Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.56310016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} + 14x^{2} - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.608430\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | ||||||||
\(3\) | −3.28715 | −1.89784 | −0.948919 | − | 0.315521i | \(-0.897821\pi\) | ||||
−0.948919 | + | 0.315521i | \(0.897821\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.93210 | 0.730263 | 0.365132 | − | 0.930956i | \(-0.381024\pi\) | ||||
0.365132 | + | 0.930956i | \(0.381024\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.80536 | 2.60179 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.62981 | −1.69745 | −0.848726 | − | 0.528832i | \(-0.822630\pi\) | ||||
−0.848726 | + | 0.528832i | \(0.822630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.07029 | −0.574195 | −0.287098 | − | 0.957901i | \(-0.592690\pi\) | ||||
−0.287098 | + | 0.957901i | \(0.592690\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.42535 | 0.830768 | 0.415384 | − | 0.909646i | \(-0.363647\pi\) | ||||
0.415384 | + | 0.909646i | \(0.363647\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.35109 | −1.38592 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.35744 | 1.11710 | 0.558552 | − | 0.829470i | \(-0.311357\pi\) | ||||
0.558552 | + | 0.829470i | \(0.311357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15.7959 | −3.03993 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.09146 | 0.202679 | 0.101340 | − | 0.994852i | \(-0.467687\pi\) | ||||
0.101340 | + | 0.994852i | \(0.467687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.09146 | −0.555243 | −0.277622 | − | 0.960691i | \(-0.589546\pi\) | ||||
−0.277622 | + | 0.960691i | \(0.589546\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.5060 | 3.22149 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.28715 | 0.540404 | 0.270202 | − | 0.962804i | \(-0.412909\pi\) | ||||
0.270202 | + | 0.962804i | \(0.412909\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.80536 | 1.08973 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.6107 | −1.81329 | −0.906645 | − | 0.421895i | \(-0.861365\pi\) | ||||
−0.906645 | + | 0.421895i | \(0.861365\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.501623 | 0.0764968 | 0.0382484 | − | 0.999268i | \(-0.487822\pi\) | ||||
0.0382484 | + | 0.999268i | \(0.487822\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.6470 | 1.84475 | 0.922376 | − | 0.386294i | \(-0.126245\pi\) | ||||
0.922376 | + | 0.386294i | \(0.126245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.26701 | −0.466715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.2596 | −1.57666 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.01076 | 0.413560 | 0.206780 | − | 0.978388i | \(-0.433702\pi\) | ||||
0.206780 | + | 0.978388i | \(0.433702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.28715 | 0.435394 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.35109 | 0.306086 | 0.153043 | − | 0.988220i | \(-0.451093\pi\) | ||||
0.153043 | + | 0.988220i | \(0.451093\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.62981 | 0.976897 | 0.488449 | − | 0.872593i | \(-0.337563\pi\) | ||||
0.488449 | + | 0.872593i | \(0.337563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.0807 | 1.89999 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2324 | −1.49442 | −0.747212 | − | 0.664585i | \(-0.768608\pi\) | ||||
−0.747212 | + | 0.664585i | \(0.768608\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17.6107 | −2.12008 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.3511 | −1.70316 | −0.851580 | − | 0.524224i | \(-0.824355\pi\) | ||||
−0.851580 | + | 0.524224i | \(0.824355\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.87256 | −0.336208 | −0.168104 | − | 0.985769i | \(-0.553764\pi\) | ||||
−0.168104 | + | 0.985769i | \(0.553764\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.8773 | −1.23959 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 28.5075 | 3.16750 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.35744 | −0.588056 | −0.294028 | − | 0.955797i | \(-0.594996\pi\) | ||||
−0.294028 | + | 0.955797i | \(0.594996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.58780 | −0.384653 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.35109 | 0.885214 | 0.442607 | − | 0.896716i | \(-0.354054\pi\) | ||||
0.442607 | + | 0.896716i | \(0.354054\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.1621 | 1.05376 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.01076 | 0.305696 | 0.152848 | − | 0.988250i | \(-0.451155\pi\) | ||||
0.152848 | + | 0.988250i | \(0.451155\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −43.9427 | −4.41641 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.80536 | −0.478151 | −0.239075 | − | 0.971001i | \(-0.576844\pi\) | ||||
−0.239075 | + | 0.971001i | \(0.576844\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.22762 | 0.416560 | 0.208280 | − | 0.978069i | \(-0.433214\pi\) | ||||
0.208280 | + | 0.978069i | \(0.433214\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.92098 | 0.862424 | 0.431212 | − | 0.902251i | \(-0.358086\pi\) | ||||
0.431212 | + | 0.902251i | \(0.358086\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.25963 | 0.503781 | 0.251890 | − | 0.967756i | \(-0.418948\pi\) | ||||
0.251890 | + | 0.967756i | \(0.418948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.8054 | −1.02560 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5088 | −1.17673 | −0.588364 | − | 0.808596i | \(-0.700228\pi\) | ||||
