Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 49x^{6} + 89x^{5} + 648x^{4} - 1023x^{3} - 1476x^{2} + 1940x - 384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.254436\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.254436 | 0.0899568 | 0.0449784 | − | 0.998988i | \(-0.485678\pi\) | ||||
0.0449784 | + | 0.998988i | \(0.485678\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −7.93526 | −0.991908 | ||||||||
\(5\) | −10.8225 | −0.967990 | −0.483995 | − | 0.875071i | \(-0.660815\pi\) | ||||
−0.483995 | + | 0.875071i | \(0.660815\pi\) | |||||||
\(6\) | −0.763309 | −0.0519366 | ||||||||
\(7\) | −23.2950 | −1.25781 | −0.628907 | − | 0.777481i | \(-0.716497\pi\) | ||||
−0.628907 | + | 0.777481i | \(0.716497\pi\) | |||||||
\(8\) | −4.05451 | −0.179186 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −2.75362 | −0.0870773 | ||||||||
\(11\) | 51.0608 | 1.39958 | 0.699791 | − | 0.714347i | \(-0.253276\pi\) | ||||
0.699791 | + | 0.714347i | \(0.253276\pi\) | |||||||
\(12\) | 23.8058 | 0.572678 | ||||||||
\(13\) | 51.8661 | 1.10654 | 0.553272 | − | 0.833001i | \(-0.313379\pi\) | ||||
0.553272 | + | 0.833001i | \(0.313379\pi\) | |||||||
\(14\) | −5.92710 | −0.113149 | ||||||||
\(15\) | 32.4674 | 0.558869 | ||||||||
\(16\) | 62.4505 | 0.975789 | ||||||||
\(17\) | −0.0421754 | −0.000601709 0 | −0.000300854 | − | 1.00000i | \(-0.500096\pi\) | ||||
−0.000300854 | 1.00000i | \(0.500096\pi\) | ||||||||
\(18\) | 2.28993 | 0.0299856 | ||||||||
\(19\) | −85.2082 | −1.02885 | −0.514424 | − | 0.857536i | \(-0.671994\pi\) | ||||
−0.514424 | + | 0.857536i | \(0.671994\pi\) | |||||||
\(20\) | 85.8790 | 0.960157 | ||||||||
\(21\) | 69.8851 | 0.726199 | ||||||||
\(22\) | 12.9917 | 0.125902 | ||||||||
\(23\) | −8.50543 | −0.0771089 | −0.0385544 | − | 0.999257i | \(-0.512275\pi\) | ||||
−0.0385544 | + | 0.999257i | \(0.512275\pi\) | |||||||
\(24\) | 12.1635 | 0.103453 | ||||||||
\(25\) | −7.87442 | −0.0629954 | ||||||||
\(26\) | 13.1966 | 0.0995411 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 184.852 | 1.24764 | ||||||||
\(29\) | −101.142 | −0.647639 | −0.323819 | − | 0.946119i | \(-0.604967\pi\) | ||||
−0.323819 | + | 0.946119i | \(0.604967\pi\) | |||||||
\(30\) | 8.26087 | 0.0502741 | ||||||||
\(31\) | 271.338 | 1.57206 | 0.786029 | − | 0.618189i | \(-0.212133\pi\) | ||||
0.786029 | + | 0.618189i | \(0.212133\pi\) | |||||||
\(32\) | 48.3257 | 0.266964 | ||||||||
\(33\) | −153.182 | −0.808049 | ||||||||
\(34\) | −0.0107310 | −5.41278e−5 0 | ||||||||
\(35\) | 252.110 | 1.21755 | ||||||||
\(36\) | −71.4174 | −0.330636 | ||||||||
\(37\) | −9.54238 | −0.0423988 | −0.0211994 | − | 0.999775i | \(-0.506748\pi\) | ||||
−0.0211994 | + | 0.999775i | \(0.506748\pi\) | |||||||
\(38\) | −21.6800 | −0.0925518 | ||||||||
\(39\) | −155.598 | −0.638863 | ||||||||
\(40\) | 43.8797 | 0.173450 | ||||||||
\(41\) | −185.363 | −0.706071 | −0.353035 | − | 0.935610i | \(-0.614850\pi\) | ||||
−0.353035 | + | 0.935610i | \(0.614850\pi\) | |||||||
\(42\) | 17.7813 | 0.0653265 | ||||||||
\(43\) | 277.532 | 0.984263 | 0.492131 | − | 0.870521i | \(-0.336218\pi\) | ||||
0.492131 | + | 0.870521i | \(0.336218\pi\) | |||||||
\(44\) | −405.181 | −1.38826 | ||||||||
\(45\) | −97.4021 | −0.322663 | ||||||||
\(46\) | −2.16409 | −0.00693647 | ||||||||
\(47\) | 309.877 | 0.961708 | 0.480854 | − | 0.876801i | \(-0.340327\pi\) | ||||
0.480854 | + | 0.876801i | \(0.340327\pi\) | |||||||
\(48\) | −187.351 | −0.563372 | ||||||||
\(49\) | 199.659 | 0.582096 | ||||||||
\(50\) | −2.00354 | −0.00566686 | ||||||||
\(51\) | 0.126526 | 0.000347397 0 | ||||||||
\(52\) | −411.571 | −1.09759 | ||||||||
\(53\) | 273.504 | 0.708842 | 0.354421 | − | 0.935086i | \(-0.384678\pi\) | ||||
0.354421 | + | 0.935086i | \(0.384678\pi\) | |||||||
\(54\) | −6.86978 | −0.0173122 | ||||||||
\(55\) | −552.603 | −1.35478 | ||||||||
\(56\) | 94.4499 | 0.225382 | ||||||||
\(57\) | 255.625 | 0.594005 | ||||||||
\(58\) | −25.7341 | −0.0582595 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | −257.637 | −0.554347 | ||||||||
\(61\) | 752.893 | 1.58030 | 0.790148 | − | 0.612916i | \(-0.210004\pi\) | ||||
0.790148 | + | 0.612916i | \(0.210004\pi\) | |||||||
\(62\) | 69.0383 | 0.141417 | ||||||||
\(63\) | −209.655 | −0.419271 | ||||||||
\(64\) | −487.308 | −0.951774 | ||||||||
\(65\) | −561.319 | −1.07112 | ||||||||
\(66\) | −38.9751 | −0.0726895 | ||||||||
\(67\) | 751.435 | 1.37018 | 0.685092 | − | 0.728456i | \(-0.259762\pi\) | ||||
0.685092 | + | 0.728456i | \(0.259762\pi\) | |||||||
\(68\) | 0.334673 | 0.000596840 0 | ||||||||
\(69\) | 25.5163 | 0.0445188 | ||||||||
\(70\) | 64.1458 | 0.109527 | ||||||||
\(71\) | −651.607 | −1.08918 | −0.544588 | − | 0.838704i | \(-0.683314\pi\) | ||||
−0.544588 | + | 0.838704i | \(0.683314\pi\) | |||||||
\(72\) | −36.4906 | −0.0597285 | ||||||||
\(73\) | 842.428 | 1.35067 | 0.675334 | − | 0.737512i | \(-0.263999\pi\) | ||||
0.675334 | + | 0.737512i | \(0.263999\pi\) | |||||||
\(74\) | −2.42793 | −0.00381406 | ||||||||
\(75\) | 23.6233 | 0.0363704 | ||||||||
\(76\) | 676.149 | 1.02052 | ||||||||
\(77\) | −1189.46 | −1.76041 | ||||||||
\(78\) | −39.5898 | −0.0574701 | ||||||||
\(79\) | −368.828 | −0.525271 | −0.262635 | − | 0.964895i | \(-0.584592\pi\) | ||||
−0.262635 | + | 0.964895i | \(0.584592\pi\) | |||||||
\(80\) | −675.868 | −0.944554 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −47.1631 | −0.0635158 | ||||||||
\(83\) | −545.888 | −0.721916 | −0.360958 | − | 0.932582i | \(-0.617550\pi\) | ||||
−0.360958 | + | 0.932582i | \(0.617550\pi\) | |||||||
\(84\) | −554.557 | −0.720323 | ||||||||
\(85\) | 0.456442 | 0.000582448 0 | ||||||||
\(86\) | 70.6143 | 0.0885411 | ||||||||
\(87\) | 303.425 | 0.373914 | ||||||||
\(88\) | −207.026 | −0.250785 | ||||||||
\(89\) | 634.328 | 0.755490 | 0.377745 | − | 0.925910i | \(-0.376700\pi\) | ||||
0.377745 | + | 0.925910i | \(0.376700\pi\) | |||||||
\(90\) | −24.7826 | −0.0290258 | ||||||||
\(91\) | −1208.22 | −1.39183 | ||||||||
\(92\) | 67.4928 | 0.0764849 | ||||||||
\(93\) | −814.015 | −0.907629 | ||||||||
\(94\) | 78.8440 | 0.0865121 | ||||||||
\(95\) | 922.162 | 0.995914 | ||||||||
\(96\) | −144.977 | −0.154132 | ||||||||
\(97\) | 316.368 | 0.331158 | 0.165579 | − | 0.986197i | \(-0.447051\pi\) | ||||
0.165579 | + | 0.986197i | \(0.447051\pi\) | |||||||
\(98\) | 50.8004 | 0.0523635 | ||||||||
\(99\) | 459.547 | 0.466528 | ||||||||
\(100\) | 62.4856 | 0.0624856 | ||||||||
\(101\) | −1615.25 | −1.59132 | −0.795662 | − | 0.605740i | \(-0.792877\pi\) | ||||
−0.795662 | + | 0.605740i | \(0.792877\pi\) | |||||||
\(102\) | 0.0321929 | 3.12507e−5 0 | ||||||||
\(103\) | 1261.07 | 1.20638 | 0.603190 | − | 0.797598i | \(-0.293896\pi\) | ||||
0.603190 | + | 0.797598i | \(0.293896\pi\) | |||||||
\(104\) | −210.291 | −0.198277 | ||||||||
\(105\) | −756.329 | −0.702954 | ||||||||
\(106\) | 69.5892 | 0.0637651 | ||||||||
\(107\) | 733.783 | 0.662967 | 0.331483 | − | 0.943461i | \(-0.392451\pi\) | ||||
0.331483 | + | 0.943461i | \(0.392451\pi\) | |||||||
\(108\) | 214.252 | 0.190893 | ||||||||
\(109\) | 582.848 | 0.512171 | 0.256086 | − | 0.966654i | \(-0.417567\pi\) | ||||
0.256086 | + | 0.966654i | \(0.417567\pi\) | |||||||
\(110\) | −140.602 | −0.121872 | ||||||||
