Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.7457527933.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.70360\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23115 | −1.57766 | −0.788829 | − | 0.614612i | \(-0.789312\pi\) | ||||
−0.788829 | + | 0.614612i | \(0.789312\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.97801 | 1.48901 | ||||||||
\(5\) | −0.893036 | −0.399378 | −0.199689 | − | 0.979859i | \(-0.563993\pi\) | ||||
−0.199689 | + | 0.979859i | \(0.563993\pi\) | |||||||
\(6\) | −2.23115 | −0.910862 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.18209 | −0.771485 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.99249 | 0.630082 | ||||||||
\(11\) | −3.03213 | −0.914220 | −0.457110 | − | 0.889410i | \(-0.651116\pi\) | ||||
−0.457110 | + | 0.889410i | \(0.651116\pi\) | |||||||
\(12\) | 2.97801 | 0.859678 | ||||||||
\(13\) | −1.02235 | −0.283548 | −0.141774 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141774 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.893036 | −0.230581 | ||||||||
\(16\) | −1.08747 | −0.271867 | ||||||||
\(17\) | −0.590534 | −0.143226 | −0.0716128 | − | 0.997433i | \(-0.522815\pi\) | ||||
−0.0716128 | + | 0.997433i | \(0.522815\pi\) | |||||||
\(18\) | −2.23115 | −0.525886 | ||||||||
\(19\) | −3.50700 | −0.804561 | −0.402281 | − | 0.915516i | \(-0.631782\pi\) | ||||
−0.402281 | + | 0.915516i | \(0.631782\pi\) | |||||||
\(20\) | −2.65947 | −0.594676 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.76512 | 1.44233 | ||||||||
\(23\) | −0.556191 | −0.115974 | −0.0579870 | − | 0.998317i | \(-0.518468\pi\) | ||||
−0.0579870 | + | 0.998317i | \(0.518468\pi\) | |||||||
\(24\) | −2.18209 | −0.445417 | ||||||||
\(25\) | −4.20249 | −0.840497 | ||||||||
\(26\) | 2.28100 | 0.447342 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.89796 | 1.46661 | 0.733307 | − | 0.679898i | \(-0.237976\pi\) | ||||
0.733307 | + | 0.679898i | \(0.237976\pi\) | |||||||
\(30\) | 1.99249 | 0.363778 | ||||||||
\(31\) | 1.28393 | 0.230601 | 0.115300 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115300 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(32\) | 6.79048 | 1.20040 | ||||||||
\(33\) | −3.03213 | −0.527825 | ||||||||
\(34\) | 1.31757 | 0.225961 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.97801 | 0.496335 | ||||||||
\(37\) | −11.5424 | −1.89756 | −0.948779 | − | 0.315940i | \(-0.897680\pi\) | ||||
−0.948779 | + | 0.315940i | \(0.897680\pi\) | |||||||
\(38\) | 7.82463 | 1.26932 | ||||||||
\(39\) | −1.02235 | −0.163706 | ||||||||
\(40\) | 1.94868 | 0.308114 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.76153 | −0.878625 | −0.439313 | − | 0.898334i | \(-0.644778\pi\) | ||||
−0.439313 | + | 0.898334i | \(0.644778\pi\) | |||||||
\(44\) | −9.02971 | −1.36128 | ||||||||
\(45\) | −0.893036 | −0.133126 | ||||||||
\(46\) | 1.24094 | 0.182967 | ||||||||
\(47\) | 0.229519 | 0.0334788 | 0.0167394 | − | 0.999860i | \(-0.494671\pi\) | ||||
0.0167394 | + | 0.999860i | \(0.494671\pi\) | |||||||
\(48\) | −1.08747 | −0.156962 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.37636 | 1.32602 | ||||||||
\(51\) | −0.590534 | −0.0826913 | ||||||||
\(52\) | −3.04456 | −0.422205 | ||||||||
\(53\) | 8.54823 | 1.17419 | 0.587095 | − | 0.809518i | \(-0.300271\pi\) | ||||
0.587095 | + | 0.809518i | \(0.300271\pi\) | |||||||
\(54\) | −2.23115 | −0.303621 | ||||||||
\(55\) | 2.70780 | 0.365119 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.50700 | −0.464514 | ||||||||
\(58\) | −17.6215 | −2.31382 | ||||||||
\(59\) | −10.6811 | −1.39056 | −0.695282 | − | 0.718737i | \(-0.744721\pi\) | ||||
−0.695282 | + | 0.718737i | \(0.744721\pi\) | |||||||
\(60\) | −2.65947 | −0.343336 | ||||||||
\(61\) | −8.09457 | −1.03640 | −0.518202 | − | 0.855258i | \(-0.673398\pi\) | ||||
−0.518202 | + | 0.855258i | \(0.673398\pi\) | |||||||
\(62\) | −2.86464 | −0.363809 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.9756 | −1.62195 | ||||||||
\(65\) | 0.912992 | 0.113243 | ||||||||
\(66\) | 6.76512 | 0.832728 | ||||||||
\(67\) | 8.13979 | 0.994434 | 0.497217 | − | 0.867626i | \(-0.334355\pi\) | ||||
0.497217 | + | 0.867626i | \(0.334355\pi\) | |||||||
\(68\) | −1.75862 | −0.213264 | ||||||||
\(69\) | −0.556191 | −0.0669576 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.38924 | 0.164873 | 0.0824363 | − | 0.996596i | \(-0.473730\pi\) | ||||
0.0824363 | + | 0.996596i | \(0.473730\pi\) | |||||||
\(72\) | −2.18209 | −0.257162 | ||||||||
\(73\) | 10.7543 | 1.25869 | 0.629345 | − | 0.777126i | \(-0.283323\pi\) | ||||
0.629345 | + | 0.777126i | \(0.283323\pi\) | |||||||
\(74\) | 25.7528 | 2.99370 | ||||||||
\(75\) | −4.20249 | −0.485261 | ||||||||
\(76\) | −10.4439 | −1.19800 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.28100 | 0.258273 | ||||||||
\(79\) | 4.67035 | 0.525456 | 0.262728 | − | 0.964870i | \(-0.415378\pi\) | ||||
0.262728 | + | 0.964870i | \(0.415378\pi\) | |||||||
\(80\) | 0.971148 | 0.108578 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.23115 | −0.246389 | ||||||||
\(83\) | 3.22689 | 0.354197 | 0.177099 | − | 0.984193i | \(-0.443329\pi\) | ||||
0.177099 | + | 0.984193i | \(0.443329\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.527368 | 0.0572011 | ||||||||
\(86\) | 12.8548 | 1.38617 | ||||||||
\(87\) | 7.89796 | 0.846750 | ||||||||
\(88\) | 6.61637 | 0.705307 | ||||||||
\(89\) | 15.9423 | 1.68989 | 0.844943 | − | 0.534857i | \(-0.179634\pi\) | ||||
0.844943 | + | 0.534857i | \(0.179634\pi\) | |||||||
\(90\) | 1.99249 | 0.210027 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.65634 | −0.172686 | ||||||||
\(93\) | 1.28393 | 0.133138 | ||||||||
\(94\) | −0.512091 | −0.0528182 | ||||||||
\(95\) | 3.13188 | 0.321324 | ||||||||
\(96\) | 6.79048 | 0.693050 | ||||||||
\(97\) | 5.16775 | 0.524706 | 0.262353 | − | 0.964972i | \(-0.415502\pi\) | ||||
0.262353 | + | 0.964972i | \(0.415502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.03213 | −0.304740 | ||||||||
\(100\) | −12.5151 | −1.25151 | ||||||||
\(101\) | 10.6304 | 1.05776 | 0.528881 | − | 0.848696i | \(-0.322612\pi\) | ||||
0.528881 | + | 0.848696i | \(0.322612\pi\) | |||||||
\(102\) | 1.31757 | 0.130459 | ||||||||
\(103\) | −3.93822 | −0.388044 | −0.194022 | − | 0.980997i | \(-0.562153\pi\) | ||||
−0.194022 | + | 0.980997i | \(0.562153\pi\) | |||||||
\(104\) | 2.23085 | 0.218753 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.0724 | −1.85247 | ||||||||
\(107\) | −10.8000 | −1.04408 | −0.522039 | − | 0.852922i | \(-0.674828\pi\) | ||||
−0.522039 | + | 0.852922i | \(0.674828\pi\) | |||||||
\(108\) | 2.97801 | 0.286559 | ||||||||
\(109\) | −13.7396 | −1.31601 | −0.658007 | − | 0.753012i | \(-0.728600\pi\) | ||||
−0.658007 | + | 0.753012i | \(0.728600\pi\) | |||||||
\(110\) | −6.04149 | −0.576034 | ||||||||
\(111\) | −11.5424 | −1.09556 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.87693 | 0.270638 | 0.135319 | − | 0.990802i | \(-0.456794\pi\) | ||||
