Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.63994\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63994 | −1.86672 | −0.933359 | − | 0.358943i | \(-0.883137\pi\) | ||||
−0.933359 | + | 0.358943i | \(0.883137\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.96928 | 2.48464 | ||||||||
\(5\) | −3.08369 | −1.37907 | −0.689534 | − | 0.724254i | \(-0.742184\pi\) | ||||
−0.689534 | + | 0.724254i | \(0.742184\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −7.83871 | −2.77140 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.14075 | 2.57433 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.64097 | −1.56452 | −0.782262 | − | 0.622949i | \(-0.785934\pi\) | ||||
−0.782262 | + | 0.622949i | \(0.785934\pi\) | |||||||
\(14\) | 2.63994 | 0.705553 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10.7552 | 2.68879 | ||||||||
\(17\) | 5.60085 | 1.35841 | 0.679203 | − | 0.733951i | \(-0.262326\pi\) | ||||
0.679203 | + | 0.733951i | \(0.262326\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.122652 | 0.0281384 | 0.0140692 | − | 0.999901i | \(-0.495521\pi\) | ||||
0.0140692 | + | 0.999901i | \(0.495521\pi\) | |||||||
\(20\) | −15.3237 | −3.42648 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.67325 | −0.348896 | −0.174448 | − | 0.984666i | \(-0.555814\pi\) | ||||
−0.174448 | + | 0.984666i | \(0.555814\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.50913 | 0.901826 | ||||||||
\(26\) | 14.8918 | 2.92053 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.96928 | −0.939105 | ||||||||
\(29\) | −8.85038 | −1.64347 | −0.821737 | − | 0.569867i | \(-0.806995\pi\) | ||||
−0.821737 | + | 0.569867i | \(0.806995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.59773 | 0.286960 | 0.143480 | − | 0.989653i | \(-0.454171\pi\) | ||||
0.143480 | + | 0.989653i | \(0.454171\pi\) | |||||||
\(32\) | −12.7156 | −2.24782 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.7859 | −2.53576 | ||||||||
\(35\) | 3.08369 | 0.521238 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.17268 | 0.685984 | 0.342992 | − | 0.939338i | \(-0.388560\pi\) | ||||
0.342992 | + | 0.939338i | \(0.388560\pi\) | |||||||
\(38\) | −0.323795 | −0.0525265 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.1721 | 3.82195 | ||||||||
\(41\) | −3.48859 | −0.544827 | −0.272413 | − | 0.962180i | \(-0.587822\pi\) | ||||
−0.272413 | + | 0.962180i | \(0.587822\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.10698 | −0.778807 | −0.389403 | − | 0.921067i | \(-0.627319\pi\) | ||||
−0.389403 | + | 0.921067i | \(0.627319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.41727 | 0.651290 | ||||||||
\(47\) | 1.59400 | 0.232509 | 0.116255 | − | 0.993219i | \(-0.462911\pi\) | ||||
0.116255 | + | 0.993219i | \(0.462911\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −11.9038 | −1.68346 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −28.0316 | −3.88728 | ||||||||
\(53\) | 11.8564 | 1.62861 | 0.814303 | − | 0.580440i | \(-0.197119\pi\) | ||||
0.814303 | + | 0.580440i | \(0.197119\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.83871 | 1.04749 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 23.3645 | 3.06790 | ||||||||
\(59\) | −6.61445 | −0.861128 | −0.430564 | − | 0.902560i | \(-0.641685\pi\) | ||||
−0.430564 | + | 0.902560i | \(0.641685\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.48918 | −1.08693 | −0.543464 | − | 0.839432i | \(-0.682888\pi\) | ||||
−0.543464 | + | 0.839432i | \(0.682888\pi\) | |||||||
\(62\) | −4.21790 | −0.535674 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.0580 | 1.50725 | ||||||||
\(65\) | 17.3950 | 2.15758 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.04949 | −0.983402 | −0.491701 | − | 0.870764i | \(-0.663625\pi\) | ||||
−0.491701 | + | 0.870764i | \(0.663625\pi\) | |||||||
\(68\) | 27.8322 | 3.37515 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.14075 | −0.973006 | ||||||||
\(71\) | −6.24379 | −0.741001 | −0.370501 | − | 0.928832i | \(-0.620814\pi\) | ||||
−0.370501 | + | 0.928832i | \(0.620814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.51005 | 0.410820 | 0.205410 | − | 0.978676i | \(-0.434147\pi\) | ||||
0.205410 | + | 0.978676i | \(0.434147\pi\) | |||||||
\(74\) | −11.0156 | −1.28054 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.609494 | 0.0699138 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.39769 | −1.05732 | −0.528661 | − | 0.848833i | \(-0.677306\pi\) | ||||
−0.528661 | + | 0.848833i | \(0.677306\pi\) | |||||||
\(80\) | −33.1656 | −3.70803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.20967 | 1.01704 | ||||||||
\(83\) | 9.43386 | 1.03550 | 0.517750 | − | 0.855532i | \(-0.326770\pi\) | ||||
0.517750 | + | 0.855532i | \(0.326770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.2713 | −1.87333 | ||||||||
\(86\) | 13.4821 | 1.45381 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.45556 | 0.896288 | 0.448144 | − | 0.893961i | \(-0.352085\pi\) | ||||
0.448144 | + | 0.893961i | \(0.352085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.64097 | 0.591335 | ||||||||
\(92\) | −8.31482 | −0.866880 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.20807 | −0.434030 | ||||||||
\(95\) | −0.378222 | −0.0388047 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.68478 | −0.577202 | −0.288601 | − | 0.957449i | \(-0.593190\pi\) | ||||
−0.288601 | + | 0.957449i | \(0.593190\pi\) | |||||||
\(98\) | −2.63994 | −0.266674 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 22.4071 | 2.24071 | ||||||||
\(101\) | −16.8776 | −1.67938 | −0.839690 | − | 0.543066i | \(-0.817263\pi\) | ||||
−0.839690 | + | 0.543066i | \(0.817263\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2172 | −1.30233 | −0.651163 | − | 0.758938i | \(-0.725719\pi\) | ||||
−0.651163 | + | 0.758938i | \(0.725719\pi\) | |||||||
\(104\) | 44.2180 | 4.33593 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −31.3003 | −3.04015 | ||||||||
\(107\) | −11.0745 | −1.07061 | −0.535307 | − | 0.844658i | \(-0.679804\pi\) | ||||
−0.535307 | + | 0.844658i | \(0.679804\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.87369 | −0.466815 | −0.233407 | − | 0.972379i | \(-0.574988\pi\) | ||||
−0.233407 | + | 0.972379i | \(0.574988\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.7552 | −1.01627 | ||||||||
\(113\) | 5.28263 | 0.496948 | 0.248474 | − | 0.968639i | \(-0.420071\pi\) | ||||
