Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(65,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.h (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} - 40335478 x^{5} + 638031136 x^{4} - 1209472584 x^{3} + \cdots + 90728724573 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 69.1 | ||
Root | \(0.500000 - 14.3199i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.69 |
Dual form | 76.5.h.a.65.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −13.1514 | + | 7.59296i | −1.46127 | + | 0.843663i | −0.999070 | − | 0.0431151i | \(-0.986272\pi\) |
−0.462196 | + | 0.886778i | \(0.652938\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 19.9265 | + | 34.5138i | 0.797061 | + | 1.38055i | 0.921522 | + | 0.388326i | \(0.126947\pi\) |
−0.124461 | + | 0.992225i | \(0.539720\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −53.3663 | −1.08911 | −0.544554 | − | 0.838726i | \(-0.683301\pi\) | ||||
−0.544554 | + | 0.838726i | \(0.683301\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 74.8062 | − | 129.568i | 0.923533 | − | 1.59961i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.01156 | 0.0744757 | 0.0372379 | − | 0.999306i | \(-0.488144\pi\) | ||||
0.0372379 | + | 0.999306i | \(0.488144\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.39539 | − | 3.11503i | −0.0319254 | − | 0.0184321i | 0.483952 | − | 0.875094i | \(-0.339201\pi\) |
−0.515878 | + | 0.856662i | \(0.672534\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −524.123 | − | 302.603i | −2.32944 | − | 1.34490i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −261.609 | − | 453.120i | −0.905222 | − | 1.56789i | −0.820619 | − | 0.571476i | \(-0.806371\pi\) |
−0.0846030 | − | 0.996415i | \(-0.526962\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −329.612 | + | 147.231i | −0.913052 | + | 0.407843i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 701.842 | − | 405.208i | 1.59148 | − | 0.918840i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 204.027 | − | 353.386i | 0.385685 | − | 0.668026i | −0.606179 | − | 0.795328i | \(-0.707299\pi\) |
0.991864 | + | 0.127302i | \(0.0406319\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −481.633 | + | 834.213i | −0.770613 | + | 1.33474i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1041.94i | 1.42928i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1176.08 | + | 679.011i | 1.39843 | + | 0.807385i | 0.994228 | − | 0.107283i | \(-0.0342152\pi\) |
0.404204 | + | 0.914669i | \(0.367549\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 214.814i | − | 0.223532i | −0.993735 | − | 0.111766i | \(-0.964349\pi\) | ||
0.993735 | − | 0.111766i | \(-0.0356506\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −118.515 | + | 68.4244i | −0.108829 | + | 0.0628324i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1063.41 | − | 1841.87i | −0.868086 | − | 1.50357i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1223.68i | 0.893851i | 0.894571 | + | 0.446925i | \(0.147481\pi\) | ||||
−0.894571 | + | 0.446925i | \(0.852519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 94.6092 | 0.0622020 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −666.384 | + | 384.737i | −0.396421 | + | 0.228874i | −0.684939 | − | 0.728601i | \(-0.740171\pi\) |
0.288517 | + | 0.957475i | \(0.406838\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1147.74 | − | 1987.94i | −0.620733 | − | 1.07514i | −0.989349 | − | 0.145560i | \(-0.953502\pi\) |
0.368616 | − | 0.929582i | \(-0.379832\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5962.51 | 2.94445 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1740.86 | + | 3015.26i | −0.788076 | + | 1.36499i | 0.139067 | + | 0.990283i | \(0.455590\pi\) |
−0.927144 | + | 0.374706i | \(0.877744\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 446.963 | 0.186157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6881.05 | + | 3972.78i | 2.64554 | + | 1.52740i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4815.71 | − | 2780.35i | −1.71438 | − | 0.989801i | −0.928422 | − | 0.371527i | \(-0.878834\pi\) |
−0.785963 | − | 0.618274i | \(-0.787832\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 179.569 | + | 311.023i | 0.0593617 | + | 0.102817i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3216.93 | − | 4439.03i | 0.990130 | − | 1.36628i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2130.74 | + | 1230.18i | −0.612105 | + | 0.353399i | −0.773789 | − | 0.633444i | \(-0.781641\pi\) |
0.161684 | + | 0.986843i | \(0.448307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1471.38 | + | 2548.51i | −0.395427 | + | 0.684900i | −0.993156 | − | 0.116799i | \(-0.962737\pi\) |
0.597728 | + | 0.801699i | \(0.296070\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3992.13 | + | 6914.57i | −1.00583 | + | 1.74214i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 248.287i | − | 0.0587661i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1474.24 | + | 851.150i | 0.328411 | + | 0.189608i | 0.655135 | − | 0.755512i | \(-0.272612\pi\) |
−0.326725 | + | 0.945120i | \(0.605945\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6196.69i | 1.30155i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2989.25 | + | 1725.84i | −0.592988 | + | 0.342361i | −0.766278 | − | 0.642509i | \(-0.777893\pi\) |
0.173290 | + | 0.984871i | \(0.444560\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4122.11 | − | 7139.70i | −0.773524 | − | 1.33978i | −0.935620 | − | 0.353008i | \(-0.885159\pi\) |
0.162097 | − | 0.986775i | \(-0.448174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 14628.1i | − | 2.60055i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −480.914 | −0.0811121 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7356.86 | − | 4247.48i | 1.17879 | − | 0.680577i | 0.223059 | − | 0.974805i | \(-0.428396\pi\) |
0.955735 | + | 0.294227i | \(0.0950623\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1852.13 | − | 3207.98i | −0.282293 | − | 0.488947i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2757.20 | −0.400233 | −0.200116 | − | 0.979772i | \(-0.564132\pi\) | ||||
−0.200116 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10425.9 | − | 18058.2i | 1.44303 | − | 2.49941i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20622.8 | −2.72464 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5987.69 | + | 3457.00i | 0.755926 | + | 0.436434i | 0.827831 | − | 0.560977i | \(-0.189574\pi\) |
−0.0719049 | + | 0.997411i | \(0.522908\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 287.932 | + | 166.238i | 0.0347702 | + | 0.0200746i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1631.07 | + | 2825.10i | 0.188585 | + | 0.326639i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11649.5 | − | 8442.33i | −1.29081 | − | 0.935438i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10519.1 | + | 6073.22i | −1.11798 | + | 0.645469i | −0.940886 | − | 0.338724i | \(-0.890005\pi\) |
−0.177099 | + | 0.984193i | \(0.556671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 674.120 | − | 1167.61i | 0.0687808 | − | 0.119132i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4704.98 | + | 8149.27i | −0.461228 | + | 0.798870i | −0.999022 | − | 0.0442061i | \(-0.985924\pi\) |
0.537795 | + | 0.843076i | \(0.319257\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15630.0i | 1.47328i | 0.676284 | + | 0.736641i | \(0.263589\pi\) | ||||
−0.676284 | + | 0.736641i | \(0.736411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 27970.5 | + | 16148.8i | 2.53701 | + | 1.46474i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1064.07i | 0.0929398i | 0.998920 | + | 0.0464699i | \(0.0147972\pi\) | ||||
−0.998920 | + | 0.0464699i | \(0.985203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2702.69 | − | 1560.40i | 0.227480 | − | 0.131336i | −0.381929 | − | 0.924192i | \(-0.624740\pi\) |
