Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,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, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
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: | \(28.3879361069\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + \cdots - 14846072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(8.66878\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.66878 | 1.35566 | 0.677831 | − | 0.735218i | \(-0.262920\pi\) | ||||
0.677831 | + | 0.735218i | \(0.262920\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 26.8102 | 0.837818 | ||||||||
\(5\) | −109.801 | −1.96417 | −0.982086 | − | 0.188434i | \(-0.939659\pi\) | ||||
−0.982086 | + | 0.188434i | \(0.939659\pi\) | |||||||
\(6\) | 69.0190 | 0.782692 | ||||||||
\(7\) | 156.301 | 1.20563 | 0.602817 | − | 0.797879i | \(-0.294045\pi\) | ||||
0.602817 | + | 0.797879i | \(0.294045\pi\) | |||||||
\(8\) | −39.7996 | −0.219864 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −842.036 | −2.66275 | ||||||||
\(11\) | −426.905 | −1.06377 | −0.531887 | − | 0.846815i | \(-0.678517\pi\) | ||||
−0.531887 | + | 0.846815i | \(0.678517\pi\) | |||||||
\(12\) | 241.292 | 0.483714 | ||||||||
\(13\) | −123.969 | −0.203449 | −0.101724 | − | 0.994813i | \(-0.532436\pi\) | ||||
−0.101724 | + | 0.994813i | \(0.532436\pi\) | |||||||
\(14\) | 1198.64 | 1.63443 | ||||||||
\(15\) | −988.205 | −1.13402 | ||||||||
\(16\) | −1163.14 | −1.13588 | ||||||||
\(17\) | −852.404 | −0.715358 | −0.357679 | − | 0.933845i | \(-0.616432\pi\) | ||||
−0.357679 | + | 0.933845i | \(0.616432\pi\) | |||||||
\(18\) | 621.171 | 0.451887 | ||||||||
\(19\) | 232.142 | 0.147526 | 0.0737631 | − | 0.997276i | \(-0.476499\pi\) | ||||
0.0737631 | + | 0.997276i | \(0.476499\pi\) | |||||||
\(20\) | −2943.77 | −1.64562 | ||||||||
\(21\) | 1406.71 | 0.696073 | ||||||||
\(22\) | −3273.84 | −1.44212 | ||||||||
\(23\) | −3642.90 | −1.43591 | −0.717956 | − | 0.696089i | \(-0.754922\pi\) | ||||
−0.717956 | + | 0.696089i | \(0.754922\pi\) | |||||||
\(24\) | −358.197 | −0.126938 | ||||||||
\(25\) | 8931.16 | 2.85797 | ||||||||
\(26\) | −950.692 | −0.275808 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 4190.45 | 1.01010 | ||||||||
\(29\) | −8173.34 | −1.80470 | −0.902349 | − | 0.431005i | \(-0.858159\pi\) | ||||
−0.902349 | + | 0.431005i | \(0.858159\pi\) | |||||||
\(30\) | −7578.33 | −1.53734 | ||||||||
\(31\) | −9358.70 | −1.74909 | −0.874544 | − | 0.484947i | \(-0.838839\pi\) | ||||
−0.874544 | + | 0.484947i | \(0.838839\pi\) | |||||||
\(32\) | −7646.28 | −1.32000 | ||||||||
\(33\) | −3842.15 | −0.614171 | ||||||||
\(34\) | −6536.90 | −0.969783 | ||||||||
\(35\) | −17161.9 | −2.36807 | ||||||||
\(36\) | 2171.62 | 0.279273 | ||||||||
\(37\) | 6317.09 | 0.758600 | 0.379300 | − | 0.925274i | \(-0.376165\pi\) | ||||
0.379300 | + | 0.925274i | \(0.376165\pi\) | |||||||
\(38\) | 1780.24 | 0.199996 | ||||||||
\(39\) | −1115.72 | −0.117461 | ||||||||
\(40\) | 4370.02 | 0.431850 | ||||||||
\(41\) | 13017.8 | 1.20942 | 0.604712 | − | 0.796444i | \(-0.293288\pi\) | ||||
0.604712 | + | 0.796444i | \(0.293288\pi\) | |||||||
\(42\) | 10787.7 | 0.943640 | ||||||||
\(43\) | 23355.0 | 1.92623 | 0.963117 | − | 0.269084i | \(-0.0867208\pi\) | ||||
0.963117 | + | 0.269084i | \(0.0867208\pi\) | |||||||
\(44\) | −11445.4 | −0.891250 | ||||||||
\(45\) | −8893.84 | −0.654724 | ||||||||
\(46\) | −27936.6 | −1.94661 | ||||||||
\(47\) | −8861.12 | −0.585119 | −0.292559 | − | 0.956247i | \(-0.594507\pi\) | ||||
−0.292559 | + | 0.956247i | \(0.594507\pi\) | |||||||
\(48\) | −10468.3 | −0.655800 | ||||||||
\(49\) | 7622.89 | 0.453554 | ||||||||
\(50\) | 68491.1 | 3.87444 | ||||||||
\(51\) | −7671.64 | −0.413012 | ||||||||
\(52\) | −3323.64 | −0.170453 | ||||||||
\(53\) | 23012.3 | 1.12531 | 0.562653 | − | 0.826693i | \(-0.309781\pi\) | ||||
0.562653 | + | 0.826693i | \(0.309781\pi\) | |||||||
\(54\) | 5590.54 | 0.260897 | ||||||||
\(55\) | 46874.4 | 2.08944 | ||||||||
\(56\) | −6220.71 | −0.265075 | ||||||||
\(57\) | 2089.28 | 0.0851743 | ||||||||
\(58\) | −62679.6 | −2.44656 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | −26493.9 | −0.950098 | ||||||||
\(61\) | 13699.8 | 0.471399 | 0.235699 | − | 0.971826i | \(-0.424262\pi\) | ||||
0.235699 | + | 0.971826i | \(0.424262\pi\) | |||||||
\(62\) | −71769.8 | −2.37117 | ||||||||
\(63\) | 12660.4 | 0.401878 | ||||||||
\(64\) | −21417.1 | −0.653599 | ||||||||
\(65\) | 13611.9 | 0.399609 | ||||||||
\(66\) | −29464.6 | −0.832607 | ||||||||
\(67\) | −1424.88 | −0.0387785 | −0.0193893 | − | 0.999812i | \(-0.506172\pi\) | ||||
−0.0193893 | + | 0.999812i | \(0.506172\pi\) | |||||||
\(68\) | −22853.1 | −0.599340 | ||||||||
\(69\) | −32786.1 | −0.829024 | ||||||||
\(70\) | −131611. | −3.21031 | ||||||||
\(71\) | 34543.2 | 0.813235 | 0.406618 | − | 0.913598i | \(-0.366708\pi\) | ||||
0.406618 | + | 0.913598i | \(0.366708\pi\) | |||||||
\(72\) | −3223.77 | −0.0732880 | ||||||||
\(73\) | −50120.2 | −1.10079 | −0.550397 | − | 0.834903i | \(-0.685524\pi\) | ||||
−0.550397 | + | 0.834903i | \(0.685524\pi\) | |||||||
\(74\) | 48444.4 | 1.02840 | ||||||||
\(75\) | 80380.4 | 1.65005 | ||||||||
\(76\) | 6223.76 | 0.123600 | ||||||||
\(77\) | −66725.5 | −1.28252 | ||||||||
\(78\) | −8556.23 | −0.159238 | ||||||||
\(79\) | −69723.6 | −1.25693 | −0.628466 | − | 0.777837i | \(-0.716317\pi\) | ||||
−0.628466 | + | 0.777837i | \(0.716317\pi\) | |||||||
\(80\) | 127713. | 2.23106 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 99830.8 | 1.63957 | ||||||||
\(83\) | 49883.0 | 0.794799 | 0.397399 | − | 0.917646i | \(-0.369913\pi\) | ||||
0.397399 | + | 0.917646i | \(0.369913\pi\) | |||||||
\(84\) | 37714.0 | 0.583183 | ||||||||
\(85\) | 93594.5 | 1.40509 | ||||||||
\(86\) | 179104. | 2.61132 | ||||||||
\(87\) | −73560.1 | −1.04194 | ||||||||
\(88\) | 16990.7 | 0.233886 | ||||||||
\(89\) | −50735.3 | −0.678946 | −0.339473 | − | 0.940616i | \(-0.610249\pi\) | ||||
−0.339473 | + | 0.940616i | \(0.610249\pi\) | |||||||
\(90\) | −68204.9 | −0.887584 | ||||||||
\(91\) | −19376.5 | −0.245285 | ||||||||
\(92\) | −97666.8 | −1.20303 | ||||||||
\(93\) | −84228.3 | −1.00984 | ||||||||
\(94\) | −67954.0 | −0.793223 | ||||||||
\(95\) | −25489.3 | −0.289767 | ||||||||
\(96\) | −68816.5 | −0.762104 | ||||||||
\(97\) | 21922.7 | 0.236573 | 0.118286 | − | 0.992980i | \(-0.462260\pi\) | ||||
0.118286 | + | 0.992980i | \(0.462260\pi\) | |||||||
\(98\) | 58458.2 | 0.614866 | ||||||||
\(99\) | −34579.3 | −0.354592 | ||||||||
\(100\) | 239446. | 2.39446 | ||||||||
\(101\) | 136749. | 1.33389 | 0.666944 | − | 0.745108i | \(-0.267602\pi\) | ||||
0.666944 | + | 0.745108i | \(0.267602\pi\) | |||||||
\(102\) | −58832.1 | −0.559905 | ||||||||
\(103\) | −45802.7 | −0.425400 | −0.212700 | − | 0.977118i | \(-0.568226\pi\) | ||||
−0.212700 | + | 0.977118i | \(0.568226\pi\) | |||||||
\(104\) | 4933.93 | 0.0447311 | ||||||||
\(105\) | −154457. | −1.36721 | ||||||||
\(106\) | 176476. | 1.52553 | ||||||||
\(107\) | 42126.7 | 0.355711 | 0.177856 | − | 0.984057i | \(-0.443084\pi\) | ||||
0.177856 | + | 0.984057i | \(0.443084\pi\) | |||||||
\(108\) | 19544.6 | 0.161238 | ||||||||
\(109\) | −184019. | −1.48353 | −0.741765 | − | 0.670660i | \(-0.766011\pi\) | ||||
−0.741765 | + | 0.670660i | \(0.766011\pi\) | |||||||
\(110\) | 359470. | 2.83257 | ||||||||