−0.588364 | + | 0.808596i | \(0.700228\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.1594 | −1.49393 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.61810 | 0.606680 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.6948 | 1.88135 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 38.1662 | 3.44133 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2952 | 1.09102 | 0.545510 | − | 0.838104i | \(-0.316336\pi\) | ||||
0.545510 | + | 0.838104i | \(0.316336\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.64891 | −0.145179 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7863 | 0.942400 | 0.471200 | − | 0.882026i | \(-0.343821\pi\) | ||||
0.471200 | + | 0.882026i | \(0.343821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.93210 | −0.167534 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.85582 | 0.414861 | 0.207430 | − | 0.978250i | \(-0.433490\pi\) | ||||
0.207430 | + | 0.978250i | \(0.433490\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2405 | 0.953409 | 0.476705 | − | 0.879064i | \(-0.341831\pi\) | ||||
0.476705 | + | 0.879064i | \(0.341831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −41.5725 | −3.50104 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.6554 | 0.974669 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7391 | 0.885750 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.62981 | 0.297366 | 0.148683 | − | 0.988885i | \(-0.452497\pi\) | ||||
0.148683 | + | 0.988885i | \(0.452497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3511 | 0.842360 | 0.421180 | − | 0.906977i | \(-0.361616\pi\) | ||||
0.421180 | + | 0.906977i | \(0.361616\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 26.7360 | 2.16148 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.12708 | −0.568803 | −0.284402 | − | 0.958705i | \(-0.591795\pi\) | ||||
−0.284402 | + | 0.958705i | \(0.591795\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.89682 | −0.784869 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3511 | 0.815780 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.21686 | 0.0953118 | 0.0476559 | − | 0.998864i | \(-0.484825\pi\) | ||||
0.0476559 | + | 0.998864i | \(0.484825\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8830 | 1.22906 | 0.614531 | − | 0.788893i | \(-0.289345\pi\) | ||||
0.614531 | + | 0.788893i | \(0.289345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.71390 | −0.670300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.80536 | −0.596891 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.7884 | 1.04831 | 0.524157 | − | 0.851622i | \(-0.324380\pi\) | ||||
0.524157 | + | 0.851622i | \(0.324380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.72838 | −0.580901 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.3511 | −0.773677 | −0.386838 | − | 0.922148i | \(-0.626433\pi\) | ||||
−0.386838 | + | 0.922148i | \(0.626433\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.0803 | −1.85399 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.2841 | −1.41019 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −30.5193 | −2.21995 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.43517 | 0.610348 | 0.305174 | − | 0.952297i | \(-0.401285\pi\) | ||||
0.305174 | + | 0.952297i | \(0.401285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.2864 | −1.67619 | −0.838097 | − | 0.545521i | \(-0.816332\pi\) | ||||
−0.838097 | + | 0.545521i | \(0.816332\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.28116 | 0.590008 | 0.295004 | − | 0.955496i | \(-0.404679\pi\) | ||||
0.295004 | + | 0.955496i | \(0.404679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7863 | 1.33172 | 0.665861 | − | 0.746076i | \(-0.268064\pi\) | ||||
0.665861 | + | 0.746076i | \(0.268064\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 40.2097 | 2.83617 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.10881 | 0.148009 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 41.8167 | 2.90646 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.62981 | 0.389422 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.7789 | 1.49932 | 0.749660 | − | 0.661823i | \(-0.230217\pi\) | ||||
0.749660 | + | 0.661823i | \(0.230217\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 47.1742 | 3.23232 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.97300 | −0.405474 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.44255 | 0.638068 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.09146 | −0.477023 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.5548 | 0.974662 | 0.487331 | − | 0.873217i | \(-0.337970\pi\) | ||||
0.487331 | + | 0.873217i | \(0.337970\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.07029 | 0.137410 | 0.0687050 | − | 0.997637i | \(-0.478113\pi\) | ||||
0.0687050 | + | 0.997637i | \(0.478113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.4616 | −1.02173 | −0.510867 | − | 0.859660i | \(-0.670676\pi\) | ||||
−0.510867 | + | 0.859660i | \(0.670676\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 35.7554 | 2.35254 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.8934 | −1.89287 | −0.946434 | − | 0.322897i | \(-0.895343\pi\) | ||||
−0.946434 | + | 0.322897i | \(0.895343\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.1486 | 0.854093 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.6181 | −1.72178 | −0.860891 | − | 0.508790i | \(-0.830093\pi\) | ||||