0.135319 | + | 0.990802i | \(0.456794\pi\) | |||||||
\(114\) | 7.82463 | 0.732844 | ||||||||
\(115\) | 0.496699 | 0.0463174 | ||||||||
\(116\) | 23.5202 | 2.18380 | ||||||||
\(117\) | −1.02235 | −0.0945160 | ||||||||
\(118\) | 23.8312 | 2.19384 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.94868 | 0.177890 | ||||||||
\(121\) | −1.80621 | −0.164201 | ||||||||
\(122\) | 18.0602 | 1.63509 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 3.82356 | 0.343366 | ||||||||
\(125\) | 8.21815 | 0.735054 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.93950 | −0.704517 | −0.352258 | − | 0.935903i | \(-0.614586\pi\) | ||||
−0.352258 | + | 0.935903i | \(0.614586\pi\) | |||||||
\(128\) | 15.3695 | 1.35849 | ||||||||
\(129\) | −5.76153 | −0.507274 | ||||||||
\(130\) | −2.03702 | −0.178658 | ||||||||
\(131\) | 1.91414 | 0.167239 | 0.0836195 | − | 0.996498i | \(-0.473352\pi\) | ||||
0.0836195 | + | 0.996498i | \(0.473352\pi\) | |||||||
\(132\) | −9.02971 | −0.785935 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −18.1611 | −1.56888 | ||||||||
\(135\) | −0.893036 | −0.0768603 | ||||||||
\(136\) | 1.28860 | 0.110496 | ||||||||
\(137\) | 10.9420 | 0.934842 | 0.467421 | − | 0.884035i | \(-0.345183\pi\) | ||||
0.467421 | + | 0.884035i | \(0.345183\pi\) | |||||||
\(138\) | 1.24094 | 0.105636 | ||||||||
\(139\) | 20.5931 | 1.74668 | 0.873341 | − | 0.487109i | \(-0.161949\pi\) | ||||
0.873341 | + | 0.487109i | \(0.161949\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.229519 | 0.0193290 | ||||||||
\(142\) | −3.09960 | −0.260112 | ||||||||
\(143\) | 3.09988 | 0.259225 | ||||||||
\(144\) | −1.08747 | −0.0906223 | ||||||||
\(145\) | −7.05316 | −0.585733 | ||||||||
\(146\) | −23.9943 | −1.98578 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −34.3734 | −2.82548 | ||||||||
\(149\) | 3.25543 | 0.266695 | 0.133347 | − | 0.991069i | \(-0.457427\pi\) | ||||
0.133347 | + | 0.991069i | \(0.457427\pi\) | |||||||
\(150\) | 9.37636 | 0.765577 | ||||||||
\(151\) | 12.0406 | 0.979852 | 0.489926 | − | 0.871764i | \(-0.337024\pi\) | ||||
0.489926 | + | 0.871764i | \(0.337024\pi\) | |||||||
\(152\) | 7.65258 | 0.620706 | ||||||||
\(153\) | −0.590534 | −0.0477418 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.14660 | −0.0920969 | ||||||||
\(156\) | −3.04456 | −0.243760 | ||||||||
\(157\) | 0.580260 | 0.0463098 | 0.0231549 | − | 0.999732i | \(-0.492629\pi\) | ||||
0.0231549 | + | 0.999732i | \(0.492629\pi\) | |||||||
\(158\) | −10.4202 | −0.828990 | ||||||||
\(159\) | 8.54823 | 0.677919 | ||||||||
\(160\) | −6.06414 | −0.479412 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.23115 | −0.175295 | ||||||||
\(163\) | 11.9654 | 0.937204 | 0.468602 | − | 0.883409i | \(-0.344758\pi\) | ||||
0.468602 | + | 0.883409i | \(0.344758\pi\) | |||||||
\(164\) | 2.97801 | 0.232544 | ||||||||
\(165\) | 2.70780 | 0.210802 | ||||||||
\(166\) | −7.19967 | −0.558802 | ||||||||
\(167\) | −16.9933 | −1.31498 | −0.657490 | − | 0.753463i | \(-0.728382\pi\) | ||||
−0.657490 | + | 0.753463i | \(0.728382\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9548 | −0.919601 | ||||||||
\(170\) | −1.17664 | −0.0902438 | ||||||||
\(171\) | −3.50700 | −0.268187 | ||||||||
\(172\) | −17.1579 | −1.30828 | ||||||||
\(173\) | 3.00321 | 0.228330 | 0.114165 | − | 0.993462i | \(-0.463581\pi\) | ||||
0.114165 | + | 0.993462i | \(0.463581\pi\) | |||||||
\(174\) | −17.6215 | −1.33588 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.29734 | 0.248546 | ||||||||
\(177\) | −10.6811 | −0.802843 | ||||||||
\(178\) | −35.5697 | −2.66606 | ||||||||
\(179\) | 10.3399 | 0.772844 | 0.386422 | − | 0.922322i | \(-0.373711\pi\) | ||||
0.386422 | + | 0.922322i | \(0.373711\pi\) | |||||||
\(180\) | −2.65947 | −0.198225 | ||||||||
\(181\) | −9.54059 | −0.709146 | −0.354573 | − | 0.935028i | \(-0.615374\pi\) | ||||
−0.354573 | + | 0.935028i | \(0.615374\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.09457 | −0.598368 | ||||||||
\(184\) | 1.21366 | 0.0894721 | ||||||||
\(185\) | 10.3078 | 0.757843 | ||||||||
\(186\) | −2.86464 | −0.210046 | ||||||||
\(187\) | 1.79057 | 0.130940 | ||||||||
\(188\) | 0.683511 | 0.0498502 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.98768 | −0.506939 | ||||||||
\(191\) | 3.85532 | 0.278961 | 0.139480 | − | 0.990225i | \(-0.455457\pi\) | ||||
0.139480 | + | 0.990225i | \(0.455457\pi\) | |||||||
\(192\) | −12.9756 | −0.936434 | ||||||||
\(193\) | 12.2524 | 0.881949 | 0.440975 | − | 0.897520i | \(-0.354633\pi\) | ||||
0.440975 | + | 0.897520i | \(0.354633\pi\) | |||||||
\(194\) | −11.5300 | −0.827806 | ||||||||
\(195\) | 0.912992 | 0.0653807 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.0578 | 1.42906 | 0.714529 | − | 0.699606i | \(-0.246641\pi\) | ||||
0.714529 | + | 0.699606i | \(0.246641\pi\) | |||||||
\(198\) | 6.76512 | 0.480776 | ||||||||
\(199\) | −8.76302 | −0.621194 | −0.310597 | − | 0.950542i | \(-0.600529\pi\) | ||||
−0.310597 | + | 0.950542i | \(0.600529\pi\) | |||||||
\(200\) | 9.17019 | 0.648431 | ||||||||
\(201\) | 8.13979 | 0.574137 | ||||||||
\(202\) | −23.7179 | −1.66879 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.75862 | −0.123128 | ||||||||
\(205\) | −0.893036 | −0.0623724 | ||||||||
\(206\) | 8.78674 | 0.612201 | ||||||||
\(207\) | −0.556191 | −0.0386580 | ||||||||
\(208\) | 1.11177 | 0.0770873 | ||||||||
\(209\) | 10.6337 | 0.735546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.8898 | 1.50696 | 0.753478 | − | 0.657473i | \(-0.228375\pi\) | ||||
0.753478 | + | 0.657473i | \(0.228375\pi\) | |||||||
\(212\) | 25.4567 | 1.74838 | ||||||||
\(213\) | 1.38924 | 0.0951892 | ||||||||
\(214\) | 24.0964 | 1.64720 | ||||||||
\(215\) | 5.14525 | 0.350903 | ||||||||
\(216\) | −2.18209 | −0.148472 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 30.6550 | 2.07622 | ||||||||
\(219\) | 10.7543 | 0.726705 | ||||||||
\(220\) | 8.06386 | 0.543665 | ||||||||
\(221\) | 0.603730 | 0.0406113 | ||||||||
\(222\) | 25.7528 | 1.72841 | ||||||||
\(223\) | 19.0053 | 1.27269 | 0.636343 | − | 0.771406i | \(-0.280446\pi\) | ||||
0.636343 | + | 0.771406i | \(0.280446\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.20249 | −0.280166 | ||||||||
\(226\) | −6.41884 | −0.426975 | ||||||||
\(227\) | 14.7021 | 0.975814 | 0.487907 | − | 0.872896i | \(-0.337761\pi\) | ||||
0.487907 | + | 0.872896i | \(0.337761\pi\) | |||||||
\(228\) | −10.4439 | −0.691664 | ||||||||
\(229\) | 22.7562 | 1.50377 | 0.751886 | − | 0.659293i | \(-0.229144\pi\) | ||||
0.751886 | + | 0.659293i | \(0.229144\pi\) | |||||||
\(230\) | −1.10821 | −0.0730731 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.2340 | −1.13147 | ||||||||
\(233\) | −27.3282 | −1.79033 | −0.895164 | − | 0.445737i | \(-0.852942\pi\) | ||||
−0.895164 | + | 0.445737i | \(0.852942\pi\) | |||||||
\(234\) | 2.28100 | 0.149114 | ||||||||
\(235\) | −0.204969 | −0.0133707 | ||||||||
\(236\) | −31.8085 | −2.07056 | ||||||||