\(111\) | 56853.8 | 0.437978 | ||||||||
\(112\) | −181800. | −1.36945 | ||||||||
\(113\) | −180222. | −1.32773 | −0.663867 | − | 0.747851i | \(-0.731086\pi\) | ||||
−0.663867 | + | 0.747851i | \(0.731086\pi\) | |||||||
\(114\) | 16022.2 | 0.115468 | ||||||||
\(115\) | 399992. | 2.82038 | ||||||||
\(116\) | −219129. | −1.51201 | ||||||||
\(117\) | −10041.5 | −0.0678163 | ||||||||
\(118\) | 26695.0 | 0.176492 | ||||||||
\(119\) | −133231. | −0.862460 | ||||||||
\(120\) | 39330.2 | 0.249329 | ||||||||
\(121\) | 21197.0 | 0.131616 | ||||||||
\(122\) | 105060. | 0.639057 | ||||||||
\(123\) | 117160. | 0.698261 | ||||||||
\(124\) | −250908. | −1.46542 | ||||||||
\(125\) | −637519. | −3.64937 | ||||||||
\(126\) | 97089.4 | 0.544811 | ||||||||
\(127\) | −25072.4 | −0.137939 | −0.0689694 | − | 0.997619i | \(-0.521971\pi\) | ||||
−0.0689694 | + | 0.997619i | \(0.521971\pi\) | |||||||
\(128\) | 80437.6 | 0.433945 | ||||||||
\(129\) | 210195. | 1.11211 | ||||||||
\(130\) | 104387. | 0.541734 | ||||||||
\(131\) | 28027.7 | 0.142695 | 0.0713475 | − | 0.997452i | \(-0.477270\pi\) | ||||
0.0713475 | + | 0.997452i | \(0.477270\pi\) | |||||||
\(132\) | −103009. | −0.514563 | ||||||||
\(133\) | 36283.9 | 0.177863 | ||||||||
\(134\) | −10927.1 | −0.0525705 | ||||||||
\(135\) | −80044.6 | −0.378005 | ||||||||
\(136\) | 33925.4 | 0.157281 | ||||||||
\(137\) | 193823. | 0.882277 | 0.441139 | − | 0.897439i | \(-0.354575\pi\) | ||||
0.441139 | + | 0.897439i | \(0.354575\pi\) | |||||||
\(138\) | −251429. | −1.12388 | ||||||||
\(139\) | −385667. | −1.69307 | −0.846536 | − | 0.532331i | \(-0.821316\pi\) | ||||
−0.846536 | + | 0.532331i | \(0.821316\pi\) | |||||||
\(140\) | −460113. | −1.98401 | ||||||||
\(141\) | −79750.1 | −0.337818 | ||||||||
\(142\) | 264904. | 1.10247 | ||||||||
\(143\) | 52923.1 | 0.216424 | ||||||||
\(144\) | −94214.3 | −0.378626 | ||||||||
\(145\) | 897438. | 3.54474 | ||||||||
\(146\) | −384361. | −1.49230 | ||||||||
\(147\) | 68606.0 | 0.261860 | ||||||||
\(148\) | 169362. | 0.635569 | ||||||||
\(149\) | −97076.0 | −0.358217 | −0.179109 | − | 0.983829i | \(-0.557321\pi\) | ||||
−0.179109 | + | 0.983829i | \(0.557321\pi\) | |||||||
\(150\) | 616420. | 2.23691 | ||||||||
\(151\) | 28312.8 | 0.101051 | 0.0505255 | − | 0.998723i | \(-0.483910\pi\) | ||||
0.0505255 | + | 0.998723i | \(0.483910\pi\) | |||||||
\(152\) | −9239.15 | −0.0324357 | ||||||||
\(153\) | −69044.8 | −0.238453 | ||||||||
\(154\) | −511703. | −1.73867 | ||||||||
\(155\) | 1.02759e6 | 3.43551 | ||||||||
\(156\) | −29912.7 | −0.0984112 | ||||||||
\(157\) | −147457. | −0.477439 | −0.238719 | − | 0.971089i | \(-0.576728\pi\) | ||||
−0.238719 | + | 0.971089i | \(0.576728\pi\) | |||||||
\(158\) | −534695. | −1.70398 | ||||||||
\(159\) | 207111. | 0.649695 | ||||||||
\(160\) | 839565. | 2.59271 | ||||||||
\(161\) | −569388. | −1.73118 | ||||||||
\(162\) | 50314.9 | 0.150629 | ||||||||
\(163\) | −140469. | −0.414105 | −0.207053 | − | 0.978330i | \(-0.566387\pi\) | ||||
−0.207053 | + | 0.978330i | \(0.566387\pi\) | |||||||
\(164\) | 349010. | 1.01328 | ||||||||
\(165\) | 421870. | 1.20634 | ||||||||
\(166\) | 382542. | 1.07748 | ||||||||
\(167\) | −33450.1 | −0.0928125 | −0.0464063 | − | 0.998923i | \(-0.514777\pi\) | ||||
−0.0464063 | + | 0.998923i | \(0.514777\pi\) | |||||||
\(168\) | −55986.3 | −0.153041 | ||||||||
\(169\) | −355925. | −0.958609 | ||||||||
\(170\) | 717755. | 1.90482 | ||||||||
\(171\) | 18803.5 | 0.0491754 | ||||||||
\(172\) | 626152. | 1.61383 | ||||||||
\(173\) | 359847. | 0.914118 | 0.457059 | − | 0.889436i | \(-0.348903\pi\) | ||||
0.457059 | + | 0.889436i | \(0.348903\pi\) | |||||||
\(174\) | −564116. | −1.41252 | ||||||||
\(175\) | 1.39595e6 | 3.44567 | ||||||||
\(176\) | 496550. | 1.20832 | ||||||||
\(177\) | 31329.0 | 0.0751646 | ||||||||
\(178\) | −389078. | −0.920422 | ||||||||
\(179\) | 51692.7 | 0.120586 | 0.0602930 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602930 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(180\) | −238446. | −0.548540 | ||||||||
\(181\) | −649652. | −1.47395 | −0.736977 | − | 0.675918i | \(-0.763748\pi\) | ||||
−0.736977 | + | 0.675918i | \(0.763748\pi\) | |||||||
\(182\) | −148594. | −0.332523 | ||||||||
\(183\) | 123298. | 0.272162 | ||||||||
\(184\) | 144986. | 0.315705 | ||||||||
\(185\) | −693620. | −1.49002 | ||||||||
\(186\) | −645928. | −1.36900 | ||||||||
\(187\) | 363896. | 0.760980 | ||||||||
\(188\) | −237568. | −0.490223 | ||||||||
\(189\) | 113943. | 0.232024 | ||||||||
\(190\) | −195472. | −0.392826 | ||||||||
\(191\) | 76790.3 | 0.152308 | 0.0761540 | − | 0.997096i | \(-0.475736\pi\) | ||||
0.0761540 | + | 0.997096i | \(0.475736\pi\) | |||||||
\(192\) | −192754. | −0.377355 | ||||||||
\(193\) | 496266. | 0.959006 | 0.479503 | − | 0.877540i | \(-0.340817\pi\) | ||||
0.479503 | + | 0.877540i | \(0.340817\pi\) | |||||||
\(194\) | 168120. | 0.320712 | ||||||||
\(195\) | 122507. | 0.230714 | ||||||||
\(196\) | 204371. | 0.379996 | ||||||||
\(197\) | −442784. | −0.812879 | −0.406439 | − | 0.913678i | \(-0.633230\pi\) | ||||
−0.406439 | + | 0.913678i | \(0.633230\pi\) | |||||||
\(198\) | −265181. | −0.480706 | ||||||||
\(199\) | 730332. | 1.30734 | 0.653668 | − | 0.756781i | \(-0.273229\pi\) | ||||
0.653668 | + | 0.756781i | \(0.273229\pi\) | |||||||
\(200\) | −355457. | −0.628365 | ||||||||
\(201\) | −12823.9 | −0.0223888 | ||||||||
\(202\) | 1.04869e6 | 1.80830 | ||||||||
\(203\) | −1.27750e6 | −2.17581 | ||||||||
\(204\) | −205678. | −0.346029 | ||||||||
\(205\) | −1.42936e6 | −2.37552 | ||||||||
\(206\) | −351251. | −0.576699 | ||||||||
\(207\) | −295075. | −0.478637 | ||||||||
\(208\) | 144194. | 0.231093 | ||||||||
\(209\) | −99102.5 | −0.156935 | ||||||||
\(210\) | −1.18450e6 | −1.85347 | ||||||||
\(211\) | 960167. | 1.48471 | 0.742353 | − | 0.670008i | \(-0.233710\pi\) | ||||
0.742353 | + | 0.670008i | \(0.233710\pi\) | |||||||
\(212\) | 616964. | 0.942801 | ||||||||
\(213\) | 310889. | 0.469522 | ||||||||
\(214\) | 323060. | 0.482224 | ||||||||
\(215\) | −2.56439e6 | −3.78345 | ||||||||
\(216\) | −29013.9 | −0.0423128 | ||||||||
\(217\) | −1.46277e6 | −2.10876 | ||||||||
\(218\) | −1.41120e6 | −2.01117 | ||||||||
\(219\) | −451082. | −0.635543 | ||||||||
\(220\) | 1.25671e6 | 1.75057 | ||||||||
\(221\) | 105672. | 0.145539 | ||||||||
\(222\) | 435999. | 0.593750 | ||||||||
\(223\) | −114848. | −0.154655 | −0.0773273 | − | 0.997006i | \(-0.524639\pi\) | ||||
−0.0773273 | + | 0.997006i | \(0.524639\pi\) | |||||||
\(224\) | −1.19512e6 | −1.59144 | ||||||||
\(225\) | 723424. | 0.952657 | ||||||||
\(226\) | −1.38208e6 | −1.79996 | ||||||||
\(227\) | −316011. | −0.407040 | −0.203520 | − | 0.979071i | \(-0.565238\pi\) | ||||
−0.203520 | + | 0.979071i | \(0.565238\pi\) | |||||||
\(228\) | 56013.9 | 0.0713606 | ||||||||
\(229\) | −110133. | −0.138781 | −0.0693903 | − | 0.997590i | \(-0.522105\pi\) | ||||
−0.0693903 | + | 0.997590i | \(0.522105\pi\) | |||||||
\(230\) | 3.06745e6 | 3.82348 | ||||||||
\(231\) | −600530. | −0.740465 | ||||||||
\(232\) | 325296. | 0.396788 | ||||||||
\(233\) | 8645.45 | 0.0104327 | 0.00521636 | − | 0.999986i | \(-0.498340\pi\) | ||||
0.00521636 | + | 0.999986i | \(0.498340\pi\) | |||||||
\(234\) | −77006.1 | −0.0919359 | ||||||||
\(235\) | 972956. | 1.14927 | ||||||||
\(236\) | 93326.2 | 0.109075 | ||||||||