0.248474 | + | 0.968639i | \(0.420071\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.15977 | 0.481151 | ||||||||
\(116\) | −43.9800 | −4.08344 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.4617 | 1.60748 | ||||||||
\(119\) | −5.60085 | −0.513429 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 22.4109 | 2.02899 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.93955 | 0.712992 | ||||||||
\(125\) | 1.51368 | 0.135388 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3400 | −1.00627 | −0.503133 | − | 0.864209i | \(-0.667819\pi\) | ||||
−0.503133 | + | 0.864209i | \(0.667819\pi\) | |||||||
\(128\) | −6.40120 | −0.565792 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −45.9217 | −4.02760 | ||||||||
\(131\) | 0.970284 | 0.0847741 | 0.0423870 | − | 0.999101i | \(-0.486504\pi\) | ||||
0.0423870 | + | 0.999101i | \(0.486504\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.122652 | −0.0106353 | ||||||||
\(134\) | 21.2502 | 1.83574 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −43.9035 | −3.76469 | ||||||||
\(137\) | 0.125101 | 0.0106881 | 0.00534403 | − | 0.999986i | \(-0.498299\pi\) | ||||
0.00534403 | + | 0.999986i | \(0.498299\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.67835 | −0.142355 | −0.0711777 | − | 0.997464i | \(-0.522676\pi\) | ||||
−0.0711777 | + | 0.997464i | \(0.522676\pi\) | |||||||
\(140\) | 15.3237 | 1.29509 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.4832 | 1.38324 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27.2918 | 2.26646 | ||||||||
\(146\) | −9.26631 | −0.766885 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.7352 | 1.70442 | ||||||||
\(149\) | −14.1791 | −1.16160 | −0.580800 | − | 0.814046i | \(-0.697260\pi\) | ||||
−0.580800 | + | 0.814046i | \(0.697260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8823 | 1.29249 | 0.646243 | − | 0.763132i | \(-0.276339\pi\) | ||||
0.646243 | + | 0.763132i | \(0.276339\pi\) | |||||||
\(152\) | −0.961437 | −0.0779829 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.92689 | −0.395737 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.19854 | −0.734124 | −0.367062 | − | 0.930197i | \(-0.619636\pi\) | ||||
−0.367062 | + | 0.930197i | \(0.619636\pi\) | |||||||
\(158\) | 24.8093 | 1.97372 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 39.2108 | 3.09989 | ||||||||
\(161\) | 1.67325 | 0.131870 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.76942 | 0.765200 | 0.382600 | − | 0.923914i | \(-0.375029\pi\) | ||||
0.382600 | + | 0.923914i | \(0.375029\pi\) | |||||||
\(164\) | −17.3358 | −1.35370 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.9048 | −1.93299 | ||||||||
\(167\) | −6.10236 | −0.472215 | −0.236107 | − | 0.971727i | \(-0.575872\pi\) | ||||
−0.236107 | + | 0.971727i | \(0.575872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.8206 | 1.44774 | ||||||||
\(170\) | 45.5951 | 3.49699 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −25.3780 | −1.93505 | ||||||||
\(173\) | −6.73818 | −0.512294 | −0.256147 | − | 0.966638i | \(-0.582453\pi\) | ||||
−0.256147 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.50913 | −0.340858 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.3222 | −1.67312 | ||||||||
\(179\) | −12.9936 | −0.971184 | −0.485592 | − | 0.874186i | \(-0.661396\pi\) | ||||
−0.485592 | + | 0.874186i | \(0.661396\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.09819 | −0.304616 | −0.152308 | − | 0.988333i | \(-0.548671\pi\) | ||||
−0.152308 | + | 0.988333i | \(0.548671\pi\) | |||||||
\(182\) | −14.8918 | −1.10386 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.1161 | 0.966931 | ||||||||
\(185\) | −12.8672 | −0.946018 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.92105 | 0.577702 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.998483 | 0.0724375 | ||||||||
\(191\) | −21.5036 | −1.55595 | −0.777973 | − | 0.628297i | \(-0.783752\pi\) | ||||
−0.777973 | + | 0.628297i | \(0.783752\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.7964 | 1.28101 | 0.640506 | − | 0.767953i | \(-0.278725\pi\) | ||||
0.640506 | + | 0.767953i | \(0.278725\pi\) | |||||||
\(194\) | 15.0075 | 1.07747 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.96928 | 0.354948 | ||||||||
\(197\) | −18.1083 | −1.29016 | −0.645080 | − | 0.764115i | \(-0.723176\pi\) | ||||
−0.645080 | + | 0.764115i | \(0.723176\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.67139 | 0.189370 | 0.0946848 | − | 0.995507i | \(-0.469816\pi\) | ||||
0.0946848 | + | 0.995507i | \(0.469816\pi\) | |||||||
\(200\) | −35.3458 | −2.49933 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 44.5557 | 3.13493 | ||||||||
\(203\) | 8.85038 | 0.621175 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.7577 | 0.751352 | ||||||||
\(206\) | 34.8925 | 2.43108 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −60.6696 | −4.20668 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.15447 | −0.561377 | −0.280688 | − | 0.959799i | \(-0.590563\pi\) | ||||
−0.280688 | + | 0.959799i | \(0.590563\pi\) | |||||||
\(212\) | 58.9179 | 4.04650 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 29.2360 | 1.99853 | ||||||||
\(215\) | 15.7483 | 1.07403 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.59773 | −0.108461 | ||||||||
\(218\) | 12.8662 | 0.871412 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.5942 | −2.12526 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.48763 | 0.568374 | 0.284187 | − | 0.958769i | \(-0.408276\pi\) | ||||
0.284187 | + | 0.958769i | \(0.408276\pi\) | |||||||
\(224\) | 12.7156 | 0.849595 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.9458 | −0.927662 | ||||||||
\(227\) | 22.1524 | 1.47031 | 0.735154 | − | 0.677900i | \(-0.237110\pi\) | ||||
0.735154 | + | 0.677900i | \(0.237110\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.98014 | −0.593424 | −0.296712 | − | 0.954967i | \(-0.595890\pi\) | ||||
−0.296712 | + | 0.954967i | \(0.595890\pi\) | |||||||
\(230\) | −13.6215 | −0.898173 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 69.3756 | 4.55473 | ||||||||
\(233\) | −19.8909 | −1.30309 | −0.651547 | − | 0.758608i | \(-0.725880\pi\) | ||||
−0.651547 | + | 0.758608i | \(0.725880\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.91541 | −0.320646 | ||||||||
\(236\) | −32.8690 | −2.13959 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.7859 | 0.958428 | ||||||||