\(237\) | 4.67035 | 0.303372 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.5731 | −0.813286 | −0.406643 | − | 0.913587i | \(-0.633301\pi\) | ||||
−0.406643 | + | 0.913587i | \(0.633301\pi\) | |||||||
\(240\) | 0.971148 | 0.0626873 | ||||||||
\(241\) | 4.30351 | 0.277214 | 0.138607 | − | 0.990347i | \(-0.455738\pi\) | ||||
0.138607 | + | 0.990347i | \(0.455738\pi\) | |||||||
\(242\) | 4.02992 | 0.259053 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −24.1057 | −1.54321 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.23115 | −0.142253 | ||||||||
\(247\) | 3.58537 | 0.228132 | ||||||||
\(248\) | −2.80165 | −0.177905 | ||||||||
\(249\) | 3.22689 | 0.204496 | ||||||||
\(250\) | −18.3359 | −1.15966 | ||||||||
\(251\) | −12.7442 | −0.804408 | −0.402204 | − | 0.915550i | \(-0.631756\pi\) | ||||
−0.402204 | + | 0.915550i | \(0.631756\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.68644 | 0.106026 | ||||||||
\(254\) | 17.7142 | 1.11149 | ||||||||
\(255\) | 0.527368 | 0.0330251 | ||||||||
\(256\) | −8.34043 | −0.521277 | ||||||||
\(257\) | −15.3531 | −0.957701 | −0.478850 | − | 0.877897i | \(-0.658946\pi\) | ||||
−0.478850 | + | 0.877897i | \(0.658946\pi\) | |||||||
\(258\) | 12.8548 | 0.800306 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.71890 | 0.168619 | ||||||||
\(261\) | 7.89796 | 0.488871 | ||||||||
\(262\) | −4.27072 | −0.263846 | ||||||||
\(263\) | 4.70180 | 0.289925 | 0.144963 | − | 0.989437i | \(-0.453694\pi\) | ||||
0.144963 | + | 0.989437i | \(0.453694\pi\) | |||||||
\(264\) | 6.61637 | 0.407209 | ||||||||
\(265\) | −7.63388 | −0.468946 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.9423 | 0.975656 | ||||||||
\(268\) | 24.2404 | 1.48072 | ||||||||
\(269\) | −17.8058 | −1.08564 | −0.542818 | − | 0.839850i | \(-0.682643\pi\) | ||||
−0.542818 | + | 0.839850i | \(0.682643\pi\) | |||||||
\(270\) | 1.99249 | 0.121259 | ||||||||
\(271\) | −5.15229 | −0.312980 | −0.156490 | − | 0.987680i | \(-0.550018\pi\) | ||||
−0.156490 | + | 0.987680i | \(0.550018\pi\) | |||||||
\(272\) | 0.642187 | 0.0389383 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.4133 | −1.47486 | ||||||||
\(275\) | 12.7425 | 0.768400 | ||||||||
\(276\) | −1.65634 | −0.0997002 | ||||||||
\(277\) | −8.01369 | −0.481496 | −0.240748 | − | 0.970588i | \(-0.577393\pi\) | ||||
−0.240748 | + | 0.970588i | \(0.577393\pi\) | |||||||
\(278\) | −45.9462 | −2.75567 | ||||||||
\(279\) | 1.28393 | 0.0768670 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.98277 | 0.297247 | 0.148624 | − | 0.988894i | \(-0.452516\pi\) | ||||
0.148624 | + | 0.988894i | \(0.452516\pi\) | |||||||
\(282\) | −0.512091 | −0.0304946 | ||||||||
\(283\) | 6.83872 | 0.406520 | 0.203260 | − | 0.979125i | \(-0.434846\pi\) | ||||
0.203260 | + | 0.979125i | \(0.434846\pi\) | |||||||
\(284\) | 4.13717 | 0.245496 | ||||||||
\(285\) | 3.13188 | 0.185516 | ||||||||
\(286\) | −6.91629 | −0.408969 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.79048 | 0.400133 | ||||||||
\(289\) | −16.6513 | −0.979486 | ||||||||
\(290\) | 15.7366 | 0.924087 | ||||||||
\(291\) | 5.16775 | 0.302939 | ||||||||
\(292\) | 32.0263 | 1.87420 | ||||||||
\(293\) | 23.1644 | 1.35328 | 0.676639 | − | 0.736315i | \(-0.263436\pi\) | ||||
0.676639 | + | 0.736315i | \(0.263436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.53863 | 0.555361 | ||||||||
\(296\) | 25.1865 | 1.46394 | ||||||||
\(297\) | −3.03213 | −0.175942 | ||||||||
\(298\) | −7.26333 | −0.420754 | ||||||||
\(299\) | 0.568620 | 0.0328842 | ||||||||
\(300\) | −12.5151 | −0.722557 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −26.8644 | −1.54587 | ||||||||
\(303\) | 10.6304 | 0.610699 | ||||||||
\(304\) | 3.81375 | 0.218734 | ||||||||
\(305\) | 7.22875 | 0.413917 | ||||||||
\(306\) | 1.31757 | 0.0753203 | ||||||||
\(307\) | −16.0121 | −0.913857 | −0.456929 | − | 0.889503i | \(-0.651051\pi\) | ||||
−0.456929 | + | 0.889503i | \(0.651051\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.93822 | −0.224037 | ||||||||
\(310\) | 2.55823 | 0.145297 | ||||||||
\(311\) | −20.7107 | −1.17440 | −0.587198 | − | 0.809443i | \(-0.699769\pi\) | ||||
−0.587198 | + | 0.809443i | \(0.699769\pi\) | |||||||
\(312\) | 2.23085 | 0.126297 | ||||||||
\(313\) | 18.5447 | 1.04821 | 0.524105 | − | 0.851653i | \(-0.324400\pi\) | ||||
0.524105 | + | 0.851653i | \(0.324400\pi\) | |||||||
\(314\) | −1.29464 | −0.0730610 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.9084 | 0.782407 | ||||||||
\(317\) | 20.6683 | 1.16085 | 0.580425 | − | 0.814314i | \(-0.302887\pi\) | ||||
0.580425 | + | 0.814314i | \(0.302887\pi\) | |||||||
\(318\) | −19.0724 | −1.06952 | ||||||||
\(319\) | −23.9476 | −1.34081 | ||||||||
\(320\) | 11.5877 | 0.647771 | ||||||||
\(321\) | −10.8000 | −0.602798 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.07100 | 0.115234 | ||||||||
\(324\) | 2.97801 | 0.165445 | ||||||||
\(325\) | 4.29640 | 0.238321 | ||||||||
\(326\) | −26.6966 | −1.47859 | ||||||||
\(327\) | −13.7396 | −0.759801 | ||||||||
\(328\) | −2.18209 | −0.120486 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.04149 | −0.332573 | ||||||||
\(331\) | 3.75882 | 0.206603 | 0.103302 | − | 0.994650i | \(-0.467059\pi\) | ||||
0.103302 | + | 0.994650i | \(0.467059\pi\) | |||||||
\(332\) | 9.60972 | 0.527402 | ||||||||
\(333\) | −11.5424 | −0.632519 | ||||||||
\(334\) | 37.9145 | 2.07459 | ||||||||
\(335\) | −7.26913 | −0.397155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.8704 | −1.46373 | −0.731863 | − | 0.681452i | \(-0.761349\pi\) | ||||
−0.731863 | + | 0.681452i | \(0.761349\pi\) | |||||||
\(338\) | 26.6729 | 1.45082 | ||||||||
\(339\) | 2.87693 | 0.156253 | ||||||||
\(340\) | 1.57051 | 0.0851728 | ||||||||
\(341\) | −3.89304 | −0.210820 | ||||||||
\(342\) | 7.82463 | 0.423108 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.5722 | 0.677846 | ||||||||
\(345\) | 0.496699 | 0.0267414 | ||||||||
\(346\) | −6.70059 | −0.360226 | ||||||||
\(347\) | −21.4572 | −1.15188 | −0.575941 | − | 0.817491i | \(-0.695364\pi\) | ||||
−0.575941 | + | 0.817491i | \(0.695364\pi\) | |||||||
\(348\) | 23.5202 | 1.26082 | ||||||||
\(349\) | 26.1532 | 1.39995 | 0.699974 | − | 0.714168i | \(-0.253195\pi\) | ||||
0.699974 | + | 0.714168i | \(0.253195\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.02235 | −0.0545688 | ||||||||
\(352\) | −20.5896 | −1.09743 | ||||||||
\(353\) | −3.71713 | −0.197843 | −0.0989216 | − | 0.995095i | \(-0.531539\pi\) | ||||
−0.0989216 | + | 0.995095i | \(0.531539\pi\) | |||||||
\(354\) | 23.8312 | 1.26661 | ||||||||
\(355\) | −1.24064 | −0.0658464 | ||||||||
\(356\) | 47.4765 | 2.51625 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.0699 | −1.21928 | ||||||||
\(359\) | 13.2589 | 0.699776 | 0.349888 | − | 0.936792i | \(-0.386220\pi\) | ||||
0.349888 | + | 0.936792i | \(0.386220\pi\) | |||||||
\(360\) | 1.94868 | 0.102705 | ||||||||
\(361\) | −6.70095 | −0.352681 | ||||||||
\(362\) | 21.2864 | 1.11879 | ||||||||