\(111\) | 28.6271 | 0.0244790 | ||||||||
\(112\) | −1454.79 | −1.22736 | ||||||||
\(113\) | −1661.78 | −1.38342 | −0.691712 | − | 0.722174i | \(-0.743143\pi\) | ||||
−0.691712 | + | 0.722174i | \(0.743143\pi\) | |||||||
\(114\) | 65.0401 | 0.0534348 | ||||||||
\(115\) | 92.0496 | 0.0746406 | ||||||||
\(116\) | 802.585 | 0.642398 | ||||||||
\(117\) | 466.795 | 0.368848 | ||||||||
\(118\) | −15.0117 | −0.0117114 | ||||||||
\(119\) | 0.982479 | 0.000756838 0 | ||||||||
\(120\) | −131.639 | −0.100141 | ||||||||
\(121\) | 1276.20 | 0.958831 | ||||||||
\(122\) | 191.563 | 0.142158 | ||||||||
\(123\) | 556.090 | 0.407650 | ||||||||
\(124\) | −2153.14 | −1.55934 | ||||||||
\(125\) | 1438.03 | 1.02897 | ||||||||
\(126\) | −53.3439 | −0.0377163 | ||||||||
\(127\) | 1560.58 | 1.09039 | 0.545193 | − | 0.838310i | \(-0.316456\pi\) | ||||
0.545193 | + | 0.838310i | \(0.316456\pi\) | |||||||
\(128\) | −510.595 | −0.352583 | ||||||||
\(129\) | −832.597 | −0.568264 | ||||||||
\(130\) | −142.820 | −0.0963548 | ||||||||
\(131\) | 2608.59 | 1.73980 | 0.869898 | − | 0.493232i | \(-0.164185\pi\) | ||||
0.869898 | + | 0.493232i | \(0.164185\pi\) | |||||||
\(132\) | 1215.54 | 0.801510 | ||||||||
\(133\) | 1984.93 | 1.29410 | ||||||||
\(134\) | 191.192 | 0.123257 | ||||||||
\(135\) | 292.206 | 0.186290 | ||||||||
\(136\) | 0.171001 | 0.000107818 0 | ||||||||
\(137\) | −2284.40 | −1.42459 | −0.712296 | − | 0.701879i | \(-0.752345\pi\) | ||||
−0.712296 | + | 0.701879i | \(0.752345\pi\) | |||||||
\(138\) | 6.49227 | 0.00400477 | ||||||||
\(139\) | −288.324 | −0.175937 | −0.0879687 | − | 0.996123i | \(-0.528038\pi\) | ||||
−0.0879687 | + | 0.996123i | \(0.528038\pi\) | |||||||
\(140\) | −2000.56 | −1.20770 | ||||||||
\(141\) | −929.632 | −0.555242 | ||||||||
\(142\) | −165.792 | −0.0979787 | ||||||||
\(143\) | 2648.32 | 1.54870 | ||||||||
\(144\) | 562.054 | 0.325263 | ||||||||
\(145\) | 1094.60 | 0.626908 | ||||||||
\(146\) | 214.344 | 0.121502 | ||||||||
\(147\) | −598.977 | −0.336073 | ||||||||
\(148\) | 75.7212 | 0.0420557 | ||||||||
\(149\) | 591.503 | 0.325220 | 0.162610 | − | 0.986690i | \(-0.448009\pi\) | ||||
0.162610 | + | 0.986690i | \(0.448009\pi\) | |||||||
\(150\) | 6.01061 | 0.00327176 | ||||||||
\(151\) | −2398.78 | −1.29278 | −0.646391 | − | 0.763007i | \(-0.723722\pi\) | ||||
−0.646391 | + | 0.763007i | \(0.723722\pi\) | |||||||
\(152\) | 345.477 | 0.184355 | ||||||||
\(153\) | −0.379579 | −0.000200570 0 | ||||||||
\(154\) | −302.642 | −0.158361 | ||||||||
\(155\) | −2936.55 | −1.52174 | ||||||||
\(156\) | 1234.71 | 0.633693 | ||||||||
\(157\) | 135.478 | 0.0688684 | 0.0344342 | − | 0.999407i | \(-0.489037\pi\) | ||||
0.0344342 | + | 0.999407i | \(0.489037\pi\) | |||||||
\(158\) | −93.8432 | −0.0472517 | ||||||||
\(159\) | −820.511 | −0.409250 | ||||||||
\(160\) | −523.003 | −0.258419 | ||||||||
\(161\) | 198.134 | 0.0969886 | ||||||||
\(162\) | 20.6093 | 0.00999520 | ||||||||
\(163\) | 1649.77 | 0.792763 | 0.396381 | − | 0.918086i | \(-0.370266\pi\) | ||||
0.396381 | + | 0.918086i | \(0.370266\pi\) | |||||||
\(164\) | 1470.91 | 0.700357 | ||||||||
\(165\) | 1657.81 | 0.782184 | ||||||||
\(166\) | −138.894 | −0.0649412 | ||||||||
\(167\) | 3500.76 | 1.62214 | 0.811070 | − | 0.584949i | \(-0.198886\pi\) | ||||
0.811070 | + | 0.584949i | \(0.198886\pi\) | |||||||
\(168\) | −283.350 | −0.130124 | ||||||||
\(169\) | 493.092 | 0.224439 | ||||||||
\(170\) | 0.116135 | 5.23951e−5 0 | ||||||||
\(171\) | −766.874 | −0.342949 | ||||||||
\(172\) | −2202.29 | −0.976298 | ||||||||
\(173\) | 2524.80 | 1.10958 | 0.554790 | − | 0.831991i | \(-0.312799\pi\) | ||||
0.554790 | + | 0.831991i | \(0.312799\pi\) | |||||||
\(174\) | 77.2023 | 0.0336361 | ||||||||
\(175\) | 183.435 | 0.0792364 | ||||||||
\(176\) | 3188.77 | 1.36570 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | 161.396 | 0.0679614 | ||||||||
\(179\) | 2717.45 | 1.13470 | 0.567351 | − | 0.823476i | \(-0.307968\pi\) | ||||
0.567351 | + | 0.823476i | \(0.307968\pi\) | |||||||
\(180\) | 772.911 | 0.320052 | ||||||||
\(181\) | 2116.30 | 0.869077 | 0.434539 | − | 0.900653i | \(-0.356911\pi\) | ||||
0.434539 | + | 0.900653i | \(0.356911\pi\) | |||||||
\(182\) | −307.416 | −0.125204 | ||||||||
\(183\) | −2258.68 | −0.912384 | ||||||||
\(184\) | 34.4853 | 0.0138168 | ||||||||
\(185\) | 103.272 | 0.0410416 | ||||||||
\(186\) | −207.115 | −0.0816473 | ||||||||
\(187\) | −2.15351 | −0.000842141 0 | ||||||||
\(188\) | −2458.96 | −0.953925 | ||||||||
\(189\) | 628.966 | 0.242066 | ||||||||
\(190\) | 234.631 | 0.0895892 | ||||||||
\(191\) | −162.049 | −0.0613899 | −0.0306950 | − | 0.999529i | \(-0.509772\pi\) | ||||
−0.0306950 | + | 0.999529i | \(0.509772\pi\) | |||||||
\(192\) | 1461.92 | 0.549507 | ||||||||
\(193\) | −1737.71 | −0.648099 | −0.324050 | − | 0.946040i | \(-0.605044\pi\) | ||||
−0.324050 | + | 0.946040i | \(0.605044\pi\) | |||||||
\(194\) | 80.4956 | 0.0297899 | ||||||||
\(195\) | 1683.96 | 0.618413 | ||||||||
\(196\) | −1584.35 | −0.577385 | ||||||||
\(197\) | −1898.32 | −0.686548 | −0.343274 | − | 0.939235i | \(-0.611536\pi\) | ||||
−0.343274 | + | 0.939235i | \(0.611536\pi\) | |||||||
\(198\) | 116.925 | 0.0419673 | ||||||||
\(199\) | −925.010 | −0.329509 | −0.164754 | − | 0.986335i | \(-0.552683\pi\) | ||||
−0.164754 | + | 0.986335i | \(0.552683\pi\) | |||||||
\(200\) | 31.9269 | 0.0112879 | ||||||||
\(201\) | −2254.30 | −0.791077 | ||||||||
\(202\) | −410.979 | −0.143150 | ||||||||
\(203\) | 2356.10 | 0.814609 | ||||||||
\(204\) | −1.00402 | −0.000344585 0 | ||||||||
\(205\) | 2006.09 | 0.683469 | ||||||||
\(206\) | 320.862 | 0.108522 | ||||||||
\(207\) | −76.5489 | −0.0257030 | ||||||||
\(208\) | 3239.06 | 1.07975 | ||||||||
\(209\) | −4350.80 | −1.43996 | ||||||||
\(210\) | −192.437 | −0.0632354 | ||||||||
\(211\) | 2553.68 | 0.833186 | 0.416593 | − | 0.909093i | \(-0.363224\pi\) | ||||
0.416593 | + | 0.909093i | \(0.363224\pi\) | |||||||
\(212\) | −2170.32 | −0.703106 | ||||||||
\(213\) | 1954.82 | 0.628836 | ||||||||
\(214\) | 186.701 | 0.0596383 | ||||||||
\(215\) | −3003.58 | −0.952756 | ||||||||
\(216\) | 109.472 | 0.0344843 | ||||||||
\(217\) | −6320.84 | −1.97736 | ||||||||
\(218\) | 148.298 | 0.0460733 | ||||||||
\(219\) | −2527.28 | −0.779809 | ||||||||
\(220\) | 4385.05 | 1.34382 | ||||||||
\(221\) | −2.18748 | −0.000665817 0 | ||||||||
\(222\) | 7.28378 | 0.00220205 | ||||||||
\(223\) | −2867.05 | −0.860949 | −0.430475 | − | 0.902603i | \(-0.641654\pi\) | ||||
−0.430475 | + | 0.902603i | \(0.641654\pi\) | |||||||
\(224\) | −1125.75 | −0.335792 | ||||||||
\(225\) | −70.8698 | −0.0209985 | ||||||||
\(226\) | −422.816 | −0.124448 | ||||||||
\(227\) | −5544.65 | −1.62120 | −0.810598 | − | 0.585603i | \(-0.800858\pi\) | ||||
−0.810598 | + | 0.585603i | \(0.800858\pi\) | |||||||
\(228\) | −2028.45 | −0.589198 | ||||||||
\(229\) | −3010.94 | −0.868857 | −0.434429 | − | 0.900706i | \(-0.643050\pi\) | ||||
−0.434429 | + | 0.900706i | \(0.643050\pi\) | |||||||
\(230\) | 23.4208 | 0.00671443 | ||||||||
\(231\) | 3568.39 | 1.01638 | ||||||||
\(232\) | 410.079 | 0.116048 | ||||||||
\(233\) | 132.563 | 0.0372724 | 0.0186362 | − | 0.999826i | \(-0.494068\pi\) | ||||
0.0186362 | + | 0.999826i | \(0.494068\pi\) | |||||||