\(239\) | 9.21976 | 0.596377 | 0.298188 | − | 0.954507i | \(-0.403618\pi\) | ||||
0.298188 | + | 0.954507i | \(0.403618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.802919 | −0.0517206 | −0.0258603 | − | 0.999666i | \(-0.508233\pi\) | ||||
−0.0258603 | + | 0.999666i | \(0.508233\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −42.1851 | −2.70062 | ||||||||
\(245\) | −3.08369 | −0.197010 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.691879 | −0.0440232 | ||||||||
\(248\) | −12.5241 | −0.795282 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.99603 | −0.252731 | ||||||||
\(251\) | −0.459277 | −0.0289893 | −0.0144947 | − | 0.999895i | \(-0.504614\pi\) | ||||
−0.0144947 | + | 0.999895i | \(0.504614\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 29.9370 | 1.87842 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.21718 | −0.451073 | ||||||||
\(257\) | 23.3574 | 1.45699 | 0.728496 | − | 0.685050i | \(-0.240220\pi\) | ||||
0.728496 | + | 0.685050i | \(0.240220\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.17268 | −0.259277 | ||||||||
\(260\) | 86.4406 | 5.36082 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.56149 | −0.158249 | ||||||||
\(263\) | 4.96169 | 0.305951 | 0.152975 | − | 0.988230i | \(-0.451114\pi\) | ||||
0.152975 | + | 0.988230i | \(0.451114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −36.5615 | −2.24596 | ||||||||
\(266\) | 0.323795 | 0.0198531 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −40.0002 | −2.44340 | ||||||||
\(269\) | −1.03203 | −0.0629239 | −0.0314620 | − | 0.999505i | \(-0.510016\pi\) | ||||
−0.0314620 | + | 0.999505i | \(0.510016\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1427 | 0.919856 | 0.459928 | − | 0.887956i | \(-0.347875\pi\) | ||||
0.459928 | + | 0.887956i | \(0.347875\pi\) | |||||||
\(272\) | 60.2381 | 3.65247 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.330258 | −0.0199516 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.07001 | −0.0642909 | −0.0321455 | − | 0.999483i | \(-0.510234\pi\) | ||||
−0.0321455 | + | 0.999483i | \(0.510234\pi\) | |||||||
\(278\) | 4.43073 | 0.265737 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −24.1721 | −1.44456 | ||||||||
\(281\) | 31.3090 | 1.86774 | 0.933868 | − | 0.357617i | \(-0.116411\pi\) | ||||
0.933868 | + | 0.357617i | \(0.116411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.9651 | 1.90013 | 0.950063 | − | 0.312059i | \(-0.101019\pi\) | ||||
0.950063 | + | 0.312059i | \(0.101019\pi\) | |||||||
\(284\) | −31.0271 | −1.84112 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.48859 | 0.205925 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.3695 | 0.845266 | ||||||||
\(290\) | −72.0487 | −4.23085 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.4424 | 1.02074 | ||||||||
\(293\) | 0.472963 | 0.0276308 | 0.0138154 | − | 0.999905i | \(-0.495602\pi\) | ||||
0.0138154 | + | 0.999905i | \(0.495602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.3969 | 1.18755 | ||||||||
\(296\) | −32.7084 | −1.90114 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 37.4321 | 2.16838 | ||||||||
\(299\) | 9.43873 | 0.545856 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.10698 | 0.294361 | ||||||||
\(302\) | −41.9284 | −2.41271 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.31915 | 0.0756583 | ||||||||
\(305\) | 26.1780 | 1.49895 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.3522 | −1.27571 | −0.637854 | − | 0.770158i | \(-0.720177\pi\) | ||||
−0.637854 | + | 0.770158i | \(0.720177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.0067 | 0.738730 | ||||||||
\(311\) | −21.9838 | −1.24659 | −0.623293 | − | 0.781988i | \(-0.714206\pi\) | ||||
−0.623293 | + | 0.781988i | \(0.714206\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.95027 | −0.449376 | −0.224688 | − | 0.974431i | \(-0.572136\pi\) | ||||
−0.224688 | + | 0.974431i | \(0.572136\pi\) | |||||||
\(314\) | 24.2836 | 1.37040 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −46.6997 | −2.62707 | ||||||||
\(317\) | 15.1227 | 0.849374 | 0.424687 | − | 0.905340i | \(-0.360384\pi\) | ||||
0.424687 | + | 0.905340i | \(0.360384\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −37.1831 | −2.07860 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.41727 | −0.246165 | ||||||||
\(323\) | 0.686958 | 0.0382234 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.4359 | −1.41093 | ||||||||
\(326\) | −25.7907 | −1.42841 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 27.3461 | 1.50993 | ||||||||
\(329\) | −1.59400 | −0.0878803 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.02542 | −0.331187 | −0.165594 | − | 0.986194i | \(-0.552954\pi\) | ||||
−0.165594 | + | 0.986194i | \(0.552954\pi\) | |||||||
\(332\) | 46.8795 | 2.57285 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.1099 | 0.881492 | ||||||||
\(335\) | 24.8221 | 1.35618 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.8494 | 1.13574 | 0.567869 | − | 0.823119i | \(-0.307768\pi\) | ||||
0.567869 | + | 0.823119i | \(0.307768\pi\) | |||||||
\(338\) | −49.6851 | −2.70252 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −85.8258 | −4.65456 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 40.0321 | 2.15839 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.7884 | 0.956309 | ||||||||
\(347\) | −1.49329 | −0.0801643 | −0.0400821 | − | 0.999196i | \(-0.512762\pi\) | ||||
−0.0400821 | + | 0.999196i | \(0.512762\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.4795 | −1.14977 | −0.574886 | − | 0.818234i | \(-0.694954\pi\) | ||||
−0.574886 | + | 0.818234i | \(0.694954\pi\) | |||||||
\(350\) | 11.9038 | 0.636287 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.4760 | −0.610808 | −0.305404 | − | 0.952223i | \(-0.598792\pi\) | ||||
−0.305404 | + | 0.952223i | \(0.598792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.2539 | 1.02189 | ||||||||
\(356\) | 42.0180 | 2.22695 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 34.3022 | 1.81293 | ||||||||
\(359\) | 5.72481 | 0.302144 | 0.151072 | − | 0.988523i | \(-0.451727\pi\) | ||||
0.151072 | + | 0.988523i | \(0.451727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9850 | −0.999208 | ||||||||
\(362\) | 10.8190 | 0.568632 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 28.0316 | 1.46925 | ||||||||
