Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [471,6,Mod(1,471)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(471, 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("471.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.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: | \(75.5407791319\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 471.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.614444 | 0.108619 | 0.0543097 | − | 0.998524i | \(-0.482704\pi\) | ||||
0.0543097 | + | 0.998524i | \(0.482704\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −31.6225 | −0.988202 | ||||||||
\(5\) | −56.4863 | −1.01046 | −0.505229 | − | 0.862985i | \(-0.668592\pi\) | ||||
−0.505229 | + | 0.862985i | \(0.668592\pi\) | |||||||
\(6\) | −5.52999 | −0.0627114 | ||||||||
\(7\) | −140.573 | −1.08432 | −0.542160 | − | 0.840275i | \(-0.682393\pi\) | ||||
−0.542160 | + | 0.840275i | \(0.682393\pi\) | |||||||
\(8\) | −39.0924 | −0.215957 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −34.7077 | −0.109755 | ||||||||
\(11\) | 344.435 | 0.858273 | 0.429137 | − | 0.903240i | \(-0.358818\pi\) | ||||
0.429137 | + | 0.903240i | \(0.358818\pi\) | |||||||
\(12\) | 284.602 | 0.570539 | ||||||||
\(13\) | −542.921 | −0.891002 | −0.445501 | − | 0.895281i | \(-0.646974\pi\) | ||||
−0.445501 | + | 0.895281i | \(0.646974\pi\) | |||||||
\(14\) | −86.3744 | −0.117778 | ||||||||
\(15\) | 508.377 | 0.583388 | ||||||||
\(16\) | 987.899 | 0.964745 | ||||||||
\(17\) | 1201.70 | 1.00849 | 0.504246 | − | 0.863560i | \(-0.331770\pi\) | ||||
0.504246 | + | 0.863560i | \(0.331770\pi\) | |||||||
\(18\) | 49.7699 | 0.0362064 | ||||||||
\(19\) | −1138.01 | −0.723205 | −0.361602 | − | 0.932332i | \(-0.617770\pi\) | ||||
−0.361602 | + | 0.932332i | \(0.617770\pi\) | |||||||
\(20\) | 1786.24 | 0.998537 | ||||||||
\(21\) | 1265.16 | 0.626033 | ||||||||
\(22\) | 211.636 | 0.0932250 | ||||||||
\(23\) | 3550.17 | 1.39936 | 0.699681 | − | 0.714456i | \(-0.253326\pi\) | ||||
0.699681 | + | 0.714456i | \(0.253326\pi\) | |||||||
\(24\) | 351.832 | 0.124683 | ||||||||
\(25\) | 65.7056 | 0.0210258 | ||||||||
\(26\) | −333.595 | −0.0967800 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 4445.27 | 1.07153 | ||||||||
\(29\) | 5307.12 | 1.17183 | 0.585914 | − | 0.810373i | \(-0.300736\pi\) | ||||
0.585914 | + | 0.810373i | \(0.300736\pi\) | |||||||
\(30\) | 312.369 | 0.0633672 | ||||||||
\(31\) | −4770.11 | −0.891506 | −0.445753 | − | 0.895156i | \(-0.647064\pi\) | ||||
−0.445753 | + | 0.895156i | \(0.647064\pi\) | |||||||
\(32\) | 1857.97 | 0.320747 | ||||||||
\(33\) | −3099.91 | −0.495524 | ||||||||
\(34\) | 738.375 | 0.109542 | ||||||||
\(35\) | 7940.47 | 1.09566 | ||||||||
\(36\) | −2561.42 | −0.329401 | ||||||||
\(37\) | 4227.38 | 0.507653 | 0.253826 | − | 0.967250i | \(-0.418311\pi\) | ||||
0.253826 | + | 0.967250i | \(0.418311\pi\) | |||||||
\(38\) | −699.242 | −0.0785540 | ||||||||
\(39\) | 4886.29 | 0.514420 | ||||||||
\(40\) | 2208.19 | 0.218216 | ||||||||
\(41\) | 5657.31 | 0.525594 | 0.262797 | − | 0.964851i | \(-0.415355\pi\) | ||||
0.262797 | + | 0.964851i | \(0.415355\pi\) | |||||||
\(42\) | 777.369 | 0.0679992 | ||||||||
\(43\) | 9591.77 | 0.791093 | 0.395547 | − | 0.918446i | \(-0.370555\pi\) | ||||
0.395547 | + | 0.918446i | \(0.370555\pi\) | |||||||
\(44\) | −10891.9 | −0.848147 | ||||||||
\(45\) | −4575.39 | −0.336819 | ||||||||
\(46\) | 2181.38 | 0.151998 | ||||||||
\(47\) | −2287.87 | −0.151073 | −0.0755365 | − | 0.997143i | \(-0.524067\pi\) | ||||
−0.0755365 | + | 0.997143i | \(0.524067\pi\) | |||||||
\(48\) | −8891.09 | −0.556996 | ||||||||
\(49\) | 2953.84 | 0.175751 | ||||||||
\(50\) | 40.3724 | 0.00228381 | ||||||||
\(51\) | −10815.3 | −0.582254 | ||||||||
\(52\) | 17168.5 | 0.880490 | ||||||||
\(53\) | −706.058 | −0.0345263 | −0.0172632 | − | 0.999851i | \(-0.505495\pi\) | ||||
−0.0172632 | + | 0.999851i | \(0.505495\pi\) | |||||||
\(54\) | −447.929 | −0.0209038 | ||||||||
\(55\) | −19455.9 | −0.867249 | ||||||||
\(56\) | 5495.35 | 0.234167 | ||||||||
\(57\) | 10242.1 | 0.417543 | ||||||||
\(58\) | 3260.93 | 0.127283 | ||||||||
\(59\) | 3971.04 | 0.148516 | 0.0742581 | − | 0.997239i | \(-0.476341\pi\) | ||||
0.0742581 | + | 0.997239i | \(0.476341\pi\) | |||||||
\(60\) | −16076.1 | −0.576505 | ||||||||
\(61\) | −45299.0 | −1.55871 | −0.779353 | − | 0.626585i | \(-0.784452\pi\) | ||||
−0.779353 | + | 0.626585i | \(0.784452\pi\) | |||||||
\(62\) | −2930.96 | −0.0968348 | ||||||||
\(63\) | −11386.4 | −0.361440 | ||||||||
\(64\) | −30471.1 | −0.929905 | ||||||||
\(65\) | 30667.6 | 0.900320 | ||||||||
\(66\) | −1904.72 | −0.0538235 | ||||||||
\(67\) | −19240.6 | −0.523638 | −0.261819 | − | 0.965117i | \(-0.584322\pi\) | ||||
−0.261819 | + | 0.965117i | \(0.584322\pi\) | |||||||
\(68\) | −38000.6 | −0.996595 | ||||||||
\(69\) | −31951.5 | −0.807921 | ||||||||
\(70\) | 4878.97 | 0.119010 | ||||||||
\(71\) | 55394.1 | 1.30412 | 0.652060 | − | 0.758167i | \(-0.273905\pi\) | ||||
0.652060 | + | 0.758167i | \(0.273905\pi\) | |||||||
\(72\) | −3166.49 | −0.0719857 | ||||||||
\(73\) | 7686.00 | 0.168808 | 0.0844040 | − | 0.996432i | \(-0.473101\pi\) | ||||
0.0844040 | + | 0.996432i | \(0.473101\pi\) | |||||||
\(74\) | 2597.48 | 0.0551409 | ||||||||
\(75\) | −591.350 | −0.0121392 | ||||||||
\(76\) | 35986.6 | 0.714672 | ||||||||
\(77\) | −48418.4 | −0.930643 | ||||||||
\(78\) | 3002.35 | 0.0558760 | ||||||||
\(79\) | 26082.4 | 0.470196 | 0.235098 | − | 0.971972i | \(-0.424459\pi\) | ||||
0.235098 | + | 0.971972i | \(0.424459\pi\) | |||||||
\(80\) | −55802.8 | −0.974834 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 3476.10 | 0.0570897 | ||||||||
\(83\) | −58429.4 | −0.930972 | −0.465486 | − | 0.885055i | \(-0.654120\pi\) | ||||
−0.465486 | + | 0.885055i | \(0.654120\pi\) | |||||||
\(84\) | −40007.5 | −0.618647 | ||||||||
\(85\) | −67879.5 | −1.01904 | ||||||||
\(86\) | 5893.61 | 0.0859280 | ||||||||
\(87\) | −47764.1 | −0.676555 | ||||||||
\(88\) | −13464.8 | −0.185350 | ||||||||
\(89\) | 16441.3 | 0.220019 | 0.110010 | − | 0.993931i | \(-0.464912\pi\) | ||||
0.110010 | + | 0.993931i | \(0.464912\pi\) | |||||||
\(90\) | −2811.32 | −0.0365851 | ||||||||
\(91\) | 76320.2 | 0.966132 | ||||||||
\(92\) | −112265. | −1.38285 | ||||||||
\(93\) | 42931.0 | 0.514711 | ||||||||
\(94\) | −1405.77 | −0.0164094 | ||||||||
\(95\) | 64281.9 | 0.730768 | ||||||||
\(96\) | −16721.7 | −0.185183 | ||||||||
\(97\) | −89938.8 | −0.970550 | −0.485275 | − | 0.874362i | \(-0.661280\pi\) | ||||
−0.485275 | + | 0.874362i | \(0.661280\pi\) | |||||||
\(98\) | 1814.97 | 0.0190899 | ||||||||
\(99\) | 27899.2 | 0.286091 | ||||||||
\(100\) | −2077.77 | −0.0207777 | ||||||||
\(101\) | 33404.4 | 0.325837 | 0.162918 | − | 0.986640i | \(-0.447909\pi\) | ||||
0.162918 | + | 0.986640i | \(0.447909\pi\) | |||||||
\(102\) | −6645.38 | −0.0632440 | ||||||||
\(103\) | −68265.5 | −0.634027 | −0.317014 | − | 0.948421i | \(-0.602680\pi\) | ||||
−0.317014 | + | 0.948421i | \(0.602680\pi\) | |||||||
\(104\) | 21224.1 | 0.192418 | ||||||||
\(105\) | −71464.2 | −0.632580 | ||||||||
\(106\) | −433.833 | −0.00375023 | ||||||||
\(107\) | 154111. | 1.30129 | 0.650645 | − | 0.759382i | \(-0.274498\pi\) | ||||
0.650645 | + | 0.759382i | \(0.274498\pi\) | |||||||
\(108\) | 23052.8 | 0.190180 | ||||||||