\(234\) | 118.770 | 0.0331804 | ||||||||
\(235\) | −3353.63 | −0.930923 | ||||||||
\(236\) | 468.180 | 0.129135 | ||||||||
\(237\) | 1106.48 | 0.303265 | ||||||||
\(238\) | 0.249978 | 6.80827e−5 0 | ||||||||
\(239\) | 7104.31 | 1.92276 | 0.961380 | − | 0.275224i | \(-0.0887519\pi\) | ||||
0.961380 | + | 0.275224i | \(0.0887519\pi\) | |||||||
\(240\) | 2027.60 | 0.545338 | ||||||||
\(241\) | 124.665 | 0.0333211 | 0.0166605 | − | 0.999861i | \(-0.494697\pi\) | ||||
0.0166605 | + | 0.999861i | \(0.494697\pi\) | |||||||
\(242\) | 324.713 | 0.0862534 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −5974.40 | −1.56751 | ||||||||
\(245\) | −2160.80 | −0.563463 | ||||||||
\(246\) | 141.489 | 0.0366709 | ||||||||
\(247\) | −4419.42 | −1.13846 | ||||||||
\(248\) | −1100.14 | −0.281690 | ||||||||
\(249\) | 1637.67 | 0.416798 | ||||||||
\(250\) | 365.886 | 0.0925627 | ||||||||
\(251\) | −6840.81 | −1.72027 | −0.860135 | − | 0.510066i | \(-0.829621\pi\) | ||||
−0.860135 | + | 0.510066i | \(0.829621\pi\) | |||||||
\(252\) | 1663.67 | 0.415878 | ||||||||
\(253\) | −434.294 | −0.107920 | ||||||||
\(254\) | 397.068 | 0.0980877 | ||||||||
\(255\) | −1.36933 | −0.000336277 0 | ||||||||
\(256\) | 3768.55 | 0.920056 | ||||||||
\(257\) | −374.942 | −0.0910049 | −0.0455024 | − | 0.998964i | \(-0.514489\pi\) | ||||
−0.0455024 | + | 0.998964i | \(0.514489\pi\) | |||||||
\(258\) | −211.843 | −0.0511192 | ||||||||
\(259\) | 222.290 | 0.0533298 | ||||||||
\(260\) | 4454.21 | 1.06246 | ||||||||
\(261\) | −910.275 | −0.215880 | ||||||||
\(262\) | 663.719 | 0.156506 | ||||||||
\(263\) | 7174.93 | 1.68222 | 0.841112 | − | 0.540861i | \(-0.181901\pi\) | ||||
0.841112 | + | 0.540861i | \(0.181901\pi\) | |||||||
\(264\) | 621.079 | 0.144791 | ||||||||
\(265\) | −2959.98 | −0.686152 | ||||||||
\(266\) | 505.038 | 0.116413 | ||||||||
\(267\) | −1902.98 | −0.436182 | ||||||||
\(268\) | −5962.83 | −1.35910 | ||||||||
\(269\) | −2997.57 | −0.679425 | −0.339713 | − | 0.940529i | \(-0.610330\pi\) | ||||
−0.339713 | + | 0.940529i | \(0.610330\pi\) | |||||||
\(270\) | 74.3479 | 0.0167580 | ||||||||
\(271\) | 5993.77 | 1.34353 | 0.671763 | − | 0.740766i | \(-0.265537\pi\) | ||||
0.671763 | + | 0.740766i | \(0.265537\pi\) | |||||||
\(272\) | −2.63388 | −0.000587141 0 | ||||||||
\(273\) | 3624.67 | 0.803571 | ||||||||
\(274\) | −581.233 | −0.128152 | ||||||||
\(275\) | −402.074 | −0.0881672 | ||||||||
\(276\) | −202.478 | −0.0441586 | ||||||||
\(277\) | −8759.33 | −1.89999 | −0.949994 | − | 0.312267i | \(-0.898912\pi\) | ||||
−0.949994 | + | 0.312267i | \(0.898912\pi\) | |||||||
\(278\) | −73.3600 | −0.0158268 | ||||||||
\(279\) | 2442.05 | 0.524020 | ||||||||
\(280\) | −1022.18 | −0.218168 | ||||||||
\(281\) | −4991.90 | −1.05976 | −0.529878 | − | 0.848074i | \(-0.677762\pi\) | ||||
−0.529878 | + | 0.848074i | \(0.677762\pi\) | |||||||
\(282\) | −236.532 | −0.0499478 | ||||||||
\(283\) | −470.303 | −0.0987866 | −0.0493933 | − | 0.998779i | \(-0.515729\pi\) | ||||
−0.0493933 | + | 0.998779i | \(0.515729\pi\) | |||||||
\(284\) | 5170.67 | 1.08036 | ||||||||
\(285\) | −2766.49 | −0.574991 | ||||||||
\(286\) | 673.829 | 0.139316 | ||||||||
\(287\) | 4318.05 | 0.888105 | ||||||||
\(288\) | 434.931 | 0.0889881 | ||||||||
\(289\) | −4913.00 | −1.00000 | ||||||||
\(290\) | 278.506 | 0.0563946 | ||||||||
\(291\) | −949.105 | −0.191194 | ||||||||
\(292\) | −6684.89 | −1.33974 | ||||||||
\(293\) | 1777.56 | 0.354425 | 0.177212 | − | 0.984173i | \(-0.443292\pi\) | ||||
0.177212 | + | 0.984173i | \(0.443292\pi\) | |||||||
\(294\) | −152.401 | −0.0302321 | ||||||||
\(295\) | 638.525 | 0.126022 | ||||||||
\(296\) | 38.6896 | 0.00759726 | ||||||||
\(297\) | −1378.64 | −0.269350 | ||||||||
\(298\) | 150.500 | 0.0292558 | ||||||||
\(299\) | −441.143 | −0.0853243 | ||||||||
\(300\) | −187.457 | −0.0360761 | ||||||||
\(301\) | −6465.13 | −1.23802 | ||||||||
\(302\) | −610.336 | −0.116294 | ||||||||
\(303\) | 4845.76 | 0.918752 | ||||||||
\(304\) | −5321.29 | −1.00394 | ||||||||
\(305\) | −8148.15 | −1.52971 | ||||||||
\(306\) | −0.0965786 | −1.80426e−5 0 | ||||||||
\(307\) | 4138.06 | 0.769289 | 0.384645 | − | 0.923065i | \(-0.374324\pi\) | ||||
0.384645 | + | 0.923065i | \(0.374324\pi\) | |||||||
\(308\) | 9438.70 | 1.74617 | ||||||||
\(309\) | −3783.21 | −0.696503 | ||||||||
\(310\) | −747.164 | −0.136891 | ||||||||
\(311\) | 7356.20 | 1.34126 | 0.670630 | − | 0.741792i | \(-0.266024\pi\) | ||||
0.670630 | + | 0.741792i | \(0.266024\pi\) | |||||||
\(312\) | 630.874 | 0.114475 | ||||||||
\(313\) | 6696.92 | 1.20937 | 0.604685 | − | 0.796465i | \(-0.293299\pi\) | ||||
0.604685 | + | 0.796465i | \(0.293299\pi\) | |||||||
\(314\) | 34.4706 | 0.00619518 | ||||||||
\(315\) | 2268.99 | 0.405850 | ||||||||
\(316\) | 2926.75 | 0.521020 | ||||||||
\(317\) | 7828.34 | 1.38701 | 0.693507 | − | 0.720450i | \(-0.256065\pi\) | ||||
0.693507 | + | 0.720450i | \(0.256065\pi\) | |||||||
\(318\) | −208.768 | −0.0368148 | ||||||||
\(319\) | −5164.37 | −0.906424 | ||||||||
\(320\) | 5273.87 | 0.921307 | ||||||||
\(321\) | −2201.35 | −0.382764 | ||||||||
\(322\) | 50.4125 | 0.00872478 | ||||||||
\(323\) | 3.59369 | 0.000619066 0 | ||||||||
\(324\) | −642.756 | −0.110212 | ||||||||
\(325\) | −408.415 | −0.0697071 | ||||||||
\(326\) | 419.762 | 0.0713144 | ||||||||
\(327\) | −1748.54 | −0.295702 | ||||||||
\(328\) | 751.557 | 0.126518 | ||||||||
\(329\) | −7218.60 | −1.20965 | ||||||||
\(330\) | 421.807 | 0.0703627 | ||||||||
\(331\) | −791.925 | −0.131505 | −0.0657525 | − | 0.997836i | \(-0.520945\pi\) | ||||
−0.0657525 | + | 0.997836i | \(0.520945\pi\) | |||||||
\(332\) | 4331.77 | 0.716074 | ||||||||
\(333\) | −85.8814 | −0.0141329 | ||||||||
\(334\) | 890.721 | 0.145922 | ||||||||
\(335\) | −8132.37 | −1.32633 | ||||||||
\(336\) | 4364.36 | 0.708617 | ||||||||
\(337\) | 3609.06 | 0.583378 | 0.291689 | − | 0.956513i | \(-0.405783\pi\) | ||||
0.291689 | + | 0.956513i | \(0.405783\pi\) | |||||||
\(338\) | 125.460 | 0.0201898 | ||||||||
\(339\) | 4985.33 | 0.798720 | ||||||||
\(340\) | −3.62199 | −0.000577735 0 | ||||||||
\(341\) | 13854.8 | 2.20023 | ||||||||
\(342\) | −195.120 | −0.0308506 | ||||||||
\(343\) | 3339.14 | 0.525646 | ||||||||
\(344\) | −1125.26 | −0.176366 | ||||||||
\(345\) | −276.149 | −0.0430938 | ||||||||
\(346\) | 642.401 | 0.0998142 | ||||||||
\(347\) | −4501.38 | −0.696389 | −0.348194 | − | 0.937422i | \(-0.613205\pi\) | ||||
−0.348194 | + | 0.937422i | \(0.613205\pi\) | |||||||
\(348\) | −2407.76 | −0.370889 | ||||||||
\(349\) | 4505.21 | 0.690998 | 0.345499 | − | 0.938419i | \(-0.387710\pi\) | ||||
0.345499 | + | 0.938419i | \(0.387710\pi\) | |||||||
\(350\) | 46.6725 | 0.00712785 | ||||||||
\(351\) | −1400.38 | −0.212954 | ||||||||
\(352\) | 2467.55 | 0.373639 | ||||||||
\(353\) | −6156.62 | −0.928282 | −0.464141 | − | 0.885761i | \(-0.653637\pi\) | ||||
−0.464141 | + | 0.885761i | \(0.653637\pi\) | |||||||
\(354\) | 45.0352 | 0.00676157 | ||||||||
\(355\) | 7051.99 | 1.05431 | ||||||||
\(356\) | −5033.56 | −0.749376 | ||||||||
\(357\) | −2.94744 | −0.000436960 0 | ||||||||
\(358\) | 691.417 | 0.102074 | ||||||||
\(359\) | 8811.87 | 1.29547 | 0.647734 | − | 0.761867i | \(-0.275717\pi\) | ||||
0.647734 | + | 0.761867i | \(0.275717\pi\) | |||||||