−0.860891 | + | 0.508790i | \(0.830093\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6107 | −1.26324 | −0.631619 | − | 0.775279i | \(-0.717609\pi\) | ||||
−0.631619 | + | 0.775279i | \(0.717609\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −46.3208 | −2.97148 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.07029 | 0.131729 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.6107 | 1.11603 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.2522 | −0.899594 | −0.449797 | − | 0.893131i | \(-0.648504\pi\) | ||||
−0.449797 | + | 0.893131i | \(0.648504\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.1614 | −1.89623 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2919 | −0.704371 | −0.352185 | − | 0.935930i | \(-0.614561\pi\) | ||||
−0.352185 | + | 0.935930i | \(0.614561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.35109 | 0.394637 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.51925 | 0.527329 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.3571 | −0.946959 | −0.473479 | − | 0.880805i | \(-0.657002\pi\) | ||||
−0.473479 | + | 0.880805i | \(0.657002\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.4513 | −1.67999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.4426 | 0.697665 | 0.348832 | − | 0.937185i | \(-0.386578\pi\) | ||||
0.348832 | + | 0.937185i | \(0.386578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.4161 | −0.754223 | −0.377111 | − | 0.926168i | \(-0.623083\pi\) | ||||
−0.377111 | + | 0.926168i | \(0.623083\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.1486 | 0.795790 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0212 | 0.962619 | 0.481309 | − | 0.876551i | \(-0.340161\pi\) | ||||
0.481309 | + | 0.876551i | \(0.340161\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.1300 | −1.44462 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.8851 | −1.48452 | −0.742260 | − | 0.670112i | \(-0.766246\pi\) | ||||
−0.742260 | + | 0.670112i | \(0.766246\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.2348 | 0.965057 | 0.482529 | − | 0.875880i | \(-0.339718\pi\) | ||||
0.482529 | + | 0.875880i | \(0.339718\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.4330 | −1.32418 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.26701 | −0.309824 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.89682 | −0.580162 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.2864 | −1.36041 | −0.680204 | − | 0.733023i | \(-0.738109\pi\) | ||||
−0.680204 | + | 0.733023i | \(0.738109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 88.9282 | 5.16013 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.0915 | −0.641436 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.969184 | 0.0558628 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.7959 | 0.907453 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.964728 | 0.0550599 | 0.0275300 | − | 0.999621i | \(-0.491236\pi\) | ||||
0.0275300 | + | 0.999621i | \(0.491236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.8968 | −0.790562 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.1638 | −1.02998 | −0.514988 | − | 0.857197i | \(-0.672204\pi\) | ||||
−0.514988 | + | 0.857197i | \(0.672204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.30116 | −0.412686 | −0.206343 | − | 0.978480i | \(-0.566156\pi\) | ||||
−0.206343 | + | 0.978480i | \(0.566156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.64135 | 0.429181 | 0.214590 | − | 0.976704i | \(-0.431158\pi\) | ||||
0.214590 | + | 0.976704i | \(0.431158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.14473 | −0.344039 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.3246 | −1.63674 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.42535 | −0.190591 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.2892 | −0.956094 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.4352 | 1.34715 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.3129 | −1.22643 | −0.613214 | − | 0.789917i | \(-0.710124\pi\) | ||||
−0.613214 | + | 0.789917i | \(0.710124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.6574 | 1.40602 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.790654 | −0.0430696 | −0.0215348 | − | 0.999768i | \(-0.506855\pi\) | ||||
−0.0215348 | + | 0.999768i | \(0.506855\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 41.1183 | 2.23324 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.4044 | 0.942499 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8368 | −1.07109 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.95361 | −0.426972 | −0.213486 | − | 0.976946i | \(-0.568482\pi\) | ||||
−0.213486 | + | 0.976946i | \(0.568482\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8777 | 0.849915 | 0.424957 | − | 0.905213i | \(-0.360289\pi\) | ||||
0.424957 | + | 0.905213i | \(0.360289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.7022 | 1.74551 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.45524 | −0.450027 | −0.225013 | − | 0.974356i | \(-0.572243\pi\) | ||||
−0.225013 | + | 0.974356i | \(0.572243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.7547 | −1.15138 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.2787 | −0.806380 | −0.403190 | − | 0.915116i | \(-0.632099\pi\) | ||||
−0.403190 | + | 0.915116i | \(0.632099\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −68.0269 | −3.57049 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.6331 | 1.33804 | 0.669019 | − | 0.743245i | \(-0.266714\pi\) | ||||