\(109\) | 155028. | 1.24981 | 0.624903 | − | 0.780702i | \(-0.285138\pi\) | ||||
0.624903 | + | 0.780702i | \(0.285138\pi\) | |||||||
\(110\) | −11954.5 | −0.0942000 | ||||||||
\(111\) | −38046.4 | −0.293093 | ||||||||
\(112\) | −138872. | −1.04609 | ||||||||
\(113\) | −29603.6 | −0.218096 | −0.109048 | − | 0.994036i | \(-0.534780\pi\) | ||||
−0.109048 | + | 0.994036i | \(0.534780\pi\) | |||||||
\(114\) | 6293.18 | 0.0453532 | ||||||||
\(115\) | −200536. | −1.41400 | ||||||||
\(116\) | −167824. | −1.15800 | ||||||||
\(117\) | −43976.6 | −0.297001 | ||||||||
\(118\) | 2439.98 | 0.0161317 | ||||||||
\(119\) | −168927. | −1.09353 | ||||||||
\(120\) | −19873.7 | −0.125987 | ||||||||
\(121\) | −42415.6 | −0.263367 | ||||||||
\(122\) | −27833.7 | −0.169306 | ||||||||
\(123\) | −50915.8 | −0.303452 | ||||||||
\(124\) | 150843. | 0.880988 | ||||||||
\(125\) | 172808. | 0.989213 | ||||||||
\(126\) | −6996.32 | −0.0392594 | ||||||||
\(127\) | −107755. | −0.592828 | −0.296414 | − | 0.955059i | \(-0.595791\pi\) | ||||
−0.296414 | + | 0.955059i | \(0.595791\pi\) | |||||||
\(128\) | −78177.7 | −0.421753 | ||||||||
\(129\) | −86326.0 | −0.456738 | ||||||||
\(130\) | 18843.5 | 0.0977922 | ||||||||
\(131\) | −193485. | −0.985076 | −0.492538 | − | 0.870291i | \(-0.663931\pi\) | ||||
−0.492538 | + | 0.870291i | \(0.663931\pi\) | |||||||
\(132\) | 98026.9 | 0.489678 | ||||||||
\(133\) | 159974. | 0.784186 | ||||||||
\(134\) | −11822.2 | −0.0568772 | ||||||||
\(135\) | 41178.5 | 0.194463 | ||||||||
\(136\) | −46977.3 | −0.217791 | ||||||||
\(137\) | −38469.5 | −0.175112 | −0.0875559 | − | 0.996160i | \(-0.527906\pi\) | ||||
−0.0875559 | + | 0.996160i | \(0.527906\pi\) | |||||||
\(138\) | −19632.4 | −0.0877559 | ||||||||
\(139\) | −140401. | −0.616359 | −0.308179 | − | 0.951328i | \(-0.599720\pi\) | ||||
−0.308179 | + | 0.951328i | \(0.599720\pi\) | |||||||
\(140\) | −251097. | −1.08273 | ||||||||
\(141\) | 20590.8 | 0.0872220 | ||||||||
\(142\) | 34036.5 | 0.141653 | ||||||||
\(143\) | −187001. | −0.764723 | ||||||||
\(144\) | 80019.8 | 0.321582 | ||||||||
\(145\) | −299780. | −1.18408 | ||||||||
\(146\) | 4722.61 | 0.0183358 | ||||||||
\(147\) | −26584.6 | −0.101470 | ||||||||
\(148\) | −133680. | −0.501663 | ||||||||
\(149\) | 67519.5 | 0.249151 | 0.124576 | − | 0.992210i | \(-0.460243\pi\) | ||||
0.124576 | + | 0.992210i | \(0.460243\pi\) | |||||||
\(150\) | −363.351 | −0.00131856 | ||||||||
\(151\) | 467866. | 1.66985 | 0.834927 | − | 0.550360i | \(-0.185510\pi\) | ||||
0.834927 | + | 0.550360i | \(0.185510\pi\) | |||||||
\(152\) | 44487.5 | 0.156181 | ||||||||
\(153\) | 97337.5 | 0.336164 | ||||||||
\(154\) | −29750.3 | −0.101086 | ||||||||
\(155\) | 269446. | 0.900830 | ||||||||
\(156\) | −154517. | −0.508351 | ||||||||
\(157\) | −24649.0 | −0.0798087 | ||||||||
\(158\) | 16026.1 | 0.0510724 | ||||||||
\(159\) | 6354.52 | 0.0199338 | ||||||||
\(160\) | −104950. | −0.324101 | ||||||||
\(161\) | −499059. | −1.51736 | ||||||||
\(162\) | 4031.36 | 0.0120688 | ||||||||
\(163\) | 68283.4 | 0.201301 | 0.100650 | − | 0.994922i | \(-0.467908\pi\) | ||||
0.100650 | + | 0.994922i | \(0.467908\pi\) | |||||||
\(164\) | −178898. | −0.519393 | ||||||||
\(165\) | 175103. | 0.500707 | ||||||||
\(166\) | −35901.6 | −0.101122 | ||||||||
\(167\) | 480226. | 1.33246 | 0.666230 | − | 0.745746i | \(-0.267907\pi\) | ||||
0.666230 | + | 0.745746i | \(0.267907\pi\) | |||||||
\(168\) | −49458.1 | −0.135196 | ||||||||
\(169\) | −76529.3 | −0.206116 | ||||||||
\(170\) | −41708.1 | −0.110687 | ||||||||
\(171\) | −92178.7 | −0.241068 | ||||||||
\(172\) | −303315. | −0.781760 | ||||||||
\(173\) | 232724. | 0.591188 | 0.295594 | − | 0.955314i | \(-0.404482\pi\) | ||||
0.295594 | + | 0.955314i | \(0.404482\pi\) | |||||||
\(174\) | −29348.3 | −0.0734869 | ||||||||
\(175\) | −9236.45 | −0.0227987 | ||||||||
\(176\) | 340267. | 0.828014 | ||||||||
\(177\) | −35739.3 | −0.0857459 | ||||||||
\(178\) | 10102.3 | 0.0238984 | ||||||||
\(179\) | −16060.7 | −0.0374656 | −0.0187328 | − | 0.999825i | \(-0.505963\pi\) | ||||
−0.0187328 | + | 0.999825i | \(0.505963\pi\) | |||||||
\(180\) | 144685. | 0.332846 | ||||||||
\(181\) | 302428. | 0.686161 | 0.343080 | − | 0.939306i | \(-0.388530\pi\) | ||||
0.343080 | + | 0.939306i | \(0.388530\pi\) | |||||||
\(182\) | 46894.5 | 0.104941 | ||||||||
\(183\) | 407691. | 0.899919 | ||||||||
\(184\) | −138785. | −0.302202 | ||||||||
\(185\) | −238789. | −0.512962 | ||||||||
\(186\) | 26378.7 | 0.0559076 | ||||||||
\(187\) | 413907. | 0.865562 | ||||||||
\(188\) | 72348.1 | 0.149291 | ||||||||
\(189\) | 102478. | 0.208678 | ||||||||
\(190\) | 39497.6 | 0.0793756 | ||||||||
\(191\) | −406930. | −0.807116 | −0.403558 | − | 0.914954i | \(-0.632227\pi\) | ||||
−0.403558 | + | 0.914954i | \(0.632227\pi\) | |||||||
\(192\) | 274240. | 0.536881 | ||||||||
\(193\) | −722066. | −1.39535 | −0.697676 | − | 0.716414i | \(-0.745782\pi\) | ||||
−0.697676 | + | 0.716414i | \(0.745782\pi\) | |||||||
\(194\) | −55262.3 | −0.105420 | ||||||||
\(195\) | −276009. | −0.519800 | ||||||||
\(196\) | −93407.8 | −0.173677 | ||||||||
\(197\) | 678698. | 1.24598 | 0.622990 | − | 0.782230i | \(-0.285918\pi\) | ||||
0.622990 | + | 0.782230i | \(0.285918\pi\) | |||||||
\(198\) | 17142.5 | 0.0310750 | ||||||||
\(199\) | −735695. | −1.31694 | −0.658469 | − | 0.752608i | \(-0.728796\pi\) | ||||
−0.658469 | + | 0.752608i | \(0.728796\pi\) | |||||||
\(200\) | −2568.59 | −0.00454067 | ||||||||
\(201\) | 173165. | 0.302322 | ||||||||
\(202\) | 20525.1 | 0.0353922 | ||||||||
\(203\) | −746039. | −1.27064 | ||||||||
\(204\) | 342006. | 0.575384 | ||||||||
\(205\) | −319561. | −0.531091 | ||||||||
\(206\) | −41945.3 | −0.0688676 | ||||||||
\(207\) | 287564. | 0.466454 | ||||||||
\(208\) | −536351. | −0.859589 | ||||||||
\(209\) | −391970. | −0.620707 | ||||||||
\(210\) | −43910.7 | −0.0687104 | ||||||||
\(211\) | −98424.3 | −0.152194 | −0.0760968 | − | 0.997100i | \(-0.524246\pi\) | ||||
−0.0760968 | + | 0.997100i | \(0.524246\pi\) | |||||||
\(212\) | 22327.3 | 0.0341190 | ||||||||
\(213\) | −498547. | −0.752934 | ||||||||
\(214\) | 94692.6 | 0.141345 | ||||||||
\(215\) | −541804. | −0.799367 | ||||||||
\(216\) | 28498.4 | 0.0415610 | ||||||||
\(217\) | 670550. | 0.966678 | ||||||||
\(218\) | 95255.7 | 0.135753 | ||||||||
\(219\) | −69174.0 | −0.0974614 | ||||||||
\(220\) | 615242. | 0.857017 | ||||||||
\(221\) | −652427. | −0.898569 | ||||||||
\(222\) | −23377.4 | −0.0318356 | ||||||||
\(223\) | −1.26864e6 | −1.70834 | −0.854171 | − | 0.519992i | \(-0.825935\pi\) | ||||
−0.854171 | + | 0.519992i | \(0.825935\pi\) | |||||||
\(224\) | −261180. | −0.347793 | ||||||||
\(225\) | 5322.15 | 0.00700860 | ||||||||
\(226\) | −18189.8 | −0.0236895 | ||||||||
\(227\) | −263274. | −0.339112 | −0.169556 | − | 0.985521i | \(-0.554233\pi\) | ||||
−0.169556 | + | 0.985521i | \(0.554233\pi\) | |||||||
\(228\) | −323880. | −0.412616 | ||||||||
\(229\) | −950204. | −1.19737 | −0.598685 | − | 0.800985i | \(-0.704310\pi\) | ||||
−0.598685 | + | 0.800985i | \(0.704310\pi\) | |||||||
\(230\) | −123218. | −0.153587 | ||||||||
\(231\) | 435765. | 0.537307 | ||||||||
\(232\) | −207468. | −0.253065 | ||||||||
\(233\) | 1.31533e6 | 1.58725 | 0.793626 | − | 0.608406i | \(-0.208191\pi\) | ||||
0.793626 | + | 0.608406i | \(0.208191\pi\) | |||||||
\(234\) | −27021.2 | −0.0322600 | ||||||||