\(360\) | 394.918 | 0.0578166 | ||||||||
\(361\) | 401.436 | 0.0585269 | ||||||||
\(362\) | 538.462 | 0.0781794 | ||||||||
\(363\) | −3828.61 | −0.553582 | ||||||||
\(364\) | 9587.56 | 1.38056 | ||||||||
\(365\) | −9117.14 | −1.30743 | ||||||||
\(366\) | −574.690 | −0.0820752 | ||||||||
\(367\) | 13290.6 | 1.89036 | 0.945181 | − | 0.326546i | \(-0.105885\pi\) | ||||
0.945181 | + | 0.326546i | \(0.105885\pi\) | |||||||
\(368\) | −531.168 | −0.0752420 | ||||||||
\(369\) | −1668.27 | −0.235357 | ||||||||
\(370\) | 26.2761 | 0.00369197 | ||||||||
\(371\) | −6371.28 | −0.891591 | ||||||||
\(372\) | 6459.43 | 0.900284 | ||||||||
\(373\) | 10006.7 | 1.38908 | 0.694541 | − | 0.719453i | \(-0.255608\pi\) | ||||
0.694541 | + | 0.719453i | \(0.255608\pi\) | |||||||
\(374\) | −0.547931 | −7.57563e−5 0 | ||||||||
\(375\) | −4314.08 | −0.594075 | ||||||||
\(376\) | −1256.40 | −0.172324 | ||||||||
\(377\) | −5245.82 | −0.716641 | ||||||||
\(378\) | 160.032 | 0.0217755 | ||||||||
\(379\) | −3895.86 | −0.528013 | −0.264006 | − | 0.964521i | \(-0.585044\pi\) | ||||
−0.264006 | + | 0.964521i | \(0.585044\pi\) | |||||||
\(380\) | −7317.60 | −0.987855 | ||||||||
\(381\) | −4681.74 | −0.629535 | ||||||||
\(382\) | −41.2312 | −0.00552244 | ||||||||
\(383\) | −3038.64 | −0.405398 | −0.202699 | − | 0.979241i | \(-0.564971\pi\) | ||||
−0.202699 | + | 0.979241i | \(0.564971\pi\) | |||||||
\(384\) | 1531.78 | 0.203564 | ||||||||
\(385\) | 12872.9 | 1.70406 | ||||||||
\(386\) | −442.136 | −0.0583009 | ||||||||
\(387\) | 2497.79 | 0.328088 | ||||||||
\(388\) | −2510.47 | −0.328478 | ||||||||
\(389\) | −13537.3 | −1.76444 | −0.882222 | − | 0.470834i | \(-0.843953\pi\) | ||||
−0.882222 | + | 0.470834i | \(0.843953\pi\) | |||||||
\(390\) | 428.459 | 0.0556305 | ||||||||
\(391\) | 0.358720 | 4.63971e−5 0 | ||||||||
\(392\) | −809.518 | −0.104303 | ||||||||
\(393\) | −7825.76 | −1.00447 | ||||||||
\(394\) | −483.002 | −0.0617597 | ||||||||
\(395\) | 3991.63 | 0.508457 | ||||||||
\(396\) | −3646.63 | −0.462752 | ||||||||
\(397\) | −3491.32 | −0.441371 | −0.220686 | − | 0.975345i | \(-0.570829\pi\) | ||||
−0.220686 | + | 0.975345i | \(0.570829\pi\) | |||||||
\(398\) | −235.356 | −0.0296415 | ||||||||
\(399\) | −5954.78 | −0.747148 | ||||||||
\(400\) | −491.761 | −0.0614702 | ||||||||
\(401\) | 12667.7 | 1.57754 | 0.788769 | − | 0.614689i | \(-0.210719\pi\) | ||||
0.788769 | + | 0.614689i | \(0.210719\pi\) | |||||||
\(402\) | −573.577 | −0.0711627 | ||||||||
\(403\) | 14073.3 | 1.73955 | ||||||||
\(404\) | 12817.5 | 1.57845 | ||||||||
\(405\) | −876.619 | −0.107554 | ||||||||
\(406\) | 599.477 | 0.0732796 | ||||||||
\(407\) | −487.241 | −0.0593407 | ||||||||
\(408\) | −0.513002 | −6.22485e−5 0 | ||||||||
\(409\) | 10431.3 | 1.26111 | 0.630557 | − | 0.776143i | \(-0.282826\pi\) | ||||
0.630557 | + | 0.776143i | \(0.282826\pi\) | |||||||
\(410\) | 510.421 | 0.0614827 | ||||||||
\(411\) | 6853.19 | 0.822488 | ||||||||
\(412\) | −10006.9 | −1.19662 | ||||||||
\(413\) | 1374.41 | 0.163753 | ||||||||
\(414\) | −19.4768 | −0.00231216 | ||||||||
\(415\) | 5907.85 | 0.698808 | ||||||||
\(416\) | 2506.47 | 0.295408 | ||||||||
\(417\) | 864.971 | 0.101578 | ||||||||
\(418\) | −1107.00 | −0.129534 | ||||||||
\(419\) | −6955.06 | −0.810923 | −0.405462 | − | 0.914112i | \(-0.632889\pi\) | ||||
−0.405462 | + | 0.914112i | \(0.632889\pi\) | |||||||
\(420\) | 6001.67 | 0.697265 | ||||||||
\(421\) | −2977.09 | −0.344643 | −0.172321 | − | 0.985041i | \(-0.555127\pi\) | ||||
−0.172321 | + | 0.985041i | \(0.555127\pi\) | |||||||
\(422\) | 649.748 | 0.0749507 | ||||||||
\(423\) | 2788.90 | 0.320569 | ||||||||
\(424\) | −1108.92 | −0.127014 | ||||||||
\(425\) | 0.332107 | 3.79049e−5 0 | ||||||||
\(426\) | 497.377 | 0.0565681 | ||||||||
\(427\) | −17538.7 | −1.98772 | ||||||||
\(428\) | −5822.76 | −0.657602 | ||||||||
\(429\) | −7944.97 | −0.894142 | ||||||||
\(430\) | −764.220 | −0.0857069 | ||||||||
\(431\) | −9721.43 | −1.08646 | −0.543230 | − | 0.839584i | \(-0.682799\pi\) | ||||
−0.543230 | + | 0.839584i | \(0.682799\pi\) | |||||||
\(432\) | −1686.16 | −0.187791 | ||||||||
\(433\) | 814.588 | 0.0904079 | 0.0452040 | − | 0.998978i | \(-0.485606\pi\) | ||||
0.0452040 | + | 0.998978i | \(0.485606\pi\) | |||||||
\(434\) | −1608.25 | −0.177877 | ||||||||
\(435\) | −3283.80 | −0.361945 | ||||||||
\(436\) | −4625.05 | −0.508027 | ||||||||
\(437\) | 724.732 | 0.0793333 | ||||||||
\(438\) | −643.033 | −0.0701491 | ||||||||
\(439\) | 15373.9 | 1.67143 | 0.835716 | − | 0.549162i | \(-0.185053\pi\) | ||||
0.835716 | + | 0.549162i | \(0.185053\pi\) | |||||||
\(440\) | 2240.53 | 0.242757 | ||||||||
\(441\) | 1796.93 | 0.194032 | ||||||||
\(442\) | −0.556573 | −5.98947e−5 0 | ||||||||
\(443\) | 5462.95 | 0.585897 | 0.292949 | − | 0.956128i | \(-0.405364\pi\) | ||||
0.292949 | + | 0.956128i | \(0.405364\pi\) | |||||||
\(444\) | −227.164 | −0.0242809 | ||||||||
\(445\) | −6864.99 | −0.731307 | ||||||||
\(446\) | −729.480 | −0.0774482 | ||||||||
\(447\) | −1774.51 | −0.187766 | ||||||||
\(448\) | 11351.9 | 1.19715 | ||||||||
\(449\) | −9408.54 | −0.988901 | −0.494451 | − | 0.869206i | \(-0.664631\pi\) | ||||
−0.494451 | + | 0.869206i | \(0.664631\pi\) | |||||||
\(450\) | −18.0318 | −0.00188895 | ||||||||
\(451\) | −9464.80 | −0.988204 | ||||||||
\(452\) | 13186.6 | 1.37223 | ||||||||
\(453\) | 7196.34 | 0.746388 | ||||||||
\(454\) | −1410.76 | −0.145838 | ||||||||
\(455\) | 13075.9 | 1.34727 | ||||||||
\(456\) | −1036.43 | −0.106437 | ||||||||
\(457\) | 1254.04 | 0.128362 | 0.0641809 | − | 0.997938i | \(-0.479557\pi\) | ||||
0.0641809 | + | 0.997938i | \(0.479557\pi\) | |||||||
\(458\) | −766.091 | −0.0781596 | ||||||||
\(459\) | 1.13874 | 0.000115799 0 | ||||||||
\(460\) | −730.438 | −0.0740366 | ||||||||
\(461\) | −15647.0 | −1.58081 | −0.790407 | − | 0.612582i | \(-0.790131\pi\) | ||||
−0.790407 | + | 0.612582i | \(0.790131\pi\) | |||||||
\(462\) | 907.927 | 0.0914299 | ||||||||
\(463\) | 18387.3 | 1.84564 | 0.922821 | − | 0.385228i | \(-0.125877\pi\) | ||||
0.922821 | + | 0.385228i | \(0.125877\pi\) | |||||||
\(464\) | −6316.34 | −0.631959 | ||||||||
\(465\) | 8809.65 | 0.878575 | ||||||||
\(466\) | 33.7287 | 0.00335290 | ||||||||
\(467\) | 13135.8 | 1.30161 | 0.650805 | − | 0.759245i | \(-0.274431\pi\) | ||||
0.650805 | + | 0.759245i | \(0.274431\pi\) | |||||||
\(468\) | −3704.14 | −0.365863 | ||||||||
\(469\) | −17504.7 | −1.72344 | ||||||||
\(470\) | −853.286 | −0.0837429 | ||||||||
\(471\) | −406.435 | −0.0397612 | ||||||||
\(472\) | 239.216 | 0.0233280 | ||||||||
\(473\) | 14171.0 | 1.37756 | ||||||||
\(474\) | 281.530 | 0.0272808 | ||||||||
\(475\) | 670.965 | 0.0648126 | ||||||||
\(476\) | −7.79623 | −0.000750713 0 | ||||||||
\(477\) | 2461.53 | 0.236281 | ||||||||
\(478\) | 1807.59 | 0.172965 | ||||||||
\(479\) | −4918.54 | −0.469173 | −0.234587 | − | 0.972095i | \(-0.575374\pi\) | ||||
−0.234587 | + | 0.972095i | \(0.575374\pi\) | |||||||
\(480\) | 1569.01 | 0.149198 | ||||||||
\(481\) | −494.926 | −0.0469162 | ||||||||
\(482\) | 31.7193 | 0.00299745 | ||||||||
\(483\) | −594.403 | −0.0559964 | ||||||||
\(484\) | −10127.0 | −0.951072 | ||||||||
\(485\) | −3423.88 | −0.320558 | ||||||||
\(486\) | −61.8280 | −0.00577073 | ||||||||