\(365\) | −10.8239 | −0.566548 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4991 | 0.913445 | 0.456723 | − | 0.889609i | \(-0.349023\pi\) | ||||
0.456723 | + | 0.889609i | \(0.349023\pi\) | |||||||
\(368\) | −17.9960 | −0.938109 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 33.9687 | 1.76595 | ||||||||
\(371\) | −11.8564 | −0.615555 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.54362 | −0.494150 | −0.247075 | − | 0.968996i | \(-0.579469\pi\) | ||||
−0.247075 | + | 0.968996i | \(0.579469\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.4949 | −0.644377 | ||||||||
\(377\) | 49.9247 | 2.57126 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.9605 | 1.64170 | 0.820850 | − | 0.571144i | \(-0.193500\pi\) | ||||
0.820850 | + | 0.571144i | \(0.193500\pi\) | |||||||
\(380\) | −1.87949 | −0.0964158 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 56.7682 | 2.90452 | ||||||||
\(383\) | 9.82236 | 0.501899 | 0.250950 | − | 0.968000i | \(-0.419257\pi\) | ||||
0.250950 | + | 0.968000i | \(0.419257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −46.9814 | −2.39129 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −28.2493 | −1.43414 | ||||||||
\(389\) | −33.1998 | −1.68330 | −0.841648 | − | 0.540027i | \(-0.818414\pi\) | ||||
−0.841648 | + | 0.540027i | \(0.818414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.37160 | −0.473942 | ||||||||
\(392\) | −7.83871 | −0.395915 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 47.8047 | 2.40837 | ||||||||
\(395\) | 28.9795 | 1.45812 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.6535 | 1.18713 | 0.593566 | − | 0.804785i | \(-0.297719\pi\) | ||||
0.593566 | + | 0.804785i | \(0.297719\pi\) | |||||||
\(398\) | −7.05230 | −0.353500 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 48.4965 | 2.42482 | ||||||||
\(401\) | −25.2737 | −1.26211 | −0.631054 | − | 0.775739i | \(-0.717377\pi\) | ||||
−0.631054 | + | 0.775739i | \(0.717377\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.01273 | −0.448956 | ||||||||
\(404\) | −83.8693 | −4.17265 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −23.3645 | −1.15956 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.9735 | 0.690947 | 0.345474 | − | 0.938428i | \(-0.387718\pi\) | ||||
0.345474 | + | 0.938428i | \(0.387718\pi\) | |||||||
\(410\) | −28.3998 | −1.40256 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −65.6798 | −3.23581 | ||||||||
\(413\) | 6.61445 | 0.325476 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.0911 | −1.42803 | ||||||||
\(416\) | 71.7282 | 3.51676 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.7445 | −1.45311 | −0.726556 | − | 0.687107i | \(-0.758880\pi\) | ||||
−0.726556 | + | 0.687107i | \(0.758880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.2675 | 1.76757 | 0.883786 | − | 0.467892i | \(-0.154986\pi\) | ||||
0.883786 | + | 0.467892i | \(0.154986\pi\) | |||||||
\(422\) | 21.5273 | 1.04793 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −92.9392 | −4.51353 | ||||||||
\(425\) | 25.2550 | 1.22505 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.48918 | 0.410820 | ||||||||
\(428\) | −55.0323 | −2.66009 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −41.5746 | −2.00491 | ||||||||
\(431\) | −35.8066 | −1.72474 | −0.862372 | − | 0.506275i | \(-0.831022\pi\) | ||||
−0.862372 | + | 0.506275i | \(0.831022\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0958 | −1.10992 | −0.554958 | − | 0.831879i | \(-0.687266\pi\) | ||||
−0.554958 | + | 0.831879i | \(0.687266\pi\) | |||||||
\(434\) | 4.21790 | 0.202466 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.2187 | −1.15987 | ||||||||
\(437\) | −0.205228 | −0.00981737 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.7837 | 1.18286 | 0.591431 | − | 0.806356i | \(-0.298563\pi\) | ||||
0.591431 | + | 0.806356i | \(0.298563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 83.4069 | 3.96726 | ||||||||
\(443\) | −13.2945 | −0.631642 | −0.315821 | − | 0.948819i | \(-0.602280\pi\) | ||||
−0.315821 | + | 0.948819i | \(0.602280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.0743 | −1.23604 | ||||||||
\(446\) | −22.4068 | −1.06099 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.0580 | −0.569686 | ||||||||
\(449\) | −20.8714 | −0.984981 | −0.492490 | − | 0.870318i | \(-0.663913\pi\) | ||||
−0.492490 | + | 0.870318i | \(0.663913\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 26.2509 | 1.23474 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −58.4810 | −2.74465 | ||||||||
\(455\) | −17.3950 | −0.815490 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.2344 | −1.32075 | −0.660375 | − | 0.750936i | \(-0.729603\pi\) | ||||
−0.660375 | + | 0.750936i | \(0.729603\pi\) | |||||||
\(458\) | 23.7070 | 1.10776 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 25.6403 | 1.19549 | ||||||||
\(461\) | 13.5432 | 0.630770 | 0.315385 | − | 0.948964i | \(-0.397866\pi\) | ||||
0.315385 | + | 0.948964i | \(0.397866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.9584 | −1.57818 | −0.789090 | − | 0.614277i | \(-0.789448\pi\) | ||||
−0.789090 | + | 0.614277i | \(0.789448\pi\) | |||||||
\(464\) | −95.1873 | −4.41896 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 52.5107 | 2.43251 | ||||||||
\(467\) | −12.5809 | −0.582172 | −0.291086 | − | 0.956697i | \(-0.594017\pi\) | ||||
−0.291086 | + | 0.956697i | \(0.594017\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.04949 | 0.371691 | ||||||||
\(470\) | 12.9764 | 0.598556 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 51.8488 | 2.38653 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.553056 | 0.0253759 | ||||||||
\(476\) | −27.8322 | −1.27569 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.3396 | −1.11327 | ||||||||
\(479\) | −28.8916 | −1.32009 | −0.660046 | − | 0.751225i | \(-0.729463\pi\) | ||||
−0.660046 | + | 0.751225i | \(0.729463\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.5380 | −1.07324 | ||||||||
\(482\) | 2.11966 | 0.0965478 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.5301 | 0.796001 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.5077 | 1.15586 | 0.577932 | − | 0.816085i | \(-0.303860\pi\) | ||||
0.577932 | + | 0.816085i | \(0.303860\pi\) | |||||||
\(488\) | 66.5443 | 3.01232 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.14075 | 0.367762 | ||||||||
\(491\) | −4.66598 | −0.210573 | −0.105286 | − | 0.994442i | \(-0.533576\pi\) | ||||