0.609409 | + | 0.792856i | \(0.291407\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9291.37 | − | 16093.1i | −0.754108 | − | 1.30615i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4559.56i | 0.357081i | 0.983933 | + | 0.178540i | \(0.0571375\pi\) | ||||
−0.983933 | + | 0.178540i | \(0.942863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16262.2 | 1.22966 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −807.216 | + | 466.047i | −0.0589683 | + | 0.0340453i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13961.1 | + | 24181.4i | 0.985885 | + | 1.70760i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14559.8 | −0.994453 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5842.59 | − | 10119.7i | 0.386185 | − | 0.668892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13480.9 | −0.862781 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16901.8 | + | 9758.24i | 1.04791 | + | 0.605012i | 0.922064 | − | 0.387038i | \(-0.126502\pi\) |
0.125848 | + | 0.992050i | \(0.459835\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 30188.7 | + | 17429.4i | 1.81411 | + | 1.04738i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9199.29 | − | 15933.6i | −0.536058 | − | 0.928479i | −0.999111 | − | 0.0421489i | \(-0.986580\pi\) |
0.463054 | − | 0.886330i | \(-0.346754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17590.2 | − | 7857.20i | 0.994413 | − | 0.444186i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −35961.3 | + | 20762.3i | −1.97319 | + | 1.13922i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9527.92 | − | 16502.8i | 0.507642 | − | 0.879261i | −0.492319 | − | 0.870415i | \(-0.663851\pi\) |
0.999961 | − | 0.00884630i | \(-0.00281590\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7531.70 | − | 13045.3i | 0.389819 | − | 0.675187i | −0.602606 | − | 0.798039i | \(-0.705871\pi\) |
0.992425 | + | 0.122852i | \(0.0392041\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 52873.2i | − | 2.65948i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −48.6209 | − | 28.0713i | −0.00237766 | − | 0.00137274i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 54121.3i | 2.57414i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5878.19 | + | 3393.78i | −0.272025 | + | 0.157054i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6317.79 | − | 10942.7i | −0.284572 | − | 0.492894i | 0.687933 | − | 0.725774i | \(-0.258518\pi\) |
−0.972505 | + | 0.232880i | \(0.925185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14119.5i | 0.619248i | 0.950859 | + | 0.309624i | \(0.100203\pi\) | ||||
−0.950859 | + | 0.309624i | \(0.899797\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −78279.9 | −3.34401 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7414.03 | − | 4280.49i | 0.308597 | − | 0.178168i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6248.53 | + | 10822.8i | 0.253500 | + | 0.439075i | 0.964487 | − | 0.264130i | \(-0.0850848\pi\) |
−0.710987 | + | 0.703205i | \(0.751751\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 84444.4 | 3.34023 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10888.2 | + | 18858.9i | −0.420053 | + | 0.727553i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 29683.1 | 1.11721 | 0.558604 | − | 0.829434i | \(-0.311337\pi\) | ||||
0.558604 | + | 0.829434i | \(0.311337\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4723.17 | − | 2726.92i | −0.173486 | − | 0.100162i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20882.9 | − | 12056.8i | −0.748788 | − | 0.432313i | 0.0764680 | − | 0.997072i | \(-0.475636\pi\) |
−0.825256 | + | 0.564759i | \(0.808969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14261.1 | − | 24700.9i | −0.499321 | − | 0.864848i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5580.50 | + | 53721.0i | −0.190845 | + | 1.83718i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −26503.6 | + | 15301.9i | −0.885550 | + | 0.511273i | −0.872484 | − | 0.488642i | \(-0.837492\pi\) |
−0.0130660 | + | 0.999915i | \(0.504159\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 25703.0 | − | 44518.9i | 0.839281 | − | 1.45368i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18681.4 | − | 32357.2i | 0.596299 | − | 1.03282i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 31622.5i | 0.986940i | 0.869763 | + | 0.493470i | \(0.164272\pi\) | ||||
−0.869763 | + | 0.493470i | \(0.835728\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2932.84 | − | 1693.28i | −0.0895223 | − | 0.0516857i | 0.454571 | − | 0.890711i | \(-0.349793\pi\) |
−0.544093 | + | 0.839025i | \(0.683126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 44688.7i | − | 1.33443i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −42233.9 | + | 24383.7i | −1.23401 | + | 0.712454i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2357.51 | − | 4083.32i | −0.0674170 | − | 0.116770i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 55604.6i | − | 1.55664i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7140.61 | −0.195735 | −0.0978675 | − | 0.995199i | \(-0.531202\pi\) | ||||
−0.0978675 | + | 0.995199i | \(0.531202\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13922.0 | + | 8037.86i | −0.373754 | + | 0.215787i | −0.675097 | − | 0.737729i | \(-0.735898\pi\) |
0.301343 | + | 0.953516i | \(0.402565\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1885.23 | + | 3265.32i | 0.0495788 | + | 0.0858729i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26545.9 | −0.684013 | −0.342007 | − | 0.939698i | \(-0.611107\pi\) | ||||
−0.342007 | + | 0.939698i | \(0.611107\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2357.02 | + | 4082.47i | −0.0595191 | + | 0.103090i | −0.894250 | − | 0.447569i | \(-0.852290\pi\) |
0.834731 | + | 0.550659i | \(0.185623\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25851.0 | −0.639861 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −62763.1 | − | 36236.3i | −1.52304 | − | 0.879330i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26557.4 | − | 15332.9i | −0.631944 | − | 0.364853i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −30525.0 | − | 52870.9i | −0.712385 | − | 1.23389i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2970.32 | + | 1326.78i | −0.0680002 | + | 0.0303744i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7586.62 | + | 4380.14i | −0.170405 | + | 0.0983836i | −0.582777 | − | 0.812632i | \(-0.698034\pi\) |
0.412372 | + | 0.911016i | \(0.364701\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26208.5 | − | 45394.5i | 0.577675 | − | 1.00056i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 45740.8 | − | 79225.3i | 0.989524 | − | 1.71391i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11463.8i | 0.243450i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 108423. | + | 62598.0i | 2.26065 | + | 1.30519i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3259.68i | 0.0667406i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 74100.7 | − | 42782.0i | 1.49009 | − | 0.860304i | 0.490154 | − | 0.871636i | \(-0.336941\pi\) |
0.999936 | + | 0.0113323i | \(0.00360726\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 72058.3 | + | 124809.i | 1.42337 | + | 2.46535i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 52738.6i | 1.02347i | 0.859142 | + | 0.511737i | \(0.170998\pi\) | ||||
−0.859142 | + | 0.511737i | \(0.829002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27552.9 | 0.525407 | 0.262704 | − | 0.964877i | \(-0.415386\pi\) | ||||
0.262704 | + | 0.964877i | \(0.415386\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6324.69 | − | 3651.56i | 0.118526 | − | 0.0684313i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29960.8 | + | 51893.6i | 0.551876 | + | 0.955877i | 0.998139 | + | 0.0609754i | \(0.0194211\pi\) |