\(235\) | 129233. | 0.152653 | ||||||||
\(236\) | −125574. | −0.146764 | ||||||||
\(237\) | −234741. | −0.271468 | ||||||||
\(238\) | −103796. | −0.118778 | ||||||||
\(239\) | −1.53549e6 | −1.73881 | −0.869403 | − | 0.494104i | \(-0.835496\pi\) | ||||
−0.869403 | + | 0.494104i | \(0.835496\pi\) | |||||||
\(240\) | 502225. | 0.562821 | ||||||||
\(241\) | 876339. | 0.971918 | 0.485959 | − | 0.873982i | \(-0.338470\pi\) | ||||
0.485959 | + | 0.873982i | \(0.338470\pi\) | |||||||
\(242\) | −26062.0 | −0.0286068 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 1.43247e6 | 1.54032 | ||||||||
\(245\) | −166852. | −0.177589 | ||||||||
\(246\) | −31284.9 | −0.0329607 | ||||||||
\(247\) | 617849. | 0.644377 | ||||||||
\(248\) | 186475. | 0.192527 | ||||||||
\(249\) | 525865. | 0.537497 | ||||||||
\(250\) | 106181. | 0.107448 | ||||||||
\(251\) | 295424. | 0.295979 | 0.147990 | − | 0.988989i | \(-0.452720\pi\) | ||||
0.147990 | + | 0.988989i | \(0.452720\pi\) | |||||||
\(252\) | 360067. | 0.357176 | ||||||||
\(253\) | 1.22280e6 | 1.20103 | ||||||||
\(254\) | −66209.5 | −0.0643926 | ||||||||
\(255\) | 610915. | 0.588343 | ||||||||
\(256\) | 927041. | 0.884095 | ||||||||
\(257\) | −867807. | −0.819578 | −0.409789 | − | 0.912180i | \(-0.634398\pi\) | ||||
−0.409789 | + | 0.912180i | \(0.634398\pi\) | |||||||
\(258\) | −53042.4 | −0.0496106 | ||||||||
\(259\) | −594256. | −0.550458 | ||||||||
\(260\) | −969786. | −0.889698 | ||||||||
\(261\) | 429877. | 0.390609 | ||||||||
\(262\) | −118886. | −0.106998 | ||||||||
\(263\) | 162256. | 0.144648 | 0.0723239 | − | 0.997381i | \(-0.476958\pi\) | ||||
0.0723239 | + | 0.997381i | \(0.476958\pi\) | |||||||
\(264\) | 121183. | 0.107012 | ||||||||
\(265\) | 39882.6 | 0.0348874 | ||||||||
\(266\) | 98294.7 | 0.0851777 | ||||||||
\(267\) | −147972. | −0.127028 | ||||||||
\(268\) | 608434. | 0.517460 | ||||||||
\(269\) | 59710.7 | 0.0503119 | 0.0251560 | − | 0.999684i | \(-0.491992\pi\) | ||||
0.0251560 | + | 0.999684i | \(0.491992\pi\) | |||||||
\(270\) | 25301.9 | 0.0211224 | ||||||||
\(271\) | 1.18076e6 | 0.976647 | 0.488324 | − | 0.872663i | \(-0.337609\pi\) | ||||
0.488324 | + | 0.872663i | \(0.337609\pi\) | |||||||
\(272\) | 1.18716e6 | 0.972938 | ||||||||
\(273\) | −686882. | −0.557796 | ||||||||
\(274\) | −23637.3 | −0.0190205 | ||||||||
\(275\) | 22631.3 | 0.0180459 | ||||||||
\(276\) | 1.01039e6 | 0.798389 | ||||||||
\(277\) | −638733. | −0.500172 | −0.250086 | − | 0.968224i | \(-0.580459\pi\) | ||||
−0.250086 | + | 0.968224i | \(0.580459\pi\) | |||||||
\(278\) | −86268.6 | −0.0669485 | ||||||||
\(279\) | −386379. | −0.297169 | ||||||||
\(280\) | −310412. | −0.236616 | ||||||||
\(281\) | 1.22272e6 | 0.923762 | 0.461881 | − | 0.886942i | \(-0.347175\pi\) | ||||
0.461881 | + | 0.886942i | \(0.347175\pi\) | |||||||
\(282\) | 12651.9 | 0.00947400 | ||||||||
\(283\) | 917909. | 0.681292 | 0.340646 | − | 0.940192i | \(-0.389354\pi\) | ||||
0.340646 | + | 0.940192i | \(0.389354\pi\) | |||||||
\(284\) | −1.75170e6 | −1.28873 | ||||||||
\(285\) | −578537. | −0.421909 | ||||||||
\(286\) | −114902. | −0.0830637 | ||||||||
\(287\) | −795267. | −0.569912 | ||||||||
\(288\) | 150495. | 0.106916 | ||||||||
\(289\) | 24219.7 | 0.0170579 | ||||||||
\(290\) | −184198. | −0.128614 | ||||||||
\(291\) | 809449. | 0.560347 | ||||||||
\(292\) | −243050. | −0.166816 | ||||||||
\(293\) | −2.27112e6 | −1.54550 | −0.772752 | − | 0.634708i | \(-0.781120\pi\) | ||||
−0.772752 | + | 0.634708i | \(0.781120\pi\) | |||||||
\(294\) | −16334.7 | −0.0110216 | ||||||||
\(295\) | −224309. | −0.150069 | ||||||||
\(296\) | −165258. | −0.109631 | ||||||||
\(297\) | −251093. | −0.165175 | ||||||||
\(298\) | 41486.9 | 0.0270627 | ||||||||
\(299\) | −1.92746e6 | −1.24683 | ||||||||
\(300\) | 18700.0 | 0.0119960 | ||||||||
\(301\) | −1.34835e6 | −0.857799 | ||||||||
\(302\) | 287477. | 0.181379 | ||||||||
\(303\) | −300640. | −0.188122 | ||||||||
\(304\) | −1.12424e6 | −0.697708 | ||||||||
\(305\) | 2.55877e6 | 1.57501 | ||||||||
\(306\) | 59808.4 | 0.0365139 | ||||||||
\(307\) | 963006. | 0.583154 | 0.291577 | − | 0.956547i | \(-0.405820\pi\) | ||||
0.291577 | + | 0.956547i | \(0.405820\pi\) | |||||||
\(308\) | 1.53111e6 | 0.919663 | ||||||||
\(309\) | 614389. | 0.366056 | ||||||||
\(310\) | 165559. | 0.0978475 | ||||||||
\(311\) | 441991. | 0.259127 | 0.129563 | − | 0.991571i | \(-0.458642\pi\) | ||||
0.129563 | + | 0.991571i | \(0.458642\pi\) | |||||||
\(312\) | −191017. | −0.111093 | ||||||||
\(313\) | 873569. | 0.504007 | 0.252003 | − | 0.967726i | \(-0.418911\pi\) | ||||
0.252003 | + | 0.967726i | \(0.418911\pi\) | |||||||
\(314\) | −15145.4 | −0.00866877 | ||||||||
\(315\) | 643178. | 0.365220 | ||||||||
\(316\) | −824789. | −0.464649 | ||||||||
\(317\) | 618512. | 0.345700 | 0.172850 | − | 0.984948i | \(-0.444702\pi\) | ||||
0.172850 | + | 0.984948i | \(0.444702\pi\) | |||||||
\(318\) | 3904.50 | 0.00216520 | ||||||||
\(319\) | 1.82796e6 | 1.00575 | ||||||||
\(320\) | 1.72120e6 | 0.939631 | ||||||||
\(321\) | −1.38700e6 | −0.751301 | ||||||||
\(322\) | −306644. | −0.164814 | ||||||||
\(323\) | −1.36754e6 | −0.729347 | ||||||||
\(324\) | −207475. | −0.109800 | ||||||||
\(325\) | −35673.0 | −0.0187340 | ||||||||
\(326\) | 41956.3 | 0.0218652 | ||||||||
\(327\) | −1.39525e6 | −0.721576 | ||||||||
\(328\) | −221158. | −0.113506 | ||||||||
\(329\) | 321613. | 0.163812 | ||||||||
\(330\) | 107591. | 0.0543864 | ||||||||
\(331\) | 1.49070e6 | 0.747860 | 0.373930 | − | 0.927457i | \(-0.378010\pi\) | ||||
0.373930 | + | 0.927457i | \(0.378010\pi\) | |||||||
\(332\) | 1.84768e6 | 0.919988 | ||||||||
\(333\) | 342418. | 0.169218 | ||||||||
\(334\) | 295072. | 0.144731 | ||||||||
\(335\) | 1.08683e6 | 0.529114 | ||||||||
\(336\) | 1.24985e6 | 0.603962 | ||||||||
\(337\) | 3.78851e6 | 1.81716 | 0.908581 | − | 0.417708i | \(-0.137167\pi\) | ||||
0.908581 | + | 0.417708i | \(0.137167\pi\) | |||||||
\(338\) | −47022.9 | −0.0223881 | ||||||||
\(339\) | 266432. | 0.125918 | ||||||||
\(340\) | 2.14652e6 | 1.00702 | ||||||||
\(341\) | −1.64299e6 | −0.765156 | ||||||||
\(342\) | −56638.6 | −0.0261847 | ||||||||
\(343\) | 1.94738e6 | 0.893750 | ||||||||
\(344\) | −374966. | −0.170842 | ||||||||
\(345\) | 1.80483e6 | 0.816371 | ||||||||
\(346\) | 142996. | 0.0642144 | ||||||||
\(347\) | 1.94084e6 | 0.865297 | 0.432649 | − | 0.901563i | \(-0.357579\pi\) | ||||
0.432649 | + | 0.901563i | \(0.357579\pi\) | |||||||
\(348\) | 1.51042e6 | 0.668573 | ||||||||
\(349\) | 249412. | 0.109611 | 0.0548055 | − | 0.998497i | \(-0.482546\pi\) | ||||
0.0548055 | + | 0.998497i | \(0.482546\pi\) | |||||||
\(350\) | −5675.28 | −0.00247638 | ||||||||
\(351\) | 395790. | 0.171473 | ||||||||
\(352\) | 639948. | 0.275289 | ||||||||
\(353\) | −3.79350e6 | −1.62033 | −0.810165 | − | 0.586201i | \(-0.800623\pi\) | ||||
−0.810165 | + | 0.586201i | \(0.800623\pi\) | |||||||
\(354\) | −21959.8 | −0.00931366 | ||||||||
\(355\) | −3.12901e6 | −1.31776 | ||||||||
\(356\) | −519914. | −0.217424 | ||||||||
\(357\) | 1.52034e6 | 0.631350 | ||||||||
\(358\) | −9868.42 | −0.00406949 | ||||||||
\(359\) | −874422. | −0.358084 | −0.179042 | − | 0.983841i | \(-0.557300\pi\) | ||||
−0.179042 | + | 0.983841i | \(0.557300\pi\) | |||||||
\(360\) | 178863. | 0.0727386 | ||||||||
\(361\) | −1.18104e6 | −0.476975 | ||||||||