\(237\) | −627512. | −0.725690 | ||||||||
\(238\) | −1.02172e6 | −1.16920 | ||||||||
\(239\) | 623677. | 0.706261 | 0.353131 | − | 0.935574i | \(-0.385117\pi\) | ||||
0.353131 | + | 0.935574i | \(0.385117\pi\) | |||||||
\(240\) | 1.14942e6 | 1.28810 | ||||||||
\(241\) | −1.73477e6 | −1.92398 | −0.961988 | − | 0.273092i | \(-0.911954\pi\) | ||||
−0.961988 | + | 0.273092i | \(0.911954\pi\) | |||||||
\(242\) | 162555. | 0.178427 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 367293. | 0.394946 | ||||||||
\(245\) | −836997. | −0.890859 | ||||||||
\(246\) | 898477. | 0.946606 | ||||||||
\(247\) | −28778.4 | −0.0300141 | ||||||||
\(248\) | 372473. | 0.384561 | ||||||||
\(249\) | 448947. | 0.458877 | ||||||||
\(250\) | −4.88900e6 | −4.94732 | ||||||||
\(251\) | 1.44679e6 | 1.44951 | 0.724755 | − | 0.689006i | \(-0.241953\pi\) | ||||
0.724755 | + | 0.689006i | \(0.241953\pi\) | |||||||
\(252\) | 339426. | 0.336701 | ||||||||
\(253\) | 1.55517e6 | 1.52749 | ||||||||
\(254\) | −192275. | −0.186998 | ||||||||
\(255\) | 842350. | 0.811227 | ||||||||
\(256\) | 1.30221e6 | 1.24188 | ||||||||
\(257\) | −177900. | −0.168013 | −0.0840064 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840064 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(258\) | 1.61194e6 | 1.50765 | ||||||||
\(259\) | 987365. | 0.914594 | ||||||||
\(260\) | 364937. | 0.334799 | ||||||||
\(261\) | −662041. | −0.601566 | ||||||||
\(262\) | 214938. | 0.193446 | ||||||||
\(263\) | −662979. | −0.591031 | −0.295515 | − | 0.955338i | \(-0.595491\pi\) | ||||
−0.295515 | + | 0.955338i | \(0.595491\pi\) | |||||||
\(264\) | 152916. | 0.135034 | ||||||||
\(265\) | −2.52676e6 | −2.21029 | ||||||||
\(266\) | 278253. | 0.241122 | ||||||||
\(267\) | −456618. | −0.391990 | ||||||||
\(268\) | −38201.3 | −0.0324893 | ||||||||
\(269\) | −1.10386e6 | −0.930105 | −0.465052 | − | 0.885283i | \(-0.653965\pi\) | ||||
−0.465052 | + | 0.885283i | \(0.653965\pi\) | |||||||
\(270\) | −613844. | −0.512447 | ||||||||
\(271\) | −1.65544e6 | −1.36927 | −0.684635 | − | 0.728886i | \(-0.740039\pi\) | ||||
−0.684635 | + | 0.728886i | \(0.740039\pi\) | |||||||
\(272\) | 991466. | 0.812560 | ||||||||
\(273\) | −174388. | −0.141615 | ||||||||
\(274\) | 1.48639e6 | 1.19607 | ||||||||
\(275\) | −3.81276e6 | −3.04024 | ||||||||
\(276\) | −879001. | −0.694571 | ||||||||
\(277\) | −87836.5 | −0.0687821 | −0.0343911 | − | 0.999408i | \(-0.510949\pi\) | ||||
−0.0343911 | + | 0.999408i | \(0.510949\pi\) | |||||||
\(278\) | −2.95760e6 | −2.29523 | ||||||||
\(279\) | −758055. | −0.583029 | ||||||||
\(280\) | 683037. | 0.520654 | ||||||||
\(281\) | −800455. | −0.604743 | −0.302372 | − | 0.953190i | \(-0.597778\pi\) | ||||
−0.302372 | + | 0.953190i | \(0.597778\pi\) | |||||||
\(282\) | −611586. | −0.457967 | ||||||||
\(283\) | −2.09590e6 | −1.55563 | −0.777813 | − | 0.628495i | \(-0.783671\pi\) | ||||
−0.777813 | + | 0.628495i | \(0.783671\pi\) | |||||||
\(284\) | 926108. | 0.681343 | ||||||||
\(285\) | −229404. | −0.167297 | ||||||||
\(286\) | 405855. | 0.293397 | ||||||||
\(287\) | 2.03469e6 | 1.45812 | ||||||||
\(288\) | −619348. | −0.440001 | ||||||||
\(289\) | −693264. | −0.488263 | ||||||||
\(290\) | 6.88225e6 | 4.80547 | ||||||||
\(291\) | 197304. | 0.136585 | ||||||||
\(292\) | −1.34373e6 | −0.922264 | ||||||||
\(293\) | 1.40390e6 | 0.955363 | 0.477681 | − | 0.878533i | \(-0.341477\pi\) | ||||
0.477681 | + | 0.878533i | \(0.341477\pi\) | |||||||
\(294\) | 526124. | 0.354993 | ||||||||
\(295\) | −382216. | −0.255713 | ||||||||
\(296\) | −251418. | −0.166789 | ||||||||
\(297\) | −311214. | −0.204724 | ||||||||
\(298\) | −744455. | −0.485621 | ||||||||
\(299\) | 451607. | 0.292135 | ||||||||
\(300\) | 2.15501e6 | 1.38244 | ||||||||
\(301\) | 3.65040e6 | 2.32233 | ||||||||
\(302\) | 217125. | 0.136991 | ||||||||
\(303\) | 1.23074e6 | 0.770121 | ||||||||
\(304\) | −270013. | −0.167572 | ||||||||
\(305\) | −1.50424e6 | −0.925908 | ||||||||
\(306\) | −529489. | −0.323261 | ||||||||
\(307\) | −1.33666e6 | −0.809422 | −0.404711 | − | 0.914445i | \(-0.632628\pi\) | ||||
−0.404711 | + | 0.914445i | \(0.632628\pi\) | |||||||
\(308\) | −1.78892e6 | −1.07452 | ||||||||
\(309\) | −412224. | −0.245605 | ||||||||
\(310\) | 7.88037e6 | 4.65739 | ||||||||
\(311\) | −2.02561e6 | −1.18756 | −0.593778 | − | 0.804629i | \(-0.702364\pi\) | ||||
−0.593778 | + | 0.804629i | \(0.702364\pi\) | |||||||
\(312\) | 44405.3 | 0.0258255 | ||||||||
\(313\) | 513441. | 0.296231 | 0.148115 | − | 0.988970i | \(-0.452679\pi\) | ||||
0.148115 | + | 0.988970i | \(0.452679\pi\) | |||||||
\(314\) | −1.13082e6 | −0.647245 | ||||||||
\(315\) | −1.39011e6 | −0.789358 | ||||||||
\(316\) | −1.86930e6 | −1.05308 | ||||||||
\(317\) | 4929.11 | 0.00275499 | 0.00137750 | − | 0.999999i | \(-0.499562\pi\) | ||||
0.00137750 | + | 0.999999i | \(0.499562\pi\) | |||||||
\(318\) | 1.58829e6 | 0.880767 | ||||||||
\(319\) | 3.48924e6 | 1.91979 | ||||||||
\(320\) | 2.35161e6 | 1.28378 | ||||||||
\(321\) | 379140. | 0.205370 | ||||||||
\(322\) | −4.36651e6 | −2.34690 | ||||||||
\(323\) | −197879. | −0.105534 | ||||||||
\(324\) | 175902. | 0.0930909 | ||||||||
\(325\) | −1.10719e6 | −0.581451 | ||||||||
\(326\) | −1.07722e6 | −0.561386 | ||||||||
\(327\) | −1.65617e6 | −0.856517 | ||||||||
\(328\) | −518104. | −0.265909 | ||||||||
\(329\) | −1.38500e6 | −0.705439 | ||||||||
\(330\) | 3.23523e6 | 1.63538 | ||||||||
\(331\) | −1.97213e6 | −0.989386 | −0.494693 | − | 0.869068i | \(-0.664719\pi\) | ||||
−0.494693 | + | 0.869068i | \(0.664719\pi\) | |||||||
\(332\) | 1.33737e6 | 0.665897 | ||||||||
\(333\) | 511684. | 0.252867 | ||||||||
\(334\) | −256522. | −0.125822 | ||||||||
\(335\) | 156453. | 0.0761676 | ||||||||
\(336\) | −1.63620e6 | −0.790655 | ||||||||
\(337\) | 2.30193e6 | 1.10412 | 0.552062 | − | 0.833803i | \(-0.313841\pi\) | ||||
0.552062 | + | 0.833803i | \(0.313841\pi\) | |||||||
\(338\) | −2.72951e6 | −1.29955 | ||||||||
\(339\) | −1.62200e6 | −0.766567 | ||||||||
\(340\) | 2.50928e6 | 1.17721 | ||||||||
\(341\) | 3.99528e6 | 1.86063 | ||||||||
\(342\) | 144200. | 0.0666652 | ||||||||
\(343\) | −1.43548e6 | −0.658814 | ||||||||
\(344\) | −929521. | −0.423509 | ||||||||
\(345\) | 3.59993e6 | 1.62835 | ||||||||
\(346\) | 2.75958e6 | 1.23923 | ||||||||
\(347\) | 947055. | 0.422232 | 0.211116 | − | 0.977461i | \(-0.432290\pi\) | ||||
0.211116 | + | 0.977461i | \(0.432290\pi\) | |||||||
\(348\) | −1.97216e6 | −0.872959 | ||||||||
\(349\) | 1.96092e6 | 0.861781 | 0.430891 | − | 0.902404i | \(-0.358199\pi\) | ||||
0.430891 | + | 0.902404i | \(0.358199\pi\) | |||||||
\(350\) | 1.07052e7 | 4.67116 | ||||||||
\(351\) | −90373.5 | −0.0391538 | ||||||||
\(352\) | 3.26423e6 | 1.40419 | ||||||||
\(353\) | 2.49167e6 | 1.06427 | 0.532137 | − | 0.846658i | \(-0.321389\pi\) | ||||
0.532137 | + | 0.846658i | \(0.321389\pi\) | |||||||
\(354\) | 240255. | 0.101898 | ||||||||
\(355\) | −3.79286e6 | −1.59733 | ||||||||
\(356\) | −1.36022e6 | −0.568834 | ||||||||
\(357\) | −1.19908e6 | −0.497942 | ||||||||
\(358\) | 396420. | 0.163474 | ||||||||
\(359\) | 282969. | 0.115878 | 0.0579392 | − | 0.998320i | \(-0.481547\pi\) | ||||
0.0579392 | + | 0.998320i | \(0.481547\pi\) | |||||||
\(360\) | 353972. | 0.143950 | ||||||||
\(361\) | −2.42221e6 | −0.978236 | ||||||||
\(362\) | −4.98203e6 | −1.99818 | ||||||||
\(363\) | 190773. | 0.0759888 | ||||||||
