440 | − | 0.862275i | \(-0.669039\pi\) | ||||
−0.506440 | + | 0.862275i | \(0.669039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.31088 | −0.0417680 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.16275 | −0.0688410 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50.6237 | −1.60974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.7101 | −1.48379 | −0.741897 | − | 0.670514i | \(-0.766074\pi\) | ||||
−0.741897 | + | 0.670514i | \(0.766074\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.3370 | −0.423236 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.99115 | −0.158230 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.6548 | −1.63592 | −0.817962 | − | 0.575273i | \(-0.804896\pi\) | ||||
−0.817962 | + | 0.575273i | \(0.804896\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 62.1127 | 1.96516 |
(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 | 9680.2.a.cy.1.6 | 6 | ||
4.3 | odd | 2 | 4840.2.a.be.1.1 | 6 | |||
11.7 | odd | 10 | 880.2.bo.j.401.1 | 12 | |||
11.8 | odd | 10 | 880.2.bo.j.801.1 | 12 | |||
11.10 | odd | 2 | 9680.2.a.cx.1.6 | 6 | |||
44.7 | even | 10 | 440.2.y.b.401.3 | yes | 12 | ||
44.19 | even | 10 | 440.2.y.b.361.3 | ✓ | 12 | ||
44.43 | even | 2 | 4840.2.a.bf.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.b.361.3 | ✓ | 12 | 44.19 | even | 10 | ||
440.2.y.b.401.3 | yes | 12 | 44.7 | even | 10 | ||
880.2.bo.j.401.1 | 12 | 11.7 | odd | 10 | |||
880.2.bo.j.801.1 | 12 | 11.8 | odd | 10 | |||
4840.2.a.be.1.1 | 6 | 4.3 | odd | 2 | |||
4840.2.a.bf.1.1 | 6 | 44.43 | even | 2 | |||
9680.2.a.cx.1.6 | 6 | 11.10 | odd | 2 | |||
9680.2.a.cy.1.6 | 6 | 1.1 | even | 1 | trivial |