\(487\) | 12272.0 | 1.14189 | 0.570944 | − | 0.820989i | \(-0.306577\pi\) | ||||
0.570944 | + | 0.820989i | \(0.306577\pi\) | |||||||
\(488\) | −3052.61 | −0.283166 | ||||||||
\(489\) | −4949.32 | −0.457702 | ||||||||
\(490\) | −549.786 | −0.0506873 | ||||||||
\(491\) | −9165.57 | −0.842437 | −0.421218 | − | 0.906959i | \(-0.638397\pi\) | ||||
−0.421218 | + | 0.906959i | \(0.638397\pi\) | |||||||
\(492\) | −4412.72 | −0.404351 | ||||||||
\(493\) | 4.26569 | 0.000389690 0 | ||||||||
\(494\) | −1124.46 | −0.102413 | ||||||||
\(495\) | −4973.43 | −0.451594 | ||||||||
\(496\) | 16945.2 | 1.53400 | ||||||||
\(497\) | 15179.2 | 1.36998 | ||||||||
\(498\) | 416.681 | 0.0374938 | ||||||||
\(499\) | −4308.93 | −0.386561 | −0.193281 | − | 0.981144i | \(-0.561913\pi\) | ||||
−0.193281 | + | 0.981144i | \(0.561913\pi\) | |||||||
\(500\) | −11411.1 | −1.02064 | ||||||||
\(501\) | −10502.3 | −0.936543 | ||||||||
\(502\) | −1740.55 | −0.154750 | ||||||||
\(503\) | −10004.0 | −0.886795 | −0.443397 | − | 0.896325i | \(-0.646227\pi\) | ||||
−0.443397 | + | 0.896325i | \(0.646227\pi\) | |||||||
\(504\) | 850.049 | 0.0751274 | ||||||||
\(505\) | 17481.0 | 1.54039 | ||||||||
\(506\) | −110.500 | −0.00970816 | ||||||||
\(507\) | −1479.28 | −0.129580 | ||||||||
\(508\) | −12383.6 | −1.08156 | ||||||||
\(509\) | −11329.0 | −0.986538 | −0.493269 | − | 0.869877i | \(-0.664198\pi\) | ||||
−0.493269 | + | 0.869877i | \(0.664198\pi\) | |||||||
\(510\) | −0.348406 | −3.02503e−5 0 | ||||||||
\(511\) | −19624.4 | −1.69889 | ||||||||
\(512\) | 5043.61 | 0.435348 | ||||||||
\(513\) | 2300.62 | 0.198002 | ||||||||
\(514\) | −95.3989 | −0.00818650 | ||||||||
\(515\) | −13647.9 | −1.16776 | ||||||||
\(516\) | 6606.88 | 0.563666 | ||||||||
\(517\) | 15822.6 | 1.34599 | ||||||||
\(518\) | 56.5586 | 0.00479738 | ||||||||
\(519\) | −7574.41 | −0.640616 | ||||||||
\(520\) | 2275.87 | 0.191930 | ||||||||
\(521\) | −578.251 | −0.0486251 | −0.0243125 | − | 0.999704i | \(-0.507740\pi\) | ||||
−0.0243125 | + | 0.999704i | \(0.507740\pi\) | |||||||
\(522\) | −231.607 | −0.0194198 | ||||||||
\(523\) | −22559.8 | −1.88618 | −0.943088 | − | 0.332543i | \(-0.892093\pi\) | ||||
−0.943088 | + | 0.332543i | \(0.892093\pi\) | |||||||
\(524\) | −20699.8 | −1.72572 | ||||||||
\(525\) | −550.305 | −0.0457472 | ||||||||
\(526\) | 1825.56 | 0.151327 | ||||||||
\(527\) | −11.4438 | −0.000945922 0 | ||||||||
\(528\) | −9566.31 | −0.788486 | ||||||||
\(529\) | −12094.7 | −0.994054 | ||||||||
\(530\) | −753.126 | −0.0617240 | ||||||||
\(531\) | −531.000 | −0.0433963 | ||||||||
\(532\) | −15750.9 | −1.28363 | ||||||||
\(533\) | −9614.07 | −0.781298 | ||||||||
\(534\) | −484.188 | −0.0392376 | ||||||||
\(535\) | −7941.33 | −0.641745 | ||||||||
\(536\) | −3046.70 | −0.245517 | ||||||||
\(537\) | −8152.34 | −0.655120 | ||||||||
\(538\) | −762.691 | −0.0611189 | ||||||||
\(539\) | 10194.7 | 0.814691 | ||||||||
\(540\) | −2318.73 | −0.184782 | ||||||||
\(541\) | −8649.61 | −0.687386 | −0.343693 | − | 0.939082i | \(-0.611678\pi\) | ||||
−0.343693 | + | 0.939082i | \(0.611678\pi\) | |||||||
\(542\) | 1525.03 | 0.120859 | ||||||||
\(543\) | −6348.89 | −0.501762 | ||||||||
\(544\) | −2.03816 | −0.000160635 0 | ||||||||
\(545\) | −6307.84 | −0.495777 | ||||||||
\(546\) | 922.247 | 0.0722867 | ||||||||
\(547\) | −9720.33 | −0.759801 | −0.379901 | − | 0.925027i | \(-0.624042\pi\) | ||||
−0.379901 | + | 0.925027i | \(0.624042\pi\) | |||||||
\(548\) | 18127.3 | 1.41306 | ||||||||
\(549\) | 6776.04 | 0.526765 | ||||||||
\(550\) | −102.302 | −0.00793124 | ||||||||
\(551\) | 8618.09 | 0.666322 | ||||||||
\(552\) | −103.456 | −0.00797713 | ||||||||
\(553\) | 8591.87 | 0.660693 | ||||||||
\(554\) | −2228.69 | −0.170917 | ||||||||
\(555\) | −309.816 | −0.0236954 | ||||||||
\(556\) | 2287.92 | 0.174514 | ||||||||
\(557\) | 14288.6 | 1.08694 | 0.543472 | − | 0.839428i | \(-0.317110\pi\) | ||||
0.543472 | + | 0.839428i | \(0.317110\pi\) | |||||||
\(558\) | 621.345 | 0.0471391 | ||||||||
\(559\) | 14394.5 | 1.08913 | ||||||||
\(560\) | 15744.4 | 1.18807 | ||||||||
\(561\) | 6.46053 | 0.000486210 0 | ||||||||
\(562\) | −1270.12 | −0.0953323 | ||||||||
\(563\) | −2067.53 | −0.154771 | −0.0773856 | − | 0.997001i | \(-0.524657\pi\) | ||||
−0.0773856 | + | 0.997001i | \(0.524657\pi\) | |||||||
\(564\) | 7376.87 | 0.550749 | ||||||||
\(565\) | 17984.5 | 1.33914 | ||||||||
\(566\) | −119.662 | −0.00888652 | ||||||||
\(567\) | −1886.90 | −0.139757 | ||||||||
\(568\) | 2641.94 | 0.195165 | ||||||||
\(569\) | −3196.60 | −0.235516 | −0.117758 | − | 0.993042i | \(-0.537571\pi\) | ||||
−0.117758 | + | 0.993042i | \(0.537571\pi\) | |||||||
\(570\) | −703.894 | −0.0517244 | ||||||||
\(571\) | −15856.8 | −1.16215 | −0.581073 | − | 0.813852i | \(-0.697367\pi\) | ||||
−0.581073 | + | 0.813852i | \(0.697367\pi\) | |||||||
\(572\) | −21015.1 | −1.53617 | ||||||||
\(573\) | 486.148 | 0.0354435 | ||||||||
\(574\) | 1098.67 | 0.0798911 | ||||||||
\(575\) | 66.9753 | 0.00485750 | ||||||||
\(576\) | −4385.77 | −0.317258 | ||||||||
\(577\) | 18096.9 | 1.30569 | 0.652846 | − | 0.757491i | \(-0.273575\pi\) | ||||
0.652846 | + | 0.757491i | \(0.273575\pi\) | |||||||
\(578\) | −1250.04 | −0.0899567 | ||||||||
\(579\) | 5213.13 | 0.374180 | ||||||||
\(580\) | −8685.94 | −0.621835 | ||||||||
\(581\) | 12716.5 | 0.908036 | ||||||||
\(582\) | −241.487 | −0.0171992 | ||||||||
\(583\) | 13965.3 | 0.992082 | ||||||||
\(584\) | −3415.63 | −0.242020 | ||||||||
\(585\) | −5051.87 | −0.357041 | ||||||||
\(586\) | 452.277 | 0.0318829 | ||||||||
\(587\) | 1903.98 | 0.133877 | 0.0669383 | − | 0.997757i | \(-0.478677\pi\) | ||||
0.0669383 | + | 0.997757i | \(0.478677\pi\) | |||||||
\(588\) | 4753.04 | 0.333354 | ||||||||
\(589\) | −23120.3 | −1.61741 | ||||||||
\(590\) | 162.464 | 0.0113365 | ||||||||
\(591\) | 5694.97 | 0.396379 | ||||||||
\(592\) | −595.926 | −0.0413723 | ||||||||
\(593\) | 16287.4 | 1.12790 | 0.563948 | − | 0.825810i | \(-0.309282\pi\) | ||||
0.563948 | + | 0.825810i | \(0.309282\pi\) | |||||||
\(594\) | −350.776 | −0.0242298 | ||||||||
\(595\) | −10.6328 | −0.000732611 0 | ||||||||
\(596\) | −4693.73 | −0.322588 | ||||||||
\(597\) | 2775.03 | 0.190242 | ||||||||
\(598\) | −112.243 | −0.00767550 | ||||||||
\(599\) | −13497.9 | −0.920715 | −0.460357 | − | 0.887734i | \(-0.652279\pi\) | ||||
−0.460357 | + | 0.887734i | \(0.652279\pi\) | |||||||
\(600\) | −95.7807 | −0.00651705 | ||||||||
\(601\) | 13860.8 | 0.940755 | 0.470378 | − | 0.882465i | \(-0.344118\pi\) | ||||
0.470378 | + | 0.882465i | \(0.344118\pi\) | |||||||
\(602\) | −1644.96 | −0.111368 | ||||||||
\(603\) | 6762.91 | 0.456728 | ||||||||
\(604\) | 19034.9 | 1.28232 | ||||||||
\(605\) | −13811.7 | −0.928139 | ||||||||
\(606\) | 1232.94 | 0.0826479 | ||||||||
\(607\) | 13140.0 | 0.878641 | 0.439321 | − | 0.898330i | \(-0.355219\pi\) | ||||
0.439321 | + | 0.898330i | \(0.355219\pi\) | |||||||
\(608\) | −4117.75 | −0.274666 | ||||||||
\(609\) | −7068.29 | −0.470315 | ||||||||
\(610\) | −2073.18 | −0.137608 | ||||||||
\(611\) | 16072.1 | 1.06417 | ||||||||
\(612\) | 3.01206 | 0.000198947 0 | ||||||||
\(613\) | −10495.5 | −0.691535 | −0.345768 | − | 0.938320i | \(-0.612381\pi\) | ||||
−0.345768 | + | 0.938320i | \(0.612381\pi\) | |||||||