\(364\) | −519486. | −0.205504 | ||||||||
\(365\) | 5.50323e6 | 2.16215 | ||||||||
\(366\) | 945544. | 0.368960 | ||||||||
\(367\) | 1.02276e6 | 0.396378 | 0.198189 | − | 0.980164i | \(-0.436494\pi\) | ||||
0.198189 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(368\) | 4.23720e6 | 1.63102 | ||||||||
\(369\) | 1.05444e6 | 0.403141 | ||||||||
\(370\) | −5.31922e6 | −2.01996 | ||||||||
\(371\) | 3.59684e6 | 1.35671 | ||||||||
\(372\) | −2.25818e6 | −0.846059 | ||||||||
\(373\) | 3.02229e6 | 1.12477 | 0.562385 | − | 0.826876i | \(-0.309884\pi\) | ||||
0.562385 | + | 0.826876i | \(0.309884\pi\) | |||||||
\(374\) | 2.79064e6 | 1.03163 | ||||||||
\(375\) | −5.73768e6 | −2.10697 | ||||||||
\(376\) | 352669. | 0.128646 | ||||||||
\(377\) | 1.01324e6 | 0.367164 | ||||||||
\(378\) | 873805. | 0.314547 | ||||||||
\(379\) | −529457. | −0.189336 | −0.0946679 | − | 0.995509i | \(-0.530179\pi\) | ||||
−0.0946679 | + | 0.995509i | \(0.530179\pi\) | |||||||
\(380\) | −683372. | −0.242772 | ||||||||
\(381\) | −225652. | −0.0796390 | ||||||||
\(382\) | 588887. | 0.206478 | ||||||||
\(383\) | −2.95011e6 | −1.02764 | −0.513820 | − | 0.857898i | \(-0.671770\pi\) | ||||
−0.513820 | + | 0.857898i | \(0.671770\pi\) | |||||||
\(384\) | 723939. | 0.250538 | ||||||||
\(385\) | 7.32650e6 | 2.51910 | ||||||||
\(386\) | 3.80575e6 | 1.30009 | ||||||||
\(387\) | 1.89176e6 | 0.642078 | ||||||||
\(388\) | 587751. | 0.198205 | ||||||||
\(389\) | −2.96852e6 | −0.994641 | −0.497321 | − | 0.867567i | \(-0.665683\pi\) | ||||
−0.497321 | + | 0.867567i | \(0.665683\pi\) | |||||||
\(390\) | 939479. | 0.312770 | ||||||||
\(391\) | 3.10522e6 | 1.02719 | ||||||||
\(392\) | −303388. | −0.0997202 | ||||||||
\(393\) | 252249. | 0.0823849 | ||||||||
\(394\) | −3.39561e6 | −1.10199 | ||||||||
\(395\) | 7.65569e6 | 2.46883 | ||||||||
\(396\) | −927077. | −0.297083 | ||||||||
\(397\) | 1.04019e6 | 0.331234 | 0.165617 | − | 0.986190i | \(-0.447038\pi\) | ||||
0.165617 | + | 0.986190i | \(0.447038\pi\) | |||||||
\(398\) | 5.60075e6 | 1.77231 | ||||||||
\(399\) | 326555. | 0.102689 | ||||||||
\(400\) | −1.03882e7 | −3.24631 | ||||||||
\(401\) | 3.31007e6 | 1.02796 | 0.513980 | − | 0.857802i | \(-0.328171\pi\) | ||||
0.513980 | + | 0.857802i | \(0.328171\pi\) | |||||||
\(402\) | −98343.8 | −0.0303516 | ||||||||
\(403\) | 1.16019e6 | 0.355850 | ||||||||
\(404\) | 3.66625e6 | 1.11756 | ||||||||
\(405\) | −720401. | −0.218241 | ||||||||
\(406\) | −9.79686e6 | −2.94966 | ||||||||
\(407\) | −2.69680e6 | −0.806979 | ||||||||
\(408\) | 305328. | 0.0908065 | ||||||||
\(409\) | −5.21191e6 | −1.54059 | −0.770297 | − | 0.637685i | \(-0.779892\pi\) | ||||
−0.770297 | + | 0.637685i | \(0.779892\pi\) | |||||||
\(410\) | −1.09615e7 | −3.22040 | ||||||||
\(411\) | 1.74441e6 | 0.509383 | ||||||||
\(412\) | −1.22798e6 | −0.356408 | ||||||||
\(413\) | 544083. | 0.156960 | ||||||||
\(414\) | −2.26286e6 | −0.648870 | ||||||||
\(415\) | −5.47718e6 | −1.56112 | ||||||||
\(416\) | 947903. | 0.268553 | ||||||||
\(417\) | −3.47100e6 | −0.977496 | ||||||||
\(418\) | −759995. | −0.212750 | ||||||||
\(419\) | −3.41630e6 | −0.950649 | −0.475325 | − | 0.879810i | \(-0.657669\pi\) | ||||
−0.475325 | + | 0.879810i | \(0.657669\pi\) | |||||||
\(420\) | −4.14102e6 | −1.14547 | ||||||||
\(421\) | 5.70486e6 | 1.56870 | 0.784350 | − | 0.620319i | \(-0.212997\pi\) | ||||
0.784350 | + | 0.620319i | \(0.212997\pi\) | |||||||
\(422\) | 7.36331e6 | 2.01276 | ||||||||
\(423\) | −717751. | −0.195040 | ||||||||
\(424\) | −915881. | −0.247414 | ||||||||
\(425\) | −7.61296e6 | −2.04447 | ||||||||
\(426\) | 2.38414e6 | 0.636513 | ||||||||
\(427\) | 2.14128e6 | 0.568335 | ||||||||
\(428\) | 1.12942e6 | 0.298021 | ||||||||
\(429\) | 476308. | 0.124952 | ||||||||
\(430\) | −1.96658e7 | −5.12908 | ||||||||
\(431\) | −2.31113e6 | −0.599281 | −0.299640 | − | 0.954052i | \(-0.596867\pi\) | ||||
−0.299640 | + | 0.954052i | \(0.596867\pi\) | |||||||
\(432\) | −847929. | −0.218600 | ||||||||
\(433\) | −55388.5 | −0.0141971 | −0.00709856 | − | 0.999975i | \(-0.502260\pi\) | ||||
−0.00709856 | + | 0.999975i | \(0.502260\pi\) | |||||||
\(434\) | −1.12177e7 | −2.85876 | ||||||||
\(435\) | 8.07694e6 | 2.04656 | ||||||||
\(436\) | −4.93358e6 | −1.24293 | ||||||||
\(437\) | −845669. | −0.211835 | ||||||||
\(438\) | −3.45925e6 | −0.861582 | ||||||||
\(439\) | −5.60645e6 | −1.38844 | −0.694219 | − | 0.719764i | \(-0.744250\pi\) | ||||
−0.694219 | + | 0.719764i | \(0.744250\pi\) | |||||||
\(440\) | −1.86558e6 | −0.459392 | ||||||||
\(441\) | 617454. | 0.151185 | ||||||||
\(442\) | 810374. | 0.197301 | ||||||||
\(443\) | 5.33809e6 | 1.29234 | 0.646170 | − | 0.763194i | \(-0.276370\pi\) | ||||
0.646170 | + | 0.763194i | \(0.276370\pi\) | |||||||
\(444\) | 1.52426e6 | 0.366946 | ||||||||
\(445\) | 5.57077e6 | 1.33357 | ||||||||
\(446\) | −880747. | −0.209659 | ||||||||
\(447\) | −873684. | −0.206817 | ||||||||
\(448\) | −3.34751e6 | −0.788001 | ||||||||
\(449\) | −3.68121e6 | −0.861737 | −0.430869 | − | 0.902415i | \(-0.641793\pi\) | ||||
−0.430869 | + | 0.902415i | \(0.641793\pi\) | |||||||
\(450\) | 5.54778e6 | 1.29148 | ||||||||
\(451\) | −5.55737e6 | −1.28655 | ||||||||
\(452\) | −4.83177e6 | −1.11240 | ||||||||
\(453\) | 254815. | 0.0583418 | ||||||||
\(454\) | −2.42342e6 | −0.551809 | ||||||||
\(455\) | 2.12755e6 | 0.481782 | ||||||||
\(456\) | −83152.4 | −0.0187268 | ||||||||
\(457\) | 3.14852e6 | 0.705205 | 0.352603 | − | 0.935773i | \(-0.385297\pi\) | ||||
0.352603 | + | 0.935773i | \(0.385297\pi\) | |||||||
\(458\) | −844585. | −0.188139 | ||||||||
\(459\) | −621403. | −0.137671 | ||||||||
\(460\) | 1.07239e7 | 2.36296 | ||||||||
\(461\) | −3.05916e6 | −0.670425 | −0.335213 | − | 0.942143i | \(-0.608808\pi\) | ||||
−0.335213 | + | 0.942143i | \(0.608808\pi\) | |||||||
\(462\) | −4.60533e6 | −1.00382 | ||||||||
\(463\) | 8.35625e6 | 1.81159 | 0.905793 | − | 0.423721i | \(-0.139276\pi\) | ||||
0.905793 | + | 0.423721i | \(0.139276\pi\) | |||||||
\(464\) | 9.50674e6 | 2.04992 | ||||||||
\(465\) | 9.24832e6 | 1.98349 | ||||||||
\(466\) | 66300.1 | 0.0141432 | ||||||||
\(467\) | 1.16583e6 | 0.247367 | 0.123683 | − | 0.992322i | \(-0.460529\pi\) | ||||
0.123683 | + | 0.992322i | \(0.460529\pi\) | |||||||
\(468\) | −269214. | −0.0568177 | ||||||||
\(469\) | −222710. | −0.0467527 | ||||||||
\(470\) | 7.46138e6 | 1.55803 | ||||||||
\(471\) | −1.32712e6 | −0.275649 | ||||||||
\(472\) | −138542. | −0.0286238 | ||||||||
\(473\) | −9.97037e6 | −2.04908 | ||||||||
\(474\) | −4.81225e6 | −0.983791 | ||||||||
\(475\) | 2.07330e6 | 0.421626 | ||||||||
\(476\) | −3.57196e6 | −0.722585 | ||||||||
\(477\) | 1.86400e6 | 0.375102 | ||||||||
\(478\) | 4.78284e6 | 0.957451 | ||||||||
\(479\) | −1.23399e6 | −0.245737 | −0.122869 | − | 0.992423i | \(-0.539209\pi\) | ||||
−0.122869 | + | 0.992423i | \(0.539209\pi\) | |||||||
\(480\) | 7.55609e6 | 1.49690 | ||||||||
\(481\) | −783124. | −0.154336 | ||||||||
\(482\) | −1.33036e7 | −2.60826 | ||||||||
\(483\) | −5.12449e6 | −0.999500 | ||||||||
\(484\) | 568294. | 0.110271 | ||||||||
\(485\) | −2.40712e6 | −0.464669 | ||||||||
\(486\) | 452834. | 0.0869657 | ||||||||
\(487\) | 1.60158e6 | 0.306004 | 0.153002 | − | 0.988226i | \(-0.451106\pi\) | ||||
0.153002 | + | 0.988226i | \(0.451106\pi\) | |||||||
\(488\) | −545245. | −0.103644 | ||||||||