0.669019 | + | 0.743245i | \(0.266714\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −90.6258 | −4.71779 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.81708 | 0.302008 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.30390 | −0.0675132 | −0.0337566 | − | 0.999430i | \(-0.510747\pi\) | ||||
−0.0337566 | + | 0.999430i | \(0.510747\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.25964 | −0.116378 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.87034 | −0.250173 | −0.125086 | − | 0.992146i | \(-0.539921\pi\) | ||||
−0.125086 | + | 0.992146i | \(0.539921\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −40.4161 | −2.07058 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.6876 | −1.05709 | −0.528544 | − | 0.848906i | \(-0.677262\pi\) | ||||
−0.528544 | + | 0.848906i | \(0.677262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.91535 | 0.199028 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.252246 | 0.0127894 | 0.00639470 | − | 0.999980i | \(-0.497964\pi\) | ||||
0.00639470 | + | 0.999980i | \(0.497964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.3511 | 0.928054 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −35.4561 | −1.78852 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1665 | 1.41364 | 0.706819 | − | 0.707395i | \(-0.250130\pi\) | ||||
0.706819 | + | 0.707395i | \(0.250130\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.35109 | 0.317952 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.25963 | 0.262653 | 0.131327 | − | 0.991339i | \(-0.458076\pi\) | ||||
0.131327 | + | 0.991339i | \(0.458076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.40023 | 0.318818 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.5060 | −0.917310 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.0533 | −1.23880 | −0.619402 | − | 0.785074i | \(-0.712625\pi\) | ||||
−0.619402 | + | 0.785074i | \(0.712625\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.9618 | −0.787338 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.54253 | 0.223523 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −36.9493 | −1.80942 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7022 | −0.620542 | −0.310271 | − | 0.950648i | \(-0.600420\pi\) | ||||
−0.310271 | + | 0.950648i | \(0.600420\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9618 | 0.680457 | 0.340228 | − | 0.940343i | \(-0.389496\pi\) | ||||
0.340228 | + | 0.940343i | \(0.389496\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 98.7142 | 4.79965 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.7415 | 0.713393 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −38.3129 | −1.84976 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.1300 | −1.74032 | −0.870160 | − | 0.492770i | \(-0.835984\pi\) | ||||
−0.870160 | + | 0.492770i | \(0.835984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.50726 | 0.264662 | 0.132331 | − | 0.991206i | \(-0.457754\pi\) | ||||
0.132331 | + | 0.991206i | \(0.457754\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.35744 | −0.256281 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.4811 | 1.64569 | 0.822846 | − | 0.568265i | \(-0.192385\pi\) | ||||
0.822846 | + | 0.568265i | \(0.192385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.5002 | −1.21429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.9562 | 1.37575 | 0.687874 | − | 0.725830i | \(-0.258544\pi\) | ||||
0.687874 | + | 0.725830i | \(0.258544\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.9317 | −0.564352 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.5725 | −0.734913 | −0.367456 | − | 0.930041i | \(-0.619771\pi\) | ||||
−0.367456 | + | 0.930041i | \(0.619771\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 65.3662 | 3.07797 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −34.0256 | −1.59866 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.715236 | 0.0334573 | 0.0167287 | − | 0.999860i | \(-0.494675\pi\) | ||||
0.0167287 | + | 0.999860i | \(0.494675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −54.1065 | −2.52548 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.7863 | −1.34071 | −0.670355 | − | 0.742041i | \(-0.733858\pi\) | ||||
−0.670355 | + | 0.742041i | \(0.733858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.1055 | −1.02733 | −0.513664 | − | 0.857991i | \(-0.671712\pi\) | ||||
−0.513664 | + | 0.857991i | \(0.671712\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.6645 | −1.74291 | −0.871454 | − | 0.490478i | \(-0.836822\pi\) | ||||
−0.871454 | + | 0.490478i | \(0.836822\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.6342 | −1.09132 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.4278 | 1.07950 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.82405 | −0.129850 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.5001 | 1.07599 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.32461 | 0.243288 | 0.121644 | − | 0.992574i | \(-0.461183\pi\) | ||||
0.121644 | + | 0.992574i | \(0.461183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.80536 | −0.310298 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −34.0256 | −1.54822 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9425 | 0.677109 | 0.338555 | − | 0.940947i | \(-0.390062\pi\) | ||||
0.338555 | + | 0.940947i | \(0.390062\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.81708 | −0.262521 | −0.131260 | − | 0.991348i | \(-0.541902\pi\) | ||||
−0.131260 | + | 0.991348i | \(0.541902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.73864 | 0.168380 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.7277 | −1.24376 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.4235 | −0.779981 | −0.389990 | − | 0.920819i | \(-0.627522\pi\) | ||||