\(363\) | −1.80621 | −0.0948015 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.60393 | −0.502693 | ||||||||
\(366\) | 18.0602 | 0.944021 | ||||||||
\(367\) | −19.4105 | −1.01322 | −0.506610 | − | 0.862175i | \(-0.669102\pi\) | ||||
−0.506610 | + | 0.862175i | \(0.669102\pi\) | |||||||
\(368\) | 0.604840 | 0.0315295 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −22.9982 | −1.19562 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.82356 | 0.198243 | ||||||||
\(373\) | 19.8031 | 1.02536 | 0.512682 | − | 0.858579i | \(-0.328652\pi\) | ||||
0.512682 | + | 0.858579i | \(0.328652\pi\) | |||||||
\(374\) | −3.99503 | −0.206578 | ||||||||
\(375\) | 8.21815 | 0.424384 | ||||||||
\(376\) | −0.500831 | −0.0258284 | ||||||||
\(377\) | −8.07445 | −0.415855 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.4729 | 0.537955 | 0.268977 | − | 0.963147i | \(-0.413314\pi\) | ||||
0.268977 | + | 0.963147i | \(0.413314\pi\) | |||||||
\(380\) | 9.32677 | 0.478453 | ||||||||
\(381\) | −7.93950 | −0.406753 | ||||||||
\(382\) | −8.60178 | −0.440105 | ||||||||
\(383\) | 17.9568 | 0.917552 | 0.458776 | − | 0.888552i | \(-0.348288\pi\) | ||||
0.458776 | + | 0.888552i | \(0.348288\pi\) | |||||||
\(384\) | 15.3695 | 0.784322 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −27.3370 | −1.39141 | ||||||||
\(387\) | −5.76153 | −0.292875 | ||||||||
\(388\) | 15.3896 | 0.781290 | ||||||||
\(389\) | 31.2703 | 1.58547 | 0.792733 | − | 0.609569i | \(-0.208657\pi\) | ||||
0.792733 | + | 0.609569i | \(0.208657\pi\) | |||||||
\(390\) | −2.03702 | −0.103148 | ||||||||
\(391\) | 0.328450 | 0.0166104 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.91414 | 0.0965555 | ||||||||
\(394\) | −44.7519 | −2.25457 | ||||||||
\(395\) | −4.17079 | −0.209855 | ||||||||
\(396\) | −9.02971 | −0.453760 | ||||||||
\(397\) | 29.4827 | 1.47969 | 0.739846 | − | 0.672776i | \(-0.234898\pi\) | ||||
0.739846 | + | 0.672776i | \(0.234898\pi\) | |||||||
\(398\) | 19.5516 | 0.980032 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.57007 | 0.228503 | ||||||||
\(401\) | −11.3149 | −0.565040 | −0.282520 | − | 0.959261i | \(-0.591170\pi\) | ||||
−0.282520 | + | 0.959261i | \(0.591170\pi\) | |||||||
\(402\) | −18.1611 | −0.905791 | ||||||||
\(403\) | −1.31262 | −0.0653864 | ||||||||
\(404\) | 31.6574 | 1.57501 | ||||||||
\(405\) | −0.893036 | −0.0443753 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.9980 | 1.73479 | ||||||||
\(408\) | 1.28860 | 0.0637951 | ||||||||
\(409\) | 18.9256 | 0.935812 | 0.467906 | − | 0.883778i | \(-0.345009\pi\) | ||||
0.467906 | + | 0.883778i | \(0.345009\pi\) | |||||||
\(410\) | 1.99249 | 0.0984023 | ||||||||
\(411\) | 10.9420 | 0.539731 | ||||||||
\(412\) | −11.7281 | −0.577800 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.24094 | 0.0609891 | ||||||||
\(415\) | −2.88173 | −0.141459 | ||||||||
\(416\) | −6.94222 | −0.340370 | ||||||||
\(417\) | 20.5931 | 1.00845 | ||||||||
\(418\) | −23.7253 | −1.16044 | ||||||||
\(419\) | 11.2826 | 0.551193 | 0.275597 | − | 0.961273i | \(-0.411125\pi\) | ||||
0.275597 | + | 0.961273i | \(0.411125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.47063 | 0.0716742 | 0.0358371 | − | 0.999358i | \(-0.488590\pi\) | ||||
0.0358371 | + | 0.999358i | \(0.488590\pi\) | |||||||
\(422\) | −48.8393 | −2.37746 | ||||||||
\(423\) | 0.229519 | 0.0111596 | ||||||||
\(424\) | −18.6530 | −0.905870 | ||||||||
\(425\) | 2.48171 | 0.120381 | ||||||||
\(426\) | −3.09960 | −0.150176 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −32.1626 | −1.55464 | ||||||||
\(429\) | 3.09988 | 0.149664 | ||||||||
\(430\) | −11.4798 | −0.553606 | ||||||||
\(431\) | −4.90425 | −0.236229 | −0.118115 | − | 0.993000i | \(-0.537685\pi\) | ||||
−0.118115 | + | 0.993000i | \(0.537685\pi\) | |||||||
\(432\) | −1.08747 | −0.0523208 | ||||||||
\(433\) | −9.20606 | −0.442415 | −0.221207 | − | 0.975227i | \(-0.571000\pi\) | ||||
−0.221207 | + | 0.975227i | \(0.571000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.05316 | −0.338173 | ||||||||
\(436\) | −40.9166 | −1.95955 | ||||||||
\(437\) | 1.95056 | 0.0933081 | ||||||||
\(438\) | −23.9943 | −1.14649 | ||||||||
\(439\) | −24.0382 | −1.14728 | −0.573641 | − | 0.819107i | \(-0.694470\pi\) | ||||
−0.573641 | + | 0.819107i | \(0.694470\pi\) | |||||||
\(440\) | −5.90865 | −0.281684 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.34701 | −0.0640708 | ||||||||
\(443\) | −22.3474 | −1.06176 | −0.530878 | − | 0.847448i | \(-0.678138\pi\) | ||||
−0.530878 | + | 0.847448i | \(0.678138\pi\) | |||||||
\(444\) | −34.3734 | −1.63129 | ||||||||
\(445\) | −14.2371 | −0.674903 | ||||||||
\(446\) | −42.4035 | −2.00786 | ||||||||
\(447\) | 3.25543 | 0.153976 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.0846 | 0.711886 | 0.355943 | − | 0.934508i | \(-0.384160\pi\) | ||||
0.355943 | + | 0.934508i | \(0.384160\pi\) | |||||||
\(450\) | 9.37636 | 0.442006 | ||||||||
\(451\) | −3.03213 | −0.142777 | ||||||||
\(452\) | 8.56752 | 0.402982 | ||||||||
\(453\) | 12.0406 | 0.565718 | ||||||||
\(454\) | −32.8026 | −1.53950 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.65258 | 0.358365 | ||||||||
\(457\) | −11.9480 | −0.558905 | −0.279453 | − | 0.960160i | \(-0.590153\pi\) | ||||
−0.279453 | + | 0.960160i | \(0.590153\pi\) | |||||||
\(458\) | −50.7724 | −2.37244 | ||||||||
\(459\) | −0.590534 | −0.0275638 | ||||||||
\(460\) | 1.47918 | 0.0689669 | ||||||||
\(461\) | −8.73937 | −0.407033 | −0.203517 | − | 0.979071i | \(-0.565237\pi\) | ||||
−0.203517 | + | 0.979071i | \(0.565237\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.3911 | −1.50534 | −0.752670 | − | 0.658398i | \(-0.771235\pi\) | ||||
−0.752670 | + | 0.658398i | \(0.771235\pi\) | |||||||
\(464\) | −8.58877 | −0.398724 | ||||||||
\(465\) | −1.14660 | −0.0531722 | ||||||||
\(466\) | 60.9731 | 2.82453 | ||||||||
\(467\) | 0.327510 | 0.0151553 | 0.00757767 | − | 0.999971i | \(-0.497588\pi\) | ||||
0.00757767 | + | 0.999971i | \(0.497588\pi\) | |||||||
\(468\) | −3.04456 | −0.140735 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.457316 | 0.0210944 | ||||||||
\(471\) | 0.580260 | 0.0267370 | ||||||||
\(472\) | 23.3072 | 1.07280 | ||||||||
\(473\) | 17.4697 | 0.803257 | ||||||||
\(474\) | −10.4202 | −0.478617 | ||||||||
\(475\) | 14.7381 | 0.676231 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.54823 | 0.391397 | ||||||||
\(478\) | 28.0524 | 1.28309 | ||||||||
\(479\) | −5.82212 | −0.266020 | −0.133010 | − | 0.991115i | \(-0.542464\pi\) | ||||
−0.133010 | + | 0.991115i | \(0.542464\pi\) | |||||||
\(480\) | −6.06414 | −0.276789 | ||||||||
\(481\) | 11.8003 | 0.538049 | ||||||||
\(482\) | −9.60177 | −0.437349 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.37892 | −0.244496 | ||||||||
\(485\) | −4.61499 | −0.209556 | ||||||||
\(486\) | −2.23115 | −0.101207 | ||||||||
\(487\) | −24.5314 | −1.11162 | −0.555811 | − | 0.831309i | \(-0.687592\pi\) | ||||
−0.555811 | + | 0.831309i | \(0.687592\pi\) | |||||||