\(489\) | −1.26422e6 | −0.239084 | ||||||||
\(490\) | −6.41875e6 | −1.20770 | ||||||||
\(491\) | 1.78594e6 | 0.334321 | 0.167161 | − | 0.985930i | \(-0.446540\pi\) | ||||
0.167161 | + | 0.985930i | \(0.446540\pi\) | |||||||
\(492\) | 3.14109e6 | 0.585016 | ||||||||
\(493\) | 6.96699e6 | 1.29101 | ||||||||
\(494\) | −220695. | −0.0406889 | ||||||||
\(495\) | 3.79683e6 | 0.696479 | ||||||||
\(496\) | 1.08855e7 | 1.98675 | ||||||||
\(497\) | 5.39912e6 | 0.980465 | ||||||||
\(498\) | 3.44287e6 | 0.622082 | ||||||||
\(499\) | 7.98618e6 | 1.43578 | 0.717889 | − | 0.696157i | \(-0.245108\pi\) | ||||
0.717889 | + | 0.696157i | \(0.245108\pi\) | |||||||
\(500\) | −1.70920e7 | −3.05751 | ||||||||
\(501\) | −301051. | −0.0535853 | ||||||||
\(502\) | 1.10951e7 | 1.96505 | ||||||||
\(503\) | −3.77866e6 | −0.665914 | −0.332957 | − | 0.942942i | \(-0.608046\pi\) | ||||
−0.332957 | + | 0.942942i | \(0.608046\pi\) | |||||||
\(504\) | −503877. | −0.0883585 | ||||||||
\(505\) | −1.50151e7 | −2.61999 | ||||||||
\(506\) | 1.19263e7 | 2.07075 | ||||||||
\(507\) | −3.20332e6 | −0.553453 | ||||||||
\(508\) | −672196. | −0.115568 | ||||||||
\(509\) | −5.46200e6 | −0.934452 | −0.467226 | − | 0.884138i | \(-0.654747\pi\) | ||||
−0.467226 | + | 0.884138i | \(0.654747\pi\) | |||||||
\(510\) | 6.45980e6 | 1.09975 | ||||||||
\(511\) | −7.83382e6 | −1.32715 | ||||||||
\(512\) | 7.41233e6 | 1.24963 | ||||||||
\(513\) | 169231. | 0.0283914 | ||||||||
\(514\) | −1.36427e6 | −0.227768 | ||||||||
\(515\) | 5.02916e6 | 0.835559 | ||||||||
\(516\) | 5.63537e6 | 0.931747 | ||||||||
\(517\) | 3.78286e6 | 0.622434 | ||||||||
\(518\) | 7.57189e6 | 1.23988 | ||||||||
\(519\) | 3.23862e6 | 0.527766 | ||||||||
\(520\) | −541748. | −0.0878595 | ||||||||
\(521\) | −3.79145e6 | −0.611944 | −0.305972 | − | 0.952041i | \(-0.598981\pi\) | ||||
−0.305972 | + | 0.952041i | \(0.598981\pi\) | |||||||
\(522\) | −5.07705e6 | −0.815520 | ||||||||
\(523\) | 2.52314e6 | 0.403355 | 0.201678 | − | 0.979452i | \(-0.435361\pi\) | ||||
0.201678 | + | 0.979452i | \(0.435361\pi\) | |||||||
\(524\) | 751426. | 0.119552 | ||||||||
\(525\) | 1.25635e7 | 1.98936 | ||||||||
\(526\) | −5.08424e6 | −0.801238 | ||||||||
\(527\) | 7.97740e6 | 1.25122 | ||||||||
\(528\) | 4.46895e6 | 0.697623 | ||||||||
\(529\) | 6.83438e6 | 1.06184 | ||||||||
\(530\) | −1.93772e7 | −2.99641 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | 972778. | 0.149017 | ||||||||
\(533\) | −1.61381e6 | −0.246056 | ||||||||
\(534\) | −3.50170e6 | −0.531406 | ||||||||
\(535\) | −4.62553e6 | −0.698678 | ||||||||
\(536\) | 56709.6 | 0.00852599 | ||||||||
\(537\) | 465235. | 0.0696204 | ||||||||
\(538\) | −8.46523e6 | −1.26091 | ||||||||
\(539\) | −3.25425e6 | −0.482480 | ||||||||
\(540\) | −2.14601e6 | −0.316699 | ||||||||
\(541\) | 3.18382e6 | 0.467687 | 0.233844 | − | 0.972274i | \(-0.424870\pi\) | ||||
0.233844 | + | 0.972274i | \(0.424870\pi\) | |||||||
\(542\) | −1.26952e7 | −1.85627 | ||||||||
\(543\) | −5.84686e6 | −0.850988 | ||||||||
\(544\) | 6.51772e6 | 0.944275 | ||||||||
\(545\) | 2.02054e7 | 2.91391 | ||||||||
\(546\) | −1.33734e6 | −0.191982 | ||||||||
\(547\) | 1.08153e7 | 1.54550 | 0.772749 | − | 0.634712i | \(-0.218881\pi\) | ||||
0.772749 | + | 0.634712i | \(0.218881\pi\) | |||||||
\(548\) | 5.19644e6 | 0.739188 | ||||||||
\(549\) | 1.10968e6 | 0.157133 | ||||||||
\(550\) | −2.92392e7 | −4.12153 | ||||||||
\(551\) | −1.89737e6 | −0.266240 | ||||||||
\(552\) | 1.30487e6 | 0.182272 | ||||||||
\(553\) | −1.08978e7 | −1.51540 | ||||||||
\(554\) | −673599. | −0.0932453 | ||||||||
\(555\) | −6.24258e6 | −0.860264 | ||||||||
\(556\) | −1.03398e7 | −1.41849 | ||||||||
\(557\) | −300600. | −0.0410536 | −0.0205268 | − | 0.999789i | \(-0.506534\pi\) | ||||
−0.0205268 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(558\) | −5.81336e6 | −0.790390 | ||||||||
\(559\) | −2.89530e6 | −0.391890 | ||||||||
\(560\) | 1.99617e7 | 2.68984 | ||||||||
\(561\) | 3.27506e6 | 0.439352 | ||||||||
\(562\) | −6.13851e6 | −0.819827 | ||||||||
\(563\) | −9.21092e6 | −1.22471 | −0.612353 | − | 0.790584i | \(-0.709777\pi\) | ||||
−0.612353 | + | 0.790584i | \(0.709777\pi\) | |||||||
\(564\) | −2.13811e6 | −0.283030 | ||||||||
\(565\) | 1.97884e7 | 2.60790 | ||||||||
\(566\) | −1.60730e7 | −2.10890 | ||||||||
\(567\) | 1.02549e6 | 0.133959 | ||||||||
\(568\) | −1.37480e6 | −0.178801 | ||||||||
\(569\) | −1.44126e6 | −0.186621 | −0.0933106 | − | 0.995637i | \(-0.529745\pi\) | ||||
−0.0933106 | + | 0.995637i | \(0.529745\pi\) | |||||||
\(570\) | −1.75925e6 | −0.226798 | ||||||||
\(571\) | 4.03264e6 | 0.517606 | 0.258803 | − | 0.965930i | \(-0.416672\pi\) | ||||
0.258803 | + | 0.965930i | \(0.416672\pi\) | |||||||
\(572\) | 1.41888e6 | 0.181324 | ||||||||
\(573\) | 691112. | 0.0879351 | ||||||||
\(574\) | 1.56036e7 | 1.97672 | ||||||||
\(575\) | −3.25353e7 | −4.10379 | ||||||||
\(576\) | −1.73479e6 | −0.217866 | ||||||||
\(577\) | 2.52617e6 | 0.315880 | 0.157940 | − | 0.987449i | \(-0.449515\pi\) | ||||
0.157940 | + | 0.987449i | \(0.449515\pi\) | |||||||
\(578\) | −5.31649e6 | −0.661919 | ||||||||
\(579\) | 4.46639e6 | 0.553682 | ||||||||
\(580\) | 2.40605e7 | 2.96985 | ||||||||
\(581\) | 7.79674e6 | 0.958237 | ||||||||
\(582\) | 1.51308e6 | 0.185163 | ||||||||
\(583\) | −9.82407e6 | −1.19707 | ||||||||
\(584\) | 1.99477e6 | 0.242025 | ||||||||
\(585\) | 1.10256e6 | 0.133203 | ||||||||
\(586\) | 1.07662e7 | 1.29515 | ||||||||
\(587\) | 5.01886e6 | 0.601188 | 0.300594 | − | 0.953752i | \(-0.402815\pi\) | ||||
0.300594 | + | 0.953752i | \(0.402815\pi\) | |||||||
\(588\) | 1.83934e6 | 0.219391 | ||||||||
\(589\) | −2.17255e6 | −0.258036 | ||||||||
\(590\) | −2.93113e6 | −0.346661 | ||||||||
\(591\) | −3.98505e6 | −0.469316 | ||||||||
\(592\) | −7.34766e6 | −0.861678 | ||||||||
\(593\) | −1.51902e7 | −1.77390 | −0.886948 | − | 0.461870i | \(-0.847179\pi\) | ||||
−0.886948 | + | 0.461870i | \(0.847179\pi\) | |||||||
\(594\) | −2.38663e6 | −0.277536 | ||||||||
\(595\) | 1.46289e7 | 1.69402 | ||||||||
\(596\) | −2.60263e6 | −0.300121 | ||||||||
\(597\) | 6.57299e6 | 0.754791 | ||||||||
\(598\) | 3.46328e6 | 0.396036 | ||||||||
\(599\) | 7.13948e6 | 0.813017 | 0.406509 | − | 0.913647i | \(-0.366746\pi\) | ||||
0.406509 | + | 0.913647i | \(0.366746\pi\) | |||||||
\(600\) | −3.19911e6 | −0.362786 | ||||||||
\(601\) | 8.80337e6 | 0.994175 | 0.497088 | − | 0.867700i | \(-0.334403\pi\) | ||||
0.497088 | + | 0.867700i | \(0.334403\pi\) | |||||||
\(602\) | 2.79941e7 | 3.14830 | ||||||||
\(603\) | −115415. | −0.0129262 | ||||||||
\(604\) | 759072. | 0.0846624 | ||||||||
\(605\) | −2.32744e6 | −0.258517 | ||||||||
\(606\) | 9.43825e6 | 1.04402 | ||||||||
\(607\) | −9.90444e6 | −1.09108 | −0.545542 | − | 0.838084i | \(-0.683676\pi\) | ||||
−0.545542 | + | 0.838084i | \(0.683676\pi\) | |||||||
\(608\) | −1.77502e6 | −0.194735 | ||||||||
\(609\) | −1.14975e7 | −1.25620 | ||||||||
\(610\) | −1.15357e7 | −1.25522 | ||||||||
\(611\) | 1.09851e6 | 0.119042 | ||||||||
\(612\) | −1.85110e6 | −0.199780 | ||||||||
\(613\) | 7.13725e6 | 0.767149 | 0.383574 | − | 0.923510i | \(-0.374693\pi\) | ||||
0.383574 | + | 0.923510i | \(0.374693\pi\) | |||||||
\(614\) | −1.02506e7 | −1.09730 | ||||||||
\(615\) | −1.28643e7 | −1.37151 | ||||||||
\(616\) | 2.65565e6 | 0.281981 | ||||||||
\(617\) | −6.15006e6 | −0.650379 | −0.325189 | − | 0.945649i | \(-0.605428\pi\) | ||||