\(362\) | 185825. | 0.0745303 | ||||||||
\(363\) | 381740. | 0.152055 | ||||||||
\(364\) | −2.41343e6 | −0.954733 | ||||||||
\(365\) | −434154. | −0.170573 | ||||||||
\(366\) | 250503. | 0.0977486 | ||||||||
\(367\) | 2.16264e6 | 0.838144 | 0.419072 | − | 0.907953i | \(-0.362355\pi\) | ||||
0.419072 | + | 0.907953i | \(0.362355\pi\) | |||||||
\(368\) | 3.50721e6 | 1.35003 | ||||||||
\(369\) | 458242. | 0.175198 | ||||||||
\(370\) | −146722. | −0.0557176 | ||||||||
\(371\) | 99252.9 | 0.0374376 | ||||||||
\(372\) | −1.35758e6 | −0.508639 | ||||||||
\(373\) | 318374. | 0.118486 | 0.0592428 | − | 0.998244i | \(-0.481131\pi\) | ||||
0.0592428 | + | 0.998244i | \(0.481131\pi\) | |||||||
\(374\) | 254322. | 0.0940168 | ||||||||
\(375\) | −1.55527e6 | −0.571122 | ||||||||
\(376\) | 89438.4 | 0.0326253 | ||||||||
\(377\) | −2.88135e6 | −1.04410 | ||||||||
\(378\) | 62966.9 | 0.0226664 | ||||||||
\(379\) | −1.96985e6 | −0.704427 | −0.352213 | − | 0.935920i | \(-0.614571\pi\) | ||||
−0.352213 | + | 0.935920i | \(0.614571\pi\) | |||||||
\(380\) | −2.03275e6 | −0.722147 | ||||||||
\(381\) | 969797. | 0.342270 | ||||||||
\(382\) | −250035. | −0.0876684 | ||||||||
\(383\) | −939792. | −0.327367 | −0.163684 | − | 0.986513i | \(-0.552338\pi\) | ||||
−0.163684 | + | 0.986513i | \(0.552338\pi\) | |||||||
\(384\) | 703599. | 0.243499 | ||||||||
\(385\) | 2.73497e6 | 0.940376 | ||||||||
\(386\) | −443669. | −0.151562 | ||||||||
\(387\) | 776934. | 0.263698 | ||||||||
\(388\) | 2.84409e6 | 0.959099 | ||||||||
\(389\) | −3.98669e6 | −1.33579 | −0.667895 | − | 0.744255i | \(-0.732805\pi\) | ||||
−0.667895 | + | 0.744255i | \(0.732805\pi\) | |||||||
\(390\) | −169592. | −0.0564603 | ||||||||
\(391\) | 4.26623e6 | 1.41125 | ||||||||
\(392\) | −115473. | −0.0379547 | ||||||||
\(393\) | 1.74137e6 | 0.568734 | ||||||||
\(394\) | 417022. | 0.135337 | ||||||||
\(395\) | −1.47330e6 | −0.475114 | ||||||||
\(396\) | −882242. | −0.282716 | ||||||||
\(397\) | 48363.5 | 0.0154007 | 0.00770036 | − | 0.999970i | \(-0.497549\pi\) | ||||
0.00770036 | + | 0.999970i | \(0.497549\pi\) | |||||||
\(398\) | −452043. | −0.143045 | ||||||||
\(399\) | −1.43976e6 | −0.452750 | ||||||||
\(400\) | 64910.5 | 0.0202845 | ||||||||
\(401\) | −1.10869e6 | −0.344310 | −0.172155 | − | 0.985070i | \(-0.555073\pi\) | ||||
−0.172155 | + | 0.985070i | \(0.555073\pi\) | |||||||
\(402\) | 106400. | 0.0328380 | ||||||||
\(403\) | 2.58980e6 | 0.794334 | ||||||||
\(404\) | −1.05633e6 | −0.321993 | ||||||||
\(405\) | −370607. | −0.112273 | ||||||||
\(406\) | −458399. | −0.138016 | ||||||||
\(407\) | 1.45606e6 | 0.435705 | ||||||||
\(408\) | 422795. | 0.125742 | ||||||||
\(409\) | −871295. | −0.257547 | −0.128774 | − | 0.991674i | \(-0.541104\pi\) | ||||
−0.128774 | + | 0.991674i | \(0.541104\pi\) | |||||||
\(410\) | −196352. | −0.0576867 | ||||||||
\(411\) | 346226. | 0.101101 | ||||||||
\(412\) | 2.15872e6 | 0.626547 | ||||||||
\(413\) | −558222. | −0.161039 | ||||||||
\(414\) | 176692. | 0.0506659 | ||||||||
\(415\) | 3.30046e6 | 0.940708 | ||||||||
\(416\) | −1.00873e6 | −0.285786 | ||||||||
\(417\) | 1.26361e6 | 0.355855 | ||||||||
\(418\) | −240843. | −0.0674208 | ||||||||
\(419\) | −1.03894e6 | −0.289105 | −0.144552 | − | 0.989497i | \(-0.546174\pi\) | ||||
−0.144552 | + | 0.989497i | \(0.546174\pi\) | |||||||
\(420\) | 2.25987e6 | 0.625117 | ||||||||
\(421\) | −4.23746e6 | −1.16520 | −0.582600 | − | 0.812759i | \(-0.697964\pi\) | ||||
−0.582600 | + | 0.812759i | \(0.697964\pi\) | |||||||
\(422\) | −60476.2 | −0.0165312 | ||||||||
\(423\) | −185317. | −0.0503577 | ||||||||
\(424\) | 27601.5 | 0.00745621 | ||||||||
\(425\) | 78958.2 | 0.0212044 | ||||||||
\(426\) | −306329. | −0.0817832 | ||||||||
\(427\) | 6.36783e6 | 1.69014 | ||||||||
\(428\) | −4.87337e6 | −1.28594 | ||||||||
\(429\) | 1.68301e6 | 0.441513 | ||||||||
\(430\) | −332908. | −0.0868267 | ||||||||
\(431\) | 137045. | 0.0355362 | 0.0177681 | − | 0.999842i | \(-0.494344\pi\) | ||||
0.0177681 | + | 0.999842i | \(0.494344\pi\) | |||||||
\(432\) | −720178. | −0.185665 | ||||||||
\(433\) | −3.25653e6 | −0.834709 | −0.417355 | − | 0.908744i | \(-0.637043\pi\) | ||||
−0.417355 | + | 0.908744i | \(0.637043\pi\) | |||||||
\(434\) | 412015. | 0.105000 | ||||||||
\(435\) | 2.69802e6 | 0.683631 | ||||||||
\(436\) | −4.90235e6 | −1.23506 | ||||||||
\(437\) | −4.04012e6 | −1.01202 | ||||||||
\(438\) | −42503.5 | −0.0105862 | ||||||||
\(439\) | −2.44288e6 | −0.604980 | −0.302490 | − | 0.953153i | \(-0.597818\pi\) | ||||
−0.302490 | + | 0.953153i | \(0.597818\pi\) | |||||||
\(440\) | 760577. | 0.187289 | ||||||||
\(441\) | 239261. | 0.0585836 | ||||||||
\(442\) | −400880. | −0.0976020 | ||||||||
\(443\) | 5.34971e6 | 1.29515 | 0.647576 | − | 0.762001i | \(-0.275783\pi\) | ||||
0.647576 | + | 0.762001i | \(0.275783\pi\) | |||||||
\(444\) | 1.20312e6 | 0.289635 | ||||||||
\(445\) | −928709. | −0.222321 | ||||||||
\(446\) | −779506. | −0.185559 | ||||||||
\(447\) | −607675. | −0.143848 | ||||||||
\(448\) | 4.28343e6 | 1.00832 | ||||||||
\(449\) | −2.70070e6 | −0.632208 | −0.316104 | − | 0.948725i | \(-0.602375\pi\) | ||||
−0.316104 | + | 0.948725i | \(0.602375\pi\) | |||||||
\(450\) | 3270.16 | 0.000761269 0 | ||||||||
\(451\) | 1.94858e6 | 0.451103 | ||||||||
\(452\) | 936139. | 0.215523 | ||||||||
\(453\) | −4.21079e6 | −0.964091 | ||||||||
\(454\) | −161767. | −0.0368341 | ||||||||
\(455\) | −4.31105e6 | −0.976236 | ||||||||
\(456\) | −400387. | −0.0901713 | ||||||||
\(457\) | 6.52433e6 | 1.46132 | 0.730660 | − | 0.682742i | \(-0.239213\pi\) | ||||
0.730660 | + | 0.682742i | \(0.239213\pi\) | |||||||
\(458\) | −583847. | −0.130057 | ||||||||
\(459\) | −876037. | −0.194085 | ||||||||
\(460\) | 6.34145e6 | 1.39731 | ||||||||
\(461\) | 7.60277e6 | 1.66617 | 0.833085 | − | 0.553144i | \(-0.186572\pi\) | ||||
0.833085 | + | 0.553144i | \(0.186572\pi\) | |||||||
\(462\) | 267753. | 0.0583619 | ||||||||
\(463\) | 1.02732e6 | 0.222718 | 0.111359 | − | 0.993780i | \(-0.464480\pi\) | ||||
0.111359 | + | 0.993780i | \(0.464480\pi\) | |||||||
\(464\) | 5.24289e6 | 1.13051 | ||||||||
\(465\) | −2.42501e6 | −0.520094 | ||||||||
\(466\) | 808198. | 0.172406 | ||||||||
\(467\) | −4.17375e6 | −0.885593 | −0.442797 | − | 0.896622i | \(-0.646014\pi\) | ||||
−0.442797 | + | 0.896622i | \(0.646014\pi\) | |||||||
\(468\) | 1.39065e6 | 0.293497 | ||||||||
\(469\) | 2.70471e6 | 0.567791 | ||||||||
\(470\) | 79406.6 | 0.0165811 | ||||||||
\(471\) | 221841. | 0.0460776 | ||||||||
\(472\) | −155237. | −0.0320731 | ||||||||
\(473\) | 3.30374e6 | 0.678974 | ||||||||
\(474\) | −144235. | −0.0294867 | ||||||||
\(475\) | −74773.5 | −0.0152060 | ||||||||
\(476\) | 5.34187e6 | 1.08063 | ||||||||
\(477\) | −57190.7 | −0.0115088 | ||||||||
\(478\) | −943469. | −0.188868 | ||||||||
\(479\) | 1.99136e6 | 0.396562 | 0.198281 | − | 0.980145i | \(-0.436464\pi\) | ||||
0.198281 | + | 0.980145i | \(0.436464\pi\) | |||||||
\(480\) | 944547. | 0.187120 | ||||||||
\(481\) | −2.29513e6 | −0.452319 | ||||||||
\(482\) | 538461. | 0.105569 | ||||||||
\(483\) | 4.49153e6 | 0.876046 | ||||||||
\(484\) | 1.34128e6 | 0.260260 | ||||||||
\(485\) | 5.08031e6 | 0.980700 | ||||||||
\(486\) | −36282.3 | −0.00696793 | ||||||||
\(487\) | −4.01402e6 | −0.766932 | −0.383466 | − | 0.923555i | \(-0.625270\pi\) | ||||
−0.383466 | + | 0.923555i | \(0.625270\pi\) | |||||||
