Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,6,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(4.00959549532\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | 4.00000 | 0.256600 | 0.128300 | − | 0.991735i | \(-0.459048\pi\) | ||||
0.128300 | + | 0.991735i | \(0.459048\pi\) | |||||||
\(4\) | −28.0000 | −0.875000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −8.00000 | −0.0907218 | ||||||||
\(7\) | −192.000 | −1.48100 | −0.740502 | − | 0.672054i | \(-0.765412\pi\) | ||||
−0.740502 | + | 0.672054i | \(0.765412\pi\) | |||||||
\(8\) | 120.000 | 0.662913 | ||||||||
\(9\) | −227.000 | −0.934156 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −148.000 | −0.368791 | −0.184395 | − | 0.982852i | \(-0.559033\pi\) | ||||
−0.184395 | + | 0.982852i | \(0.559033\pi\) | |||||||
\(12\) | −112.000 | −0.224525 | ||||||||
\(13\) | −286.000 | −0.469362 | −0.234681 | − | 0.972072i | \(-0.575405\pi\) | ||||
−0.234681 | + | 0.972072i | \(0.575405\pi\) | |||||||
\(14\) | 384.000 | 0.523614 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 656.000 | 0.640625 | ||||||||
\(17\) | 1678.00 | 1.40822 | 0.704109 | − | 0.710092i | \(-0.251347\pi\) | ||||
0.704109 | + | 0.710092i | \(0.251347\pi\) | |||||||
\(18\) | 454.000 | 0.330274 | ||||||||
\(19\) | 1060.00 | 0.673631 | 0.336815 | − | 0.941571i | \(-0.390650\pi\) | ||||
0.336815 | + | 0.941571i | \(0.390650\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −768.000 | −0.380026 | ||||||||
\(22\) | 296.000 | 0.130387 | ||||||||
\(23\) | −2976.00 | −1.17304 | −0.586521 | − | 0.809934i | \(-0.699503\pi\) | ||||
−0.586521 | + | 0.809934i | \(0.699503\pi\) | |||||||
\(24\) | 480.000 | 0.170103 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 572.000 | 0.165944 | ||||||||
\(27\) | −1880.00 | −0.496305 | ||||||||
\(28\) | 5376.00 | 1.29588 | ||||||||
\(29\) | −3410.00 | −0.752938 | −0.376469 | − | 0.926429i | \(-0.622862\pi\) | ||||
−0.376469 | + | 0.926429i | \(0.622862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2448.00 | −0.457517 | −0.228758 | − | 0.973483i | \(-0.573467\pi\) | ||||
−0.228758 | + | 0.973483i | \(0.573467\pi\) | |||||||
\(32\) | −5152.00 | −0.889408 | ||||||||
\(33\) | −592.000 | −0.0946317 | ||||||||
\(34\) | −3356.00 | −0.497880 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6356.00 | 0.817387 | ||||||||
\(37\) | −182.000 | −0.0218558 | −0.0109279 | − | 0.999940i | \(-0.503479\pi\) | ||||
−0.0109279 | + | 0.999940i | \(0.503479\pi\) | |||||||
\(38\) | −2120.00 | −0.238164 | ||||||||
\(39\) | −1144.00 | −0.120438 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9398.00 | −0.873124 | −0.436562 | − | 0.899674i | \(-0.643804\pi\) | ||||
−0.436562 | + | 0.899674i | \(0.643804\pi\) | |||||||
\(42\) | 1536.00 | 0.134359 | ||||||||
\(43\) | 1244.00 | 0.102600 | 0.0513002 | − | 0.998683i | \(-0.483663\pi\) | ||||
0.0513002 | + | 0.998683i | \(0.483663\pi\) | |||||||
\(44\) | 4144.00 | 0.322692 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5952.00 | 0.414733 | ||||||||
\(47\) | 12088.0 | 0.798196 | 0.399098 | − | 0.916908i | \(-0.369323\pi\) | ||||
0.399098 | + | 0.916908i | \(0.369323\pi\) | |||||||
\(48\) | 2624.00 | 0.164384 | ||||||||
\(49\) | 20057.0 | 1.19337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6712.00 | 0.361349 | ||||||||
\(52\) | 8008.00 | 0.410691 | ||||||||
\(53\) | −23846.0 | −1.16607 | −0.583037 | − | 0.812446i | \(-0.698136\pi\) | ||||