−0.325189 | + | 0.945649i | \(0.605428\pi\) | |||||||
\(618\) | −3.16125e6 | −0.332957 | ||||||||
\(619\) | −749330. | −0.0786043 | −0.0393022 | − | 0.999227i | \(-0.512513\pi\) | ||||
−0.0393022 | + | 0.999227i | \(0.512513\pi\) | |||||||
\(620\) | 2.75499e7 | 2.87833 | ||||||||
\(621\) | −2.65567e6 | −0.276341 | ||||||||
\(622\) | −1.55339e7 | −1.60992 | ||||||||
\(623\) | −7.92997e6 | −0.818561 | ||||||||
\(624\) | 1.29774e6 | 0.133422 | ||||||||
\(625\) | 4.20901e7 | 4.31003 | ||||||||
\(626\) | 3.93747e6 | 0.401588 | ||||||||
\(627\) | −891923. | −0.0906063 | ||||||||
\(628\) | −3.95336e6 | −0.400007 | ||||||||
\(629\) | −5.38472e6 | −0.542670 | ||||||||
\(630\) | −1.06605e7 | −1.07010 | ||||||||
\(631\) | −2.06221e6 | −0.206186 | −0.103093 | − | 0.994672i | \(-0.532874\pi\) | ||||
−0.103093 | + | 0.994672i | \(0.532874\pi\) | |||||||
\(632\) | 2.77497e6 | 0.276354 | ||||||||
\(633\) | 8.64150e6 | 0.857196 | ||||||||
\(634\) | 37800.2 | 0.00373483 | ||||||||
\(635\) | 2.75296e6 | 0.270936 | ||||||||
\(636\) | 5.55267e6 | 0.544326 | ||||||||
\(637\) | −945003. | −0.0922751 | ||||||||
\(638\) | 2.67582e7 | 2.60259 | ||||||||
\(639\) | 2.79800e6 | 0.271078 | ||||||||
\(640\) | −8.83210e6 | −0.852342 | ||||||||
\(641\) | −3.59859e6 | −0.345929 | −0.172964 | − | 0.984928i | \(-0.555335\pi\) | ||||
−0.172964 | + | 0.984928i | \(0.555335\pi\) | |||||||
\(642\) | 2.90754e6 | 0.278412 | ||||||||
\(643\) | 1.37456e7 | 1.31110 | 0.655549 | − | 0.755153i | \(-0.272437\pi\) | ||||
0.655549 | + | 0.755153i | \(0.272437\pi\) | |||||||
\(644\) | −1.52654e7 | −1.45042 | ||||||||
\(645\) | −2.30795e7 | −2.18438 | ||||||||
\(646\) | −1.51749e6 | −0.143068 | ||||||||
\(647\) | 5.03818e6 | 0.473165 | 0.236583 | − | 0.971611i | \(-0.423973\pi\) | ||||
0.236583 | + | 0.971611i | \(0.423973\pi\) | |||||||
\(648\) | −261125. | −0.0244293 | ||||||||
\(649\) | −1.48606e6 | −0.138492 | ||||||||
\(650\) | −8.49078e6 | −0.788251 | ||||||||
\(651\) | −1.31649e7 | −1.21749 | ||||||||
\(652\) | −3.76599e6 | −0.346945 | ||||||||
\(653\) | 1.53399e7 | 1.40780 | 0.703898 | − | 0.710301i | \(-0.251441\pi\) | ||||
0.703898 | + | 0.710301i | \(0.251441\pi\) | |||||||
\(654\) | −1.27008e7 | −1.16115 | ||||||||
\(655\) | −3.07745e6 | −0.280277 | ||||||||
\(656\) | −1.51415e7 | −1.37376 | ||||||||
\(657\) | −4.05974e6 | −0.366931 | ||||||||
\(658\) | −1.06212e7 | −0.956337 | ||||||||
\(659\) | −3.56478e6 | −0.319756 | −0.159878 | − | 0.987137i | \(-0.551110\pi\) | ||||
−0.159878 | + | 0.987137i | \(0.551110\pi\) | |||||||
\(660\) | 1.13104e7 | 1.01069 | ||||||||
\(661\) | −1.62245e7 | −1.44434 | −0.722168 | − | 0.691718i | \(-0.756854\pi\) | ||||
−0.722168 | + | 0.691718i | \(0.756854\pi\) | |||||||
\(662\) | −1.51238e7 | −1.34127 | ||||||||
\(663\) | 951047. | 0.0840269 | ||||||||
\(664\) | −1.98532e6 | −0.174748 | ||||||||
\(665\) | −3.98399e6 | −0.349353 | ||||||||
\(666\) | 3.92399e6 | 0.342802 | ||||||||
\(667\) | 2.97747e7 | 2.59139 | ||||||||
\(668\) | −896804. | −0.0777600 | ||||||||
\(669\) | −1.03364e6 | −0.0892899 | ||||||||
\(670\) | 1.19980e6 | 0.103258 | ||||||||
\(671\) | −5.84850e6 | −0.501462 | ||||||||
\(672\) | −1.07561e7 | −0.918819 | ||||||||
\(673\) | 3.40408e6 | 0.289709 | 0.144854 | − | 0.989453i | \(-0.453729\pi\) | ||||
0.144854 | + | 0.989453i | \(0.453729\pi\) | |||||||
\(674\) | 1.76530e7 | 1.49682 | ||||||||
\(675\) | 6.51082e6 | 0.550017 | ||||||||
\(676\) | −9.54240e6 | −0.803139 | ||||||||
\(677\) | 1.17767e7 | 0.987531 | 0.493766 | − | 0.869595i | \(-0.335620\pi\) | ||||
0.493766 | + | 0.869595i | \(0.335620\pi\) | |||||||
\(678\) | −1.24387e7 | −1.03921 | ||||||||
\(679\) | 3.42653e6 | 0.285220 | ||||||||
\(680\) | −3.72502e6 | −0.308928 | ||||||||
\(681\) | −2.84410e6 | −0.235005 | ||||||||
\(682\) | 3.06389e7 | 2.52239 | ||||||||
\(683\) | 1.47519e7 | 1.21003 | 0.605015 | − | 0.796214i | \(-0.293167\pi\) | ||||
0.605015 | + | 0.796214i | \(0.293167\pi\) | |||||||
\(684\) | 504125. | 0.0412000 | ||||||||
\(685\) | −2.12819e7 | −1.73294 | ||||||||
\(686\) | −1.10084e7 | −0.893128 | ||||||||
\(687\) | −991196. | −0.0801250 | ||||||||
\(688\) | −2.71652e7 | −2.18797 | ||||||||
\(689\) | −2.85282e6 | −0.228942 | ||||||||
\(690\) | 2.76071e7 | 2.20749 | ||||||||
\(691\) | −1.18621e6 | −0.0945079 | −0.0472539 | − | 0.998883i | \(-0.515047\pi\) | ||||
−0.0472539 | + | 0.998883i | \(0.515047\pi\) | |||||||
\(692\) | 9.64755e6 | 0.765864 | ||||||||
\(693\) | −5.40477e6 | −0.427508 | ||||||||
\(694\) | 7.26275e6 | 0.572404 | ||||||||
\(695\) | 4.23465e7 | 3.32549 | ||||||||
\(696\) | 2.92766e6 | 0.229086 | ||||||||
\(697\) | −1.10964e7 | −0.865171 | ||||||||
\(698\) | 1.50379e7 | 1.16828 | ||||||||
\(699\) | 77809.1 | 0.00602334 | ||||||||
\(700\) | 3.74256e7 | 2.88684 | ||||||||
\(701\) | −1.36391e7 | −1.04831 | −0.524155 | − | 0.851623i | \(-0.675619\pi\) | ||||
−0.524155 | + | 0.851623i | \(0.675619\pi\) | |||||||
\(702\) | −693055. | −0.0530792 | ||||||||
\(703\) | 1.46646e6 | 0.111913 | ||||||||
\(704\) | 9.14308e6 | 0.695282 | ||||||||
\(705\) | 8.75660e6 | 0.663534 | ||||||||
\(706\) | 1.91081e7 | 1.44280 | ||||||||
\(707\) | 2.13739e7 | 1.60818 | ||||||||
\(708\) | 839936. | 0.0629743 | ||||||||
\(709\) | −1.43919e7 | −1.07524 | −0.537618 | − | 0.843189i | \(-0.680676\pi\) | ||||
−0.537618 | + | 0.843189i | \(0.680676\pi\) | |||||||
\(710\) | −2.90866e7 | −2.16544 | ||||||||
\(711\) | −5.64761e6 | −0.418978 | ||||||||
\(712\) | 2.01925e6 | 0.149276 | ||||||||
\(713\) | 3.40928e7 | 2.51153 | ||||||||
\(714\) | −9.19550e6 | −0.675040 | ||||||||
\(715\) | −5.81098e6 | −0.425093 | ||||||||
\(716\) | 1.38589e6 | 0.101029 | ||||||||
\(717\) | 5.61310e6 | 0.407760 | ||||||||
\(718\) | 2.17003e6 | 0.157092 | ||||||||
\(719\) | 1.64117e7 | 1.18395 | 0.591974 | − | 0.805957i | \(-0.298349\pi\) | ||||
0.591974 | + | 0.805957i | \(0.298349\pi\) | |||||||
\(720\) | 1.03448e7 | 0.743687 | ||||||||
\(721\) | −7.15899e6 | −0.512877 | ||||||||
\(722\) | −1.85754e7 | −1.32616 | ||||||||
\(723\) | −1.56129e7 | −1.11081 | ||||||||
\(724\) | −1.74173e7 | −1.23491 | ||||||||
\(725\) | −7.29974e7 | −5.15778 | ||||||||
\(726\) | 1.46299e6 | 0.103015 | ||||||||
\(727\) | −1.31438e7 | −0.922328 | −0.461164 | − | 0.887315i | \(-0.652568\pi\) | ||||
−0.461164 | + | 0.887315i | \(0.652568\pi\) | |||||||
\(728\) | 771176. | 0.0539293 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 4.22030e7 | 2.93114 | ||||||||
\(731\) | −1.99079e7 | −1.37795 | ||||||||
\(732\) | 3.30564e6 | 0.228022 | ||||||||
\(733\) | 2.02772e6 | 0.139395 | 0.0696977 | − | 0.997568i | \(-0.477797\pi\) | ||||
0.0696977 | + | 0.997568i | \(0.477797\pi\) | |||||||
\(734\) | 7.84333e6 | 0.537354 | ||||||||
\(735\) | −7.53298e6 | −0.514338 | ||||||||
\(736\) | 2.78546e7 | 1.89541 | ||||||||
\(737\) | 608288. | 0.0412516 | ||||||||
\(738\) | 8.08629e6 | 0.546523 | ||||||||
\(739\) | −1.39245e7 | −0.937929 | −0.468964 | − | 0.883217i | \(-0.655373\pi\) | ||||
−0.468964 | + | 0.883217i | \(0.655373\pi\) | |||||||
\(740\) | −1.85961e7 | −1.24837 | ||||||||
\(741\) | −259006. | −0.0173286 | ||||||||
\(742\) | 2.75834e7 | 1.83924 | ||||||||
\(743\) | −1.13430e6 | −0.0753800 | −0.0376900 | − | 0.999289i | \(-0.512000\pi\) | ||||
−0.0376900 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(744\) | 3.35226e6 | 0.222026 | ||||||||