−0.389990 | + | 0.920819i | \(0.627522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −52.2097 | −2.33256 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.490004 | −0.0218482 | −0.0109241 | − | 0.999940i | \(-0.503477\pi\) | ||||
−0.0109241 | + | 0.999940i | \(0.503477\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.6439 | 1.27212 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.4811 | 0.730510 | 0.365255 | − | 0.930908i | \(-0.380982\pi\) | ||||
0.365255 | + | 0.930908i | \(0.380982\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.55007 | −0.245521 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.7959 | 0.697407 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −71.2001 | −3.13138 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −45.3246 | −1.98953 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0533 | 0.747117 | 0.373559 | − | 0.927607i | \(-0.378137\pi\) | ||||
0.373559 | + | 0.927607i | \(0.378137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.2777 | −1.49886 | −0.749430 | − | 0.662084i | \(-0.769672\pi\) | ||||
−0.749430 | + | 0.662084i | \(0.769672\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.5893 | −0.461278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.70218 | 0.247921 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.3511 | 0.796369 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0376 | 1.04118 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.0256 | 1.46831 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.3926 | 0.792227 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.9427 | 1.28734 | 0.643669 | − | 0.765304i | \(-0.277411\pi\) | ||||
0.643669 | + | 0.765304i | \(0.277411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.57430 | 0.282130 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.1339 | −1.24568 | −0.622838 | − | 0.782351i | \(-0.714020\pi\) | ||||
−0.622838 | + | 0.782351i | \(0.714020\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 59.5534 | 2.54168 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.09146 | −0.0464979 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.72838 | −0.328644 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.4542 | −1.62936 | −0.814678 | − | 0.579914i | \(-0.803086\pi\) | ||||
−0.814678 | + | 0.579914i | \(0.803086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.03851 | −0.0439241 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 63.3896 | 2.67631 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.58181 | 0.361680 | 0.180840 | − | 0.983512i | \(-0.442118\pi\) | ||||
0.180840 | + | 0.983512i | \(0.442118\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 55.0793 | 2.31311 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.221120 | −0.00926985 | −0.00463492 | − | 0.999989i | \(-0.501475\pi\) | ||||
−0.00463492 | + | 0.999989i | \(0.501475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.23315 | −0.0934544 | −0.0467272 | − | 0.998908i | \(-0.514879\pi\) | ||||
−0.0467272 | + | 0.998908i | \(0.514879\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.7277 | −1.15834 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.6225 | −0.692002 | −0.346001 | − | 0.938234i | \(-0.612461\pi\) | ||||
−0.346001 | + | 0.938234i | \(0.612461\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 76.5460 | 3.18114 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3511 | −0.429436 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9500 | −0.701998 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.2213 | −0.793347 | −0.396674 | − | 0.917960i | \(-0.629835\pi\) | ||||
−0.396674 | + | 0.917960i | \(0.629835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.09146 | 0.127381 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.2214 | −1.11974 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0230 | 0.534792 | 0.267396 | − | 0.963587i | \(-0.413837\pi\) | ||||
0.267396 | + | 0.963587i | \(0.413837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −61.7533 | −2.52739 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.0915 | −1.10693 | −0.553464 | − | 0.832873i | \(-0.686694\pi\) | ||||
−0.553464 | + | 0.832873i | \(0.686694\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.42779 | −0.221404 | −0.110702 | − | 0.993854i | \(-0.535310\pi\) | ||||
−0.110702 | + | 0.993854i | \(0.535310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −95.4782 | −3.88817 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.0663 | −0.855056 | −0.427528 | − | 0.904002i | \(-0.640616\pi\) | ||||
−0.427528 | + | 0.904002i | \(0.640616\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.93197 | −0.280898 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.1829 | −1.05925 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.2753 | −1.22281 | −0.611405 | − | 0.791318i | \(-0.709395\pi\) | ||||
−0.611405 | + | 0.791318i | \(0.709395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45.3049 | −1.82391 | −0.911953 | − | 0.410295i | \(-0.865426\pi\) | ||||
−0.911953 | + | 0.410295i | \(0.865426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.2331 | −0.732852 | −0.366426 | − | 0.930447i | \(-0.619419\pi\) | ||||