−0.105286 | + | 0.994442i | \(0.533576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −49.5697 | −2.23250 | ||||||||
\(494\) | 1.82652 | 0.0821789 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.1838 | 0.771576 | ||||||||
\(497\) | 6.24379 | 0.280072 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.4958 | −0.827987 | −0.413994 | − | 0.910280i | \(-0.635866\pi\) | ||||
−0.413994 | + | 0.910280i | \(0.635866\pi\) | |||||||
\(500\) | 7.52191 | 0.336390 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.21246 | 0.0541149 | ||||||||
\(503\) | 23.1076 | 1.03032 | 0.515159 | − | 0.857094i | \(-0.327733\pi\) | ||||
0.515159 | + | 0.857094i | \(0.327733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 52.0451 | 2.31598 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −56.3518 | −2.50021 | ||||||||
\(509\) | 28.6541 | 1.27007 | 0.635036 | − | 0.772483i | \(-0.280985\pi\) | ||||
0.635036 | + | 0.772483i | \(0.280985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.51005 | −0.155275 | ||||||||
\(512\) | 31.8553 | 1.40782 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −61.6620 | −2.71979 | ||||||||
\(515\) | 40.7576 | 1.79600 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.0156 | 0.483998 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −136.354 | −5.97954 | ||||||||
\(521\) | 7.99220 | 0.350144 | 0.175072 | − | 0.984556i | \(-0.443984\pi\) | ||||
0.175072 | + | 0.984556i | \(0.443984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.2399 | 1.62839 | 0.814194 | − | 0.580592i | \(-0.197179\pi\) | ||||
0.814194 | + | 0.580592i | \(0.197179\pi\) | |||||||
\(524\) | 4.82161 | 0.210633 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.0986 | −0.571124 | ||||||||
\(527\) | 8.94863 | 0.389808 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2002 | −0.878272 | ||||||||
\(530\) | 96.5202 | 4.19257 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.609494 | −0.0264249 | ||||||||
\(533\) | 19.6791 | 0.852394 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.1503 | 1.47645 | ||||||||
\(536\) | 63.0977 | 2.72541 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.72449 | 0.117461 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9890 | −0.988376 | −0.494188 | − | 0.869355i | \(-0.664535\pi\) | ||||
−0.494188 | + | 0.869355i | \(0.664535\pi\) | |||||||
\(542\) | −39.9759 | −1.71711 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −71.2180 | −3.05345 | ||||||||
\(545\) | 15.0289 | 0.643769 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.4285 | 1.30103 | 0.650515 | − | 0.759493i | \(-0.274553\pi\) | ||||
0.650515 | + | 0.759493i | \(0.274553\pi\) | |||||||
\(548\) | 0.621660 | 0.0265560 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.08552 | −0.0462447 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.39769 | 0.399630 | ||||||||
\(554\) | 2.82477 | 0.120013 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.34016 | −0.353702 | ||||||||
\(557\) | 42.4812 | 1.79998 | 0.899992 | − | 0.435906i | \(-0.143572\pi\) | ||||
0.899992 | + | 0.435906i | \(0.143572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.8083 | 1.21846 | ||||||||
\(560\) | 33.1656 | 1.40150 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −82.6538 | −3.48654 | ||||||||
\(563\) | −12.0958 | −0.509777 | −0.254888 | − | 0.966971i | \(-0.582039\pi\) | ||||
−0.254888 | + | 0.966971i | \(0.582039\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.2900 | −0.685325 | ||||||||
\(566\) | −84.3858 | −3.54700 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 48.9433 | 2.05361 | ||||||||
\(569\) | 34.0054 | 1.42558 | 0.712789 | − | 0.701378i | \(-0.247432\pi\) | ||||
0.712789 | + | 0.701378i | \(0.247432\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0762 | 0.672767 | 0.336383 | − | 0.941725i | \(-0.390796\pi\) | ||||
0.336383 | + | 0.941725i | \(0.390796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.20967 | −0.384404 | ||||||||
\(575\) | −7.54489 | −0.314643 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.94068 | 0.164053 | 0.0820264 | − | 0.996630i | \(-0.473861\pi\) | ||||
0.0820264 | + | 0.996630i | \(0.473861\pi\) | |||||||
\(578\) | −37.9347 | −1.57787 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 135.621 | 5.63134 | ||||||||
\(581\) | −9.43386 | −0.391383 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −27.5142 | −1.13855 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.24859 | −0.0515789 | ||||||||
\(587\) | −9.92820 | −0.409781 | −0.204890 | − | 0.978785i | \(-0.565684\pi\) | ||||
−0.204890 | + | 0.978785i | \(0.565684\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.195965 | 0.00807460 | ||||||||
\(590\) | −53.8466 | −2.21683 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 44.8778 | 1.84447 | ||||||||
\(593\) | −1.35512 | −0.0556480 | −0.0278240 | − | 0.999613i | \(-0.508858\pi\) | ||||
−0.0278240 | + | 0.999613i | \(0.508858\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.2713 | 0.708053 | ||||||||
\(596\) | −70.4601 | −2.88616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.9177 | −1.01896 | ||||||||
\(599\) | 30.7682 | 1.25716 | 0.628578 | − | 0.777747i | \(-0.283637\pi\) | ||||
0.628578 | + | 0.777747i | \(0.283637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.2165 | −0.539113 | −0.269557 | − | 0.962985i | \(-0.586877\pi\) | ||||
−0.269557 | + | 0.962985i | \(0.586877\pi\) | |||||||
\(602\) | −13.4821 | −0.549490 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 78.9237 | 3.21136 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.83308 | −0.236757 | −0.118379 | − | 0.992969i | \(-0.537770\pi\) | ||||
−0.118379 | + | 0.992969i | \(0.537770\pi\) | |||||||
\(608\) | −1.55960 | −0.0632499 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −69.1083 | −2.79811 | ||||||||
\(611\) | −8.99173 | −0.363767 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.67731 | 0.269694 | 0.134847 | − | 0.990866i | \(-0.456946\pi\) | ||||
0.134847 | + | 0.990866i | \(0.456946\pi\) | |||||||
\(614\) | 59.0084 | 2.38139 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.1716 | −0.610785 | −0.305392 | − | 0.952227i | \(-0.598788\pi\) | ||||
−0.305392 | + | 0.952227i | \(0.598788\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.9902 | 1.12502 | 0.562510 | − | 0.826790i | \(-0.309836\pi\) | ||||
0.562510 | + | 0.826790i | \(0.309836\pi\) | |||||||