−0.446263 | + | 0.894902i | \(0.647246\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −138757. | −2.51258 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −64502.0 | + | 111721.i | −1.14836 | + | 1.98901i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18546.4 | 0.324686 | 0.162343 | − | 0.986734i | \(-0.448095\pi\) | ||||
0.162343 | + | 0.986734i | \(0.448095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 51352.4 | + | 29648.3i | 0.884152 | + | 0.510465i | 0.872025 | − | 0.489461i | \(-0.162807\pi\) |
0.0121266 | + | 0.999926i | \(0.496140\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −24374.1 | − | 14072.4i | −0.412777 | − | 0.238317i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8906.43 | + | 15426.4i | 0.148379 | + | 0.256999i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2237.01 | + | 232.379i | 0.0366669 | + | 0.00380893i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 36261.1 | − | 20935.3i | 0.584847 | − | 0.337661i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13531.1 | + | 23436.6i | −0.214776 | + | 0.372003i | −0.953203 | − | 0.302330i | \(-0.902235\pi\) |
0.738427 | + | 0.674333i | \(0.235569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1838.60 | − | 3184.56i | 0.0287242 | − | 0.0497517i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 316655.i | 4.86974i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −43689.8 | − | 25224.3i | −0.661475 | − | 0.381903i | 0.131364 | − | 0.991334i | \(-0.458064\pi\) |
−0.792839 | + | 0.609431i | \(0.791398\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 65303.4i | − | 0.973500i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 175956. | − | 101588.i | 2.58300 | − | 1.49129i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1642.93 | − | 2845.63i | −0.0237523 | − | 0.0411403i | 0.853905 | − | 0.520429i | \(-0.174228\pi\) |
−0.877657 | + | 0.479289i | \(0.840895\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 221611.i | − | 3.15573i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −104995. | −1.47281 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14796.8 | + | 8542.92i | −0.204486 | + | 0.118060i | −0.598746 | − | 0.800939i | \(-0.704334\pi\) |
0.394260 | + | 0.918999i | \(0.371001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10303.0 | − | 17845.4i | −0.140290 | − | 0.242989i | 0.787316 | − | 0.616550i | \(-0.211470\pi\) |
−0.927606 | + | 0.373561i | \(0.878137\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5048.94 | −0.0677447 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4340.27 | + | 7517.56i | −0.0573919 | + | 0.0994058i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24421.2 | −0.318278 | −0.159139 | − | 0.987256i | \(-0.550872\pi\) | ||||
−0.159139 | + | 0.987256i | \(0.550872\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27833.0 | − | 16069.4i | −0.357562 | − | 0.206439i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6075.51 | − | 3507.70i | −0.0769431 | − | 0.0444231i | 0.461035 | − | 0.887382i | \(-0.347478\pi\) |
−0.537978 | + | 0.842959i | \(0.680812\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 47805.3 | + | 82801.3i | 0.596903 | + | 1.03387i | 0.993275 | + | 0.115776i | \(0.0369354\pi\) |
−0.396373 | + | 0.918090i | \(0.629731\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 217310. | + | 22574.0i | 2.67541 | + | 0.277919i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35562.5 | − | 20532.0i | 0.431746 | − | 0.249269i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −95118.2 | + | 164750.i | −1.13885 | + | 1.97255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 92227.4 | − | 159743.i | 1.08912 | − | 1.88640i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 110120.i | − | 1.28272i | −0.767239 | − | 0.641361i | \(-0.778370\pi\) | ||
0.767239 | − | 0.641361i | \(-0.221630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −84916.4 | − | 49026.5i | −0.975770 | − | 0.563361i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9389.52i | 0.106446i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2201.61 | + | 1271.10i | −0.0246263 | + | 0.0142180i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 61250.4 | + | 106089.i | 0.676046 | + | 1.17095i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 142899.i | − | 1.55648i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −117278. | −1.26072 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 37032.8 | − | 21380.9i | 0.392925 | − | 0.226855i | −0.290502 | − | 0.956874i | \(-0.593822\pi\) |
0.683427 | + | 0.730019i | \(0.260489\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −118678. | − | 205557.i | −1.24295 | − | 2.15286i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −62672.8 | −0.647976 | −0.323988 | − | 0.946061i | \(-0.605024\pi\) | ||||
−0.323988 | + | 0.946061i | \(0.605024\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −87372.5 | + | 151334.i | −0.891838 | + | 1.54471i | −0.0541679 | + | 0.998532i | \(0.517251\pi\) |
−0.837670 | + | 0.546177i | \(0.816083\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −318197. | −3.20682 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26126.0 | + | 15083.9i | 0.259989 | + | 0.150105i | 0.624329 | − | 0.781161i | \(-0.285372\pi\) |
−0.364341 | + | 0.931266i | \(0.618706\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10598.3 | + | 6118.95i | 0.104149 | + | 0.0601306i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8079.42 | − | 13994.0i | −0.0784098 | − | 0.135810i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 152943. | + | 110837.i | 1.46597 | + | 1.06238i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5197.19 | − | 3000.60i | 0.0492042 | − | 0.0284081i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23696.1 | + | 41042.9i | −0.221606 | + | 0.383833i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 92903.3 | − | 160913.i | 0.858301 | − | 1.48662i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 63185.8i | 0.576718i | 0.957522 | + | 0.288359i | \(0.0931096\pi\) | ||||
−0.957522 | + | 0.288359i | \(0.906890\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 158550. | + | 91538.9i | 1.42981 | + | 0.825501i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 67841.9i | 0.604517i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −125600. | + | 72515.1i | −1.10593 | + | 0.638511i | −0.937773 | − | 0.347249i | \(-0.887116\pi\) |
−0.168160 | + | 0.985760i | \(0.553783\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −34620.6 | − | 59964.6i | −0.301256 | − | 0.521790i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1935.81i | − | 0.0166477i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 104280. | 0.886363 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −213871. | + | 123478.i | −1.79686 | + | 1.03742i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1089.43 | + | 1886.95i | 0.00904776 | + | 0.0156712i | 0.870514 | − | 0.492144i | \(-0.163787\pi\) |
−0.861466 | + | 0.507815i | \(0.830453\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 88628.2 | 0.727647 | 0.363824 | − | 0.931468i | \(-0.381471\pi\) | ||||
0.363824 | + | 0.931468i | \(0.381471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3245.68 | − | 5621.68i | 0.0263446 | − | 0.0456302i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 197267. | 1.58309 | 0.791545 | − | 0.611111i | \(-0.209277\pi\) | ||||
0.791545 | + | 0.611111i | \(0.209277\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −119131. | − | 68780.2i | −0.945295 | − | 0.545766i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −367216. | − | 212012.i | −2.88128 | − | 1.66351i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −69978.8 | − | 121207.i | −0.542972 | − | 0.940455i | −0.998732 | − | 0.0503521i | \(-0.983966\pi\) |