−0.583037 | + | 0.812446i | \(0.698136\pi\) | |||||||
\(54\) | 3760.00 | 0.175470 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −23040.0 | −0.981776 | ||||||||
\(57\) | 4240.00 | 0.172854 | ||||||||
\(58\) | 6820.00 | 0.266204 | ||||||||
\(59\) | −20020.0 | −0.748745 | −0.374373 | − | 0.927278i | \(-0.622142\pi\) | ||||
−0.374373 | + | 0.927278i | \(0.622142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32302.0 | 1.11149 | 0.555744 | − | 0.831353i | \(-0.312433\pi\) | ||||
0.555744 | + | 0.831353i | \(0.312433\pi\) | |||||||
\(62\) | 4896.00 | 0.161757 | ||||||||
\(63\) | 43584.0 | 1.38349 | ||||||||
\(64\) | −10688.0 | −0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1184.00 | 0.0334574 | ||||||||
\(67\) | −60972.0 | −1.65937 | −0.829685 | − | 0.558231i | \(-0.811480\pi\) | ||||
−0.829685 | + | 0.558231i | \(0.811480\pi\) | |||||||
\(68\) | −46984.0 | −1.23219 | ||||||||
\(69\) | −11904.0 | −0.301003 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −32648.0 | −0.768618 | −0.384309 | − | 0.923204i | \(-0.625560\pi\) | ||||
−0.384309 | + | 0.923204i | \(0.625560\pi\) | |||||||
\(72\) | −27240.0 | −0.619264 | ||||||||
\(73\) | 38774.0 | 0.851596 | 0.425798 | − | 0.904818i | \(-0.359993\pi\) | ||||
0.425798 | + | 0.904818i | \(0.359993\pi\) | |||||||
\(74\) | 364.000 | 0.00772720 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −29680.0 | −0.589427 | ||||||||
\(77\) | 28416.0 | 0.546180 | ||||||||
\(78\) | 2288.00 | 0.0425814 | ||||||||
\(79\) | −33360.0 | −0.601393 | −0.300696 | − | 0.953720i | \(-0.597219\pi\) | ||||
−0.300696 | + | 0.953720i | \(0.597219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 47641.0 | 0.806805 | ||||||||
\(82\) | 18796.0 | 0.308696 | ||||||||
\(83\) | −16716.0 | −0.266340 | −0.133170 | − | 0.991093i | \(-0.542516\pi\) | ||||
−0.133170 | + | 0.991093i | \(0.542516\pi\) | |||||||
\(84\) | 21504.0 | 0.332522 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2488.00 | −0.0362747 | ||||||||
\(87\) | −13640.0 | −0.193204 | ||||||||
\(88\) | −17760.0 | −0.244476 | ||||||||
\(89\) | 101370. | 1.35655 | 0.678273 | − | 0.734810i | \(-0.262729\pi\) | ||||
0.678273 | + | 0.734810i | \(0.262729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 54912.0 | 0.695126 | ||||||||
\(92\) | 83328.0 | 1.02641 | ||||||||
\(93\) | −9792.00 | −0.117399 | ||||||||
\(94\) | −24176.0 | −0.282205 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −20608.0 | −0.228222 | ||||||||
\(97\) | 119038. | 1.28457 | 0.642283 | − | 0.766468i | \(-0.277987\pi\) | ||||
0.642283 | + | 0.766468i | \(0.277987\pi\) | |||||||
\(98\) | −40114.0 | −0.421921 | ||||||||
\(99\) | 33596.0 | 0.344508 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −89898.0 | −0.876893 | −0.438446 | − | 0.898757i | \(-0.644471\pi\) | ||||
−0.438446 | + | 0.898757i | \(0.644471\pi\) | |||||||
\(102\) | −13424.0 | −0.127756 | ||||||||
\(103\) | 19504.0 | 0.181147 | 0.0905734 | − | 0.995890i | \(-0.471130\pi\) | ||||
0.0905734 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(104\) | −34320.0 | −0.311146 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 47692.0 | 0.412269 | ||||||||
\(107\) | −158292. | −1.33659 | −0.668297 | − | 0.743895i | \(-0.732976\pi\) | ||||
−0.668297 | + | 0.743895i | \(0.732976\pi\) | |||||||
\(108\) | 52640.0 | 0.434267 | ||||||||
\(109\) | 36830.0 | 0.296917 | 0.148459 | − | 0.988919i | \(-0.452569\pi\) | ||||