\(614\) | 1052.87 | 0.0692028 | ||||||||
\(615\) | −6018.26 | −0.394601 | ||||||||
\(616\) | 4822.69 | 0.315441 | ||||||||
\(617\) | 9157.76 | 0.597533 | 0.298766 | − | 0.954326i | \(-0.403425\pi\) | ||||
0.298766 | + | 0.954326i | \(0.403425\pi\) | |||||||
\(618\) | −962.586 | −0.0626552 | ||||||||
\(619\) | 15266.3 | 0.991286 | 0.495643 | − | 0.868526i | \(-0.334932\pi\) | ||||
0.495643 | + | 0.868526i | \(0.334932\pi\) | |||||||
\(620\) | 23302.3 | 1.50942 | ||||||||
\(621\) | 229.647 | 0.0148396 | ||||||||
\(622\) | 1871.68 | 0.120655 | ||||||||
\(623\) | −14776.7 | −0.950266 | ||||||||
\(624\) | −9717.19 | −0.623396 | ||||||||
\(625\) | −14578.7 | −0.933036 | ||||||||
\(626\) | 1703.94 | 0.108791 | ||||||||
\(627\) | 13052.4 | 0.831359 | ||||||||
\(628\) | −1075.06 | −0.0683111 | ||||||||
\(629\) | 0.402454 | 2.55117e−5 0 | ||||||||
\(630\) | 577.312 | 0.0365090 | ||||||||
\(631\) | 6869.98 | 0.433422 | 0.216711 | − | 0.976236i | \(-0.430467\pi\) | ||||
0.216711 | + | 0.976236i | \(0.430467\pi\) | |||||||
\(632\) | 1495.42 | 0.0941210 | ||||||||
\(633\) | −7661.03 | −0.481040 | ||||||||
\(634\) | 1991.81 | 0.124771 | ||||||||
\(635\) | −16889.3 | −1.05548 | ||||||||
\(636\) | 6510.97 | 0.405938 | ||||||||
\(637\) | 10355.5 | 0.644114 | ||||||||
\(638\) | −1314.00 | −0.0815390 | ||||||||
\(639\) | −5864.46 | −0.363059 | ||||||||
\(640\) | 5525.89 | 0.341297 | ||||||||
\(641\) | 14205.2 | 0.875306 | 0.437653 | − | 0.899144i | \(-0.355810\pi\) | ||||
0.437653 | + | 0.899144i | \(0.355810\pi\) | |||||||
\(642\) | −560.102 | −0.0344322 | ||||||||
\(643\) | 32050.2 | 1.96569 | 0.982843 | − | 0.184442i | \(-0.0590479\pi\) | ||||
0.982843 | + | 0.184442i | \(0.0590479\pi\) | |||||||
\(644\) | −1572.25 | −0.0962038 | ||||||||
\(645\) | 9010.75 | 0.550074 | ||||||||
\(646\) | 0.914366 | 5.56892e−5 0 | ||||||||
\(647\) | 27275.5 | 1.65736 | 0.828679 | − | 0.559725i | \(-0.189093\pi\) | ||||
0.828679 | + | 0.559725i | \(0.189093\pi\) | |||||||
\(648\) | −328.415 | −0.0199095 | ||||||||
\(649\) | −3012.59 | −0.182210 | ||||||||
\(650\) | −103.916 | −0.00627063 | ||||||||
\(651\) | 18962.5 | 1.14163 | ||||||||
\(652\) | −13091.4 | −0.786347 | ||||||||
\(653\) | −6694.40 | −0.401182 | −0.200591 | − | 0.979675i | \(-0.564286\pi\) | ||||
−0.200591 | + | 0.979675i | \(0.564286\pi\) | |||||||
\(654\) | −444.893 | −0.0266004 | ||||||||
\(655\) | −28231.3 | −1.68411 | ||||||||
\(656\) | −11576.0 | −0.688976 | ||||||||
\(657\) | 7581.85 | 0.450223 | ||||||||
\(658\) | −1836.67 | −0.108816 | ||||||||
\(659\) | 1828.61 | 0.108092 | 0.0540460 | − | 0.998538i | \(-0.482788\pi\) | ||||
0.0540460 | + | 0.998538i | \(0.482788\pi\) | |||||||
\(660\) | −13155.2 | −0.775854 | ||||||||
\(661\) | 3994.07 | 0.235025 | 0.117512 | − | 0.993071i | \(-0.462508\pi\) | ||||
0.117512 | + | 0.993071i | \(0.462508\pi\) | |||||||
\(662\) | −201.494 | −0.0118298 | ||||||||
\(663\) | 6.56243 | 0.000384410 0 | ||||||||
\(664\) | 2213.31 | 0.129357 | ||||||||
\(665\) | −21481.8 | −1.25267 | ||||||||
\(666\) | −21.8513 | −0.00127135 | ||||||||
\(667\) | 860.253 | 0.0499387 | ||||||||
\(668\) | −27779.5 | −1.60901 | ||||||||
\(669\) | 8601.14 | 0.497069 | ||||||||
\(670\) | −2069.17 | −0.119312 | ||||||||
\(671\) | 38443.3 | 2.21175 | ||||||||
\(672\) | 3377.25 | 0.193869 | ||||||||
\(673\) | 1511.93 | 0.0865980 | 0.0432990 | − | 0.999062i | \(-0.486213\pi\) | ||||
0.0432990 | + | 0.999062i | \(0.486213\pi\) | |||||||
\(674\) | 918.276 | 0.0524788 | ||||||||
\(675\) | 212.609 | 0.0121235 | ||||||||
\(676\) | −3912.81 | −0.222623 | ||||||||
\(677\) | 105.944 | 0.00601442 | 0.00300721 | − | 0.999995i | \(-0.499043\pi\) | ||||
0.00300721 | + | 0.999995i | \(0.499043\pi\) | |||||||
\(678\) | 1268.45 | 0.0718503 | ||||||||
\(679\) | −7369.81 | −0.416535 | ||||||||
\(680\) | −1.85065 | −0.000104366 0 | ||||||||
\(681\) | 16634.0 | 0.935998 | ||||||||
\(682\) | 3525.15 | 0.197925 | ||||||||
\(683\) | −5370.44 | −0.300870 | −0.150435 | − | 0.988620i | \(-0.548067\pi\) | ||||
−0.150435 | + | 0.988620i | \(0.548067\pi\) | |||||||
\(684\) | 6085.34 | 0.340174 | ||||||||
\(685\) | 24722.8 | 1.37899 | ||||||||
\(686\) | 849.597 | 0.0472854 | ||||||||
\(687\) | 9032.81 | 0.501635 | ||||||||
\(688\) | 17332.0 | 0.960433 | ||||||||
\(689\) | 14185.6 | 0.784364 | ||||||||
\(690\) | −70.2623 | −0.00387658 | ||||||||
\(691\) | −11938.4 | −0.657246 | −0.328623 | − | 0.944461i | \(-0.606584\pi\) | ||||
−0.328623 | + | 0.944461i | \(0.606584\pi\) | |||||||
\(692\) | −20035.0 | −1.10060 | ||||||||
\(693\) | −10705.2 | −0.586805 | ||||||||
\(694\) | −1145.31 | −0.0626449 | ||||||||
\(695\) | 3120.37 | 0.170306 | ||||||||
\(696\) | −1230.24 | −0.0670001 | ||||||||
\(697\) | 7.81778 | 0.000424849 0 | ||||||||
\(698\) | 1146.29 | 0.0621599 | ||||||||
\(699\) | −397.688 | −0.0215192 | ||||||||
\(700\) | −1455.60 | −0.0785952 | ||||||||
\(701\) | 20482.4 | 1.10358 | 0.551791 | − | 0.833982i | \(-0.313945\pi\) | ||||
0.551791 | + | 0.833982i | \(0.313945\pi\) | |||||||
\(702\) | −356.309 | −0.0191567 | ||||||||
\(703\) | 813.089 | 0.0436219 | ||||||||
\(704\) | −24882.3 | −1.33209 | ||||||||
\(705\) | 10060.9 | 0.537469 | ||||||||
\(706\) | −1566.47 | −0.0835053 | ||||||||
\(707\) | 37627.4 | 2.00159 | ||||||||
\(708\) | −1404.54 | −0.0745564 | ||||||||
\(709\) | −9508.25 | −0.503653 | −0.251826 | − | 0.967772i | \(-0.581031\pi\) | ||||
−0.251826 | + | 0.967772i | \(0.581031\pi\) | |||||||
\(710\) | 1794.28 | 0.0948424 | ||||||||
\(711\) | −3319.45 | −0.175090 | ||||||||
\(712\) | −2571.89 | −0.135373 | ||||||||
\(713\) | −2307.85 | −0.121220 | ||||||||
\(714\) | −0.749934 | −3.93075e−5 0 | ||||||||
\(715\) | −28661.4 | −1.49913 | ||||||||
\(716\) | −21563.7 | −1.12552 | ||||||||
\(717\) | −21312.9 | −1.11011 | ||||||||
\(718\) | 2242.06 | 0.116536 | ||||||||
\(719\) | 7683.75 | 0.398547 | 0.199274 | − | 0.979944i | \(-0.436142\pi\) | ||||
0.199274 | + | 0.979944i | \(0.436142\pi\) | |||||||
\(720\) | −6082.81 | −0.314851 | ||||||||
\(721\) | −29376.7 | −1.51740 | ||||||||
\(722\) | 102.140 | 0.00526489 | ||||||||
\(723\) | −373.995 | −0.0192379 | ||||||||
\(724\) | −16793.4 | −0.862044 | ||||||||
\(725\) | 796.432 | 0.0407982 | ||||||||
\(726\) | −974.138 | −0.0497984 | ||||||||
\(727\) | −28207.9 | −1.43903 | −0.719515 | − | 0.694477i | \(-0.755636\pi\) | ||||
−0.719515 | + | 0.694477i | \(0.755636\pi\) | |||||||
\(728\) | 4898.75 | 0.249395 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −2319.73 | −0.117612 | ||||||||
\(731\) | −11.7051 | −0.000592239 0 | ||||||||
\(732\) | 17923.2 | 0.905001 | ||||||||
\(733\) | −21546.7 | −1.08574 | −0.542870 | − | 0.839817i | \(-0.682662\pi\) | ||||
−0.542870 | + | 0.839817i | \(0.682662\pi\) | |||||||
\(734\) | 3381.61 | 0.170051 | ||||||||
\(735\) | 6482.40 | 0.325316 | ||||||||
\(736\) | −411.031 | −0.0205853 | ||||||||
\(737\) | 38368.9 | 1.91769 | ||||||||
\(738\) | −424.468 | −0.0211719 | ||||||||
\(739\) | 13254.6 | 0.659780 | 0.329890 | − | 0.944019i | \(-0.392988\pi\) | ||||
0.329890 | + | 0.944019i | \(0.392988\pi\) | |||||||
\(740\) | −819.490 | −0.0407095 | ||||||||
\(741\) | 13258.2 | 0.657293 | ||||||||
\(742\) | −1621.08 | −0.0802046 | ||||||||