0.455760 | − | 0.890103i | \(-0.349368\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 86966.8 | − | 97058.4i | 0.667328 | − | 0.744764i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 191482. | − | 110552.i | 1.45316 | − | 0.838983i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 164279. | − | 284539.i | 1.23309 | − | 2.13578i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16609.2 | − | 28768.0i | 0.123315 | − | 0.213588i | −0.797758 | − | 0.602978i | \(-0.793981\pi\) |
0.921073 | + | 0.389390i | \(0.127314\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 115123.i | 0.845491i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 256997. | + | 148377.i | 1.86715 | + | 1.07800i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23103.2i | 0.166056i | 0.996547 | + | 0.0830281i | \(0.0264591\pi\) | ||||
−0.996547 | + | 0.0830281i | \(0.973541\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 177293. | − | 102360.i | 1.26075 | − | 0.727896i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4230.28 | − | 7327.06i | −0.0297636 | − | 0.0515521i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 32221.6i | − | 0.224321i | −0.993690 | − | 0.112160i | \(-0.964223\pi\) | ||
0.993690 | − | 0.112160i | \(-0.0357770\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −296376. | −2.04170 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −195003. | + | 112585.i | −1.32936 | + | 0.767509i | −0.985201 | − | 0.171401i | \(-0.945171\pi\) |
−0.344163 | + | 0.938910i | \(0.611837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9582.94 | − | 16598.1i | −0.0646513 | − | 0.111979i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −343431. | −2.29307 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14122.8 | − | 24461.4i | 0.0933302 | − | 0.161653i | −0.815580 | − | 0.578644i | \(-0.803582\pi\) |
0.908910 | + | 0.416991i | \(0.136915\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −213502. | −1.39652 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 241967. | + | 139700.i | 1.56665 | + | 0.904504i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 293193. | + | 169275.i | 1.87914 | + | 1.08492i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 97341.9 | + | 168601.i | 0.617616 | + | 1.06974i | 0.989919 | + | 0.141632i | \(0.0452349\pi\) |
−0.372303 | + | 0.928111i | \(0.621432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −171676. | + | 236895.i | −1.07836 | + | 1.48802i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20526.9 | + | 11851.2i | −0.127654 | + | 0.0737012i | −0.562467 | − | 0.826820i | \(-0.690148\pi\) |
0.434813 | + | 0.900521i | \(0.356814\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −669.151 | + | 1159.00i | −0.00412016 | + | 0.00713633i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 73812.9 | − | 127848.i | 0.450010 | − | 0.779441i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11027.3i | 0.0665702i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 142037. | + | 82004.9i | 0.849090 | + | 0.490222i | 0.860344 | − | 0.509715i | \(-0.170249\pi\) |
−0.0112539 | + | 0.999937i | \(0.503582\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 289381.i | 1.71311i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 113710. | − | 65650.3i | 0.666649 | − | 0.384890i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −54941.5 | − | 95161.5i | −0.319010 | − | 0.552542i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 228752.i | 1.31550i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 60552.8 | 0.344910 | 0.172455 | − | 0.985017i | \(-0.444830\pi\) | ||||
0.172455 | + | 0.985017i | \(0.444830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 116808. | − | 67439.2i | 0.659036 | − | 0.380494i | −0.132874 | − | 0.991133i | \(-0.542420\pi\) |
0.791909 | + | 0.610638i | \(0.209087\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 260454. | + | 451120.i | 1.45563 | + | 2.52122i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 503999. | 2.79030 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 78522.4 | − | 136005.i | 0.430663 | − | 0.745931i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 852.576 | 0.00463253 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −93228.7 | − | 53825.6i | −0.501874 | − | 0.289757i | 0.227613 | − | 0.973752i | \(-0.426908\pi\) |
−0.729487 | + | 0.683994i | \(0.760241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 82985.3 | + | 47911.6i | 0.442614 | + | 0.255543i | 0.704706 | − | 0.709500i | \(-0.251079\pi\) |
−0.262092 | + | 0.965043i | \(0.584412\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −410941. | − | 711771.i | −2.17171 | − | 3.76151i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15220.3 | + | 146519.i | −0.0797005 | + | 0.767241i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −220263. | + | 127169.i | −1.14291 | + | 0.659859i | −0.947149 | − | 0.320793i | \(-0.896051\pi\) |
−0.195760 | + | 0.980652i | \(0.562717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33435.6 | − | 57912.2i | 0.171922 | − | 0.297778i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −146103. | + | 253058.i | −0.744479 | + | 1.28947i | 0.205959 | + | 0.978561i | \(0.433969\pi\) |
−0.950438 | + | 0.310914i | \(0.899365\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 275544.i | 1.39146i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 166176. | + | 95941.5i | 0.831672 | + | 0.480166i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 123714.i | − | 0.613657i | −0.951765 | − | 0.306828i | \(-0.900732\pi\) | ||
0.951765 | − | 0.306828i | \(-0.0992677\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6005.16 | + | 3467.08i | −0.0295238 | + | 0.0170455i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −107209. | − | 185691.i | −0.522437 | − | 0.904887i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13250.2i | 0.0640027i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −249320. | −1.19378 | −0.596890 | − | 0.802323i | \(-0.703597\pi\) | ||||
−0.596890 | + | 0.802323i | \(0.703597\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 472125. | − | 272582.i | 2.24095 | − | 1.29381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 63180.9 | + | 109432.i | 0.297292 | + | 0.514925i | 0.975516 | − | 0.219931i | \(-0.0705831\pi\) |
−0.678223 | + | 0.734856i | \(0.737250\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −86701.1 | −0.404448 | −0.202224 | − | 0.979339i | \(-0.564817\pi\) | ||||
−0.202224 | + | 0.979339i | \(0.564817\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −65003.3 | + | 112589.i | −0.300628 | + | 0.520703i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 226847. | 1.04016 | 0.520078 | − | 0.854119i | \(-0.325903\pi\) | ||||
0.520078 | + | 0.854119i | \(0.325903\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −78674.5 | − | 45422.7i | −0.357675 | − | 0.206504i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −164354. | − | 94889.6i | −0.740863 | − | 0.427737i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10342.9 | − | 17914.4i | −0.0462295 | − | 0.0800719i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35929.6 | − | 345878.i | 0.159245 | − | 1.53298i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −720489. | + | 415975.i | −3.16658 | + | 1.82823i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 130496. | − | 226026.i | 0.568757 | − | 0.985117i | −0.427932 | − | 0.903811i | \(-0.640758\pi\) |
0.996689 | − | 0.0813056i | \(-0.0259090\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3811.80 | − | 6602.24i | 0.0164756 | − | 0.0285365i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 330694.i | − | 1.41753i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −419219. | − | 242036.i | −1.78220 | − | 1.02896i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 402444.i | − | 1.69687i | −0.529303 | − | 0.848433i | \(-0.677547\pi\) | ||