\(620\) | −24.4831 | −0.983264 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 58.0359 | 2.32703 | ||||||||
\(623\) | −8.45556 | −0.338765 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.2134 | −1.08854 | ||||||||
\(626\) | 20.9882 | 0.838858 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −45.7101 | −1.82403 | ||||||||
\(629\) | 23.3705 | 0.931844 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.58035 | −0.222150 | −0.111075 | − | 0.993812i | \(-0.535429\pi\) | ||||
−0.111075 | + | 0.993812i | \(0.535429\pi\) | |||||||
\(632\) | 73.6658 | 2.93027 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −39.9230 | −1.58554 | ||||||||
\(635\) | 34.9692 | 1.38771 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.64097 | −0.223503 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19.7393 | 0.780265 | ||||||||
\(641\) | −10.9667 | −0.433158 | −0.216579 | − | 0.976265i | \(-0.569490\pi\) | ||||
−0.216579 | + | 0.976265i | \(0.569490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.399143 | 0.0157406 | 0.00787032 | − | 0.999969i | \(-0.497495\pi\) | ||||
0.00787032 | + | 0.999969i | \(0.497495\pi\) | |||||||
\(644\) | 8.31482 | 0.327650 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.81353 | −0.0713523 | ||||||||
\(647\) | −31.2956 | −1.23036 | −0.615178 | − | 0.788389i | \(-0.710916\pi\) | ||||
−0.615178 | + | 0.788389i | \(0.710916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 67.1492 | 2.63381 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 48.5470 | 1.90125 | ||||||||
\(653\) | 26.1788 | 1.02446 | 0.512228 | − | 0.858849i | \(-0.328820\pi\) | ||||
0.512228 | + | 0.858849i | \(0.328820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.99205 | −0.116909 | ||||||||
\(656\) | −37.5204 | −1.46493 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.20807 | 0.164048 | ||||||||
\(659\) | 5.84482 | 0.227682 | 0.113841 | − | 0.993499i | \(-0.463685\pi\) | ||||
0.113841 | + | 0.993499i | \(0.463685\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.32811 | −0.246135 | −0.123067 | − | 0.992398i | \(-0.539273\pi\) | ||||
−0.123067 | + | 0.992398i | \(0.539273\pi\) | |||||||
\(662\) | 15.9067 | 0.618233 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −73.9494 | −2.86979 | ||||||||
\(665\) | 0.378222 | 0.0146668 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.8089 | 0.573401 | ||||||||
\(668\) | −30.3243 | −1.17328 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −65.5289 | −2.53160 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.21912 | 0.162635 | 0.0813176 | − | 0.996688i | \(-0.474087\pi\) | ||||
0.0813176 | + | 0.996688i | \(0.474087\pi\) | |||||||
\(674\) | −55.0411 | −2.12010 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 93.5246 | 3.59710 | ||||||||
\(677\) | −17.9247 | −0.688902 | −0.344451 | − | 0.938804i | \(-0.611935\pi\) | ||||
−0.344451 | + | 0.938804i | \(0.611935\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.68478 | 0.218162 | ||||||||
\(680\) | 135.385 | 5.19176 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.96513 | 0.228249 | 0.114125 | − | 0.993466i | \(-0.463594\pi\) | ||||
0.114125 | + | 0.993466i | \(0.463594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.385771 | −0.0147396 | ||||||||
\(686\) | 2.63994 | 0.100793 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −54.9264 | −2.09405 | ||||||||
\(689\) | −66.8818 | −2.54799 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.4084 | −1.49917 | −0.749583 | − | 0.661910i | \(-0.769746\pi\) | ||||
−0.749583 | + | 0.661910i | \(0.769746\pi\) | |||||||
\(692\) | −33.4839 | −1.27287 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.94221 | 0.149644 | ||||||||
\(695\) | 5.17549 | 0.196318 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.5391 | −0.740096 | ||||||||
\(698\) | 56.7046 | 2.14630 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −22.4071 | −0.846910 | ||||||||
\(701\) | 25.4284 | 0.960417 | 0.480208 | − | 0.877154i | \(-0.340561\pi\) | ||||
0.480208 | + | 0.877154i | \(0.340561\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.511789 | 0.0193025 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.2961 | 1.14021 | ||||||||
\(707\) | 16.8776 | 0.634746 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.08068 | 0.265921 | 0.132960 | − | 0.991121i | \(-0.457552\pi\) | ||||
0.132960 | + | 0.991121i | \(0.457552\pi\) | |||||||
\(710\) | −50.8291 | −1.90758 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −66.2807 | −2.48398 | ||||||||
\(713\) | −2.67339 | −0.100119 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −64.5686 | −2.41304 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.1132 | −0.564018 | ||||||||
\(719\) | 21.5811 | 0.804840 | 0.402420 | − | 0.915455i | \(-0.368169\pi\) | ||||
0.402420 | + | 0.915455i | \(0.368169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.2172 | 0.492233 | ||||||||
\(722\) | 50.1191 | 1.86524 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.3650 | −0.756861 | ||||||||
\(725\) | −39.9075 | −1.48213 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.7114 | 1.32446 | 0.662231 | − | 0.749300i | \(-0.269610\pi\) | ||||
0.662231 | + | 0.749300i | \(0.269610\pi\) | |||||||
\(728\) | −44.2180 | −1.63883 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 28.5744 | 1.05759 | ||||||||
\(731\) | −28.6034 | −1.05794 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.34501 | 0.234358 | 0.117179 | − | 0.993111i | \(-0.462615\pi\) | ||||
0.117179 | + | 0.993111i | \(0.462615\pi\) | |||||||
\(734\) | −46.1965 | −1.70515 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.2763 | 0.784254 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.9804 | 0.403922 | 0.201961 | − | 0.979394i | \(-0.435269\pi\) | ||||
0.201961 | + | 0.979394i | \(0.435269\pi\) | |||||||
\(740\) | −63.9409 | −2.35051 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 31.3003 | 1.14907 | ||||||||
\(743\) | 18.4186 | 0.675711 | 0.337856 | − | 0.941198i | \(-0.390298\pi\) | ||||
0.337856 | + | 0.941198i | \(0.390298\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.7240 | 1.60192 | ||||||||
\(746\) | 25.1946 | 0.922438 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.0745 | 0.404654 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.96566 | 0.181200 | 0.0905998 | − | 0.995887i | \(-0.471122\pi\) | ||||
0.0905998 | + | 0.995887i | \(0.471122\pi\) | |||||||