\(488\) | 1.77085e6 | 0.336614 | ||||||||
\(489\) | −614550. | −0.116221 | ||||||||
\(490\) | −102521. | −0.0192896 | ||||||||
\(491\) | −7.56267e6 | −1.41570 | −0.707851 | − | 0.706362i | \(-0.750335\pi\) | ||||
−0.707851 | + | 0.706362i | \(0.750335\pi\) | |||||||
\(492\) | 1.61008e6 | 0.299872 | ||||||||
\(493\) | 6.37755e6 | 1.18178 | ||||||||
\(494\) | 379633. | 0.0699918 | ||||||||
\(495\) | −1.57593e6 | −0.289083 | ||||||||
\(496\) | −4.71239e6 | −0.860076 | ||||||||
\(497\) | −7.78693e6 | −1.41408 | ||||||||
\(498\) | 323114. | 0.0583825 | ||||||||
\(499\) | 5.49280e6 | 0.987512 | 0.493756 | − | 0.869600i | \(-0.335624\pi\) | ||||
0.493756 | + | 0.869600i | \(0.335624\pi\) | |||||||
\(500\) | −5.46462e6 | −0.977542 | ||||||||
\(501\) | −4.32203e6 | −0.769296 | ||||||||
\(502\) | 181521. | 0.0321490 | ||||||||
\(503\) | 1.40108e6 | 0.246913 | 0.123457 | − | 0.992350i | \(-0.460602\pi\) | ||||
0.123457 | + | 0.992350i | \(0.460602\pi\) | |||||||
\(504\) | 445123. | 0.0780556 | ||||||||
\(505\) | −1.88689e6 | −0.329244 | ||||||||
\(506\) | 751344. | 0.130455 | ||||||||
\(507\) | 688763. | 0.119001 | ||||||||
\(508\) | 3.40748e6 | 0.585834 | ||||||||
\(509\) | 4.24891e6 | 0.726914 | 0.363457 | − | 0.931611i | \(-0.381596\pi\) | ||||
0.363457 | + | 0.931611i | \(0.381596\pi\) | |||||||
\(510\) | 375373. | 0.0639054 | ||||||||
\(511\) | −1.08045e6 | −0.183042 | ||||||||
\(512\) | 3.07130e6 | 0.517783 | ||||||||
\(513\) | 829608. | 0.139181 | ||||||||
\(514\) | −533219. | −0.0890220 | ||||||||
\(515\) | 3.85607e6 | 0.640658 | ||||||||
\(516\) | 2.72984e6 | 0.451349 | ||||||||
\(517\) | −788023. | −0.129662 | ||||||||
\(518\) | −365137. | −0.0597904 | ||||||||
\(519\) | −2.09451e6 | −0.341323 | ||||||||
\(520\) | −1.19887e6 | −0.194431 | ||||||||
\(521\) | −5.74220e6 | −0.926796 | −0.463398 | − | 0.886150i | \(-0.653370\pi\) | ||||
−0.463398 | + | 0.886150i | \(0.653370\pi\) | |||||||
\(522\) | 264135. | 0.0424277 | ||||||||
\(523\) | −8.93255e6 | −1.42798 | −0.713988 | − | 0.700158i | \(-0.753113\pi\) | ||||
−0.713988 | + | 0.700158i | \(0.753113\pi\) | |||||||
\(524\) | 6.11848e6 | 0.973454 | ||||||||
\(525\) | 83128.1 | 0.0131628 | ||||||||
\(526\) | 99697.3 | 0.0157115 | ||||||||
\(527\) | −5.73223e6 | −0.899077 | ||||||||
\(528\) | −3.06240e6 | −0.478054 | ||||||||
\(529\) | 6.16738e6 | 0.958211 | ||||||||
\(530\) | 24505.6 | 0.00378945 | ||||||||
\(531\) | 321654. | 0.0495054 | ||||||||
\(532\) | −5.05876e6 | −0.774934 | ||||||||
\(533\) | −3.07148e6 | −0.468305 | ||||||||
\(534\) | −90920.3 | −0.0137977 | ||||||||
\(535\) | −8.70517e6 | −1.31490 | ||||||||
\(536\) | 752160. | 0.113083 | ||||||||
\(537\) | 144547. | 0.0216308 | ||||||||
\(538\) | 36688.8 | 0.00546485 | ||||||||
\(539\) | 1.01741e6 | 0.150842 | ||||||||
\(540\) | −1.30217e6 | −0.192168 | ||||||||
\(541\) | −1.21222e7 | −1.78069 | −0.890347 | − | 0.455283i | \(-0.849538\pi\) | ||||
−0.890347 | + | 0.455283i | \(0.849538\pi\) | |||||||
\(542\) | 725509. | 0.106083 | ||||||||
\(543\) | −2.72185e6 | −0.396155 | ||||||||
\(544\) | 2.23271e6 | 0.323471 | ||||||||
\(545\) | −8.75694e6 | −1.26288 | ||||||||
\(546\) | −422050. | −0.0605875 | ||||||||
\(547\) | −4.58544e6 | −0.655259 | −0.327630 | − | 0.944806i | \(-0.606250\pi\) | ||||
−0.327630 | + | 0.944806i | \(0.606250\pi\) | |||||||
\(548\) | 1.21650e6 | 0.173046 | ||||||||
\(549\) | −3.66922e6 | −0.519569 | ||||||||
\(550\) | 13905.7 | 0.00196013 | ||||||||
\(551\) | −6.03954e6 | −0.847472 | ||||||||
\(552\) | 1.24906e6 | 0.174476 | ||||||||
\(553\) | −3.66648e6 | −0.509844 | ||||||||
\(554\) | −392465. | −0.0543284 | ||||||||
\(555\) | 2.14910e6 | 0.296159 | ||||||||
\(556\) | 4.43983e6 | 0.609087 | ||||||||
\(557\) | 72367.7 | 0.00988341 | 0.00494171 | − | 0.999988i | \(-0.498427\pi\) | ||||
0.00494171 | + | 0.999988i | \(0.498427\pi\) | |||||||
\(558\) | −237408. | −0.0322783 | ||||||||
\(559\) | −5.20758e6 | −0.704866 | ||||||||
\(560\) | 7.84438e6 | 1.05703 | ||||||||
\(561\) | −3.72516e6 | −0.499733 | ||||||||
\(562\) | 751291. | 0.100338 | ||||||||
\(563\) | −2.90372e6 | −0.386086 | −0.193043 | − | 0.981190i | \(-0.561836\pi\) | ||||
−0.193043 | + | 0.981190i | \(0.561836\pi\) | |||||||
\(564\) | −651133. | −0.0861930 | ||||||||
\(565\) | 1.67220e6 | 0.220377 | ||||||||
\(566\) | 564003. | 0.0740015 | ||||||||
\(567\) | −922301. | −0.120480 | ||||||||
\(568\) | −2.16549e6 | −0.281634 | ||||||||
\(569\) | −1.44699e7 | −1.87363 | −0.936816 | − | 0.349824i | \(-0.886241\pi\) | ||||
−0.936816 | + | 0.349824i | \(0.886241\pi\) | |||||||
\(570\) | −355478. | −0.0458275 | ||||||||
\(571\) | 305861. | 0.0392585 | 0.0196293 | − | 0.999807i | \(-0.493751\pi\) | ||||
0.0196293 | + | 0.999807i | \(0.493751\pi\) | |||||||
\(572\) | 5.91344e6 | 0.755701 | ||||||||
\(573\) | 3.66237e6 | 0.465989 | ||||||||
\(574\) | −488647. | −0.0619035 | ||||||||
\(575\) | 233266. | 0.0294227 | ||||||||
\(576\) | −2.46816e6 | −0.309968 | ||||||||
\(577\) | −1.30522e7 | −1.63209 | −0.816045 | − | 0.577988i | \(-0.803838\pi\) | ||||
−0.816045 | + | 0.577988i | \(0.803838\pi\) | |||||||
\(578\) | 14881.6 | 0.00185281 | ||||||||
\(579\) | 6.49860e6 | 0.805607 | ||||||||
\(580\) | 9.47977e6 | 1.17011 | ||||||||
\(581\) | 8.21362e6 | 1.00947 | ||||||||
\(582\) | 497361. | 0.0608645 | ||||||||
\(583\) | −243191. | −0.0296330 | ||||||||
\(584\) | −300464. | −0.0364553 | ||||||||
\(585\) | 2.48408e6 | 0.300107 | ||||||||
\(586\) | −1.39547e6 | −0.167872 | ||||||||
\(587\) | −5.83915e6 | −0.699447 | −0.349723 | − | 0.936853i | \(-0.613724\pi\) | ||||
−0.349723 | + | 0.936853i | \(0.613724\pi\) | |||||||
\(588\) | 840671. | 0.100273 | ||||||||
\(589\) | 5.42843e6 | 0.644742 | ||||||||
\(590\) | −137825. | −0.0163004 | ||||||||
\(591\) | −6.10828e6 | −0.719367 | ||||||||
\(592\) | 4.17622e6 | 0.489755 | ||||||||
\(593\) | 4.87510e6 | 0.569307 | 0.284654 | − | 0.958630i | \(-0.408121\pi\) | ||||
0.284654 | + | 0.958630i | \(0.408121\pi\) | |||||||
\(594\) | −154283. | −0.0179412 | ||||||||
\(595\) | 9.54204e6 | 1.10497 | ||||||||
\(596\) | −2.13513e6 | −0.246212 | ||||||||
\(597\) | 6.62126e6 | 0.760334 | ||||||||
\(598\) | −1.18432e6 | −0.135430 | ||||||||
\(599\) | −1.44821e7 | −1.64916 | −0.824582 | − | 0.565743i | \(-0.808590\pi\) | ||||
−0.824582 | + | 0.565743i | \(0.808590\pi\) | |||||||
\(600\) | 23117.3 | 0.00262156 | ||||||||
\(601\) | −1.46459e7 | −1.65398 | −0.826988 | − | 0.562219i | \(-0.809948\pi\) | ||||
−0.826988 | + | 0.562219i | \(0.809948\pi\) | |||||||
\(602\) | −828483. | −0.0931735 | ||||||||
\(603\) | −1.55849e6 | −0.174546 | ||||||||
\(604\) | −1.47951e7 | −1.65015 | ||||||||
\(605\) | 2.39590e6 | 0.266122 | ||||||||
\(606\) | −184726. | −0.0204337 | ||||||||
\(607\) | −5.72602e6 | −0.630785 | −0.315392 | − | 0.948961i | \(-0.602136\pi\) | ||||
−0.315392 | + | 0.948961i | \(0.602136\pi\) | |||||||
\(608\) | −2.11438e6 | −0.231966 | ||||||||
\(609\) | 6.71435e6 | 0.733602 | ||||||||
\(610\) | 1.57222e6 | 0.171076 | ||||||||
\(611\) | 1.24213e6 | 0.134606 | ||||||||
\(612\) | −3.07805e6 | −0.332198 | ||||||||
\(613\) | −9.47872e6 | −1.01882 | −0.509411 | − | 0.860523i | \(-0.670137\pi\) | ||||
−0.509411 | + | 0.860523i | \(0.670137\pi\) | |||||||
\(614\) | 591713. | 0.0633417 | ||||||||
\(615\) | 2.87605e6 | 0.306625 | ||||||||
\(616\) | 1.89279e6 | 0.200979 | ||||||||