0.529303 | − | 0.848433i | \(-0.322453\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −390374. | + | 225383.i | −1.63254 | + | 0.942547i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8446.75 | + | 14630.2i | 0.0350370 | + | 0.0606858i | 0.883012 | − | 0.469350i | \(-0.155512\pi\) |
−0.847975 | + | 0.530036i | \(0.822178\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 710542.i | − | 2.92345i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 53731.5 | 0.219290 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 159525. | − | 92101.9i | 0.645828 | − | 0.372869i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 96752.2 | + | 167580.i | 0.388562 | + | 0.673009i | 0.992256 | − | 0.124207i | \(-0.0396387\pi\) |
−0.603695 | + | 0.797216i | \(0.706305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 366186. | 1.45890 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7000.74 | + | 12125.6i | −0.0276699 | + | 0.0479257i | −0.879529 | − | 0.475846i | \(-0.842142\pi\) |
0.851859 | + | 0.523771i | \(0.175475\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −375016. | −1.47051 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 375107. | + | 216568.i | 1.45928 | + | 0.842516i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 68947.5 | + | 39806.9i | 0.266123 | + | 0.153646i | 0.627125 | − | 0.778919i | \(-0.284232\pi\) |
−0.361001 | + | 0.932565i | \(0.617565\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 219982. | + | 381020.i | 0.842451 | + | 1.45917i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −153407. | − | 343436.i | −0.582921 | − | 1.30500i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −539451. | + | 311452.i | −2.03394 | + | 1.17430i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15687.9 | + | 27172.2i | −0.0586925 | + | 0.101658i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 232373. | − | 402482.i | 0.862683 | − | 1.49421i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 358410.i | − | 1.32040i | −0.751090 | − | 0.660200i | \(-0.770472\pi\) | ||
0.751090 | − | 0.660200i | \(-0.229528\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 194918. | + | 112536.i | 0.712606 | + | 0.411423i | 0.812025 | − | 0.583622i | \(-0.198365\pi\) |
−0.0994192 | + | 0.995046i | \(0.531698\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 780647.i | 2.83228i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −97336.5 | + | 56197.3i | −0.350473 | + | 0.202346i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56666.2 | + | 98148.8i | 0.202494 | + | 0.350731i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 368101.i | 1.30550i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4793.87 | 0.0168745 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36725.0 | + | 21203.2i | −0.128308 | + | 0.0740787i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −240109. | − | 415881.i | −0.832644 | − | 1.44218i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4027.84 | 0.0138642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 122595. | − | 212341.i | 0.418870 | − | 0.725504i | −0.576956 | − | 0.816775i | \(-0.695760\pi\) |
0.995826 | + | 0.0912713i | \(0.0290930\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 51427.9 | 0.174421 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 107711. | + | 62186.8i | 0.362631 | + | 0.209365i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 381981. | + | 220537.i | 1.27664 | + | 0.737067i | 0.976229 | − | 0.216744i | \(-0.0695436\pi\) |
0.300409 | + | 0.953811i | \(0.402877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 220137. | + | 381289.i | 0.730380 | + | 1.26506i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −487622. | − | 50653.8i | −1.60613 | − | 0.166843i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −392608. | + | 226673.i | −1.28384 | + | 0.741223i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 370290. | − | 641360.i | 1.20214 | − | 2.08217i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −161284. | + | 279353.i | −0.519855 | + | 0.900415i | 0.479879 | + | 0.877335i | \(0.340681\pi\) |
−0.999734 | + | 0.0230804i | \(0.992653\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14300.9i | 0.0457657i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 62009.0 | + | 35800.9i | 0.197029 | + | 0.113754i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 35055.3i | − | 0.110595i | −0.998470 | − | 0.0552977i | \(-0.982389\pi\) | ||
0.998470 | − | 0.0552977i | \(-0.0176108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −157368. | + | 90856.2i | −0.492968 | + | 0.284615i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 98841.2 | + | 171198.i | 0.307448 | + | 0.532516i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 510214.i | − | 1.57590i | −0.615742 | − | 0.787948i | \(-0.711144\pi\) | ||
0.615742 | − | 0.787948i | \(-0.288856\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −191075. | −0.586047 | −0.293023 | − | 0.956105i | \(-0.594661\pi\) | ||||
−0.293023 | + | 0.956105i | \(0.594661\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 93909.0 | − | 54218.4i | 0.286021 | − | 0.165134i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 196533. | + | 340404.i | 0.594428 | + | 1.02958i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −397878. | −1.19508 | −0.597542 | − | 0.801838i | \(-0.703856\pi\) | ||||
−0.597542 | + | 0.801838i | \(0.703856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 122062. | − | 211418.i | 0.364103 | − | 0.630645i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 147142. | 0.435897 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −43397.0 | − | 25055.3i | −0.127680 | − | 0.0737161i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −32170.0 | − | 18573.4i | −0.0940026 | − | 0.0542724i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −294687. | − | 510414.i | −0.855235 | − | 1.48131i | −0.876427 | − | 0.481535i | \(-0.840079\pi\) |
0.0211920 | − | 0.999775i | \(-0.493254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31627.3 | + | 70805.2i | 0.0911658 | + | 0.204096i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 349115. | − | 201562.i | 0.999526 | − | 0.577077i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −153979. | + | 266700.i | −0.437878 | + | 0.758426i | −0.997526 | − | 0.0703041i | \(-0.977603\pi\) |
0.559648 | + | 0.828730i | \(0.310936\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −556393. | + | 963701.i | −1.57162 | + | 2.72213i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 71587.0i | − | 0.200856i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 529620. | + | 305776.i | 1.47608 | + | 0.852217i | 0.999636 | − | 0.0269863i | \(-0.00859106\pi\) |
0.476447 | + | 0.879203i | \(0.341924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 374521.i | − | 1.03688i | −0.855115 | − | 0.518439i | \(-0.826513\pi\) | ||
0.855115 | − | 0.518439i | \(-0.173487\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 220564. | − | 127343.i | 0.606596 | − | 0.350218i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −290126. | − | 502513.i | −0.792640 | − | 1.37289i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 66013.3i | − | 0.179165i | −0.995979 | − | 0.0895827i | \(-0.971447\pi\) | ||
0.995979 | − | 0.0895827i | \(-0.0285533\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.10056e6 | 2.96743 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18785.2 | − | 10845.7i | 0.0503193 | − | 0.0290518i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18704.7 | + | 32397.6i | 0.0497772 | + | 0.0862167i | 0.889840 | − | 0.456272i | \(-0.150816\pi\) |
−0.840063 | + | 0.542489i | \(0.817482\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 465690. | 1.23125 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 56603.6 | − | 98040.4i | 0.148687 | − | 0.257534i | −0.782055 | − | 0.623209i | \(-0.785829\pi\) |