\(745\) | 1.06590e7 | 0.703600 | ||||||||
\(746\) | 2.31772e7 | 1.52481 | ||||||||
\(747\) | 4.04052e6 | 0.264933 | ||||||||
\(748\) | 9.75611e6 | 0.637562 | ||||||||
\(749\) | 6.58442e6 | 0.428858 | ||||||||
\(750\) | −4.40010e7 | −2.85633 | ||||||||
\(751\) | −2.62894e7 | −1.70091 | −0.850456 | − | 0.526047i | \(-0.823674\pi\) | ||||
−0.850456 | + | 0.526047i | \(0.823674\pi\) | |||||||
\(752\) | 1.03067e7 | 0.664624 | ||||||||
\(753\) | 1.30211e7 | 0.836875 | ||||||||
\(754\) | 7.77033e6 | 0.497750 | ||||||||
\(755\) | −3.10876e6 | −0.198482 | ||||||||
\(756\) | 3.05484e6 | 0.194394 | ||||||||
\(757\) | 2.04231e7 | 1.29534 | 0.647668 | − | 0.761923i | \(-0.275744\pi\) | ||||
0.647668 | + | 0.761923i | \(0.275744\pi\) | |||||||
\(758\) | −4.06029e6 | −0.256675 | ||||||||
\(759\) | 1.39966e7 | 0.881895 | ||||||||
\(760\) | 1.01446e6 | 0.0637093 | ||||||||
\(761\) | 671201. | 0.0420137 | 0.0210068 | − | 0.999779i | \(-0.493313\pi\) | ||||
0.0210068 | + | 0.999779i | \(0.493313\pi\) | |||||||
\(762\) | −1.73047e6 | −0.107964 | ||||||||
\(763\) | −2.87623e7 | −1.78860 | ||||||||
\(764\) | 2.05876e6 | 0.127606 | ||||||||
\(765\) | 7.58115e6 | 0.468362 | ||||||||
\(766\) | −2.26237e7 | −1.39313 | ||||||||
\(767\) | −431537. | −0.0264868 | ||||||||
\(768\) | 1.17199e7 | 0.717000 | ||||||||
\(769\) | 5.15936e6 | 0.314616 | 0.157308 | − | 0.987550i | \(-0.449719\pi\) | ||||
0.157308 | + | 0.987550i | \(0.449719\pi\) | |||||||
\(770\) | 5.61853e7 | 3.41504 | ||||||||
\(771\) | −1.60110e6 | −0.0970022 | ||||||||
\(772\) | 1.33050e7 | 0.803472 | ||||||||
\(773\) | 1.30533e7 | 0.785727 | 0.392863 | − | 0.919597i | \(-0.371485\pi\) | ||||
0.392863 | + | 0.919597i | \(0.371485\pi\) | |||||||
\(774\) | 1.45075e7 | 0.870440 | ||||||||
\(775\) | −8.35841e7 | −4.99884 | ||||||||
\(776\) | −872515. | −0.0520138 | ||||||||
\(777\) | 8.88629e6 | 0.528041 | ||||||||
\(778\) | −2.27650e7 | −1.34840 | ||||||||
\(779\) | 3.02198e6 | 0.178422 | ||||||||
\(780\) | 3.28443e6 | 0.193296 | ||||||||
\(781\) | −1.47467e7 | −0.865099 | ||||||||
\(782\) | 2.38133e7 | 1.39252 | ||||||||
\(783\) | −5.95837e6 | −0.347314 | ||||||||
\(784\) | −8.86649e6 | −0.515183 | ||||||||
\(785\) | 1.61909e7 | 0.937772 | ||||||||
\(786\) | 1.93444e6 | 0.111686 | ||||||||
\(787\) | −1.77189e7 | −1.01977 | −0.509883 | − | 0.860244i | \(-0.670311\pi\) | ||||
−0.509883 | + | 0.860244i | \(0.670311\pi\) | |||||||
\(788\) | −1.18711e7 | −0.681045 | ||||||||
\(789\) | −5.96681e6 | −0.341232 | ||||||||
\(790\) | 5.87098e7 | 3.34690 | ||||||||
\(791\) | −2.81688e7 | −1.60076 | ||||||||
\(792\) | 1.37624e6 | 0.0779619 | ||||||||
\(793\) | −1.69835e6 | −0.0959056 | ||||||||
\(794\) | 7.97695e6 | 0.449041 | ||||||||
\(795\) | −2.27409e7 | −1.27611 | ||||||||
\(796\) | 1.95803e7 | 1.09531 | ||||||||
\(797\) | 1.81052e7 | 1.00962 | 0.504809 | − | 0.863231i | \(-0.331563\pi\) | ||||
0.504809 | + | 0.863231i | \(0.331563\pi\) | |||||||
\(798\) | 2.50428e6 | 0.139212 | ||||||||
\(799\) | 7.55326e6 | 0.418569 | ||||||||
\(800\) | −6.82901e7 | −3.77253 | ||||||||
\(801\) | −4.10956e6 | −0.226315 | ||||||||
\(802\) | 2.53842e7 | 1.39357 | ||||||||
\(803\) | 2.13966e7 | 1.17100 | ||||||||
\(804\) | −343811. | −0.0187577 | ||||||||
\(805\) | 6.25191e7 | 3.40034 | ||||||||
\(806\) | 8.89725e6 | 0.482412 | ||||||||
\(807\) | −9.93471e6 | −0.536996 | ||||||||
\(808\) | −5.44254e6 | −0.293274 | ||||||||
\(809\) | −1.50822e7 | −0.810204 | −0.405102 | − | 0.914272i | \(-0.632764\pi\) | ||||
−0.405102 | + | 0.914272i | \(0.632764\pi\) | |||||||
\(810\) | −5.52460e6 | −0.295861 | ||||||||
\(811\) | 3.23070e7 | 1.72482 | 0.862411 | − | 0.506209i | \(-0.168954\pi\) | ||||
0.862411 | + | 0.506209i | \(0.168954\pi\) | |||||||
\(812\) | −3.42500e7 | −1.82293 | ||||||||
\(813\) | −1.48989e7 | −0.790549 | ||||||||
\(814\) | −2.06811e7 | −1.09399 | ||||||||
\(815\) | 1.54235e7 | 0.813374 | ||||||||
\(816\) | 8.92319e6 | 0.469132 | ||||||||
\(817\) | 5.42167e6 | 0.284170 | ||||||||
\(818\) | −3.99690e7 | −2.08852 | ||||||||
\(819\) | −1.56949e6 | −0.0817617 | ||||||||
\(820\) | −3.83215e7 | −1.99025 | ||||||||
\(821\) | −3.33802e7 | −1.72835 | −0.864175 | − | 0.503191i | \(-0.832159\pi\) | ||||
−0.864175 | + | 0.503191i | \(0.832159\pi\) | |||||||
\(822\) | 1.33775e7 | 0.690551 | ||||||||
\(823\) | 3.38256e7 | 1.74079 | 0.870393 | − | 0.492357i | \(-0.163865\pi\) | ||||
0.870393 | + | 0.492357i | \(0.163865\pi\) | |||||||
\(824\) | 1.82293e6 | 0.0935301 | ||||||||
\(825\) | −3.43148e7 | −1.75528 | ||||||||
\(826\) | 4.17245e6 | 0.212785 | ||||||||
\(827\) | 3.25009e7 | 1.65246 | 0.826231 | − | 0.563332i | \(-0.190481\pi\) | ||||
0.826231 | + | 0.563332i | \(0.190481\pi\) | |||||||
\(828\) | −7.91101e6 | −0.401011 | ||||||||
\(829\) | −508321. | −0.0256893 | −0.0128446 | − | 0.999918i | \(-0.504089\pi\) | ||||
−0.0128446 | + | 0.999918i | \(0.504089\pi\) | |||||||
\(830\) | −4.20033e7 | −2.11635 | ||||||||
\(831\) | −790529. | −0.0397114 | ||||||||
\(832\) | 2.65506e6 | 0.132974 | ||||||||
\(833\) | −6.49778e6 | −0.324454 | ||||||||
\(834\) | −2.66184e7 | −1.32515 | ||||||||
\(835\) | 3.67284e6 | 0.182300 | ||||||||
\(836\) | −2.65696e6 | −0.131483 | ||||||||
\(837\) | −6.82249e6 | −0.336612 | ||||||||
\(838\) | −2.61988e7 | −1.28876 | ||||||||
\(839\) | −583710. | −0.0286281 | −0.0143140 | − | 0.999898i | \(-0.504556\pi\) | ||||
−0.0143140 | + | 0.999898i | \(0.504556\pi\) | |||||||
\(840\) | 6.14733e6 | 0.300600 | ||||||||
\(841\) | 4.62924e7 | 2.25694 | ||||||||
\(842\) | 4.37493e7 | 2.12663 | ||||||||
\(843\) | −7.20409e6 | −0.349149 | ||||||||
\(844\) | 2.57423e7 | 1.24391 | ||||||||
\(845\) | 3.90807e7 | 1.88287 | ||||||||
\(846\) | −5.50427e6 | −0.264408 | ||||||||
\(847\) | 3.31310e6 | 0.158681 | ||||||||
\(848\) | −2.67665e7 | −1.27821 | ||||||||
\(849\) | −1.88631e7 | −0.898141 | ||||||||
\(850\) | −5.83821e7 | −2.77161 | ||||||||
\(851\) | −2.30125e7 | −1.08928 | ||||||||
\(852\) | 8.33498e6 | 0.393374 | ||||||||
\(853\) | 9.83319e6 | 0.462724 | 0.231362 | − | 0.972868i | \(-0.425682\pi\) | ||||
0.231362 | + | 0.972868i | \(0.425682\pi\) | |||||||
\(854\) | 1.64210e7 | 0.770469 | ||||||||
\(855\) | −2.06463e6 | −0.0965890 | ||||||||
\(856\) | −1.67662e6 | −0.0782081 | ||||||||
\(857\) | 1.07762e7 | 0.501201 | 0.250601 | − | 0.968091i | \(-0.419372\pi\) | ||||
0.250601 | + | 0.968091i | \(0.419372\pi\) | |||||||
\(858\) | 3.65270e6 | 0.169393 | ||||||||
\(859\) | −3.47029e7 | −1.60466 | −0.802329 | − | 0.596883i | \(-0.796406\pi\) | ||||
−0.802329 | + | 0.596883i | \(0.796406\pi\) | |||||||
\(860\) | −6.87518e7 | −3.16985 | ||||||||
\(861\) | 1.83122e7 | 0.841848 | ||||||||
\(862\) | −1.77235e7 | −0.812422 | ||||||||
\(863\) | −2.34351e7 | −1.07112 | −0.535561 | − | 0.844496i | \(-0.679900\pi\) | ||||
−0.535561 | + | 0.844496i | \(0.679900\pi\) | |||||||
\(864\) | −5.57414e6 | −0.254035 | ||||||||
\(865\) | −3.95114e7 | −1.79548 | ||||||||
\(866\) | −424762. | −0.0192465 | ||||||||
\(867\) | −6.23937e6 | −0.281899 | ||||||||
\(868\) | −3.92172e7 | −1.76676 | ||||||||
\(869\) | 2.97654e7 | 1.33709 | ||||||||
\(870\) | 6.19403e7 | 2.77444 | ||||||||
\(871\) | 176641. | 0.00788944 | ||||||||
\(872\) | 7.32389e6 | 0.326175 | ||||||||
\(873\) | 1.77574e6 | 0.0788575 | ||||||||
\(874\) | −6.48525e6 | −0.287176 | ||||||||
\(875\) | −9.96447e7 | −4.39981 | ||||||||