\(617\) | −1.80423e7 | −1.90800 | −0.954000 | − | 0.299806i | \(-0.903078\pi\) | ||||
−0.954000 | + | 0.299806i | \(0.903078\pi\) | |||||||
\(618\) | 377508. | 0.0397607 | ||||||||
\(619\) | 5.10552e6 | 0.535566 | 0.267783 | − | 0.963479i | \(-0.413709\pi\) | ||||
0.267783 | + | 0.963479i | \(0.413709\pi\) | |||||||
\(620\) | −8.52055e6 | −0.890201 | ||||||||
\(621\) | −2.58808e6 | −0.269307 | ||||||||
\(622\) | 271579. | 0.0281462 | ||||||||
\(623\) | −2.31121e6 | −0.238572 | ||||||||
\(624\) | 4.82716e6 | 0.496284 | ||||||||
\(625\) | −9.96664e6 | −1.02058 | ||||||||
\(626\) | 536759. | 0.0547449 | ||||||||
\(627\) | 3.52773e6 | 0.358366 | ||||||||
\(628\) | 779462. | 0.0788671 | ||||||||
\(629\) | 5.08003e6 | 0.511964 | ||||||||
\(630\) | 395197. | 0.0396700 | ||||||||
\(631\) | −9.73882e6 | −0.973717 | −0.486858 | − | 0.873481i | \(-0.661857\pi\) | ||||
−0.486858 | + | 0.873481i | \(0.661857\pi\) | |||||||
\(632\) | −1.01962e6 | −0.101542 | ||||||||
\(633\) | 885819. | 0.0878690 | ||||||||
\(634\) | 380041. | 0.0375497 | ||||||||
\(635\) | 6.08670e6 | 0.599028 | ||||||||
\(636\) | −200946. | −0.0196986 | ||||||||
\(637\) | −1.60371e6 | −0.156594 | ||||||||
\(638\) | 1.12318e6 | 0.109244 | ||||||||
\(639\) | 4.48692e6 | 0.434707 | ||||||||
\(640\) | 4.41597e6 | 0.426164 | ||||||||
\(641\) | −6.96903e6 | −0.669927 | −0.334963 | − | 0.942231i | \(-0.608724\pi\) | ||||
−0.334963 | + | 0.942231i | \(0.608724\pi\) | |||||||
\(642\) | −852233. | −0.0816058 | ||||||||
\(643\) | −8.53787e6 | −0.814370 | −0.407185 | − | 0.913346i | \(-0.633490\pi\) | ||||
−0.407185 | + | 0.913346i | \(0.633490\pi\) | |||||||
\(644\) | 1.57815e7 | 1.49945 | ||||||||
\(645\) | 4.87624e6 | 0.461515 | ||||||||
\(646\) | −840277. | −0.0792212 | ||||||||
\(647\) | 9.86040e6 | 0.926048 | 0.463024 | − | 0.886346i | \(-0.346764\pi\) | ||||
0.463024 | + | 0.886346i | \(0.346764\pi\) | |||||||
\(648\) | −256485. | −0.0239952 | ||||||||
\(649\) | 1.36776e6 | 0.127468 | ||||||||
\(650\) | −21919.0 | −0.00203488 | ||||||||
\(651\) | −6.03495e6 | −0.558112 | ||||||||
\(652\) | −2.15929e6 | −0.198926 | ||||||||
\(653\) | −9.68284e6 | −0.888628 | −0.444314 | − | 0.895871i | \(-0.646552\pi\) | ||||
−0.444314 | + | 0.895871i | \(0.646552\pi\) | |||||||
\(654\) | −857302. | −0.0783771 | ||||||||
\(655\) | 1.09293e7 | 0.995378 | ||||||||
\(656\) | 5.58885e6 | 0.507064 | ||||||||
\(657\) | 622566. | 0.0562694 | ||||||||
\(658\) | 197613. | 0.0177931 | ||||||||
\(659\) | −9.25872e6 | −0.830496 | −0.415248 | − | 0.909708i | \(-0.636305\pi\) | ||||
−0.415248 | + | 0.909708i | \(0.636305\pi\) | |||||||
\(660\) | −5.53718e6 | −0.494799 | ||||||||
\(661\) | 5.66019e6 | 0.503880 | 0.251940 | − | 0.967743i | \(-0.418931\pi\) | ||||
0.251940 | + | 0.967743i | \(0.418931\pi\) | |||||||
\(662\) | 915951. | 0.0812321 | ||||||||
\(663\) | 5.87185e6 | 0.518789 | ||||||||
\(664\) | 2.28415e6 | 0.201050 | ||||||||
\(665\) | −9.03632e6 | −0.792387 | ||||||||
\(666\) | 210396. | 0.0183803 | ||||||||
\(667\) | 1.88412e7 | 1.63981 | ||||||||
\(668\) | −1.51859e7 | −1.31674 | ||||||||
\(669\) | 1.14177e7 | 0.986312 | ||||||||
\(670\) | 667795. | 0.0574720 | ||||||||
\(671\) | −1.56026e7 | −1.33780 | ||||||||
\(672\) | 2.35062e6 | 0.200798 | ||||||||
\(673\) | −1.30413e7 | −1.10990 | −0.554949 | − | 0.831884i | \(-0.687262\pi\) | ||||
−0.554949 | + | 0.831884i | \(0.687262\pi\) | |||||||
\(674\) | 2.32783e6 | 0.197379 | ||||||||
\(675\) | −47899.4 | −0.00404642 | ||||||||
\(676\) | 2.42004e6 | 0.203684 | ||||||||
\(677\) | 7.00449e6 | 0.587361 | 0.293680 | − | 0.955904i | \(-0.405120\pi\) | ||||
0.293680 | + | 0.955904i | \(0.405120\pi\) | |||||||
\(678\) | 163708. | 0.0136771 | ||||||||
\(679\) | 1.26430e7 | 1.05239 | ||||||||
\(680\) | 2.65357e6 | 0.220069 | ||||||||
\(681\) | 2.36946e6 | 0.195786 | ||||||||
\(682\) | −1.00953e6 | −0.0831107 | ||||||||
\(683\) | −1.79286e7 | −1.47060 | −0.735299 | − | 0.677743i | \(-0.762958\pi\) | ||||
−0.735299 | + | 0.677743i | \(0.762958\pi\) | |||||||
\(684\) | 2.91492e6 | 0.238224 | ||||||||
\(685\) | 2.17300e6 | 0.176943 | ||||||||
\(686\) | 1.19656e6 | 0.0970785 | ||||||||
\(687\) | 8.55184e6 | 0.691302 | ||||||||
\(688\) | 9.47570e6 | 0.763203 | ||||||||
\(689\) | 383334. | 0.0307630 | ||||||||
\(690\) | 1.10896e6 | 0.0886737 | ||||||||
\(691\) | −1.01169e7 | −0.806035 | −0.403018 | − | 0.915192i | \(-0.632039\pi\) | ||||
−0.403018 | + | 0.915192i | \(0.632039\pi\) | |||||||
\(692\) | −7.35930e6 | −0.584213 | ||||||||
\(693\) | −3.92189e6 | −0.310214 | ||||||||
\(694\) | 1.19253e6 | 0.0939880 | ||||||||
\(695\) | 7.93074e6 | 0.622805 | ||||||||
\(696\) | 1.86721e6 | 0.146107 | ||||||||
\(697\) | 6.79838e6 | 0.530058 | ||||||||
\(698\) | 153250. | 0.0119059 | ||||||||
\(699\) | −1.18380e7 | −0.916400 | ||||||||
\(700\) | 292079. | 0.0225297 | ||||||||
\(701\) | −4.39775e6 | −0.338015 | −0.169007 | − | 0.985615i | \(-0.554056\pi\) | ||||
−0.169007 | + | 0.985615i | \(0.554056\pi\) | |||||||
\(702\) | 243191. | 0.0186253 | ||||||||
\(703\) | −4.81079e6 | −0.367137 | ||||||||
\(704\) | −1.04953e7 | −0.798113 | ||||||||
\(705\) | −1.16310e6 | −0.0881342 | ||||||||
\(706\) | −2.33089e6 | −0.175999 | ||||||||
\(707\) | −4.69576e6 | −0.353311 | ||||||||
\(708\) | 1.13017e6 | 0.0847343 | ||||||||
\(709\) | 1.79270e7 | 1.33934 | 0.669671 | − | 0.742658i | \(-0.266435\pi\) | ||||
0.669671 | + | 0.742658i | \(0.266435\pi\) | |||||||
\(710\) | −1.92260e6 | −0.143134 | ||||||||
\(711\) | 2.11267e6 | 0.156732 | ||||||||
\(712\) | −642730. | −0.0475148 | ||||||||
\(713\) | −1.69347e7 | −1.24754 | ||||||||
\(714\) | 934163. | 0.0685768 | ||||||||
\(715\) | 1.05630e7 | 0.772721 | ||||||||
\(716\) | 507880. | 0.0370236 | ||||||||
\(717\) | 1.38194e7 | 1.00390 | ||||||||
\(718\) | −537283. | −0.0388948 | ||||||||
\(719\) | −2.48736e6 | −0.179439 | −0.0897196 | − | 0.995967i | \(-0.528597\pi\) | ||||
−0.0897196 | + | 0.995967i | \(0.528597\pi\) | |||||||
\(720\) | −4.52002e6 | −0.324945 | ||||||||
\(721\) | 9.59630e6 | 0.687489 | ||||||||
\(722\) | −725680. | −0.0518087 | ||||||||
\(723\) | −7.88705e6 | −0.561137 | ||||||||
\(724\) | −9.56353e6 | −0.678065 | ||||||||
\(725\) | 348707. | 0.0246386 | ||||||||
\(726\) | 234558. | 0.0165161 | ||||||||
\(727\) | 1.11908e7 | 0.785279 | 0.392640 | − | 0.919692i | \(-0.371562\pi\) | ||||
0.392640 | + | 0.919692i | \(0.371562\pi\) | |||||||
\(728\) | −2.98354e6 | −0.208643 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −266763. | −0.0185276 | ||||||||
\(731\) | 1.15264e7 | 0.797812 | ||||||||
\(732\) | −1.28922e7 | −0.889302 | ||||||||
\(733\) | 8.00809e6 | 0.550515 | 0.275257 | − | 0.961371i | \(-0.411237\pi\) | ||||
0.275257 | + | 0.961371i | \(0.411237\pi\) | |||||||
\(734\) | 1.32882e6 | 0.0910387 | ||||||||
\(735\) | 1.50167e6 | 0.102531 | ||||||||
\(736\) | 6.59610e6 | 0.448841 | ||||||||
\(737\) | −6.62712e6 | −0.449424 | ||||||||
\(738\) | 281564. | 0.0190299 | ||||||||
\(739\) | 6.18443e6 | 0.416571 | 0.208285 | − | 0.978068i | \(-0.433212\pi\) | ||||
0.208285 | + | 0.978068i | \(0.433212\pi\) | |||||||
\(740\) | 7.55110e6 | 0.506910 | ||||||||
\(741\) | −5.56064e6 | −0.372031 | ||||||||
\(742\) | 60985.3 | 0.00406645 | ||||||||
\(743\) | 1.64958e7 | 1.09623 | 0.548113 | − | 0.836404i | \(-0.315346\pi\) | ||||
0.548113 | + | 0.836404i | \(0.315346\pi\) | |||||||