0.930743 | + | 0.365675i | \(0.119162\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 313267. | 0.817586 | 0.408793 | − | 0.912627i | \(-0.365950\pi\) | ||||
0.408793 | + | 0.912627i | \(0.365950\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 368207. | + | 212585.i | 0.954793 | + | 0.551250i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −319541. | − | 184487.i | −0.823286 | − | 0.475324i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 32392.2 | + | 56105.0i | 0.0829241 | + | 0.143629i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 28989.6 | − | 40002.6i | 0.0737406 | − | 0.101754i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 554475. | − | 320126.i | 1.40146 | − | 0.809133i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −246290. | + | 426586.i | −0.618568 | + | 1.07139i | 0.371180 | + | 0.928561i | \(0.378953\pi\) |
−0.989747 | + | 0.142830i | \(0.954380\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 66516.4 | − | 115210.i | 0.166005 | − | 0.287529i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 777791.i | 1.92893i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2411.54 | − | 1392.30i | −0.00594314 | − | 0.00343127i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 516415.i | 1.26473i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −168128. | + | 97068.9i | −0.409190 | + | 0.236246i | −0.690441 | − | 0.723388i | \(-0.742584\pi\) |
0.281252 | + | 0.959634i | \(0.409250\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43796.5 | − | 75857.7i | −0.105930 | − | 0.183475i | 0.808188 | − | 0.588925i | \(-0.200448\pi\) |
−0.914118 | + | 0.405449i | \(0.867115\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.38923e6i | 3.33930i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −636027. | −1.51938 | −0.759690 | − | 0.650285i | \(-0.774650\pi\) | ||||
−0.759690 | + | 0.650285i | \(0.774650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19201.3 | + | 11085.9i | −0.0455869 | + | 0.0263196i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −87044.4 | − | 150765.i | −0.205390 | − | 0.355745i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 46609.6 | 0.109307 | 0.0546536 | − | 0.998505i | \(-0.482595\pi\) | ||||
0.0546536 | + | 0.998505i | \(0.482595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 366620. | − | 635004.i | 0.854542 | − | 1.48011i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.23344e6 | −2.85750 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −577704. | − | 333537.i | −1.33025 | − | 0.768022i | −0.344915 | − | 0.938634i | \(-0.612092\pi\) |
−0.985338 | + | 0.170612i | \(0.945426\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 387846. | + | 223923.i | 0.887681 | + | 0.512503i | 0.873183 | − | 0.487392i | \(-0.162052\pi\) |
0.0144975 | + | 0.999895i | \(0.495385\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24750.6 | − | 42869.3i | −0.0563066 | − | 0.0975258i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 621692. | + | 450536.i | 1.40583 | + | 1.01879i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 479906. | − | 277074.i | 1.07871 | − | 0.622793i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −649685. | + | 1.12529e6i | −1.45161 | + | 2.51427i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13259.5 | + | 22966.1i | −0.0294497 | + | 0.0510084i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 146080.i | − | 0.322522i | −0.986912 | − | 0.161261i | \(-0.948444\pi\) | ||
0.986912 | − | 0.161261i | \(-0.0515561\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −869202. | − | 501834.i | −1.90771 | − | 1.10142i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 383372.i | − | 0.836456i | −0.908342 | − | 0.418228i | \(-0.862651\pi\) | ||
0.908342 | − | 0.418228i | \(-0.137349\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 561367. | − | 324105.i | 1.21761 | − | 0.702986i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −400442. | − | 693586.i | −0.863466 | − | 1.49557i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 828560.i | 1.77616i | 0.459687 | + | 0.888081i | \(0.347962\pi\) | ||||
−0.459687 | + | 0.888081i | \(0.652038\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 759434. | 1.61849 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −362359. | + | 209208.i | −0.767760 | + | 0.443266i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17321.7 | + | 30002.1i | 0.0364882 | + | 0.0631995i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −734197. | −1.53765 | −0.768824 | − | 0.639461i | \(-0.779158\pi\) | ||||
−0.768824 | + | 0.639461i | \(0.779158\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −35975.3 | + | 62311.1i | −0.0749097 | + | 0.129747i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 600322. | 1.24284 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 348664. | + | 201301.i | 0.717699 | + | 0.414363i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −788053. | − | 454982.i | −1.61288 | − | 0.931194i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −86328.7 | − | 149526.i | −0.175679 | − | 0.304284i | 0.764717 | − | 0.644366i | \(-0.222879\pi\) |
−0.940396 | + | 0.340082i | \(0.889545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −180164. | − | 403340.i | −0.364551 | − | 0.816132i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.82485e6 | − | 1.05358e6i | 3.67155 | − | 2.11977i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 251088. | − | 434896.i | 0.502327 | − | 0.870056i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 81982.8 | − | 141998.i | 0.163091 | − | 0.282482i | −0.772885 | − | 0.634547i | \(-0.781187\pi\) |
0.935976 | + | 0.352064i | \(0.114520\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.27095e6i | − | 2.51414i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −75912.1 | − | 43827.9i | −0.149325 | − | 0.0862127i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2237.45i | − | 0.00437665i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −243911. | + | 140822.i | −0.474453 | + | 0.273925i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −309781. | − | 536556.i | −0.599234 | − | 1.03790i | −0.992934 | − | 0.118665i | \(-0.962138\pi\) |
0.393700 | − | 0.919239i | \(-0.371195\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 834118.i | − | 1.60456i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −900475. | −1.72264 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.13288e6 | + | 654069.i | −2.15530 | + | 1.24436i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −95900.8 | − | 166105.i | −0.181449 | − | 0.314278i | 0.760925 | − | 0.648839i | \(-0.224745\pi\) |
−0.942374 | + | 0.334561i | \(0.891412\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 727449. | 1.36882 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −600516. | + | 1.04012e6i | −1.12380 | + | 1.94648i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 589533. | 1.09724 | 0.548618 | − | 0.836073i | \(-0.315154\pi\) | ||||
0.548618 | + | 0.836073i | \(0.315154\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −234264. | − | 135252.i | −0.433642 | − | 0.250363i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13285.2 | + | 7670.19i | 0.0244586 | + | 0.0141212i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 415929. | + | 720409.i | 0.761605 | + | 1.31914i | 0.942023 | + | 0.335549i | \(0.108922\pi\) |
−0.180418 | + | 0.983590i | \(0.557745\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31184.3 | + | 13929.4i | −0.0567936 | + | 0.0253686i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 79675.6 | − | 46000.7i | 0.144327 | − | 0.0833273i | −0.426098 | − | 0.904677i | \(-0.640112\pi\) |
0.570425 | + | 0.821350i | \(0.306779\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 251783. | − | 436101.i | 0.453643 | − | 0.785733i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −206256. | + | 357246.i | −0.369628 | + | 0.640215i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 56785.4i | − | 0.101221i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −807256. | − | 466069.i | −1.43130 | − | 0.826362i | −0.434082 | − | 0.900874i | \(-0.642927\pi\) |