−0.366426 | + | 0.930447i | \(0.619419\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −84.6258 | −3.39592 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.1351 | 0.646439 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.5060 | −0.739060 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.2596 | 0.448951 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.4087 | 0.454173 | 0.227086 | − | 0.973875i | \(-0.427080\pi\) | ||||
0.227086 | + | 0.973875i | \(0.427080\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −71.5905 | −2.84547 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.76365 | 0.267986 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −112.015 | −4.43126 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.92330 | 0.194459 | 0.0972293 | − | 0.995262i | \(-0.469002\pi\) | ||||
0.0972293 | + | 0.995262i | \(0.469002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.4136 | −0.962779 | −0.481390 | − | 0.876507i | \(-0.659868\pi\) | ||||
−0.481390 | + | 0.876507i | \(0.659868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.0424 | 0.434123 | 0.217061 | − | 0.976158i | \(-0.430353\pi\) | ||||
0.217061 | + | 0.976158i | \(0.430353\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.2362 | −0.519566 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.6342 | 0.769523 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.1665 | 1.10224 | 0.551121 | − | 0.834426i | \(-0.314200\pi\) | ||||
0.551121 | + | 0.834426i | \(0.314200\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.4214 | −0.874742 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.74037 | −0.184659 | −0.0923294 | − | 0.995729i | \(-0.529431\pi\) | ||||
−0.0923294 | + | 0.995729i | \(0.529431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4426 | −0.756228 | −0.378114 | − | 0.925759i | \(-0.623427\pi\) | ||||
−0.378114 | + | 0.925759i | \(0.623427\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.3107 | 0.905313 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.84744 | 0.226414 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −47.8439 | −1.84975 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.9544 | −1.65824 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5088 | 0.482178 | 0.241089 | − | 0.970503i | \(-0.422495\pi\) | ||||
0.241089 | + | 0.970503i | \(0.422495\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.7265 | −1.56525 | −0.782623 | − | 0.622497i | \(-0.786118\pi\) | ||||
−0.782623 | + | 0.622497i | \(0.786118\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.81708 | 0.223239 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.80536 | −0.260782 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.8312 | −0.567500 | −0.283750 | − | 0.958898i | \(-0.591579\pi\) | ||||
−0.283750 | + | 0.958898i | \(0.591579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.8248 | 1.93909 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.23315 | −0.237464 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.0958 | −0.498188 | −0.249094 | − | 0.968479i | \(-0.580133\pi\) | ||||
−0.249094 | + | 0.968479i | \(0.580133\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −84.9015 | −3.22514 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.7707 | −1.50642 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 94.9769 | 3.59236 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.0797 | −0.531785 | −0.265892 | − | 0.964003i | \(-0.585667\pi\) | ||||
−0.265892 | + | 0.964003i | \(0.585667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.28715 | −0.123977 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.28441 | −0.349176 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.38928 | 0.315066 | 0.157533 | − | 0.987514i | \(-0.449646\pi\) | ||||
0.157533 | + | 0.987514i | \(0.449646\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −31.2214 | −1.17090 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.5623 | −0.620264 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 87.4977 | 3.26766 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.70652 | −0.250111 | −0.125055 | − | 0.992150i | \(-0.539911\pi\) | ||||
−0.125055 | + | 0.992150i | \(0.539911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.16816 | 0.304198 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 64.4634 | 2.39742 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.5009 | 0.760337 | 0.380168 | − | 0.924917i | \(-0.375866\pi\) | ||||
0.380168 | + | 0.924917i | \(0.375866\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 66.7407 | 2.47188 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.71823 | 0.0635512 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.4323 | 1.56727 | 0.783636 | − | 0.621220i | \(-0.213363\pi\) | ||||
0.783636 | + | 0.621220i | \(0.213363\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 68.8661 | 2.53671 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.4352 | −1.63457 | −0.817287 | − | 0.576231i | \(-0.804523\pi\) | ||||
−0.817287 | + | 0.576231i | \(0.804523\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.80536 | −0.250001 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.4350 | −1.33667 | −0.668336 | − | 0.743859i | \(-0.732993\pi\) | ||||
−0.668336 | + | 0.743859i | \(0.732993\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −41.8167 | −1.52999 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.2362 | 0.629797 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.6107 | 1.08051 | 0.540255 | − | 0.841501i | \(-0.318328\pi\) | ||||
0.540255 | + | 0.841501i | \(0.318328\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 46.8493 | 1.70728 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.0252 | 1.60012 | 0.800062 | − | 0.599917i | \(-0.204800\pi\) | ||||