\(488\) | 17.6631 | 0.799570 | ||||||||
\(489\) | 11.9654 | 0.541095 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.0462 | 0.949801 | 0.474900 | − | 0.880040i | \(-0.342484\pi\) | ||||
0.474900 | + | 0.880040i | \(0.342484\pi\) | |||||||
\(492\) | 2.97801 | 0.134259 | ||||||||
\(493\) | −4.66401 | −0.210057 | ||||||||
\(494\) | −7.99948 | −0.359914 | ||||||||
\(495\) | 2.70780 | 0.121706 | ||||||||
\(496\) | −1.39623 | −0.0626928 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.19967 | −0.322625 | ||||||||
\(499\) | 21.4488 | 0.960181 | 0.480090 | − | 0.877219i | \(-0.340604\pi\) | ||||
0.480090 | + | 0.877219i | \(0.340604\pi\) | |||||||
\(500\) | 24.4738 | 1.09450 | ||||||||
\(501\) | −16.9933 | −0.759204 | ||||||||
\(502\) | 28.4342 | 1.26908 | ||||||||
\(503\) | 33.1070 | 1.47617 | 0.738084 | − | 0.674708i | \(-0.235731\pi\) | ||||
0.738084 | + | 0.674708i | \(0.235731\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.49330 | −0.422446 | ||||||||
\(506\) | −3.76270 | −0.167272 | ||||||||
\(507\) | −11.9548 | −0.530932 | ||||||||
\(508\) | −23.6439 | −1.04903 | ||||||||
\(509\) | 13.7852 | 0.611018 | 0.305509 | − | 0.952189i | \(-0.401173\pi\) | ||||
0.305509 | + | 0.952189i | \(0.401173\pi\) | |||||||
\(510\) | −1.17664 | −0.0521023 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −12.1303 | −0.536090 | ||||||||
\(513\) | −3.50700 | −0.154838 | ||||||||
\(514\) | 34.2550 | 1.51092 | ||||||||
\(515\) | 3.51697 | 0.154976 | ||||||||
\(516\) | −17.1579 | −0.755335 | ||||||||
\(517\) | −0.695932 | −0.0306070 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.00321 | 0.131826 | ||||||||
\(520\) | −1.99223 | −0.0873651 | ||||||||
\(521\) | 27.8521 | 1.22022 | 0.610112 | − | 0.792315i | \(-0.291124\pi\) | ||||
0.610112 | + | 0.792315i | \(0.291124\pi\) | |||||||
\(522\) | −17.6215 | −0.771272 | ||||||||
\(523\) | 25.6651 | 1.12226 | 0.561128 | − | 0.827729i | \(-0.310367\pi\) | ||||
0.561128 | + | 0.827729i | \(0.310367\pi\) | |||||||
\(524\) | 5.70033 | 0.249020 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.4904 | −0.457403 | ||||||||
\(527\) | −0.758205 | −0.0330279 | ||||||||
\(528\) | 3.29734 | 0.143498 | ||||||||
\(529\) | −22.6907 | −0.986550 | ||||||||
\(530\) | 17.0323 | 0.739836 | ||||||||
\(531\) | −10.6811 | −0.463521 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.02235 | −0.0442827 | ||||||||
\(534\) | −35.5697 | −1.53925 | ||||||||
\(535\) | 9.64481 | 0.416981 | ||||||||
\(536\) | −17.7617 | −0.767190 | ||||||||
\(537\) | 10.3399 | 0.446202 | ||||||||
\(538\) | 39.7273 | 1.71276 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.65947 | −0.114445 | ||||||||
\(541\) | −24.9672 | −1.07342 | −0.536711 | − | 0.843766i | \(-0.680333\pi\) | ||||
−0.536711 | + | 0.843766i | \(0.680333\pi\) | |||||||
\(542\) | 11.4955 | 0.493775 | ||||||||
\(543\) | −9.54059 | −0.409426 | ||||||||
\(544\) | −4.01001 | −0.171928 | ||||||||
\(545\) | 12.2699 | 0.525587 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.176971 | 0.00756675 | 0.00378338 | − | 0.999993i | \(-0.498796\pi\) | ||||
0.00378338 | + | 0.999993i | \(0.498796\pi\) | |||||||
\(548\) | 32.5855 | 1.39198 | ||||||||
\(549\) | −8.09457 | −0.345468 | ||||||||
\(550\) | −28.4303 | −1.21227 | ||||||||
\(551\) | −27.6981 | −1.17998 | ||||||||
\(552\) | 1.21366 | 0.0516567 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 17.8797 | 0.759636 | ||||||||
\(555\) | 10.3078 | 0.437541 | ||||||||
\(556\) | 61.3264 | 2.60082 | ||||||||
\(557\) | 28.8231 | 1.22127 | 0.610636 | − | 0.791911i | \(-0.290914\pi\) | ||||
0.610636 | + | 0.791911i | \(0.290914\pi\) | |||||||
\(558\) | −2.86464 | −0.121270 | ||||||||
\(559\) | 5.89028 | 0.249132 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.79057 | 0.0755981 | ||||||||
\(562\) | −11.1173 | −0.468954 | ||||||||
\(563\) | 28.9563 | 1.22036 | 0.610181 | − | 0.792262i | \(-0.291097\pi\) | ||||
0.610181 | + | 0.792262i | \(0.291097\pi\) | |||||||
\(564\) | 0.683511 | 0.0287810 | ||||||||
\(565\) | −2.56920 | −0.108087 | ||||||||
\(566\) | −15.2582 | −0.641350 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.03144 | −0.127197 | ||||||||
\(569\) | 2.87743 | 0.120628 | 0.0603140 | − | 0.998179i | \(-0.480790\pi\) | ||||
0.0603140 | + | 0.998179i | \(0.480790\pi\) | |||||||
\(570\) | −6.98768 | −0.292682 | ||||||||
\(571\) | −23.6968 | −0.991680 | −0.495840 | − | 0.868414i | \(-0.665140\pi\) | ||||
−0.495840 | + | 0.868414i | \(0.665140\pi\) | |||||||
\(572\) | 9.23149 | 0.385988 | ||||||||
\(573\) | 3.85532 | 0.161058 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.33739 | 0.0974758 | ||||||||
\(576\) | −12.9756 | −0.540650 | ||||||||
\(577\) | 25.8656 | 1.07680 | 0.538399 | − | 0.842690i | \(-0.319029\pi\) | ||||
0.538399 | + | 0.842690i | \(0.319029\pi\) | |||||||
\(578\) | 37.1514 | 1.54530 | ||||||||
\(579\) | 12.2524 | 0.509194 | ||||||||
\(580\) | −21.0044 | −0.872160 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.5300 | −0.477934 | ||||||||
\(583\) | −25.9193 | −1.07347 | ||||||||
\(584\) | −23.4667 | −0.971060 | ||||||||
\(585\) | 0.912992 | 0.0377476 | ||||||||
\(586\) | −51.6831 | −2.13501 | ||||||||
\(587\) | 42.3285 | 1.74708 | 0.873542 | − | 0.486750i | \(-0.161818\pi\) | ||||
0.873542 | + | 0.486750i | \(0.161818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.50275 | −0.185533 | ||||||||
\(590\) | −21.2821 | −0.876170 | ||||||||
\(591\) | 20.0578 | 0.825067 | ||||||||
\(592\) | 12.5520 | 0.515883 | ||||||||
\(593\) | 32.3171 | 1.32711 | 0.663553 | − | 0.748129i | \(-0.269048\pi\) | ||||
0.663553 | + | 0.748129i | \(0.269048\pi\) | |||||||
\(594\) | 6.76512 | 0.277576 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.69470 | 0.397110 | ||||||||
\(597\) | −8.76302 | −0.358647 | ||||||||
\(598\) | −1.26868 | −0.0518800 | ||||||||
\(599\) | −34.5668 | −1.41236 | −0.706181 | − | 0.708032i | \(-0.749583\pi\) | ||||
−0.706181 | + | 0.708032i | \(0.749583\pi\) | |||||||
\(600\) | 9.17019 | 0.374372 | ||||||||
\(601\) | 21.2165 | 0.865439 | 0.432720 | − | 0.901529i | \(-0.357554\pi\) | ||||
0.432720 | + | 0.901529i | \(0.357554\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.13979 | 0.331478 | ||||||||
\(604\) | 35.8571 | 1.45900 | ||||||||
\(605\) | 1.61301 | 0.0655783 | ||||||||
\(606\) | −23.7179 | −0.963474 | ||||||||
\(607\) | −14.5087 | −0.588890 | −0.294445 | − | 0.955668i | \(-0.595135\pi\) | ||||
−0.294445 | + | 0.955668i | \(0.595135\pi\) | |||||||
\(608\) | −23.8142 | −0.965793 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.1284 | −0.653020 | ||||||||
\(611\) | −0.234648 | −0.00949285 | ||||||||
\(612\) | −1.75862 | −0.0710879 | ||||||||
\(613\) | −32.3488 | −1.30656 | −0.653278 | − | 0.757118i | \(-0.726607\pi\) | ||||
−0.653278 | + | 0.757118i | \(0.726607\pi\) | |||||||
\(614\) | 35.7253 | 1.44175 | ||||||||
\(615\) | −0.893036 | −0.0360107 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.742674 | 0.0298989 | 0.0149495 | − | 0.999888i | \(-0.495241\pi\) | ||||