−0.997220 | + | 0.0745111i | \(0.976260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 410965.i | − | 0.724794i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −487316. | + | 281352.i | −0.854904 | + | 0.493579i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 286555. | + | 496329.i | 0.500054 | + | 0.866119i | 1.00000 | 6.22515e-5i | \(1.98153e-5\pi\) | |
−0.499946 | + | 0.866057i | \(0.666647\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 55841.8i | 0.0969340i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 250379. | 0.432342 | 0.216171 | − | 0.976355i | \(-0.430643\pi\) | ||||
0.216171 | + | 0.976355i | \(0.430643\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −144233. | + | 83272.8i | −0.247751 | + | 0.143039i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.55985e6 | − | 2.70173e6i | −2.66538 | − | 4.61657i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15328.2 | 0.0260556 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −330979. | + | 573272.i | −0.559690 | + | 0.969411i | 0.437832 | + | 0.899057i | \(0.355746\pi\) |
−0.997522 | + | 0.0703546i | \(0.977587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 766109. | 1.28879 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −519862. | − | 300143.i | −0.870020 | − | 0.502306i | −0.00266520 | − | 0.999996i | \(-0.500848\pi\) |
−0.867355 | + | 0.497690i | \(0.834182\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 179201. | + | 103461.i | 0.298357 | + | 0.172256i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 495846. | + | 858831.i | 0.821306 | + | 1.42254i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 163003. | − | 224927.i | 0.268609 | − | 0.370652i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26937.8 | + | 15552.5i | −0.0441632 | + | 0.0254976i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −707490. | + | 1.22541e6i | −1.15398 | + | 1.99875i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −249023. | + | 431320.i | −0.404110 | + | 0.699940i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 51876.0i | − | 0.0837563i | −0.999123 | − | 0.0418781i | \(-0.986666\pi\) | ||
0.999123 | − | 0.0418781i | \(-0.0133341\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 43213.5 | + | 24949.3i | 0.0694170 | + | 0.0400779i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 243327.i | − | 0.388899i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15877.4 | − | 9166.81i | 0.0252483 | − | 0.0145771i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.68268e6 | + | 2.91449e6i | 2.66237 | + | 4.61136i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 532921.i | 0.838969i | 0.907762 | + | 0.419485i | \(0.137789\pi\) | ||||
−0.907762 | + | 0.419485i | \(0.862211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.82170e6 | 2.85354 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 895833. | − | 517209.i | 1.39625 | − | 0.806123i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37146.6 | − | 64339.8i | −0.0576087 | − | 0.0997812i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −867855. | −1.33923 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 129732. | − | 224703.i | 0.199205 | − | 0.345034i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −253863. | −0.387884 | −0.193942 | − | 0.981013i | \(-0.562127\pi\) | ||||
−0.193942 | + | 0.981013i | \(0.562127\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45687.4 | + | 26377.7i | 0.0694632 | + | 0.0401046i | 0.534329 | − | 0.845276i | \(-0.320564\pi\) |
−0.464866 | + | 0.885381i | \(0.653898\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 270998. | + | 156461.i | 0.410002 | + | 0.236715i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 591481. | + | 1.02448e6i | 0.890483 | + | 1.54236i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 670994. | + | 486264.i | 1.00525 | + | 0.728498i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 43078.2 | − | 24871.2i | 0.0642228 | − | 0.0370791i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −432787. | + | 749609.i | −0.642078 | + | 1.11211i | 0.342890 | + | 0.939376i | \(0.388594\pi\) |
−0.984968 | + | 0.172737i | \(0.944739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 564220. | − | 977258.i | 0.833008 | − | 1.44281i | −0.0626344 | − | 0.998037i | \(-0.519950\pi\) |
0.895642 | − | 0.444775i | \(-0.146716\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 131822.i | − | 0.193678i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −878302. | − | 507088.i | −1.28420 | − | 0.741434i | −0.306587 | − | 0.951843i | \(-0.599187\pi\) |
−0.977614 | + | 0.210409i | \(0.932521\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 561580.i | 0.817152i | 0.912724 | + | 0.408576i | \(0.133975\pi\) | ||||
−0.912724 | + | 0.408576i | \(0.866025\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 321172. | − | 185429.i | 0.465089 | − | 0.268519i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −116930. | − | 202528.i | −0.168514 | − | 0.291874i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 960998.i | − | 1.37832i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 223824. | 0.319488 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −647385. | + | 373768.i | −0.919685 | + | 0.530980i | −0.883534 | − | 0.468366i | \(-0.844843\pi\) |
−0.0361502 | + | 0.999346i | \(0.511509\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 568472. | + | 984622.i | 0.803742 | + | 1.39212i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 106535. | 0.149913 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 568348. | − | 984408.i | 0.795978 | − | 1.37867i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 777002. | 1.08307 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.25741e6 | − | 725968.i | −1.74447 | − | 1.00717i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 432432. | + | 249664.i | 0.597115 | + | 0.344745i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −190927. | − | 330696.i | −0.262404 | − | 0.454496i | 0.704477 | − | 0.709727i | \(-0.251182\pi\) |
−0.966880 | + | 0.255231i | \(0.917849\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.96531e6 | + | 877869.i | −2.68844 | + | 1.20087i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.10306e6 | − | 636854.i | 1.50189 | − | 0.867119i | 0.501896 | − | 0.864928i | \(-0.332636\pi\) |
0.999998 | − | 0.00219068i | \(-0.000697317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 235569. | − | 408017.i | 0.319250 | − | 0.552957i | −0.661082 | − | 0.750314i | \(-0.729902\pi\) |
0.980332 | + | 0.197357i | \(0.0632357\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −311797. | + | 540049.i | −0.420597 | + | 0.728495i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 25220.7i | − | 0.0338638i | −0.999857 | − | 0.0169319i | \(-0.994610\pi\) | ||
0.999857 | − | 0.0169319i | \(-0.00538985\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.05625e6 | − | 609827.i | −1.41168 | − | 0.815031i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2.88892e6i | − | 3.84323i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66296.8 | − | 38276.5i | 0.0877916 | − | 0.0506865i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5302.71 | − | 9184.57i | −0.00698975 | − | 0.0121066i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.81726e6i | 2.38445i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 719428. | 0.939662 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 883407. | − | 510035.i | 1.14858 | − | 0.663134i | 0.200040 | − | 0.979788i | \(-0.435893\pi\) |