\(876\) | −1.20936e7 | −0.532470 | ||||||||
\(877\) | 5.93447e6 | 0.260545 | 0.130273 | − | 0.991478i | \(-0.458415\pi\) | ||||
0.130273 | + | 0.991478i | \(0.458415\pi\) | |||||||
\(878\) | −4.29946e7 | −1.88225 | ||||||||
\(879\) | 1.26351e7 | 0.551579 | ||||||||
\(880\) | −5.45215e7 | −2.37335 | ||||||||
\(881\) | −7.45973e6 | −0.323805 | −0.161902 | − | 0.986807i | \(-0.551763\pi\) | ||||
−0.161902 | + | 0.986807i | \(0.551763\pi\) | |||||||
\(882\) | 4.73512e6 | 0.204955 | ||||||||
\(883\) | −2.46902e7 | −1.06567 | −0.532835 | − | 0.846219i | \(-0.678873\pi\) | ||||
−0.532835 | + | 0.846219i | \(0.678873\pi\) | |||||||
\(884\) | 2.83308e6 | 0.121935 | ||||||||
\(885\) | −3.43994e6 | −0.147636 | ||||||||
\(886\) | 4.09366e7 | 1.75198 | ||||||||
\(887\) | 2.56140e7 | 1.09312 | 0.546562 | − | 0.837419i | \(-0.315936\pi\) | ||||
0.546562 | + | 0.837419i | \(0.315936\pi\) | |||||||
\(888\) | −2.26276e6 | −0.0962955 | ||||||||
\(889\) | −3.91883e6 | −0.166304 | ||||||||
\(890\) | 4.27210e7 | 1.80787 | ||||||||
\(891\) | −2.80092e6 | −0.118197 | ||||||||
\(892\) | −3.07911e6 | −0.129572 | ||||||||
\(893\) | −2.05704e6 | −0.0863204 | ||||||||
\(894\) | −6.70009e6 | −0.280374 | ||||||||
\(895\) | −5.67589e6 | −0.236852 | ||||||||
\(896\) | 1.25725e7 | 0.523179 | ||||||||
\(897\) | 4.06447e6 | 0.168664 | ||||||||
\(898\) | −2.82304e7 | −1.16822 | ||||||||
\(899\) | 7.64919e7 | 3.15658 | ||||||||
\(900\) | 1.93951e7 | 0.798153 | ||||||||
\(901\) | −1.96158e7 | −0.804996 | ||||||||
\(902\) | −4.26183e7 | −1.74413 | ||||||||
\(903\) | 3.28536e7 | 1.34080 | ||||||||
\(904\) | 7.17275e6 | 0.291921 | ||||||||
\(905\) | 7.13321e7 | 2.89510 | ||||||||
\(906\) | 1.95412e6 | 0.0790918 | ||||||||
\(907\) | −1.05309e7 | −0.425055 | −0.212528 | − | 0.977155i | \(-0.568170\pi\) | ||||
−0.212528 | + | 0.977155i | \(0.568170\pi\) | |||||||
\(908\) | −8.47231e6 | −0.341026 | ||||||||
\(909\) | 1.10766e7 | 0.444629 | ||||||||
\(910\) | 1.63157e7 | 0.653133 | ||||||||
\(911\) | 8.73649e6 | 0.348772 | 0.174386 | − | 0.984677i | \(-0.444206\pi\) | ||||
0.174386 | + | 0.984677i | \(0.444206\pi\) | |||||||
\(912\) | −2.43012e6 | −0.0967477 | ||||||||
\(913\) | −2.12953e7 | −0.845487 | ||||||||
\(914\) | 2.41453e7 | 0.956019 | ||||||||
\(915\) | −1.35382e7 | −0.534573 | ||||||||
\(916\) | −2.95268e6 | −0.116273 | ||||||||
\(917\) | 4.38074e6 | 0.172038 | ||||||||
\(918\) | −4.76540e6 | −0.186635 | ||||||||
\(919\) | −1.11596e7 | −0.435874 | −0.217937 | − | 0.975963i | \(-0.569933\pi\) | ||||
−0.217937 | + | 0.975963i | \(0.569933\pi\) | |||||||
\(920\) | −1.59195e7 | −0.620099 | ||||||||
\(921\) | −1.20299e7 | −0.467320 | ||||||||
\(922\) | −2.34600e7 | −0.908870 | ||||||||
\(923\) | −4.28229e6 | −0.165452 | ||||||||
\(924\) | −1.61003e7 | −0.620375 | ||||||||
\(925\) | 5.64189e7 | 2.16806 | ||||||||
\(926\) | 6.40822e7 | 2.45590 | ||||||||
\(927\) | −3.71002e6 | −0.141800 | ||||||||
\(928\) | 6.24957e7 | 2.38221 | ||||||||
\(929\) | 334818. | 0.0127283 | 0.00636415 | − | 0.999980i | \(-0.497974\pi\) | ||||
0.00636415 | + | 0.999980i | \(0.497974\pi\) | |||||||
\(930\) | 7.09233e7 | 2.68894 | ||||||||
\(931\) | 1.76959e6 | 0.0669112 | ||||||||
\(932\) | 231786. | 0.00874073 | ||||||||
\(933\) | −1.82305e7 | −0.685636 | ||||||||
\(934\) | 8.94046e6 | 0.335345 | ||||||||
\(935\) | −3.99560e7 | −1.49469 | ||||||||
\(936\) | 399648. | 0.0149104 | ||||||||
\(937\) | −4.10034e6 | −0.152571 | −0.0762853 | − | 0.997086i | \(-0.524306\pi\) | ||||
−0.0762853 | + | 0.997086i | \(0.524306\pi\) | |||||||
\(938\) | −1.70791e6 | −0.0633808 | ||||||||
\(939\) | 4.62097e6 | 0.171029 | ||||||||
\(940\) | 2.60851e7 | 0.962882 | ||||||||
\(941\) | −760066. | −0.0279819 | −0.0139910 | − | 0.999902i | \(-0.504454\pi\) | ||||
−0.0139910 | + | 0.999902i | \(0.504454\pi\) | |||||||
\(942\) | −1.01774e7 | −0.373687 | ||||||||
\(943\) | −4.74226e7 | −1.73663 | ||||||||
\(944\) | −4.04889e6 | −0.147879 | ||||||||
\(945\) | −1.25110e7 | −0.455736 | ||||||||
\(946\) | −7.64606e7 | −2.77786 | ||||||||
\(947\) | 2.02978e7 | 0.735486 | 0.367743 | − | 0.929927i | \(-0.380131\pi\) | ||||
0.367743 | + | 0.929927i | \(0.380131\pi\) | |||||||
\(948\) | −1.68237e7 | −0.607997 | ||||||||
\(949\) | 6.21336e6 | 0.223955 | ||||||||
\(950\) | 1.58996e7 | 0.571582 | ||||||||
\(951\) | 44362.0 | 0.00159059 | ||||||||
\(952\) | 5.30256e6 | 0.189624 | ||||||||
\(953\) | −7.64595e6 | −0.272709 | −0.136354 | − | 0.990660i | \(-0.543539\pi\) | ||||
−0.136354 | + | 0.990660i | \(0.543539\pi\) | |||||||
\(954\) | 1.42946e7 | 0.508511 | ||||||||
\(955\) | −8.43161e6 | −0.299159 | ||||||||
\(956\) | 1.67209e7 | 0.591718 | ||||||||
\(957\) | 3.14032e7 | 1.10839 | ||||||||
\(958\) | −9.46316e6 | −0.333137 | ||||||||
\(959\) | 3.02947e7 | 1.06370 | ||||||||
\(960\) | 2.11645e7 | 0.741191 | ||||||||
\(961\) | 5.89562e7 | 2.05931 | ||||||||
\(962\) | −6.00561e6 | −0.209228 | ||||||||
\(963\) | 3.41226e6 | 0.118570 | ||||||||
\(964\) | −4.65095e7 | −1.61194 | ||||||||
\(965\) | −5.44903e7 | −1.88365 | ||||||||
\(966\) | −3.92986e7 | −1.35498 | ||||||||
\(967\) | −362592. | −0.0124696 | −0.00623479 | − | 0.999981i | \(-0.501985\pi\) | ||||
−0.00623479 | + | 0.999981i | \(0.501985\pi\) | |||||||
\(968\) | −843631. | −0.0289377 | ||||||||
\(969\) | −1.78091e6 | −0.0609301 | ||||||||
\(970\) | −1.84597e7 | −0.629934 | ||||||||
\(971\) | −4.16836e7 | −1.41879 | −0.709393 | − | 0.704813i | \(-0.751031\pi\) | ||||
−0.709393 | + | 0.704813i | \(0.751031\pi\) | |||||||
\(972\) | 1.58311e6 | 0.0537460 | ||||||||
\(973\) | −6.02800e7 | −2.04123 | ||||||||
\(974\) | 1.22822e7 | 0.414838 | ||||||||
\(975\) | −9.96470e6 | −0.335701 | ||||||||
\(976\) | −1.59347e7 | −0.535452 | ||||||||
\(977\) | −2.63657e7 | −0.883695 | −0.441847 | − | 0.897090i | \(-0.645677\pi\) | ||||
−0.441847 | + | 0.897090i | \(0.645677\pi\) | |||||||
\(978\) | −9.69501e6 | −0.324117 | ||||||||
\(979\) | 2.16592e7 | 0.722246 | ||||||||
\(980\) | −2.24400e7 | −0.746377 | ||||||||
\(981\) | −1.49055e7 | −0.494510 | ||||||||
\(982\) | 1.36960e7 | 0.453227 | ||||||||
\(983\) | 3.95927e6 | 0.130687 | 0.0653433 | − | 0.997863i | \(-0.479186\pi\) | ||||
0.0653433 | + | 0.997863i | \(0.479186\pi\) | |||||||
\(984\) | −4.66294e6 | −0.153522 | ||||||||
\(985\) | 4.86179e7 | 1.59663 | ||||||||
\(986\) | 5.34283e7 | 1.75017 | ||||||||
\(987\) | −1.24650e7 | −0.407286 | ||||||||
\(988\) | −771555. | −0.0251463 | ||||||||
\(989\) | −8.50800e7 | −2.76590 | ||||||||
\(990\) | 2.91170e7 | 0.944189 | ||||||||
\(991\) | −3.87210e7 | −1.25246 | −0.626228 | − | 0.779640i | \(-0.715402\pi\) | ||||
−0.626228 | + | 0.779640i | \(0.715402\pi\) | |||||||
\(992\) | 7.15592e7 | 2.30880 | ||||||||
\(993\) | −1.77492e7 | −0.571222 | ||||||||
\(994\) | 4.14047e7 | 1.32918 | ||||||||
\(995\) | −8.01908e7 | −2.56783 | ||||||||
\(996\) | 1.20363e7 | 0.384456 | ||||||||
\(997\) | 3.15392e7 | 1.00488 | 0.502438 | − | 0.864613i | \(-0.332436\pi\) | ||||
0.502438 | + | 0.864613i | \(0.332436\pi\) | |||||||
\(998\) | 6.12442e7 | 1.94643 | ||||||||
\(999\) | 4.60516e6 | 0.145993 |
(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 | 177.6.a.a.1.10 | ✓ | 11 | |
3.2 | odd | 2 | 531.6.a.b.1.2 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.a.1.10 | ✓ | 11 | 1.1 | even | 1 | trivial | |
531.6.a.b.1.2 | 11 | 3.2 | odd | 2 |