0.800062 | + | 0.599917i | \(0.204800\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 99.1450 | 3.59874 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.9809 | 0.941807 | 0.470903 | − | 0.882185i | \(-0.343928\pi\) | ||||
0.470903 | + | 0.882185i | \(0.343928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.1621 | 0.367893 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.86744 | −0.175753 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.68308 | 0.0967543 | 0.0483772 | − | 0.998829i | \(-0.484595\pi\) | ||||
0.0483772 | + | 0.998829i | \(0.484595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.1183 | 1.33678 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.5328 | −1.42190 | −0.710949 | − | 0.703244i | \(-0.751734\pi\) | ||||
−0.710949 | + | 0.703244i | \(0.751734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.8770 | −0.748958 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.6107 | 0.415997 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 80.7940 | 2.89103 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.2407 | −0.616131 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.15783 | −0.326442 | −0.163221 | − | 0.986590i | \(-0.552188\pi\) | ||||
−0.163221 | + | 0.986590i | \(0.552188\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 50.4811 | 1.79717 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.1682 | −0.859321 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.7959 | −0.560930 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.5581 | −0.551095 | −0.275547 | − | 0.961287i | \(-0.588859\pi\) | ||||
−0.275547 | + | 0.961287i | \(0.588859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.3203 | 1.53256 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 65.1832 | 2.30314 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.1720 | 0.570698 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.6134 | −1.32405 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.6184 | −1.46323 | −0.731613 | − | 0.681721i | \(-0.761232\pi\) | ||||
−0.731613 | + | 0.681721i | \(0.761232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.1685 | 1.72654 | 0.863269 | − | 0.504744i | \(-0.168413\pi\) | ||||
0.863269 | + | 0.504744i | \(0.168413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.8135 | 1.43139 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.501623 | −0.0175496 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −31.2214 | −1.09097 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.9012 | −0.485154 | −0.242577 | − | 0.970132i | \(-0.577993\pi\) | ||||
−0.242577 | + | 0.970132i | \(0.577993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.0704 | 0.664754 | 0.332377 | − | 0.943147i | \(-0.392149\pi\) | ||||
0.332377 | + | 0.943147i | \(0.392149\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.7712 | −1.62639 | −0.813197 | − | 0.581988i | \(-0.802275\pi\) | ||||
−0.813197 | + | 0.581988i | \(0.802275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.37452 | 0.0824706 | 0.0412353 | − | 0.999149i | \(-0.486871\pi\) | ||||
0.0412353 | + | 0.999149i | \(0.486871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −52.6640 | −1.82689 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.1906 | −0.387732 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 48.8325 | 1.68790 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.57252 | 0.0542894 | 0.0271447 | − | 0.999632i | \(-0.491359\pi\) | ||||
0.0271447 | + | 0.999632i | \(0.491359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8087 | −0.958921 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 81.8011 | 2.81738 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.9843 | 1.37388 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −53.3662 | −1.83152 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.6107 | 0.603688 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.88094 | −0.0644021 | −0.0322010 | − | 0.999481i | \(-0.510252\pi\) | ||||
−0.0322010 | + | 0.999481i | \(0.510252\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.0371 | −0.581975 | −0.290987 | − | 0.956727i | \(-0.593984\pi\) | ||||
−0.290987 | + | 0.956727i | \(0.593984\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.8395 | −1.70050 | −0.850251 | − | 0.526377i | \(-0.823550\pi\) | ||||
−0.850251 | + | 0.526377i | \(0.823550\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 73.7407 | 2.51308 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.1696 | 0.414258 | 0.207129 | − | 0.978314i | \(-0.433588\pi\) | ||||
0.207129 | + | 0.978314i | \(0.433588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.3134 | 0.587995 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.5193 | 0.763913 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.3246 | 0.858092 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.5001 | 0.795356 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.2287 | 1.42596 | 0.712981 | − | 0.701184i | \(-0.247345\pi\) | ||||
0.712981 | + | 0.701184i | \(0.247345\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 76.5460 | 2.58183 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.6683 | −0.426807 | −0.213403 | − | 0.976964i | \(-0.568455\pi\) | ||||
−0.213403 | + | 0.976964i | \(0.568455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.5414 | −0.388400 | −0.194200 | − | 0.980962i | \(-0.562211\pi\) | ||||
−0.194200 | + | 0.980962i | \(0.562211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.36171 | 0.213605 | 0.106803 | − | 0.994280i | \(-0.465939\pi\) | ||||