0.0149495 | + | 0.999888i | \(0.495241\pi\) | |||||||
\(618\) | 8.78674 | 0.353455 | ||||||||
\(619\) | 26.3539 | 1.05925 | 0.529627 | − | 0.848231i | \(-0.322332\pi\) | ||||
0.529627 | + | 0.848231i | \(0.322332\pi\) | |||||||
\(620\) | −3.41458 | −0.137133 | ||||||||
\(621\) | −0.556191 | −0.0223192 | ||||||||
\(622\) | 46.2086 | 1.85280 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.11177 | 0.0445064 | ||||||||
\(625\) | 13.6733 | 0.546933 | ||||||||
\(626\) | −41.3760 | −1.65372 | ||||||||
\(627\) | 10.6337 | 0.424668 | ||||||||
\(628\) | 1.72802 | 0.0689556 | ||||||||
\(629\) | 6.81618 | 0.271779 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.2431 | −0.805867 | −0.402933 | − | 0.915229i | \(-0.632009\pi\) | ||||
−0.402933 | + | 0.915229i | \(0.632009\pi\) | |||||||
\(632\) | −10.1911 | −0.405381 | ||||||||
\(633\) | 21.8898 | 0.870042 | ||||||||
\(634\) | −46.1141 | −1.83142 | ||||||||
\(635\) | 7.09026 | 0.281368 | ||||||||
\(636\) | 25.4567 | 1.00943 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 53.4306 | 2.11534 | ||||||||
\(639\) | 1.38924 | 0.0549575 | ||||||||
\(640\) | −13.7255 | −0.542549 | ||||||||
\(641\) | 18.2442 | 0.720604 | 0.360302 | − | 0.932836i | \(-0.382674\pi\) | ||||
0.360302 | + | 0.932836i | \(0.382674\pi\) | |||||||
\(642\) | 24.0964 | 0.951010 | ||||||||
\(643\) | −16.3210 | −0.643637 | −0.321819 | − | 0.946801i | \(-0.604294\pi\) | ||||
−0.321819 | + | 0.946801i | \(0.604294\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.14525 | 0.202594 | ||||||||
\(646\) | −4.62071 | −0.181799 | ||||||||
\(647\) | 47.4111 | 1.86392 | 0.931962 | − | 0.362556i | \(-0.118096\pi\) | ||||
0.931962 | + | 0.362556i | \(0.118096\pi\) | |||||||
\(648\) | −2.18209 | −0.0857205 | ||||||||
\(649\) | 32.3865 | 1.27128 | ||||||||
\(650\) | −9.58589 | −0.375990 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 35.6332 | 1.39550 | ||||||||
\(653\) | −16.4495 | −0.643720 | −0.321860 | − | 0.946787i | \(-0.604308\pi\) | ||||
−0.321860 | + | 0.946787i | \(0.604308\pi\) | |||||||
\(654\) | 30.6550 | 1.19871 | ||||||||
\(655\) | −1.70940 | −0.0667916 | ||||||||
\(656\) | −1.08747 | −0.0424585 | ||||||||
\(657\) | 10.7543 | 0.419563 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.4662 | 0.758297 | 0.379148 | − | 0.925336i | \(-0.376217\pi\) | ||||
0.379148 | + | 0.925336i | \(0.376217\pi\) | |||||||
\(660\) | 8.06386 | 0.313885 | ||||||||
\(661\) | 29.5252 | 1.14840 | 0.574198 | − | 0.818716i | \(-0.305314\pi\) | ||||
0.574198 | + | 0.818716i | \(0.305314\pi\) | |||||||
\(662\) | −8.38648 | −0.325950 | ||||||||
\(663\) | 0.603730 | 0.0234469 | ||||||||
\(664\) | −7.04136 | −0.273258 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 25.7528 | 0.997900 | ||||||||
\(667\) | −4.39278 | −0.170089 | ||||||||
\(668\) | −50.6062 | −1.95801 | ||||||||
\(669\) | 19.0053 | 0.734786 | ||||||||
\(670\) | 16.2185 | 0.626575 | ||||||||
\(671\) | 24.5438 | 0.947502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0433 | 1.00390 | 0.501948 | − | 0.864898i | \(-0.332617\pi\) | ||||
0.501948 | + | 0.864898i | \(0.332617\pi\) | |||||||
\(674\) | 59.9519 | 2.30926 | ||||||||
\(675\) | −4.20249 | −0.161754 | ||||||||
\(676\) | −35.6016 | −1.36929 | ||||||||
\(677\) | 1.23438 | 0.0474410 | 0.0237205 | − | 0.999719i | \(-0.492449\pi\) | ||||
0.0237205 | + | 0.999719i | \(0.492449\pi\) | |||||||
\(678\) | −6.41884 | −0.246514 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.15076 | −0.0441298 | ||||||||
\(681\) | 14.7021 | 0.563386 | ||||||||
\(682\) | 8.68595 | 0.332602 | ||||||||
\(683\) | −9.24065 | −0.353584 | −0.176792 | − | 0.984248i | \(-0.556572\pi\) | ||||
−0.176792 | + | 0.984248i | \(0.556572\pi\) | |||||||
\(684\) | −10.4439 | −0.399332 | ||||||||
\(685\) | −9.77164 | −0.373355 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.7562 | 0.868203 | ||||||||
\(688\) | 6.26548 | 0.238869 | ||||||||
\(689\) | −8.73926 | −0.332939 | ||||||||
\(690\) | −1.10821 | −0.0421888 | ||||||||
\(691\) | 12.5139 | 0.476051 | 0.238026 | − | 0.971259i | \(-0.423500\pi\) | ||||
0.238026 | + | 0.971259i | \(0.423500\pi\) | |||||||
\(692\) | 8.94359 | 0.339984 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 47.8741 | 1.81728 | ||||||||
\(695\) | −18.3904 | −0.697586 | ||||||||
\(696\) | −17.2340 | −0.653254 | ||||||||
\(697\) | −0.590534 | −0.0223681 | ||||||||
\(698\) | −58.3516 | −2.20864 | ||||||||
\(699\) | −27.3282 | −1.03365 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.7565 | −1.01058 | −0.505289 | − | 0.862950i | \(-0.668614\pi\) | ||||
−0.505289 | + | 0.862950i | \(0.668614\pi\) | |||||||
\(702\) | 2.28100 | 0.0860910 | ||||||||
\(703\) | 40.4792 | 1.52670 | ||||||||
\(704\) | 39.3437 | 1.48282 | ||||||||
\(705\) | −0.204969 | −0.00771958 | ||||||||
\(706\) | 8.29347 | 0.312129 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −31.8085 | −1.19544 | ||||||||
\(709\) | 25.9800 | 0.975698 | 0.487849 | − | 0.872928i | \(-0.337782\pi\) | ||||
0.487849 | + | 0.872928i | \(0.337782\pi\) | |||||||
\(710\) | 2.76805 | 0.103883 | ||||||||
\(711\) | 4.67035 | 0.175152 | ||||||||
\(712\) | −34.7876 | −1.30372 | ||||||||
\(713\) | −0.714112 | −0.0267437 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.76831 | −0.103529 | ||||||||
\(716\) | 30.7925 | 1.15077 | ||||||||
\(717\) | −12.5731 | −0.469551 | ||||||||
\(718\) | −29.5824 | −1.10401 | ||||||||
\(719\) | −23.7887 | −0.887169 | −0.443585 | − | 0.896232i | \(-0.646293\pi\) | ||||
−0.443585 | + | 0.896232i | \(0.646293\pi\) | |||||||
\(720\) | 0.971148 | 0.0361926 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.9508 | 0.556411 | ||||||||
\(723\) | 4.30351 | 0.160049 | ||||||||
\(724\) | −28.4120 | −1.05592 | ||||||||
\(725\) | −33.1911 | −1.23268 | ||||||||
\(726\) | 4.02992 | 0.149564 | ||||||||
\(727\) | −34.9164 | −1.29498 | −0.647489 | − | 0.762074i | \(-0.724181\pi\) | ||||
−0.647489 | + | 0.762074i | \(0.724181\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.4278 | 0.793078 | ||||||||
\(731\) | 3.40238 | 0.125842 | ||||||||
\(732\) | −24.1057 | −0.890974 | ||||||||
\(733\) | −1.49359 | −0.0551670 | −0.0275835 | − | 0.999620i | \(-0.508781\pi\) | ||||
−0.0275835 | + | 0.999620i | \(0.508781\pi\) | |||||||
\(734\) | 43.3077 | 1.59852 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.77680 | −0.139215 | ||||||||
\(737\) | −24.6809 | −0.909132 | ||||||||
\(738\) | −2.23115 | −0.0821296 | ||||||||
\(739\) | 35.3095 | 1.29888 | 0.649440 | − | 0.760413i | \(-0.275003\pi\) | ||||
0.649440 | + | 0.760413i | \(0.275003\pi\) | |||||||
\(740\) | 30.6967 | 1.12843 | ||||||||
\(741\) | 3.58537 | 0.131712 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.1868 | 0.740582 | 0.370291 | − | 0.928916i | \(-0.379258\pi\) | ||||
0.370291 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(744\) | −2.80165 | −0.102714 | ||||||||
\(745\) | −2.90721 | −0.106512 | ||||||||