0.148459 | + | 0.988919i | \(0.452569\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −728.000 | −0.00560821 | ||||||||
\(112\) | −125952. | −0.948768 | ||||||||
\(113\) | −11186.0 | −0.0824098 | −0.0412049 | − | 0.999151i | \(-0.513120\pi\) | ||||
−0.0412049 | + | 0.999151i | \(0.513120\pi\) | |||||||
\(114\) | −8480.00 | −0.0611130 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 95480.0 | 0.658821 | ||||||||
\(117\) | 64922.0 | 0.438457 | ||||||||
\(118\) | 40040.0 | 0.264721 | ||||||||
\(119\) | −322176. | −2.08557 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139147. | −0.863993 | ||||||||
\(122\) | −64604.0 | −0.392970 | ||||||||
\(123\) | −37592.0 | −0.224044 | ||||||||
\(124\) | 68544.0 | 0.400327 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −87168.0 | −0.489137 | ||||||||
\(127\) | −70552.0 | −0.388150 | −0.194075 | − | 0.980987i | \(-0.562171\pi\) | ||||
−0.194075 | + | 0.980987i | \(0.562171\pi\) | |||||||
\(128\) | 186240. | 1.00473 | ||||||||
\(129\) | 4976.00 | 0.0263273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 76452.0 | 0.389234 | 0.194617 | − | 0.980879i | \(-0.437654\pi\) | ||||
0.194617 | + | 0.980879i | \(0.437654\pi\) | |||||||
\(132\) | 16576.0 | 0.0828028 | ||||||||
\(133\) | −203520. | −0.997650 | ||||||||
\(134\) | 121944. | 0.586676 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 201360. | 0.933525 | ||||||||
\(137\) | 144918. | 0.659661 | 0.329831 | − | 0.944040i | \(-0.393008\pi\) | ||||
0.329831 | + | 0.944040i | \(0.393008\pi\) | |||||||
\(138\) | 23808.0 | 0.106420 | ||||||||
\(139\) | 112220. | 0.492644 | 0.246322 | − | 0.969188i | \(-0.420778\pi\) | ||||
0.246322 | + | 0.969188i | \(0.420778\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 48352.0 | 0.204817 | ||||||||
\(142\) | 65296.0 | 0.271748 | ||||||||
\(143\) | 42328.0 | 0.173096 | ||||||||
\(144\) | −148912. | −0.598444 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −77548.0 | −0.301085 | ||||||||
\(147\) | 80228.0 | 0.306219 | ||||||||
\(148\) | 5096.00 | 0.0191238 | ||||||||
\(149\) | 403750. | 1.48986 | 0.744932 | − | 0.667140i | \(-0.232482\pi\) | ||||
0.744932 | + | 0.667140i | \(0.232482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −446648. | −1.59413 | −0.797064 | − | 0.603895i | \(-0.793615\pi\) | ||||
−0.797064 | + | 0.603895i | \(0.793615\pi\) | |||||||
\(152\) | 127200. | 0.446558 | ||||||||
\(153\) | −380906. | −1.31550 | ||||||||
\(154\) | −56832.0 | −0.193104 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 32032.0 | 0.105383 | ||||||||
\(157\) | 262258. | 0.849141 | 0.424570 | − | 0.905395i | \(-0.360425\pi\) | ||||
0.424570 | + | 0.905395i | \(0.360425\pi\) | |||||||
\(158\) | 66720.0 | 0.212625 | ||||||||
\(159\) | −95384.0 | −0.299215 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 571392. | 1.73728 | ||||||||
\(162\) | −95282.0 | −0.285248 | ||||||||
\(163\) | 154564. | 0.455658 | 0.227829 | − | 0.973701i | \(-0.426837\pi\) | ||||
0.227829 | + | 0.973701i | \(0.426837\pi\) | |||||||
\(164\) | 263144. | 0.763983 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 33432.0 | 0.0941656 | ||||||||
\(167\) | −396672. | −1.10063 | −0.550314 | − | 0.834958i | \(-0.685492\pi\) | ||||
−0.550314 | + | 0.834958i | \(0.685492\pi\) | |||||||
\(168\) | −92160.0 | −0.251924 | ||||||||