\(752\) | 17.1438 | 0.625170 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −131.798 | −4.79981 | ||||||||
\(755\) | −48.9761 | −1.78242 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.04107 | −0.0378384 | −0.0189192 | − | 0.999821i | \(-0.506023\pi\) | ||||
−0.0189192 | + | 0.999821i | \(0.506023\pi\) | |||||||
\(758\) | −84.3737 | −3.06459 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.96477 | 0.107544 | ||||||||
\(761\) | 42.0282 | 1.52352 | 0.761760 | − | 0.647860i | \(-0.224336\pi\) | ||||
0.761760 | + | 0.647860i | \(0.224336\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.87369 | 0.176439 | ||||||||
\(764\) | −106.857 | −3.86597 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.9304 | −0.936905 | ||||||||
\(767\) | 37.3119 | 1.34726 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.1300 | 1.59137 | 0.795684 | − | 0.605712i | \(-0.207112\pi\) | ||||
0.795684 | + | 0.605712i | \(0.207112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 88.4352 | 3.18285 | ||||||||
\(773\) | 37.3027 | 1.34168 | 0.670842 | − | 0.741600i | \(-0.265933\pi\) | ||||
0.670842 | + | 0.741600i | \(0.265933\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.20436 | 0.258788 | ||||||||
\(776\) | 44.5614 | 1.59966 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 87.6454 | 3.14224 | ||||||||
\(779\) | −0.427884 | −0.0153305 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 24.7404 | 0.884717 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.7552 | 0.384113 | ||||||||
\(785\) | 28.3654 | 1.01241 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.35809 | 0.262288 | 0.131144 | − | 0.991363i | \(-0.458135\pi\) | ||||
0.131144 | + | 0.991363i | \(0.458135\pi\) | |||||||
\(788\) | −89.9850 | −3.20558 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −76.5042 | −2.72190 | ||||||||
\(791\) | −5.28263 | −0.187829 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.8872 | 1.70053 | ||||||||
\(794\) | −62.4437 | −2.21604 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.2749 | 0.470515 | ||||||||
\(797\) | −6.00177 | −0.212594 | −0.106297 | − | 0.994334i | \(-0.533899\pi\) | ||||
−0.106297 | + | 0.994334i | \(0.533899\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.92778 | 0.315842 | ||||||||
\(800\) | −57.3362 | −2.02714 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 66.7210 | 2.35600 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.15977 | −0.181858 | ||||||||
\(806\) | 23.7931 | 0.838075 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 132.298 | 4.65424 | ||||||||
\(809\) | 28.3939 | 0.998278 | 0.499139 | − | 0.866522i | \(-0.333650\pi\) | ||||
0.499139 | + | 0.866522i | \(0.333650\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.9066 | 1.12039 | 0.560196 | − | 0.828360i | \(-0.310726\pi\) | ||||
0.560196 | + | 0.828360i | \(0.310726\pi\) | |||||||
\(812\) | 43.9800 | 1.54340 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.1259 | −1.05526 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.626383 | −0.0219144 | ||||||||
\(818\) | −36.8893 | −1.28980 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 53.4582 | 1.86684 | ||||||||
\(821\) | 4.55941 | 0.159125 | 0.0795623 | − | 0.996830i | \(-0.474648\pi\) | ||||
0.0795623 | + | 0.996830i | \(0.474648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.5932 | 1.62414 | 0.812069 | − | 0.583562i | \(-0.198341\pi\) | ||||
0.812069 | + | 0.583562i | \(0.198341\pi\) | |||||||
\(824\) | 103.606 | 3.60927 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.4617 | −0.607572 | ||||||||
\(827\) | 1.00246 | 0.0348589 | 0.0174294 | − | 0.999848i | \(-0.494452\pi\) | ||||
0.0174294 | + | 0.999848i | \(0.494452\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.4845 | −1.75340 | −0.876699 | − | 0.481039i | \(-0.840260\pi\) | ||||
−0.876699 | + | 0.481039i | \(0.840260\pi\) | |||||||
\(830\) | 76.7987 | 2.66572 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −68.0187 | −2.35813 | ||||||||
\(833\) | 5.60085 | 0.194058 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.8178 | 0.651216 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 78.5236 | 2.71255 | ||||||||
\(839\) | 26.0614 | 0.899739 | 0.449869 | − | 0.893094i | \(-0.351471\pi\) | ||||
0.449869 | + | 0.893094i | \(0.351471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.3292 | 1.70101 | ||||||||
\(842\) | −95.7441 | −3.29956 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −40.5218 | −1.39482 | ||||||||
\(845\) | −58.0368 | −1.99652 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 127.518 | 4.37898 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −66.6716 | −2.28682 | ||||||||
\(851\) | −6.98191 | −0.239337 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.1888 | −1.03364 | −0.516822 | − | 0.856093i | \(-0.672885\pi\) | ||||
−0.516822 | + | 0.856093i | \(0.672885\pi\) | |||||||
\(854\) | −22.4109 | −0.766886 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 86.8099 | 2.96710 | ||||||||
\(857\) | 25.3151 | 0.864748 | 0.432374 | − | 0.901694i | \(-0.357676\pi\) | ||||
0.432374 | + | 0.901694i | \(0.357676\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.7680 | −0.367399 | −0.183699 | − | 0.982982i | \(-0.558807\pi\) | ||||
−0.183699 | + | 0.982982i | \(0.558807\pi\) | |||||||
\(860\) | 78.2578 | 2.66857 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 94.5273 | 3.21961 | ||||||||
\(863\) | 35.3003 | 1.20163 | 0.600817 | − | 0.799386i | \(-0.294842\pi\) | ||||
0.600817 | + | 0.799386i | \(0.294842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.7784 | 0.706488 | ||||||||
\(866\) | 60.9716 | 2.07190 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.93955 | −0.269486 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.4070 | 1.53856 | ||||||||
\(872\) | 38.2035 | 1.29373 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.541788 | 0.0183263 | ||||||||
\(875\) | −1.51368 | −0.0511718 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.16706 | −0.140712 | −0.0703558 | − | 0.997522i | \(-0.522413\pi\) | ||||
−0.0703558 | + | 0.997522i | \(0.522413\pi\) | |||||||
\(878\) | −65.4275 | −2.20807 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.6561 | 1.36974 | 0.684870 | − | 0.728665i | \(-0.259859\pi\) | ||||
0.684870 | + | 0.728665i | \(0.259859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.1697 | −0.645113 | −0.322556 | − | 0.946550i | \(-0.604542\pi\) | ||||