\(744\) | −1.67828e6 | −0.111156 | ||||||||
\(745\) | −3.81393e6 | −0.251757 | ||||||||
\(746\) | 195623. | 0.0128698 | ||||||||
\(747\) | −4.73278e6 | −0.310324 | ||||||||
\(748\) | −1.30887e7 | −0.855350 | ||||||||
\(749\) | −2.16639e7 | −1.41102 | ||||||||
\(750\) | −955629. | −0.0620349 | ||||||||
\(751\) | −1.77128e7 | −1.14601 | −0.573003 | − | 0.819553i | \(-0.694222\pi\) | ||||
−0.573003 | + | 0.819553i | \(0.694222\pi\) | |||||||
\(752\) | −2.26018e6 | −0.145747 | ||||||||
\(753\) | −2.65881e6 | −0.170884 | ||||||||
\(754\) | −1.77043e6 | −0.113410 | ||||||||
\(755\) | −2.64280e7 | −1.68732 | ||||||||
\(756\) | −3.24060e6 | −0.206216 | ||||||||
\(757\) | −5.07500e6 | −0.321882 | −0.160941 | − | 0.986964i | \(-0.551453\pi\) | ||||
−0.160941 | + | 0.986964i | \(0.551453\pi\) | |||||||
\(758\) | −1.21036e6 | −0.0765144 | ||||||||
\(759\) | −1.10052e7 | −0.693417 | ||||||||
\(760\) | −2.51294e6 | −0.157815 | ||||||||
\(761\) | 7.70337e6 | 0.482191 | 0.241095 | − | 0.970501i | \(-0.422493\pi\) | ||||
0.241095 | + | 0.970501i | \(0.422493\pi\) | |||||||
\(762\) | 595886. | 0.0371771 | ||||||||
\(763\) | −2.17927e7 | −1.35519 | ||||||||
\(764\) | 1.28681e7 | 0.797593 | ||||||||
\(765\) | −5.49824e6 | −0.339680 | ||||||||
\(766\) | −577449. | −0.0355584 | ||||||||
\(767\) | −2.15596e6 | −0.132328 | ||||||||
\(768\) | −8.34337e6 | −0.510432 | ||||||||
\(769\) | −1.94770e7 | −1.18770 | −0.593849 | − | 0.804576i | \(-0.702392\pi\) | ||||
−0.593849 | + | 0.804576i | \(0.702392\pi\) | |||||||
\(770\) | 1.68049e6 | 0.102143 | ||||||||
\(771\) | 7.81026e6 | 0.473184 | ||||||||
\(772\) | 2.28335e7 | 1.37889 | ||||||||
\(773\) | 1.96554e7 | 1.18313 | 0.591564 | − | 0.806258i | \(-0.298511\pi\) | ||||
0.591564 | + | 0.806258i | \(0.298511\pi\) | |||||||
\(774\) | 477382. | 0.0286427 | ||||||||
\(775\) | −313423. | −0.0187446 | ||||||||
\(776\) | 3.51593e6 | 0.209597 | ||||||||
\(777\) | 5.34831e6 | 0.317807 | ||||||||
\(778\) | −2.44960e6 | −0.145093 | ||||||||
\(779\) | −6.43807e6 | −0.380112 | ||||||||
\(780\) | 8.72808e6 | 0.513667 | ||||||||
\(781\) | 1.90797e7 | 1.11929 | ||||||||
\(782\) | 2.62136e6 | 0.153289 | ||||||||
\(783\) | −3.86889e6 | −0.225518 | ||||||||
\(784\) | 2.91810e6 | 0.169555 | ||||||||
\(785\) | 1.39233e6 | 0.0806433 | ||||||||
\(786\) | 1.06997e6 | 0.0617755 | ||||||||
\(787\) | −1.70676e6 | −0.0982281 | −0.0491140 | − | 0.998793i | \(-0.515640\pi\) | ||||
−0.0491140 | + | 0.998793i | \(0.515640\pi\) | |||||||
\(788\) | −2.14621e7 | −1.23128 | ||||||||
\(789\) | −1.46031e6 | −0.0835125 | ||||||||
\(790\) | −905258. | −0.0516065 | ||||||||
\(791\) | 4.16148e6 | 0.236486 | ||||||||
\(792\) | −1.09065e6 | −0.0617834 | ||||||||
\(793\) | 2.45938e7 | 1.38881 | ||||||||
\(794\) | 29716.6 | 0.00167282 | ||||||||
\(795\) | −358944. | −0.0201423 | ||||||||
\(796\) | 2.32645e7 | 1.30140 | ||||||||
\(797\) | 6.14860e6 | 0.342871 | 0.171435 | − | 0.985195i | \(-0.445160\pi\) | ||||
0.171435 | + | 0.985195i | \(0.445160\pi\) | |||||||
\(798\) | −884653. | −0.0491774 | ||||||||
\(799\) | −2.74933e6 | −0.152356 | ||||||||
\(800\) | 122079. | 0.00674396 | ||||||||
\(801\) | 1.33175e6 | 0.0733398 | ||||||||
\(802\) | −681229. | −0.0373987 | ||||||||
\(803\) | 2.64733e6 | 0.144883 | ||||||||
\(804\) | −5.47591e6 | −0.298755 | ||||||||
\(805\) | 2.81900e7 | 1.53322 | ||||||||
\(806\) | 1.59128e6 | 0.0862800 | ||||||||
\(807\) | −537396. | −0.0290476 | ||||||||
\(808\) | −1.30586e6 | −0.0703668 | ||||||||
\(809\) | 2.45160e7 | 1.31698 | 0.658488 | − | 0.752592i | \(-0.271196\pi\) | ||||
0.658488 | + | 0.752592i | \(0.271196\pi\) | |||||||
\(810\) | −227717. | −0.0121950 | ||||||||
\(811\) | 1.22682e7 | 0.654982 | 0.327491 | − | 0.944854i | \(-0.393797\pi\) | ||||
0.327491 | + | 0.944854i | \(0.393797\pi\) | |||||||
\(812\) | 2.35916e7 | 1.25565 | ||||||||
\(813\) | −1.06268e7 | −0.563868 | ||||||||
\(814\) | 894665. | 0.0473259 | ||||||||
\(815\) | −3.85708e6 | −0.203406 | ||||||||
\(816\) | −1.06844e7 | −0.561726 | ||||||||
\(817\) | −1.09155e7 | −0.572123 | ||||||||
\(818\) | −535362. | −0.0279746 | ||||||||
\(819\) | 6.18194e6 | 0.322044 | ||||||||
\(820\) | 1.01053e7 | 0.524825 | ||||||||
\(821\) | −1.21032e7 | −0.626674 | −0.313337 | − | 0.949642i | \(-0.601447\pi\) | ||||
−0.313337 | + | 0.949642i | \(0.601447\pi\) | |||||||
\(822\) | 212736. | 0.0109815 | ||||||||
\(823\) | 1.52695e7 | 0.785823 | 0.392911 | − | 0.919576i | \(-0.371468\pi\) | ||||
0.392911 | + | 0.919576i | \(0.371468\pi\) | |||||||
\(824\) | 2.66866e6 | 0.136923 | ||||||||
\(825\) | −203682. | −0.0104188 | ||||||||
\(826\) | −342996. | −0.0174920 | ||||||||
\(827\) | 7.12088e6 | 0.362051 | 0.181026 | − | 0.983478i | \(-0.442058\pi\) | ||||
0.181026 | + | 0.983478i | \(0.442058\pi\) | |||||||
\(828\) | −9.09348e6 | −0.460950 | ||||||||
\(829\) | −3.88862e7 | −1.96521 | −0.982605 | − | 0.185709i | \(-0.940542\pi\) | ||||
−0.982605 | + | 0.185709i | \(0.940542\pi\) | |||||||
\(830\) | 2.02795e6 | 0.102179 | ||||||||
\(831\) | 5.74859e6 | 0.288775 | ||||||||
\(832\) | 1.65434e7 | 0.828547 | ||||||||
\(833\) | 3.54963e6 | 0.177243 | ||||||||
\(834\) | 776417. | 0.0386527 | ||||||||
\(835\) | −2.71262e7 | −1.34639 | ||||||||
\(836\) | 1.23950e7 | 0.613384 | ||||||||
\(837\) | 3.47741e6 | 0.171570 | ||||||||
\(838\) | −638370. | −0.0314023 | ||||||||
\(839\) | 1.23151e7 | 0.603992 | 0.301996 | − | 0.953309i | \(-0.402347\pi\) | ||||
0.301996 | + | 0.953309i | \(0.402347\pi\) | |||||||
\(840\) | 2.79371e6 | 0.136610 | ||||||||
\(841\) | 7.65435e6 | 0.373180 | ||||||||
\(842\) | −2.60368e6 | −0.126563 | ||||||||
\(843\) | −1.10045e7 | −0.533334 | ||||||||
\(844\) | 3.11242e6 | 0.150398 | ||||||||
\(845\) | 4.32286e6 | 0.208271 | ||||||||
\(846\) | −113867. | −0.00546981 | ||||||||
\(847\) | 5.96249e6 | 0.285574 | ||||||||
\(848\) | −697514. | −0.0333091 | ||||||||
\(849\) | −8.26118e6 | −0.393344 | ||||||||
\(850\) | 48515.4 | 0.00230320 | ||||||||
\(851\) | 1.50079e7 | 0.710389 | ||||||||
\(852\) | 1.57653e7 | 0.744051 | ||||||||
\(853\) | 1.66080e7 | 0.781527 | 0.390763 | − | 0.920491i | \(-0.372211\pi\) | ||||
0.390763 | + | 0.920491i | \(0.372211\pi\) | |||||||
\(854\) | 3.91267e6 | 0.183581 | ||||||||
\(855\) | 5.20683e6 | 0.243589 | ||||||||
\(856\) | −6.02457e6 | −0.281023 | ||||||||
\(857\) | 3.85279e7 | 1.79194 | 0.895969 | − | 0.444116i | \(-0.146482\pi\) | ||||
0.895969 | + | 0.444116i | \(0.146482\pi\) | |||||||
\(858\) | 1.03411e6 | 0.0479568 | ||||||||
\(859\) | −2.42173e7 | −1.11981 | −0.559904 | − | 0.828558i | \(-0.689162\pi\) | ||||
−0.559904 | + | 0.828558i | \(0.689162\pi\) | |||||||
\(860\) | 1.71332e7 | 0.789936 | ||||||||
\(861\) | 7.15740e6 | 0.329039 | ||||||||
\(862\) | 84206.6 | 0.00385992 | ||||||||
\(863\) | −2.38422e7 | −1.08973 | −0.544866 | − | 0.838523i | \(-0.683420\pi\) | ||||
−0.544866 | + | 0.838523i | \(0.683420\pi\) | |||||||
\(864\) | −1.35446e6 | −0.0617278 | ||||||||
\(865\) | −1.31457e7 | −0.597371 | ||||||||
\(866\) | −2.00095e6 | −0.0906655 | ||||||||
\(867\) | −217977. | −0.00984836 | ||||||||
\(868\) | −2.12044e7 | −0.955273 | ||||||||
\(869\) | 8.98368e6 | 0.403557 | ||||||||
\(870\) | 1.65778e6 | 0.0742555 | ||||||||
\(871\) | 1.04461e7 | 0.466562 | ||||||||
\(872\) | −6.06040e6 | −0.269905 | ||||||||
\(873\) | −7.28504e6 | −0.323517 | ||||||||