\(169\) | −289497. | −0.779700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −240620. | −0.629276 | ||||||||
\(172\) | −34832.0 | −0.0897754 | ||||||||
\(173\) | 573474. | 1.45680 | 0.728398 | − | 0.685155i | \(-0.240265\pi\) | ||||
0.728398 | + | 0.685155i | \(0.240265\pi\) | |||||||
\(174\) | 27280.0 | 0.0683079 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −97088.0 | −0.236257 | ||||||||
\(177\) | −80080.0 | −0.192128 | ||||||||
\(178\) | −202740. | −0.479611 | ||||||||
\(179\) | −594460. | −1.38672 | −0.693362 | − | 0.720589i | \(-0.743871\pi\) | ||||
−0.693362 | + | 0.720589i | \(0.743871\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −107098. | −0.242988 | −0.121494 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121494 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(182\) | −109824. | −0.245764 | ||||||||
\(183\) | 129208. | 0.285208 | ||||||||
\(184\) | −357120. | −0.777624 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 19584.0 | 0.0415068 | ||||||||
\(187\) | −248344. | −0.519337 | ||||||||
\(188\) | −338464. | −0.698422 | ||||||||
\(189\) | 360960. | 0.735029 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 469552. | 0.931323 | 0.465661 | − | 0.884963i | \(-0.345816\pi\) | ||||
0.465661 | + | 0.884963i | \(0.345816\pi\) | |||||||
\(192\) | −42752.0 | −0.0836957 | ||||||||
\(193\) | −52706.0 | −0.101851 | −0.0509257 | − | 0.998702i | \(-0.516217\pi\) | ||||
−0.0509257 | + | 0.998702i | \(0.516217\pi\) | |||||||
\(194\) | −238076. | −0.454163 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −561596. | −1.04420 | ||||||||
\(197\) | −455862. | −0.836889 | −0.418444 | − | 0.908242i | \(-0.637425\pi\) | ||||
−0.418444 | + | 0.908242i | \(0.637425\pi\) | |||||||
\(198\) | −67192.0 | −0.121802 | ||||||||
\(199\) | 865000. | 1.54840 | 0.774200 | − | 0.632940i | \(-0.218152\pi\) | ||||
0.774200 | + | 0.632940i | \(0.218152\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −243888. | −0.425795 | ||||||||
\(202\) | 179796. | 0.310028 | ||||||||
\(203\) | 654720. | 1.11510 | ||||||||
\(204\) | −187936. | −0.316180 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −39008.0 | −0.0640451 | ||||||||
\(207\) | 675552. | 1.09580 | ||||||||
\(208\) | −187616. | −0.300685 | ||||||||
\(209\) | −156880. | −0.248429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.10565e6 | 1.70967 | 0.854835 | − | 0.518900i | \(-0.173658\pi\) | ||||
0.854835 | + | 0.518900i | \(0.173658\pi\) | |||||||
\(212\) | 667688. | 1.02031 | ||||||||
\(213\) | −130592. | −0.197228 | ||||||||
\(214\) | 316584. | 0.472557 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −225600. | −0.329007 | ||||||||
\(217\) | 470016. | 0.677584 | ||||||||
\(218\) | −73660.0 | −0.104976 | ||||||||
\(219\) | 155096. | 0.218520 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −479908. | −0.660963 | ||||||||
\(222\) | 1456.00 | 0.00198280 | ||||||||
\(223\) | −1.12158e6 | −1.51031 | −0.755156 | − | 0.655545i | \(-0.772439\pi\) | ||||
−0.755156 | + | 0.655545i | \(0.772439\pi\) | |||||||
\(224\) | 989184. | 1.31722 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 22372.0 | 0.0291363 | ||||||||
\(227\) | 23348.0 | 0.0300736 | 0.0150368 | − | 0.999887i | \(-0.495213\pi\) | ||||
0.0150368 | + | 0.999887i | \(0.495213\pi\) | |||||||
\(228\) | −118720. | −0.151247 | ||||||||
\(229\) | −596010. | −0.751043 | −0.375522 | − | 0.926814i | \(-0.622536\pi\) | ||||