0.106803 | + | 0.994280i | \(0.465939\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.7554 | 0.796732 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −160.492 | −5.37669 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.6470 | −0.423215 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.4593 | 1.21734 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.37421 | −0.112536 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3129 | 0.343572 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.18585 | −0.106019 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.9538 | 0.828576 | 0.414288 | − | 0.910146i | \(-0.364031\pi\) | ||||
0.414288 | + | 0.910146i | \(0.364031\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.5075 | −1.24405 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.6640 | 0.949680 | 0.474840 | − | 0.880072i | \(-0.342506\pi\) | ||||
0.474840 | + | 0.880072i | \(0.342506\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.1614 | 0.998196 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.8401 | 0.688200 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0385 | 0.825944 | 0.412972 | − | 0.910744i | \(-0.364491\pi\) | ||||
0.412972 | + | 0.910744i | \(0.364491\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.17121 | −0.104495 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.7109 | 0.977947 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.9981 | 1.08380 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.2744 | 0.894844 | 0.447422 | − | 0.894323i | \(-0.352342\pi\) | ||||
0.447422 | + | 0.894323i | \(0.352342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.26701 | 0.107072 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 59.7072 | 1.95473 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.7193 | 0.938219 | 0.469109 | − | 0.883140i | \(-0.344575\pi\) | ||||
0.469109 | + | 0.883140i | \(0.344575\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.81708 | 0.254829 | 0.127415 | − | 0.991850i | \(-0.459332\pi\) | ||||
0.127415 | + | 0.991850i | \(0.459332\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −62.2037 | −2.02563 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.4886 | −1.31570 | −0.657851 | − | 0.753148i | \(-0.728534\pi\) | ||||
−0.657851 | + | 0.753148i | \(0.728534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.94704 | 0.193049 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.1183 | −0.814515 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.57857 | 0.245494 | 0.122747 | − | 0.992438i | \(-0.460830\pi\) | ||||
0.122747 | + | 0.992438i | \(0.460830\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.1986 | 0.652930 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.38190 | 0.302958 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.4429 | −0.691705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 69.6315 | 2.24384 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.5195 | −0.499075 | −0.249537 | − | 0.968365i | \(-0.580279\pi\) | ||||
−0.249537 | + | 0.968365i | \(0.580279\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.2596 | 0.361711 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.81708 | −0.0583127 | −0.0291564 | − | 0.999575i | \(-0.509282\pi\) | ||||
−0.0291564 | + | 0.999575i | \(0.509282\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.7178 | 0.696240 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.0178 | 0.672420 | 0.336210 | − | 0.941787i | \(-0.390855\pi\) | ||||
0.336210 | + | 0.941787i | \(0.390855\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −47.0151 | −1.50261 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.0533 | 1.31073 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.2339 | −0.613467 | −0.306733 | − | 0.951795i | \(-0.599236\pi\) | ||||
−0.306733 | + | 0.951795i | \(0.599236\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −80.3221 | −2.55668 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.68742 | 0.0854549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.1682 | −1.14892 | −0.574460 | − | 0.818533i | \(-0.694788\pi\) | ||||
−0.574460 | + | 0.818533i | \(0.694788\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 73.3458 | 2.32756 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.6955 | −1.13049 | −0.565245 | − | 0.824923i | \(-0.691218\pi\) | ||||
−0.565245 | + | 0.824923i | \(0.691218\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −51.9236 | −1.64279 |
(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 | 7600.2.a.cj.1.1 | 6 | ||
4.3 | odd | 2 | 1900.2.a.k.1.6 | 6 | |||
5.2 | odd | 4 | 1520.2.d.i.609.6 | 6 | |||
5.3 | odd | 4 | 1520.2.d.i.609.1 | 6 | |||
5.4 | even | 2 | inner | 7600.2.a.cj.1.6 | 6 | ||
20.3 | even | 4 | 380.2.c.b.229.6 | yes | 6 | ||
20.7 | even | 4 | 380.2.c.b.229.1 | ✓ | 6 | ||
20.19 | odd | 2 | 1900.2.a.k.1.1 | 6 | |||
60.23 | odd | 4 | 3420.2.f.c.1369.1 | 6 | |||
60.47 | odd | 4 | 3420.2.f.c.1369.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.b.229.1 | ✓ | 6 | 20.7 | even | 4 | ||
380.2.c.b.229.6 | yes | 6 | 20.3 | even | 4 | ||
1520.2.d.i.609.1 | 6 | 5.3 | odd | 4 | |||
1520.2.d.i.609.6 | 6 | 5.2 | odd | 4 | |||
1900.2.a.k.1.1 | 6 | 20.19 | odd | 2 | |||
1900.2.a.k.1.6 | 6 | 4.3 | odd | 2 | |||
3420.2.f.c.1369.1 | 6 | 60.23 | odd | 4 | |||
3420.2.f.c.1369.2 | 6 | 60.47 | odd | 4 | |||
7600.2.a.cj.1.1 | 6 | 1.1 | even | 1 | trivial | ||
7600.2.a.cj.1.6 | 6 | 5.4 | even | 2 | inner |