\(746\) | −44.1835 | −1.61767 | ||||||||
\(747\) | 3.22689 | 0.118066 | ||||||||
\(748\) | 5.33235 | 0.194970 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −18.3359 | −0.669532 | ||||||||
\(751\) | 43.9665 | 1.60436 | 0.802180 | − | 0.597083i | \(-0.203674\pi\) | ||||
0.802180 | + | 0.597083i | \(0.203674\pi\) | |||||||
\(752\) | −0.249595 | −0.00910179 | ||||||||
\(753\) | −12.7442 | −0.464425 | ||||||||
\(754\) | 18.0153 | 0.656078 | ||||||||
\(755\) | −10.7527 | −0.391331 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.4722 | 0.635040 | 0.317520 | − | 0.948252i | \(-0.397150\pi\) | ||||
0.317520 | + | 0.948252i | \(0.397150\pi\) | |||||||
\(758\) | −23.3665 | −0.848709 | ||||||||
\(759\) | 1.68644 | 0.0612140 | ||||||||
\(760\) | −6.83403 | −0.247896 | ||||||||
\(761\) | −8.70835 | −0.315677 | −0.157839 | − | 0.987465i | \(-0.550453\pi\) | ||||
−0.157839 | + | 0.987465i | \(0.550453\pi\) | |||||||
\(762\) | 17.7142 | 0.641717 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.4812 | 0.415375 | ||||||||
\(765\) | 0.527368 | 0.0190670 | ||||||||
\(766\) | −40.0643 | −1.44758 | ||||||||
\(767\) | 10.9198 | 0.394292 | ||||||||
\(768\) | −8.34043 | −0.300959 | ||||||||
\(769\) | −18.9265 | −0.682507 | −0.341253 | − | 0.939971i | \(-0.610851\pi\) | ||||
−0.341253 | + | 0.939971i | \(0.610851\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.3531 | −0.552929 | ||||||||
\(772\) | 36.4879 | 1.31323 | ||||||||
\(773\) | 32.6886 | 1.17573 | 0.587864 | − | 0.808960i | \(-0.299969\pi\) | ||||
0.587864 | + | 0.808960i | \(0.299969\pi\) | |||||||
\(774\) | 12.8548 | 0.462057 | ||||||||
\(775\) | −5.39570 | −0.193819 | ||||||||
\(776\) | −11.2765 | −0.404802 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −69.7686 | −2.50132 | ||||||||
\(779\) | −3.50700 | −0.125651 | ||||||||
\(780\) | 2.71890 | 0.0973523 | ||||||||
\(781\) | −4.21235 | −0.150730 | ||||||||
\(782\) | −0.732820 | −0.0262056 | ||||||||
\(783\) | 7.89796 | 0.282250 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.518193 | −0.0184951 | ||||||||
\(786\) | −4.27072 | −0.152332 | ||||||||
\(787\) | 54.7501 | 1.95163 | 0.975814 | − | 0.218601i | \(-0.0701494\pi\) | ||||
0.975814 | + | 0.218601i | \(0.0701494\pi\) | |||||||
\(788\) | 59.7323 | 2.12788 | ||||||||
\(789\) | 4.70180 | 0.167388 | ||||||||
\(790\) | 9.30565 | 0.331080 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.61637 | 0.235102 | ||||||||
\(793\) | 8.27546 | 0.293870 | ||||||||
\(794\) | −65.7801 | −2.33445 | ||||||||
\(795\) | −7.63388 | −0.270746 | ||||||||
\(796\) | −26.0964 | −0.924962 | ||||||||
\(797\) | 44.9819 | 1.59334 | 0.796671 | − | 0.604414i | \(-0.206593\pi\) | ||||
0.796671 | + | 0.604414i | \(0.206593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.135539 | −0.00479502 | ||||||||
\(800\) | −28.5369 | −1.00893 | ||||||||
\(801\) | 15.9423 | 0.563295 | ||||||||
\(802\) | 25.2452 | 0.891439 | ||||||||
\(803\) | −32.6082 | −1.15072 | ||||||||
\(804\) | 24.2404 | 0.854893 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.92865 | 0.103157 | ||||||||
\(807\) | −17.8058 | −0.626792 | ||||||||
\(808\) | −23.1964 | −0.816046 | ||||||||
\(809\) | 11.9297 | 0.419425 | 0.209713 | − | 0.977763i | \(-0.432747\pi\) | ||||
0.209713 | + | 0.977763i | \(0.432747\pi\) | |||||||
\(810\) | 1.99249 | 0.0700091 | ||||||||
\(811\) | 6.14692 | 0.215848 | 0.107924 | − | 0.994159i | \(-0.465580\pi\) | ||||
0.107924 | + | 0.994159i | \(0.465580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.15229 | −0.180699 | ||||||||
\(814\) | −78.0857 | −2.73690 | ||||||||
\(815\) | −10.6856 | −0.374299 | ||||||||
\(816\) | 0.642187 | 0.0224810 | ||||||||
\(817\) | 20.2057 | 0.706908 | ||||||||
\(818\) | −42.2258 | −1.47639 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.65947 | −0.0928728 | ||||||||
\(821\) | 28.1002 | 0.980702 | 0.490351 | − | 0.871525i | \(-0.336869\pi\) | ||||
0.490351 | + | 0.871525i | \(0.336869\pi\) | |||||||
\(822\) | −24.4133 | −0.851511 | ||||||||
\(823\) | 10.2799 | 0.358334 | 0.179167 | − | 0.983819i | \(-0.442660\pi\) | ||||
0.179167 | + | 0.983819i | \(0.442660\pi\) | |||||||
\(824\) | 8.59354 | 0.299370 | ||||||||
\(825\) | 12.7425 | 0.443636 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.5878 | −1.48092 | −0.740462 | − | 0.672098i | \(-0.765393\pi\) | ||||
−0.740462 | + | 0.672098i | \(0.765393\pi\) | |||||||
\(828\) | −1.65634 | −0.0575620 | ||||||||
\(829\) | −15.6799 | −0.544586 | −0.272293 | − | 0.962214i | \(-0.587782\pi\) | ||||
−0.272293 | + | 0.962214i | \(0.587782\pi\) | |||||||
\(830\) | 6.42956 | 0.223173 | ||||||||
\(831\) | −8.01369 | −0.277992 | ||||||||
\(832\) | 13.2656 | 0.459901 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −45.9462 | −1.59099 | ||||||||
\(835\) | 15.1756 | 0.525174 | ||||||||
\(836\) | 31.6672 | 1.09523 | ||||||||
\(837\) | 1.28393 | 0.0443792 | ||||||||
\(838\) | −25.1732 | −0.869595 | ||||||||
\(839\) | 46.4057 | 1.60210 | 0.801052 | − | 0.598595i | \(-0.204274\pi\) | ||||
0.801052 | + | 0.598595i | \(0.204274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.3777 | 1.15096 | ||||||||
\(842\) | −3.28119 | −0.113077 | ||||||||
\(843\) | 4.98277 | 0.171616 | ||||||||
\(844\) | 65.1881 | 2.24387 | ||||||||
\(845\) | 10.6761 | 0.367268 | ||||||||
\(846\) | −0.512091 | −0.0176061 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.29593 | −0.319224 | ||||||||
\(849\) | 6.83872 | 0.234704 | ||||||||
\(850\) | −5.53706 | −0.189920 | ||||||||
\(851\) | 6.41978 | 0.220067 | ||||||||
\(852\) | 4.13717 | 0.141737 | ||||||||
\(853\) | 23.0031 | 0.787611 | 0.393805 | − | 0.919194i | \(-0.371158\pi\) | ||||
0.393805 | + | 0.919194i | \(0.371158\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.13188 | 0.107108 | ||||||||
\(856\) | 23.5666 | 0.805489 | ||||||||
\(857\) | −4.92156 | −0.168117 | −0.0840587 | − | 0.996461i | \(-0.526788\pi\) | ||||
−0.0840587 | + | 0.996461i | \(0.526788\pi\) | |||||||
\(858\) | −6.91629 | −0.236118 | ||||||||
\(859\) | 7.76979 | 0.265102 | 0.132551 | − | 0.991176i | \(-0.457683\pi\) | ||||
0.132551 | + | 0.991176i | \(0.457683\pi\) | |||||||
\(860\) | 15.3226 | 0.522497 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.9421 | 0.372689 | ||||||||
\(863\) | −12.3757 | −0.421274 | −0.210637 | − | 0.977564i | \(-0.567554\pi\) | ||||
−0.210637 | + | 0.977564i | \(0.567554\pi\) | |||||||
\(864\) | 6.79048 | 0.231017 | ||||||||
\(865\) | −2.68197 | −0.0911898 | ||||||||
\(866\) | 20.5401 | 0.697980 | ||||||||
\(867\) | −16.6513 | −0.565507 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.1611 | −0.480382 | ||||||||
\(870\) | 15.7366 | 0.533522 | ||||||||
\(871\) | −8.32169 | −0.281970 | ||||||||
\(872\) | 29.9810 | 1.01528 | ||||||||
\(873\) | 5.16775 | 0.174902 | ||||||||
\(874\) | −4.35199 | −0.147208 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 32.0263 | 1.08207 | ||||||||
\(877\) | −31.0076 | −1.04705 | −0.523526 | − | 0.852010i | \(-0.675384\pi\) | ||||