−0.375522 | + | 0.926814i | \(0.622536\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 113664. | 0.140150 | ||||||||
\(232\) | −409200. | −0.499132 | ||||||||
\(233\) | 485334. | 0.585667 | 0.292834 | − | 0.956163i | \(-0.405402\pi\) | ||||
0.292834 | + | 0.956163i | \(0.405402\pi\) | |||||||
\(234\) | −129844. | −0.155018 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 560560. | 0.655152 | ||||||||
\(237\) | −133440. | −0.154317 | ||||||||
\(238\) | 644352. | 0.737362 | ||||||||
\(239\) | −48880.0 | −0.0553524 | −0.0276762 | − | 0.999617i | \(-0.508811\pi\) | ||||
−0.0276762 | + | 0.999617i | \(0.508811\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −110798. | −0.122882 | −0.0614411 | − | 0.998111i | \(-0.519570\pi\) | ||||
−0.0614411 | + | 0.998111i | \(0.519570\pi\) | |||||||
\(242\) | 278294. | 0.305468 | ||||||||
\(243\) | 647404. | 0.703331 | ||||||||
\(244\) | −904456. | −0.972552 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 75184.0 | 0.0792114 | ||||||||
\(247\) | −303160. | −0.316176 | ||||||||
\(248\) | −293760. | −0.303294 | ||||||||
\(249\) | −66864.0 | −0.0683430 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.64375e6 | −1.64684 | −0.823419 | − | 0.567434i | \(-0.807936\pi\) | ||||
−0.823419 | + | 0.567434i | \(0.807936\pi\) | |||||||
\(252\) | −1.22035e6 | −1.21055 | ||||||||
\(253\) | 440448. | 0.432607 | ||||||||
\(254\) | 141104. | 0.137232 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30464.0 | −0.0290527 | ||||||||
\(257\) | −1.30624e6 | −1.23365 | −0.616823 | − | 0.787102i | \(-0.711581\pi\) | ||||
−0.616823 | + | 0.787102i | \(0.711581\pi\) | |||||||
\(258\) | −9952.00 | −0.00930810 | ||||||||
\(259\) | 34944.0 | 0.0323685 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 774070. | 0.703362 | ||||||||
\(262\) | −152904. | −0.137615 | ||||||||
\(263\) | −2.12834e6 | −1.89736 | −0.948682 | − | 0.316231i | \(-0.897583\pi\) | ||||
−0.948682 | + | 0.316231i | \(0.897583\pi\) | |||||||
\(264\) | −71040.0 | −0.0627326 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 407040. | 0.352722 | ||||||||
\(267\) | 405480. | 0.348090 | ||||||||
\(268\) | 1.70722e6 | 1.45195 | ||||||||
\(269\) | −1.44109e6 | −1.21426 | −0.607128 | − | 0.794604i | \(-0.707679\pi\) | ||||
−0.607128 | + | 0.794604i | \(0.707679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −93248.0 | −0.0771288 | −0.0385644 | − | 0.999256i | \(-0.512278\pi\) | ||||
−0.0385644 | + | 0.999256i | \(0.512278\pi\) | |||||||
\(272\) | 1.10077e6 | 0.902139 | ||||||||
\(273\) | 219648. | 0.178370 | ||||||||
\(274\) | −289836. | −0.233225 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 333312. | 0.263377 | ||||||||
\(277\) | 110298. | 0.0863711 | 0.0431855 | − | 0.999067i | \(-0.486249\pi\) | ||||
0.0431855 | + | 0.999067i | \(0.486249\pi\) | |||||||
\(278\) | −224440. | −0.174176 | ||||||||
\(279\) | 555696. | 0.427392 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −192198. | −0.145205 | −0.0726027 | − | 0.997361i | \(-0.523131\pi\) | ||||
−0.0726027 | + | 0.997361i | \(0.523131\pi\) | |||||||
\(282\) | −96704.0 | −0.0724139 | ||||||||
\(283\) | 331884. | 0.246332 | 0.123166 | − | 0.992386i | \(-0.460695\pi\) | ||||
0.123166 | + | 0.992386i | \(0.460695\pi\) | |||||||
\(284\) | 914144. | 0.672541 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −84656.0 | −0.0611988 | ||||||||
\(287\) | 1.80442e6 | 1.29310 | ||||||||