\(874\) | −2.48243e6 | −0.109925 | ||||||||
\(875\) | −2.42922e7 | −1.07262 | ||||||||
\(876\) | 2.18745e6 | 0.0963115 | ||||||||
\(877\) | −3.02587e7 | −1.32847 | −0.664234 | − | 0.747524i | \(-0.731242\pi\) | ||||
−0.664234 | + | 0.747524i | \(0.731242\pi\) | |||||||
\(878\) | −1.50101e6 | −0.0657125 | ||||||||
\(879\) | 2.04400e7 | 0.892297 | ||||||||
\(880\) | −1.92204e7 | −0.836674 | ||||||||
\(881\) | 1.03568e7 | 0.449557 | 0.224778 | − | 0.974410i | \(-0.427834\pi\) | ||||
0.224778 | + | 0.974410i | \(0.427834\pi\) | |||||||
\(882\) | 147013. | 0.00636331 | ||||||||
\(883\) | 3.13258e7 | 1.35207 | 0.676036 | − | 0.736868i | \(-0.263696\pi\) | ||||
0.676036 | + | 0.736868i | \(0.263696\pi\) | |||||||
\(884\) | 2.06314e7 | 0.887968 | ||||||||
\(885\) | 2.01878e6 | 0.0866427 | ||||||||
\(886\) | 3.28709e6 | 0.140678 | ||||||||
\(887\) | −2.57569e7 | −1.09922 | −0.549611 | − | 0.835421i | \(-0.685224\pi\) | ||||
−0.549611 | + | 0.835421i | \(0.685224\pi\) | |||||||
\(888\) | 1.48733e6 | 0.0632956 | ||||||||
\(889\) | 1.51475e7 | 0.642816 | ||||||||
\(890\) | −570639. | −0.0241483 | ||||||||
\(891\) | 2.25984e6 | 0.0953637 | ||||||||
\(892\) | 4.01174e7 | 1.68819 | ||||||||
\(893\) | 2.60362e6 | 0.109257 | ||||||||
\(894\) | −373382. | −0.0156246 | ||||||||
\(895\) | 907212. | 0.0378574 | ||||||||
\(896\) | 1.09897e7 | 0.457315 | ||||||||
\(897\) | 1.73472e7 | 0.719860 | ||||||||
\(898\) | −1.65943e6 | −0.0686700 | ||||||||
\(899\) | −2.53155e7 | −1.04469 | ||||||||
\(900\) | −168300. | −0.00692591 | ||||||||
\(901\) | −848468. | −0.0348196 | ||||||||
\(902\) | 1.19729e6 | 0.0489985 | ||||||||
\(903\) | 1.21351e7 | 0.495250 | ||||||||
\(904\) | 1.15728e6 | 0.0470995 | ||||||||
\(905\) | −1.70831e7 | −0.693337 | ||||||||
\(906\) | −2.58729e6 | −0.104719 | ||||||||
\(907\) | −2.94599e7 | −1.18909 | −0.594543 | − | 0.804064i | \(-0.702667\pi\) | ||||
−0.594543 | + | 0.804064i | \(0.702667\pi\) | |||||||
\(908\) | 8.32536e6 | 0.335111 | ||||||||
\(909\) | 2.70576e6 | 0.108612 | ||||||||
\(910\) | −2.64890e6 | −0.106038 | ||||||||
\(911\) | 4.73174e7 | 1.88897 | 0.944484 | − | 0.328557i | \(-0.106562\pi\) | ||||
0.944484 | + | 0.328557i | \(0.106562\pi\) | |||||||
\(912\) | 1.01181e7 | 0.402822 | ||||||||
\(913\) | −2.01251e7 | −0.799028 | ||||||||
\(914\) | 4.00883e6 | 0.158728 | ||||||||
\(915\) | −2.30290e7 | −0.909331 | ||||||||
\(916\) | 3.00478e7 | 1.18324 | ||||||||
\(917\) | 2.71989e7 | 1.06814 | ||||||||
\(918\) | −538276. | −0.0210813 | ||||||||
\(919\) | 1.40506e7 | 0.548789 | 0.274394 | − | 0.961617i | \(-0.411523\pi\) | ||||
0.274394 | + | 0.961617i | \(0.411523\pi\) | |||||||
\(920\) | 7.83944e6 | 0.305362 | ||||||||
\(921\) | −8.66705e6 | −0.336684 | ||||||||
\(922\) | 4.67147e6 | 0.180978 | ||||||||
\(923\) | −3.00746e7 | −1.16197 | ||||||||
\(924\) | −1.37800e7 | −0.530968 | ||||||||
\(925\) | 277762. | 0.0106738 | ||||||||
\(926\) | 631232. | 0.0241914 | ||||||||
\(927\) | −5.52950e6 | −0.211342 | ||||||||
\(928\) | 9.86044e6 | 0.375860 | ||||||||
\(929\) | 1.56511e7 | 0.594984 | 0.297492 | − | 0.954724i | \(-0.403850\pi\) | ||||
0.297492 | + | 0.954724i | \(0.403850\pi\) | |||||||
\(930\) | −1.49004e6 | −0.0564923 | ||||||||
\(931\) | −3.36150e6 | −0.127104 | ||||||||
\(932\) | −4.15940e7 | −1.56852 | ||||||||
\(933\) | −3.97792e6 | −0.149607 | ||||||||
\(934\) | −2.56453e6 | −0.0961925 | ||||||||
\(935\) | −2.33801e7 | −0.874615 | ||||||||
\(936\) | 1.71915e6 | 0.0641394 | ||||||||
\(937\) | −4.40124e7 | −1.63767 | −0.818835 | − | 0.574029i | \(-0.805380\pi\) | ||||
−0.818835 | + | 0.574029i | \(0.805380\pi\) | |||||||
\(938\) | 1.66189e6 | 0.0616731 | ||||||||
\(939\) | −7.86212e6 | −0.290988 | ||||||||
\(940\) | −4.08668e6 | −0.150852 | ||||||||
\(941\) | 5.03967e7 | 1.85536 | 0.927680 | − | 0.373377i | \(-0.121800\pi\) | ||||
0.927680 | + | 0.373377i | \(0.121800\pi\) | |||||||
\(942\) | 136309. | 0.00500491 | ||||||||
\(943\) | 2.00844e7 | 0.735496 | ||||||||
\(944\) | 3.92298e6 | 0.143280 | ||||||||
\(945\) | −5.78860e6 | −0.210860 | ||||||||
\(946\) | 2.02996e6 | 0.0737497 | ||||||||
\(947\) | 4.88209e7 | 1.76901 | 0.884507 | − | 0.466527i | \(-0.154495\pi\) | ||||
0.884507 | + | 0.466527i | \(0.154495\pi\) | |||||||
\(948\) | 7.42310e6 | 0.268265 | ||||||||
\(949\) | −4.17289e6 | −0.150408 | ||||||||
\(950\) | −45944.1 | −0.00165166 | ||||||||
\(951\) | −5.56661e6 | −0.199590 | ||||||||
\(952\) | 6.60375e6 | 0.236155 | ||||||||
\(953\) | −2.90983e6 | −0.103785 | −0.0518926 | − | 0.998653i | \(-0.516525\pi\) | ||||
−0.0518926 | + | 0.998653i | \(0.516525\pi\) | |||||||
\(954\) | −35140.5 | −0.00125008 | ||||||||
\(955\) | 2.29860e7 | 0.815557 | ||||||||
\(956\) | 4.85558e7 | 1.71829 | ||||||||
\(957\) | −1.64516e7 | −0.580669 | ||||||||
\(958\) | 1.22358e6 | 0.0430743 | ||||||||
\(959\) | 5.40778e6 | 0.189877 | ||||||||
\(960\) | −1.54908e7 | −0.542496 | ||||||||
\(961\) | −5.87519e6 | −0.205217 | ||||||||
\(962\) | −1.41023e6 | −0.0491306 | ||||||||
\(963\) | 1.24830e7 | 0.433764 | ||||||||
\(964\) | −2.77120e7 | −0.960451 | ||||||||
\(965\) | 4.07869e7 | 1.40994 | ||||||||
\(966\) | 2.75979e6 | 0.0951555 | ||||||||
\(967\) | 4.31477e7 | 1.48386 | 0.741928 | − | 0.670480i | \(-0.233912\pi\) | ||||
0.741928 | + | 0.670480i | \(0.233912\pi\) | |||||||
\(968\) | 1.65813e6 | 0.0568760 | ||||||||
\(969\) | 1.23079e7 | 0.421089 | ||||||||
\(970\) | 3.12157e6 | 0.106523 | ||||||||
\(971\) | −3.68680e6 | −0.125488 | −0.0627439 | − | 0.998030i | \(-0.519985\pi\) | ||||
−0.0627439 | + | 0.998030i | \(0.519985\pi\) | |||||||
\(972\) | 1.86727e6 | 0.0633932 | ||||||||
\(973\) | 1.97366e7 | 0.668330 | ||||||||
\(974\) | −2.46639e6 | −0.0833036 | ||||||||
\(975\) | 321057. | 0.0108161 | ||||||||
\(976\) | −4.47508e7 | −1.50375 | ||||||||
\(977\) | 9.86495e6 | 0.330642 | 0.165321 | − | 0.986240i | \(-0.447134\pi\) | ||||
0.165321 | + | 0.986240i | \(0.447134\pi\) | |||||||
\(978\) | −377606. | −0.0126239 | ||||||||
\(979\) | 5.66296e6 | 0.188837 | ||||||||
\(980\) | 5.27627e6 | 0.175494 | ||||||||
\(981\) | 1.25572e7 | 0.416602 | ||||||||
\(982\) | −4.64684e6 | −0.153773 | ||||||||
\(983\) | 3.98220e7 | 1.31444 | 0.657218 | − | 0.753700i | \(-0.271733\pi\) | ||||
0.657218 | + | 0.753700i | \(0.271733\pi\) | |||||||
\(984\) | 1.99042e6 | 0.0655326 | ||||||||
\(985\) | −3.83372e7 | −1.25901 | ||||||||
\(986\) | 3.91865e6 | 0.128364 | ||||||||
\(987\) | −2.89452e6 | −0.0945766 | ||||||||
\(988\) | −1.95379e7 | −0.636775 | ||||||||
\(989\) | 3.40524e7 | 1.10703 | ||||||||
\(990\) | −968317. | −0.0314000 | ||||||||
\(991\) | −1.89214e6 | −0.0612026 | −0.0306013 | − | 0.999532i | \(-0.509742\pi\) | ||||
−0.0306013 | + | 0.999532i | \(0.509742\pi\) | |||||||
\(992\) | −8.86270e6 | −0.285948 | ||||||||
\(993\) | −1.34163e7 | −0.431777 | ||||||||
\(994\) | −4.78463e6 | −0.153597 | ||||||||
\(995\) | 4.15567e7 | 1.33071 | ||||||||
\(996\) | −1.66291e7 | −0.531155 | ||||||||
\(997\) | −1.15061e7 | −0.366598 | −0.183299 | − | 0.983057i | \(-0.558678\pi\) | ||||
−0.183299 | + | 0.983057i | \(0.558678\pi\) | |||||||
\(998\) | 3.37502e6 | 0.107263 | ||||||||
\(999\) | −3.08176e6 | −0.0976978 |
(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 | 471.6.a.b.1.16 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
471.6.a.b.1.16 | ✓ | 30 | 1.1 | even | 1 | trivial |