\(743\) | −13311.7 | −0.657280 | −0.328640 | − | 0.944455i | \(-0.606590\pi\) | ||||
−0.328640 | + | 0.944455i | \(0.606590\pi\) | |||||||
\(744\) | 3300.43 | 0.162634 | ||||||||
\(745\) | −6401.51 | −0.314810 | ||||||||
\(746\) | 2546.07 | 0.124957 | ||||||||
\(747\) | −4913.00 | −0.240639 | ||||||||
\(748\) | 17.0887 | 0.000835326 0 | ||||||||
\(749\) | −17093.5 | −0.833889 | ||||||||
\(750\) | −1097.66 | −0.0534411 | ||||||||
\(751\) | 30067.0 | 1.46093 | 0.730467 | − | 0.682948i | \(-0.239302\pi\) | ||||
0.730467 | + | 0.682948i | \(0.239302\pi\) | |||||||
\(752\) | 19352.0 | 0.938423 | ||||||||
\(753\) | 20522.4 | 0.993199 | ||||||||
\(754\) | −1334.73 | −0.0644667 | ||||||||
\(755\) | 25960.7 | 1.25140 | ||||||||
\(756\) | −4991.01 | −0.240108 | ||||||||
\(757\) | −40542.2 | −1.94654 | −0.973269 | − | 0.229666i | \(-0.926236\pi\) | ||||
−0.973269 | + | 0.229666i | \(0.926236\pi\) | |||||||
\(758\) | −991.247 | −0.0474983 | ||||||||
\(759\) | 1302.88 | 0.0623078 | ||||||||
\(760\) | −3738.91 | −0.178453 | ||||||||
\(761\) | −35970.2 | −1.71343 | −0.856713 | − | 0.515793i | \(-0.827498\pi\) | ||||
−0.856713 | + | 0.515793i | \(0.827498\pi\) | |||||||
\(762\) | −1191.20 | −0.0566310 | ||||||||
\(763\) | −13577.5 | −0.644216 | ||||||||
\(764\) | 1285.90 | 0.0608931 | ||||||||
\(765\) | 4.10798 | 0.000194149 0 | ||||||||
\(766\) | −773.140 | −0.0364683 | ||||||||
\(767\) | −3060.10 | −0.144060 | ||||||||
\(768\) | −11305.7 | −0.531195 | ||||||||
\(769\) | 29540.6 | 1.38525 | 0.692627 | − | 0.721296i | \(-0.256453\pi\) | ||||
0.692627 | + | 0.721296i | \(0.256453\pi\) | |||||||
\(770\) | 3275.34 | 0.153292 | ||||||||
\(771\) | 1124.83 | 0.0525417 | ||||||||
\(772\) | 13789.2 | 0.642854 | ||||||||
\(773\) | 31936.1 | 1.48598 | 0.742989 | − | 0.669304i | \(-0.233408\pi\) | ||||
0.742989 | + | 0.669304i | \(0.233408\pi\) | |||||||
\(774\) | 635.529 | 0.0295137 | ||||||||
\(775\) | −2136.63 | −0.0990324 | ||||||||
\(776\) | −1282.72 | −0.0593388 | ||||||||
\(777\) | −666.870 | −0.0307900 | ||||||||
\(778\) | −3444.38 | −0.158724 | ||||||||
\(779\) | 15794.5 | 0.726439 | ||||||||
\(780\) | −13362.6 | −0.613409 | ||||||||
\(781\) | −33271.6 | −1.52439 | ||||||||
\(782\) | 0.0912714 | 4.17373e−6 0 | ||||||||
\(783\) | 2730.82 | 0.124638 | ||||||||
\(784\) | 12468.8 | 0.568003 | ||||||||
\(785\) | −1466.21 | −0.0666640 | ||||||||
\(786\) | −1991.16 | −0.0903590 | ||||||||
\(787\) | 19554.7 | 0.885705 | 0.442853 | − | 0.896594i | \(-0.353966\pi\) | ||||
0.442853 | + | 0.896594i | \(0.353966\pi\) | |||||||
\(788\) | 15063.7 | 0.680993 | ||||||||
\(789\) | −21524.8 | −0.971232 | ||||||||
\(790\) | 1015.61 | 0.0457391 | ||||||||
\(791\) | 38711.2 | 1.74009 | ||||||||
\(792\) | −1863.24 | −0.0835950 | ||||||||
\(793\) | 39049.6 | 1.74867 | ||||||||
\(794\) | −888.319 | −0.0397043 | ||||||||
\(795\) | 8879.94 | 0.396150 | ||||||||
\(796\) | 7340.19 | 0.326842 | ||||||||
\(797\) | −19917.3 | −0.885202 | −0.442601 | − | 0.896719i | \(-0.645944\pi\) | ||||
−0.442601 | + | 0.896719i | \(0.645944\pi\) | |||||||
\(798\) | −1515.11 | −0.0672110 | ||||||||
\(799\) | −13.0692 | −0.000578668 0 | ||||||||
\(800\) | −380.537 | −0.0168175 | ||||||||
\(801\) | 5708.95 | 0.251830 | ||||||||
\(802\) | 3223.11 | 0.141910 | ||||||||
\(803\) | 43015.1 | 1.89037 | ||||||||
\(804\) | 17888.5 | 0.784675 | ||||||||
\(805\) | −2144.30 | −0.0938840 | ||||||||
\(806\) | 3580.75 | 0.156484 | ||||||||
\(807\) | 8992.72 | 0.392266 | ||||||||
\(808\) | 6549.06 | 0.285142 | ||||||||
\(809\) | −23172.3 | −1.00704 | −0.503520 | − | 0.863984i | \(-0.667962\pi\) | ||||
−0.503520 | + | 0.863984i | \(0.667962\pi\) | |||||||
\(810\) | −223.044 | −0.00967525 | ||||||||
\(811\) | −9763.58 | −0.422744 | −0.211372 | − | 0.977406i | \(-0.567793\pi\) | ||||
−0.211372 | + | 0.977406i | \(0.567793\pi\) | |||||||
\(812\) | −18696.3 | −0.808017 | ||||||||
\(813\) | −17981.3 | −0.775685 | ||||||||
\(814\) | −123.972 | −0.00533809 | ||||||||
\(815\) | −17854.6 | −0.767386 | ||||||||
\(816\) | 7.90163 | 0.000338986 0 | ||||||||
\(817\) | −23648.0 | −1.01266 | ||||||||
\(818\) | 2654.11 | 0.113446 | ||||||||
\(819\) | −10874.0 | −0.463942 | ||||||||
\(820\) | −15918.8 | −0.677939 | ||||||||
\(821\) | 24006.4 | 1.02050 | 0.510249 | − | 0.860026i | \(-0.329553\pi\) | ||||
0.510249 | + | 0.860026i | \(0.329553\pi\) | |||||||
\(822\) | 1743.70 | 0.0739884 | ||||||||
\(823\) | 36909.5 | 1.56329 | 0.781643 | − | 0.623726i | \(-0.214382\pi\) | ||||
0.781643 | + | 0.623726i | \(0.214382\pi\) | |||||||
\(824\) | −5113.02 | −0.216166 | ||||||||
\(825\) | 1206.22 | 0.0509034 | ||||||||
\(826\) | 349.699 | 0.0147307 | ||||||||
\(827\) | −17834.8 | −0.749912 | −0.374956 | − | 0.927043i | \(-0.622342\pi\) | ||||
−0.374956 | + | 0.927043i | \(0.622342\pi\) | |||||||
\(828\) | 607.435 | 0.0254950 | ||||||||
\(829\) | −7164.05 | −0.300142 | −0.150071 | − | 0.988675i | \(-0.547950\pi\) | ||||
−0.150071 | + | 0.988675i | \(0.547950\pi\) | |||||||
\(830\) | 1503.17 | 0.0628625 | ||||||||
\(831\) | 26278.0 | 1.09696 | ||||||||
\(832\) | −25274.8 | −1.05318 | ||||||||
\(833\) | −8.42070 | −0.000350252 0 | ||||||||
\(834\) | 220.080 | 0.00913758 | ||||||||
\(835\) | −37886.9 | −1.57021 | ||||||||
\(836\) | 34524.7 | 1.42830 | ||||||||
\(837\) | −7326.14 | −0.302543 | ||||||||
\(838\) | −1769.62 | −0.0729480 | ||||||||
\(839\) | −30792.5 | −1.26708 | −0.633538 | − | 0.773712i | \(-0.718398\pi\) | ||||
−0.633538 | + | 0.773712i | \(0.718398\pi\) | |||||||
\(840\) | 3066.54 | 0.125959 | ||||||||
\(841\) | −14159.4 | −0.580564 | ||||||||
\(842\) | −757.480 | −0.0310030 | ||||||||
\(843\) | 14975.7 | 0.611851 | ||||||||
\(844\) | −20264.1 | −0.826444 | ||||||||
\(845\) | −5336.47 | −0.217254 | ||||||||
\(846\) | 709.596 | 0.0288374 | ||||||||
\(847\) | −29729.2 | −1.20603 | ||||||||
\(848\) | 17080.4 | 0.691680 | ||||||||
\(849\) | 1410.91 | 0.0570345 | ||||||||
\(850\) | 0.0845001 | 3.40980e−6 0 | ||||||||
\(851\) | 81.1620 | 0.00326933 | ||||||||
\(852\) | −15512.0 | −0.623747 | ||||||||
\(853\) | 31914.3 | 1.28104 | 0.640519 | − | 0.767942i | \(-0.278719\pi\) | ||||
0.640519 | + | 0.767942i | \(0.278719\pi\) | |||||||
\(854\) | −4462.47 | −0.178809 | ||||||||
\(855\) | 8299.46 | 0.331971 | ||||||||
\(856\) | −2975.13 | −0.118794 | ||||||||
\(857\) | −48527.1 | −1.93425 | −0.967126 | − | 0.254296i | \(-0.918156\pi\) | ||||
−0.967126 | + | 0.254296i | \(0.918156\pi\) | |||||||
\(858\) | −2021.49 | −0.0804341 | ||||||||
\(859\) | −5570.19 | −0.221249 | −0.110624 | − | 0.993862i | \(-0.535285\pi\) | ||||
−0.110624 | + | 0.993862i | \(0.535285\pi\) | |||||||
\(860\) | 23834.2 | 0.945047 | ||||||||
\(861\) | −12954.1 | −0.512748 | ||||||||
\(862\) | −2473.48 | −0.0977345 | ||||||||
\(863\) | −45442.4 | −1.79244 | −0.896221 | − | 0.443607i | \(-0.853699\pi\) | ||||
−0.896221 | + | 0.443607i | \(0.853699\pi\) | |||||||
\(864\) | −1304.79 | −0.0513773 | ||||||||
\(865\) | −27324.6 | −1.07406 | ||||||||
\(866\) | 207.261 | 0.00813280 | ||||||||
\(867\) | 14739.0 | 0.577350 | ||||||||
\(868\) | 50157.5 | 1.96136 | ||||||||
\(869\) | −18832.7 | −0.735160 | ||||||||
\(870\) | −835.518 | −0.0325594 | ||||||||
\(871\) | 38974.0 | 1.51617 | ||||||||
\(872\) | −2363.16 | −0.0917737 | ||||||||