−0.523526 | + | 0.852010i | \(0.675384\pi\) | |||||||
\(878\) | 53.6328 | 1.81002 | ||||||||
\(879\) | 23.1644 | 0.781315 | ||||||||
\(880\) | −2.94464 | −0.0992639 | ||||||||
\(881\) | 49.0117 | 1.65125 | 0.825624 | − | 0.564221i | \(-0.190824\pi\) | ||||
0.825624 | + | 0.564221i | \(0.190824\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.3902 | 1.76307 | 0.881535 | − | 0.472119i | \(-0.156511\pi\) | ||||
0.881535 | + | 0.472119i | \(0.156511\pi\) | |||||||
\(884\) | 1.79792 | 0.0604705 | ||||||||
\(885\) | 9.53863 | 0.320638 | ||||||||
\(886\) | 49.8603 | 1.67509 | ||||||||
\(887\) | 49.6047 | 1.66556 | 0.832781 | − | 0.553603i | \(-0.186747\pi\) | ||||
0.832781 | + | 0.553603i | \(0.186747\pi\) | |||||||
\(888\) | 25.1865 | 0.845204 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 31.7650 | 1.06477 | ||||||||
\(891\) | −3.03213 | −0.101580 | ||||||||
\(892\) | 56.5979 | 1.89504 | ||||||||
\(893\) | −0.804924 | −0.0269358 | ||||||||
\(894\) | −7.26333 | −0.242922 | ||||||||
\(895\) | −9.23395 | −0.308657 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.568620 | 0.0189857 | ||||||||
\(898\) | −33.6559 | −1.12311 | ||||||||
\(899\) | 10.1404 | 0.338202 | ||||||||
\(900\) | −12.5151 | −0.417169 | ||||||||
\(901\) | −5.04802 | −0.168174 | ||||||||
\(902\) | 6.76512 | 0.225254 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.27771 | −0.208793 | ||||||||
\(905\) | 8.52009 | 0.283217 | ||||||||
\(906\) | −26.8644 | −0.892509 | ||||||||
\(907\) | 1.69849 | 0.0563974 | 0.0281987 | − | 0.999602i | \(-0.491023\pi\) | ||||
0.0281987 | + | 0.999602i | \(0.491023\pi\) | |||||||
\(908\) | 43.7831 | 1.45299 | ||||||||
\(909\) | 10.6304 | 0.352587 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.66674 | −0.254010 | −0.127005 | − | 0.991902i | \(-0.540537\pi\) | ||||
−0.127005 | + | 0.991902i | \(0.540537\pi\) | |||||||
\(912\) | 3.81375 | 0.126286 | ||||||||
\(913\) | −9.78434 | −0.323814 | ||||||||
\(914\) | 26.6578 | 0.881761 | ||||||||
\(915\) | 7.22875 | 0.238975 | ||||||||
\(916\) | 67.7682 | 2.23913 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.31757 | 0.0434862 | ||||||||
\(919\) | 29.6626 | 0.978480 | 0.489240 | − | 0.872149i | \(-0.337274\pi\) | ||||
0.489240 | + | 0.872149i | \(0.337274\pi\) | |||||||
\(920\) | −1.08384 | −0.0357332 | ||||||||
\(921\) | −16.0121 | −0.527616 | ||||||||
\(922\) | 19.4988 | 0.642159 | ||||||||
\(923\) | −1.42029 | −0.0467493 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.5068 | 1.59489 | ||||||||
\(926\) | 72.2692 | 2.37491 | ||||||||
\(927\) | −3.93822 | −0.129348 | ||||||||
\(928\) | 53.6309 | 1.76052 | ||||||||
\(929\) | −46.0046 | −1.50936 | −0.754681 | − | 0.656091i | \(-0.772209\pi\) | ||||
−0.754681 | + | 0.656091i | \(0.772209\pi\) | |||||||
\(930\) | 2.55823 | 0.0838875 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −81.3836 | −2.66581 | ||||||||
\(933\) | −20.7107 | −0.678038 | ||||||||
\(934\) | −0.730722 | −0.0239100 | ||||||||
\(935\) | −1.59905 | −0.0522944 | ||||||||
\(936\) | 2.23085 | 0.0729176 | ||||||||
\(937\) | 21.8284 | 0.713102 | 0.356551 | − | 0.934276i | \(-0.383953\pi\) | ||||
0.356551 | + | 0.934276i | \(0.383953\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.5447 | 0.605185 | ||||||||
\(940\) | −0.610400 | −0.0199091 | ||||||||
\(941\) | −27.7442 | −0.904435 | −0.452217 | − | 0.891908i | \(-0.649367\pi\) | ||||
−0.452217 | + | 0.891908i | \(0.649367\pi\) | |||||||
\(942\) | −1.29464 | −0.0421818 | ||||||||
\(943\) | −0.556191 | −0.0181121 | ||||||||
\(944\) | 11.6154 | 0.378049 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.9774 | −1.26727 | ||||||||
\(947\) | −12.5298 | −0.407163 | −0.203581 | − | 0.979058i | \(-0.565258\pi\) | ||||
−0.203581 | + | 0.979058i | \(0.565258\pi\) | |||||||
\(948\) | 13.9084 | 0.451723 | ||||||||
\(949\) | −10.9946 | −0.356899 | ||||||||
\(950\) | −32.8829 | −1.06686 | ||||||||
\(951\) | 20.6683 | 0.670217 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.2076 | −0.686981 | −0.343491 | − | 0.939156i | \(-0.611609\pi\) | ||||
−0.343491 | + | 0.939156i | \(0.611609\pi\) | |||||||
\(954\) | −19.0724 | −0.617490 | ||||||||
\(955\) | −3.44294 | −0.111411 | ||||||||
\(956\) | −37.4428 | −1.21099 | ||||||||
\(957\) | −23.9476 | −0.774116 | ||||||||
\(958\) | 12.9900 | 0.419688 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 11.5877 | 0.373991 | ||||||||
\(961\) | −29.3515 | −0.946823 | ||||||||
\(962\) | −26.3283 | −0.848857 | ||||||||
\(963\) | −10.8000 | −0.348026 | ||||||||
\(964\) | 12.8159 | 0.412773 | ||||||||
\(965\) | −10.9419 | −0.352231 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.6750 | −0.504073 | −0.252037 | − | 0.967718i | \(-0.581100\pi\) | ||||
−0.252037 | + | 0.967718i | \(0.581100\pi\) | |||||||
\(968\) | 3.94131 | 0.126679 | ||||||||
\(969\) | 2.07100 | 0.0665302 | ||||||||
\(970\) | 10.2967 | 0.330608 | ||||||||
\(971\) | −32.1713 | −1.03243 | −0.516214 | − | 0.856460i | \(-0.672659\pi\) | ||||
−0.516214 | + | 0.856460i | \(0.672659\pi\) | |||||||
\(972\) | 2.97801 | 0.0955198 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 54.7330 | 1.75376 | ||||||||
\(975\) | 4.29640 | 0.137595 | ||||||||
\(976\) | 8.80259 | 0.281764 | ||||||||
\(977\) | −21.8155 | −0.697940 | −0.348970 | − | 0.937134i | \(-0.613468\pi\) | ||||
−0.348970 | + | 0.937134i | \(0.613468\pi\) | |||||||
\(978\) | −26.6966 | −0.853663 | ||||||||
\(979\) | −48.3392 | −1.54493 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.7396 | −0.438671 | ||||||||
\(982\) | −46.9571 | −1.49846 | ||||||||
\(983\) | 42.4637 | 1.35438 | 0.677191 | − | 0.735808i | \(-0.263197\pi\) | ||||
0.677191 | + | 0.735808i | \(0.263197\pi\) | |||||||
\(984\) | −2.18209 | −0.0695624 | ||||||||
\(985\) | −17.9123 | −0.570734 | ||||||||
\(986\) | 10.4061 | 0.331397 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.6773 | 0.339689 | ||||||||
\(989\) | 3.20451 | 0.101898 | ||||||||
\(990\) | −6.04149 | −0.192011 | ||||||||
\(991\) | −60.9054 | −1.93473 | −0.967363 | − | 0.253396i | \(-0.918452\pi\) | ||||
−0.967363 | + | 0.253396i | \(0.918452\pi\) | |||||||
\(992\) | 8.71851 | 0.276813 | ||||||||
\(993\) | 3.75882 | 0.119283 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.82569 | 0.248091 | ||||||||
\(996\) | 9.60972 | 0.304496 | ||||||||
\(997\) | 19.4303 | 0.615363 | 0.307681 | − | 0.951489i | \(-0.400447\pi\) | ||||
0.307681 | + | 0.951489i | \(0.400447\pi\) | |||||||
\(998\) | −47.8554 | −1.51484 | ||||||||
\(999\) | −11.5424 | −0.365185 |
(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 | 6027.2.a.bc.1.1 | 8 | ||
7.3 | odd | 6 | 861.2.i.d.247.8 | ✓ | 16 | ||
7.5 | odd | 6 | 861.2.i.d.739.8 | yes | 16 | ||
7.6 | odd | 2 | 6027.2.a.bb.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.d.247.8 | ✓ | 16 | 7.3 | odd | 6 | ||
861.2.i.d.739.8 | yes | 16 | 7.5 | odd | 6 | ||
6027.2.a.bb.1.1 | 8 | 7.6 | odd | 2 | |||
6027.2.a.bc.1.1 | 8 | 1.1 | even | 1 | trivial |