−0.322556 | + | 0.946550i | \(0.604542\pi\) | |||||||
\(884\) | −157.001 | −5.28050 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.0967 | 1.17910 | ||||||||
\(887\) | 37.0380 | 1.24362 | 0.621808 | − | 0.783170i | \(-0.286398\pi\) | ||||
0.621808 | + | 0.783170i | \(0.286398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.3400 | 0.380333 | ||||||||
\(890\) | 68.8346 | 2.30734 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 42.1774 | 1.41220 | ||||||||
\(893\) | 0.195508 | 0.00654244 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.0681 | 1.33933 | ||||||||
\(896\) | 6.40120 | 0.213849 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 55.0992 | 1.83868 | ||||||||
\(899\) | −14.1405 | −0.471612 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66.4061 | 2.21231 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41.4090 | −1.37724 | ||||||||
\(905\) | 12.6375 | 0.420086 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.7583 | −0.954905 | −0.477452 | − | 0.878658i | \(-0.658440\pi\) | ||||
−0.477452 | + | 0.878658i | \(0.658440\pi\) | |||||||
\(908\) | 110.082 | 3.65318 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 45.9217 | 1.52229 | ||||||||
\(911\) | −44.7716 | −1.48335 | −0.741675 | − | 0.670759i | \(-0.765968\pi\) | ||||
−0.741675 | + | 0.670759i | \(0.765968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 74.5371 | 2.46547 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −44.6248 | −1.47445 | ||||||||
\(917\) | −0.970284 | −0.0320416 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.3392 | 0.637943 | 0.318971 | − | 0.947764i | \(-0.396663\pi\) | ||||
0.318971 | + | 0.947764i | \(0.396663\pi\) | |||||||
\(920\) | −40.4459 | −1.33346 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −35.7533 | −1.17747 | ||||||||
\(923\) | 35.2210 | 1.15931 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.8152 | 0.618638 | ||||||||
\(926\) | 89.6481 | 2.94602 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 112.538 | 3.69423 | ||||||||
\(929\) | 26.9129 | 0.882985 | 0.441493 | − | 0.897265i | \(-0.354449\pi\) | ||||
0.441493 | + | 0.897265i | \(0.354449\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.122652 | 0.00401977 | ||||||||
\(932\) | −98.8433 | −3.23772 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.2127 | 1.08675 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.5349 | 1.38956 | 0.694778 | − | 0.719224i | \(-0.255503\pi\) | ||||
0.694778 | + | 0.719224i | \(0.255503\pi\) | |||||||
\(938\) | −21.2502 | −0.693843 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −24.4260 | −0.796690 | ||||||||
\(941\) | 48.7704 | 1.58987 | 0.794934 | − | 0.606695i | \(-0.207505\pi\) | ||||
0.794934 | + | 0.606695i | \(0.207505\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.83727 | 0.190088 | ||||||||
\(944\) | −71.1395 | −2.31540 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.641845 | −0.0208572 | −0.0104286 | − | 0.999946i | \(-0.503320\pi\) | ||||
−0.0104286 | + | 0.999946i | \(0.503320\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.8001 | −0.642738 | ||||||||
\(950\) | −1.46003 | −0.0473698 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 43.9035 | 1.42292 | ||||||||
\(953\) | −7.65944 | −0.248114 | −0.124057 | − | 0.992275i | \(-0.539591\pi\) | ||||
−0.124057 | + | 0.992275i | \(0.539591\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 66.3104 | 2.14576 | ||||||||
\(956\) | 45.8156 | 1.48178 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 76.2721 | 2.46424 | ||||||||
\(959\) | −0.125101 | −0.00403971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4473 | −0.917654 | ||||||||
\(962\) | 62.1388 | 2.00343 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.98993 | −0.128507 | ||||||||
\(965\) | −54.8785 | −1.76660 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.7387 | −0.956333 | −0.478166 | − | 0.878269i | \(-0.658698\pi\) | ||||
−0.478166 | + | 0.878269i | \(0.658698\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −46.2784 | −1.48591 | ||||||||
\(971\) | 34.9188 | 1.12060 | 0.560299 | − | 0.828291i | \(-0.310686\pi\) | ||||
0.560299 | + | 0.828291i | \(0.310686\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.67835 | 0.0538053 | ||||||||
\(974\) | −67.3388 | −2.15767 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −91.3026 | −2.92253 | ||||||||
\(977\) | −31.9341 | −1.02166 | −0.510832 | − | 0.859681i | \(-0.670662\pi\) | ||||
−0.510832 | + | 0.859681i | \(0.670662\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −15.3237 | −0.489498 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.3179 | 0.393080 | ||||||||
\(983\) | 33.9111 | 1.08159 | 0.540797 | − | 0.841153i | \(-0.318123\pi\) | ||||
0.540797 | + | 0.841153i | \(0.318123\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.8402 | 1.77922 | ||||||||
\(986\) | 130.861 | 4.16746 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.43814 | −0.109382 | ||||||||
\(989\) | 8.54523 | 0.271722 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3101 | −0.422809 | −0.211404 | − | 0.977399i | \(-0.567804\pi\) | ||||
−0.211404 | + | 0.977399i | \(0.567804\pi\) | |||||||
\(992\) | −20.3160 | −0.645034 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.4832 | −0.522816 | ||||||||
\(995\) | −8.23772 | −0.261153 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.95257 | −0.0935088 | −0.0467544 | − | 0.998906i | \(-0.514888\pi\) | ||||
−0.0467544 | + | 0.998906i | \(0.514888\pi\) | |||||||
\(998\) | 48.8279 | 1.54562 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7623.2.a.cx.1.2 | 10 | ||
3.2 | odd | 2 | 2541.2.a.bq.1.9 | 10 | |||
11.5 | even | 5 | 693.2.m.j.190.5 | 20 | |||
11.9 | even | 5 | 693.2.m.j.631.5 | 20 | |||
11.10 | odd | 2 | 7623.2.a.cy.1.9 | 10 | |||
33.5 | odd | 10 | 231.2.j.g.190.1 | yes | 20 | ||
33.20 | odd | 10 | 231.2.j.g.169.1 | ✓ | 20 | ||
33.32 | even | 2 | 2541.2.a.br.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.g.169.1 | ✓ | 20 | 33.20 | odd | 10 | ||
231.2.j.g.190.1 | yes | 20 | 33.5 | odd | 10 | ||
693.2.m.j.190.5 | 20 | 11.5 | even | 5 | |||
693.2.m.j.631.5 | 20 | 11.9 | even | 5 | |||
2541.2.a.bq.1.9 | 10 | 3.2 | odd | 2 | |||
2541.2.a.br.1.2 | 10 | 33.32 | even | 2 | |||
7623.2.a.cx.1.2 | 10 | 1.1 | even | 1 | trivial | ||
7623.2.a.cy.1.9 | 10 | 11.10 | odd | 2 |