\(873\) | 2847.32 | 0.110386 | ||||||||
\(874\) | 184.398 | 0.00713657 | ||||||||
\(875\) | −33498.9 | −1.29425 | ||||||||
\(876\) | 20054.7 | 0.773498 | ||||||||
\(877\) | −23890.4 | −0.919865 | −0.459932 | − | 0.887954i | \(-0.652126\pi\) | ||||
−0.459932 | + | 0.887954i | \(0.652126\pi\) | |||||||
\(878\) | 3911.69 | 0.150357 | ||||||||
\(879\) | −5332.69 | −0.204627 | ||||||||
\(880\) | −34510.3 | −1.32198 | ||||||||
\(881\) | −9587.92 | −0.366657 | −0.183329 | − | 0.983052i | \(-0.558687\pi\) | ||||
−0.183329 | + | 0.983052i | \(0.558687\pi\) | |||||||
\(882\) | 457.204 | 0.0174545 | ||||||||
\(883\) | −50410.3 | −1.92122 | −0.960612 | − | 0.277893i | \(-0.910364\pi\) | ||||
−0.960612 | + | 0.277893i | \(0.910364\pi\) | |||||||
\(884\) | 17.3582 | 0.000660429 0 | ||||||||
\(885\) | −1915.57 | −0.0727586 | ||||||||
\(886\) | 1389.97 | 0.0527054 | ||||||||
\(887\) | 7413.01 | 0.280614 | 0.140307 | − | 0.990108i | \(-0.455191\pi\) | ||||
0.140307 | + | 0.990108i | \(0.455191\pi\) | |||||||
\(888\) | −116.069 | −0.00438628 | ||||||||
\(889\) | −36353.8 | −1.37150 | ||||||||
\(890\) | −1746.70 | −0.0657860 | ||||||||
\(891\) | 4135.92 | 0.155509 | ||||||||
\(892\) | 22750.8 | 0.853982 | ||||||||
\(893\) | −26404.1 | −0.989450 | ||||||||
\(894\) | −451.499 | −0.0168908 | ||||||||
\(895\) | −29409.5 | −1.09838 | ||||||||
\(896\) | 11894.3 | 0.443484 | ||||||||
\(897\) | 1323.43 | 0.0492620 | ||||||||
\(898\) | −2393.87 | −0.0889584 | ||||||||
\(899\) | −27443.6 | −1.01813 | ||||||||
\(900\) | 562.370 | 0.0208285 | ||||||||
\(901\) | −11.5351 | −0.000426516 0 | ||||||||
\(902\) | −2408.19 | −0.0888957 | ||||||||
\(903\) | 19395.4 | 0.714771 | ||||||||
\(904\) | 6737.69 | 0.247890 | ||||||||
\(905\) | −22903.5 | −0.841258 | ||||||||
\(906\) | 1831.01 | 0.0671426 | ||||||||
\(907\) | −13964.2 | −0.511216 | −0.255608 | − | 0.966781i | \(-0.582276\pi\) | ||||
−0.255608 | + | 0.966781i | \(0.582276\pi\) | |||||||
\(908\) | 43998.3 | 1.60808 | ||||||||
\(909\) | −14537.3 | −0.530442 | ||||||||
\(910\) | 3326.99 | 0.121196 | ||||||||
\(911\) | 48214.6 | 1.75348 | 0.876740 | − | 0.480965i | \(-0.159714\pi\) | ||||
0.876740 | + | 0.480965i | \(0.159714\pi\) | |||||||
\(912\) | 15963.9 | 0.579624 | ||||||||
\(913\) | −27873.5 | −1.01038 | ||||||||
\(914\) | 319.072 | 0.0115470 | ||||||||
\(915\) | 24444.5 | 0.883179 | ||||||||
\(916\) | 23892.6 | 0.861826 | ||||||||
\(917\) | −60767.1 | −2.18834 | ||||||||
\(918\) | 0.289736 | 1.04169e−5 0 | ||||||||
\(919\) | −41258.5 | −1.48095 | −0.740475 | − | 0.672084i | \(-0.765399\pi\) | ||||
−0.740475 | + | 0.672084i | \(0.765399\pi\) | |||||||
\(920\) | −373.216 | −0.0133745 | ||||||||
\(921\) | −12414.2 | −0.444149 | ||||||||
\(922\) | −3981.17 | −0.142205 | ||||||||
\(923\) | −33796.3 | −1.20522 | ||||||||
\(924\) | −28316.1 | −1.00815 | ||||||||
\(925\) | 75.1407 | 0.00267093 | ||||||||
\(926\) | 4678.41 | 0.166028 | ||||||||
\(927\) | 11349.6 | 0.402126 | ||||||||
\(928\) | −4887.74 | −0.172897 | ||||||||
\(929\) | 2682.75 | 0.0947451 | 0.0473726 | − | 0.998877i | \(-0.484915\pi\) | ||||
0.0473726 | + | 0.998877i | \(0.484915\pi\) | |||||||
\(930\) | 2241.49 | 0.0790338 | ||||||||
\(931\) | −17012.6 | −0.598888 | ||||||||
\(932\) | −1051.92 | −0.0369708 | ||||||||
\(933\) | −22068.6 | −0.774376 | ||||||||
\(934\) | 3342.22 | 0.117089 | ||||||||
\(935\) | 23.3063 | 0.000815184 0 | ||||||||
\(936\) | −1892.62 | −0.0660922 | ||||||||
\(937\) | 12243.8 | 0.426883 | 0.213441 | − | 0.976956i | \(-0.431533\pi\) | ||||
0.213441 | + | 0.976956i | \(0.431533\pi\) | |||||||
\(938\) | −4453.83 | −0.155035 | ||||||||
\(939\) | −20090.8 | −0.698230 | ||||||||
\(940\) | 26612.0 | 0.923390 | ||||||||
\(941\) | 29701.6 | 1.02895 | 0.514476 | − | 0.857505i | \(-0.327986\pi\) | ||||
0.514476 | + | 0.857505i | \(0.327986\pi\) | |||||||
\(942\) | −103.412 | −0.00357679 | ||||||||
\(943\) | 1576.59 | 0.0544443 | ||||||||
\(944\) | −3684.58 | −0.127037 | ||||||||
\(945\) | −6806.96 | −0.234318 | ||||||||
\(946\) | 3605.62 | 0.123921 | ||||||||
\(947\) | 11974.6 | 0.410899 | 0.205450 | − | 0.978668i | \(-0.434134\pi\) | ||||
0.205450 | + | 0.978668i | \(0.434134\pi\) | |||||||
\(948\) | −8780.24 | −0.300811 | ||||||||
\(949\) | 43693.5 | 1.49457 | ||||||||
\(950\) | 170.718 | 0.00583033 | ||||||||
\(951\) | −23485.0 | −0.800793 | ||||||||
\(952\) | −3.98347 | −0.000135614 0 | ||||||||
\(953\) | 23437.4 | 0.796655 | 0.398327 | − | 0.917243i | \(-0.369591\pi\) | ||||
0.398327 | + | 0.917243i | \(0.369591\pi\) | |||||||
\(954\) | 626.303 | 0.0212550 | ||||||||
\(955\) | 1753.77 | 0.0594248 | ||||||||
\(956\) | −56374.6 | −1.90720 | ||||||||
\(957\) | 15493.1 | 0.523324 | ||||||||
\(958\) | −1251.46 | −0.0422053 | ||||||||
\(959\) | 53215.1 | 1.79187 | ||||||||
\(960\) | −15821.6 | −0.531917 | ||||||||
\(961\) | 43833.6 | 1.47137 | ||||||||
\(962\) | −125.927 | −0.00422043 | ||||||||
\(963\) | 6604.04 | 0.220989 | ||||||||
\(964\) | −989.249 | −0.0330514 | ||||||||
\(965\) | 18806.3 | 0.627353 | ||||||||
\(966\) | −151.238 | −0.00503726 | ||||||||
\(967\) | 8006.86 | 0.266270 | 0.133135 | − | 0.991098i | \(-0.457496\pi\) | ||||
0.133135 | + | 0.991098i | \(0.457496\pi\) | |||||||
\(968\) | −5174.38 | −0.171809 | ||||||||
\(969\) | −10.7811 | −0.000357418 0 | ||||||||
\(970\) | −871.160 | −0.0288363 | ||||||||
\(971\) | −13457.8 | −0.444780 | −0.222390 | − | 0.974958i | \(-0.571386\pi\) | ||||
−0.222390 | + | 0.974958i | \(0.571386\pi\) | |||||||
\(972\) | 1928.27 | 0.0636309 | ||||||||
\(973\) | 6716.51 | 0.221297 | ||||||||
\(974\) | 3122.45 | 0.102721 | ||||||||
\(975\) | 1225.25 | 0.0402454 | ||||||||
\(976\) | 47018.5 | 1.54204 | ||||||||
\(977\) | 25366.7 | 0.830659 | 0.415329 | − | 0.909671i | \(-0.363666\pi\) | ||||
0.415329 | + | 0.909671i | \(0.363666\pi\) | |||||||
\(978\) | −1259.29 | −0.0411734 | ||||||||
\(979\) | 32389.3 | 1.05737 | ||||||||
\(980\) | 17146.5 | 0.558903 | ||||||||
\(981\) | 5245.63 | 0.170724 | ||||||||
\(982\) | −2332.05 | −0.0757829 | ||||||||
\(983\) | 5778.72 | 0.187500 | 0.0937500 | − | 0.995596i | \(-0.470115\pi\) | ||||
0.0937500 | + | 0.995596i | \(0.470115\pi\) | |||||||
\(984\) | −2254.67 | −0.0730450 | ||||||||
\(985\) | 20544.5 | 0.664572 | ||||||||
\(986\) | 1.08535 | 3.50552e−5 0 | ||||||||
\(987\) | 21655.8 | 0.698391 | ||||||||
\(988\) | 35069.2 | 1.12925 | ||||||||
\(989\) | −2360.53 | −0.0758954 | ||||||||
\(990\) | −1265.42 | −0.0406239 | ||||||||
\(991\) | 24959.9 | 0.800079 | 0.400039 | − | 0.916498i | \(-0.368996\pi\) | ||||
0.400039 | + | 0.916498i | \(0.368996\pi\) | |||||||
\(992\) | 13112.6 | 0.419684 | ||||||||
\(993\) | 2375.78 | 0.0759244 | ||||||||
\(994\) | 3862.14 | 0.123239 | ||||||||
\(995\) | 10010.9 | 0.318961 | ||||||||
\(996\) | −12995.3 | −0.413426 | ||||||||
\(997\) | 29815.3 | 0.947101 | 0.473550 | − | 0.880767i | \(-0.342972\pi\) | ||||
0.473550 | + | 0.880767i | \(0.342972\pi\) | |||||||
\(998\) | −1096.35 | −0.0347738 | ||||||||
\(999\) | 257.644 | 0.00815966 |
(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 | 177.4.a.c.1.4 | ✓ | 8 | |
3.2 | odd | 2 | 531.4.a.f.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.c.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
531.4.a.f.1.5 | 8 | 3.2 | odd | 2 |