0.948541 | + | 0.316654i | \(0.102559\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 836140. | + | 1.44824e6i | 1.08218 | + | 1.87440i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.23116e6 | −1.58621 | −0.793107 | − | 0.609082i | \(-0.791538\pi\) | ||||
−0.793107 | + | 0.609082i | \(0.791538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −225170. | + | 390006.i | −0.288794 | + | 0.500207i | −0.973522 | − | 0.228592i | \(-0.926588\pi\) |
0.684728 | + | 0.728799i | \(0.259921\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.48903e6 | 1.90115 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 82480.8 | + | 47620.3i | 0.104835 | + | 0.0605264i | 0.551501 | − | 0.834174i | \(-0.314055\pi\) |
−0.446666 | + | 0.894701i | \(0.647389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −901985. | − | 520761.i | −1.14129 | − | 0.658924i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16690.6 | − | 28908.9i | −0.0210240 | − | 0.0364146i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 129867. | − | 1.25017e6i | 0.162853 | − | 1.56772i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.09141e6 | + | 630128.i | −1.36252 | + | 0.786652i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19302.9 | − | 33433.5i | 0.0239904 | − | 0.0415525i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 145861. | − | 252639.i | 0.180476 | − | 0.312594i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.90946e6i | 3.58396i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.61106e6 | − | 930144.i | −1.97577 | − | 1.14071i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 134964.i | − | 0.164787i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −780267. | + | 450487.i | −0.948481 | + | 0.547606i | −0.892609 | − | 0.450832i | \(-0.851127\pi\) |
−0.0558723 | + | 0.998438i | \(0.517794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 703923. | + | 1.21923e6i | 0.851918 | + | 1.47556i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 317691.i | − | 0.382797i | −0.981512 | − | 0.191398i | \(-0.938698\pi\) | ||
0.981512 | − | 0.191398i | \(-0.0613022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24846.7 | −0.0298076 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.54237e6 | − | 890490.i | 1.84225 | − | 1.06362i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 490932. | + | 850319.i | 0.583825 | + | 1.01121i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −371224. | −0.439547 | −0.219774 | − | 0.975551i | \(-0.570532\pi\) | ||||
−0.219774 | + | 0.975551i | \(0.570532\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −324689. | + | 562377.i | −0.382779 | + | 0.662993i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21504.2 | 0.0252418 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.02081e6 | − | 589366.i | −1.19306 | − | 0.688813i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.02515e6 | + | 1.16922e6i | 2.35667 | + | 1.36062i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31626.7 | − | 54779.0i | −0.0366456 | − | 0.0634721i | 0.847121 | − | 0.531400i | \(-0.178334\pi\) |
−0.883767 | + | 0.467928i | \(0.845001\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −147324. | + | 65807.1i | −0.169971 | + | 0.0759230i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 824235. | − | 475873.i | 0.946865 | − | 0.546673i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 93953.8 | − | 162733.i | 0.107471 | − | 0.186145i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −578958. | + | 1.00279e6i | −0.659429 | + | 1.14216i | 0.321335 | + | 0.946966i | \(0.395869\pi\) |
−0.980764 | + | 0.195199i | \(0.937465\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2.65366e6i | − | 3.00964i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −295283. | − | 170482.i | −0.333472 | − | 0.192530i | 0.323910 | − | 0.946088i | \(-0.395003\pi\) |
−0.657381 | + | 0.753558i | \(0.728336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 313987.i | 0.353093i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.91912e6 | − | 1.10801e6i | 2.14901 | − | 1.24073i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −236902. | − | 410326.i | −0.264161 | − | 0.457541i | 0.703182 | − | 0.711010i | \(-0.251762\pi\) |
−0.967344 | + | 0.253469i | \(0.918428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51361.9i | 0.0570307i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −458125. | −0.506550 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 305054. | − | 176123.i | 0.335885 | − | 0.193923i | −0.322566 | − | 0.946547i | \(-0.604545\pi\) |
0.658451 | + | 0.752624i | \(0.271212\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −142288. | − | 246449.i | −0.156013 | − | 0.270222i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −185844. | −0.202920 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −508470. | + | 880696.i | −0.552877 | + | 0.957611i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 877376. | 0.950034 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 137869. | + | 79598.8i | 0.148667 | + | 0.0858329i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −554833. | − | 320333.i | −0.595810 | − | 0.343991i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −342618. | − | 593431.i | −0.366401 | − | 0.634626i | 0.622599 | − | 0.782541i | \(-0.286077\pi\) |
−0.989000 | + | 0.147916i | \(0.952744\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.85299e6 | − | 296367.i | −3.03846 | − | 0.315633i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −114126. | + | 65890.5i | −0.121045 | + | 0.0698851i | −0.559300 | − | 0.828965i | \(-0.688930\pi\) |
0.438255 | + | 0.898851i | \(0.355597\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −401939. | + | 696179.i | −0.424555 | + | 0.735352i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −45566.9 | + | 78924.2i | −0.0479336 | + | 0.0830235i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 853791.i | − | 0.894463i | −0.894418 | − | 0.447231i | \(-0.852410\pi\) | ||
0.894418 | − | 0.447231i | \(-0.147590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53958.5 | + | 31152.9i | 0.0562981 | + | 0.0325038i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 466910.i | − | 0.485172i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −63978.8 | + | 36938.2i | −0.0662108 | + | 0.0382268i | −0.532740 | − | 0.846279i | \(-0.678838\pi\) |
0.466529 | + | 0.884506i | \(0.345504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −528967. | − | 916198.i | −0.545201 | − | 0.944315i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.82165e6i | 2.89646i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −936677. | −0.957629 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.57948e6 | + | 911914.i | −1.60830 | + | 0.928553i | −0.618550 | + | 0.785745i | \(0.712280\pi\) |
−0.989750 | + | 0.142808i | \(0.954387\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −479767. | − | 830981.i | −0.486555 | − | 0.842738i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −187869. | −0.189762 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 639728. | − | 1.10804e6i | 0.643583 | − | 1.11472i | −0.341043 | − | 0.940048i | \(-0.610780\pi\) |
0.984627 | − | 0.174672i | \(-0.0558864\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.27501e6 | −1.27756 |
(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 | 76.5.h.a.69.1 | yes | 12 | |
3.2 | odd | 2 | 684.5.y.c.145.1 | 12 | |||
4.3 | odd | 2 | 304.5.r.b.145.6 | 12 | |||
19.8 | odd | 6 | inner | 76.5.h.a.65.1 | ✓ | 12 | |
57.8 | even | 6 | 684.5.y.c.217.1 | 12 | |||
76.27 | even | 6 | 304.5.r.b.65.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.h.a.65.1 | ✓ | 12 | 19.8 | odd | 6 | inner | |
76.5.h.a.69.1 | yes | 12 | 1.1 | even | 1 | trivial | |
304.5.r.b.65.6 | 12 | 76.27 | even | 6 | |||
304.5.r.b.145.6 | 12 | 4.3 | odd | 2 | |||
684.5.y.c.145.1 | 12 | 3.2 | odd | 2 | |||
684.5.y.c.217.1 | 12 | 57.8 | even | 6 |