\(288\) | 1.16950e6 | 0.830846 | ||||||||
\(289\) | 1.39583e6 | 0.983076 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 476152. | 0.329620 | ||||||||
\(292\) | −1.08567e6 | −0.745146 | ||||||||
\(293\) | −2.19481e6 | −1.49358 | −0.746788 | − | 0.665063i | \(-0.768405\pi\) | ||||
−0.746788 | + | 0.665063i | \(0.768405\pi\) | |||||||
\(294\) | −160456. | −0.108265 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −21840.0 | −0.0144885 | ||||||||
\(297\) | 278240. | 0.183033 | ||||||||
\(298\) | −807500. | −0.526747 | ||||||||
\(299\) | 851136. | 0.550581 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −238848. | −0.151952 | ||||||||
\(302\) | 893296. | 0.563609 | ||||||||
\(303\) | −359592. | −0.225011 | ||||||||
\(304\) | 695360. | 0.431545 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 761812. | 0.465098 | ||||||||
\(307\) | 2.37751e6 | 1.43971 | 0.719857 | − | 0.694123i | \(-0.244207\pi\) | ||||
0.719857 | + | 0.694123i | \(0.244207\pi\) | |||||||
\(308\) | −795648. | −0.477908 | ||||||||
\(309\) | 78016.0 | 0.0464823 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.37305e6 | −1.39125 | −0.695626 | − | 0.718405i | \(-0.744873\pi\) | ||||
−0.695626 | + | 0.718405i | \(0.744873\pi\) | |||||||
\(312\) | −137280. | −0.0798400 | ||||||||
\(313\) | 1.42941e6 | 0.824702 | 0.412351 | − | 0.911025i | \(-0.364708\pi\) | ||||
0.412351 | + | 0.911025i | \(0.364708\pi\) | |||||||
\(314\) | −524516. | −0.300217 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 934080. | 0.526219 | ||||||||
\(317\) | −2.12462e6 | −1.18750 | −0.593750 | − | 0.804650i | \(-0.702353\pi\) | ||||
−0.593750 | + | 0.804650i | \(0.702353\pi\) | |||||||
\(318\) | 190768. | 0.105788 | ||||||||
\(319\) | 504680. | 0.277677 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −633168. | −0.342970 | ||||||||
\(322\) | −1.14278e6 | −0.614221 | ||||||||
\(323\) | 1.77868e6 | 0.948618 | ||||||||
\(324\) | −1.33395e6 | −0.705954 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −309128. | −0.161100 | ||||||||
\(327\) | 147320. | 0.0761890 | ||||||||
\(328\) | −1.12776e6 | −0.578805 | ||||||||
\(329\) | −2.32090e6 | −1.18213 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.09985e6 | 1.55515 | 0.777573 | − | 0.628793i | \(-0.216451\pi\) | ||||
0.777573 | + | 0.628793i | \(0.216451\pi\) | |||||||
\(332\) | 468048. | 0.233048 | ||||||||
\(333\) | 41314.0 | 0.0204168 | ||||||||
\(334\) | 793344. | 0.389131 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −503808. | −0.243454 | ||||||||
\(337\) | −2.40008e6 | −1.15120 | −0.575601 | − | 0.817731i | \(-0.695232\pi\) | ||||
−0.575601 | + | 0.817731i | \(0.695232\pi\) | |||||||
\(338\) | 578994. | 0.275665 | ||||||||
\(339\) | −44744.0 | −0.0211464 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 362304. | 0.168728 | ||||||||
\(342\) | 481240. | 0.222483 | ||||||||
\(343\) | −624000. | −0.286384 | ||||||||
\(344\) | 149280. | 0.0680151 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.14695e6 | −0.515055 | ||||||||
\(347\) | −1.77741e6 | −0.792436 | −0.396218 | − | 0.918156i | \(-0.629678\pi\) | ||||
−0.396218 | + | 0.918156i | \(0.629678\pi\) | |||||||
\(348\) | 381920. | 0.169054 | ||||||||
\(349\) | −2.14805e6 | −0.944019 | −0.472010 | − | 0.881593i | \(-0.656471\pi\) | ||||
−0.472010 | + | 0.881593i | \(0.656471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 537680. | 0.232946 | ||||||||
\(352\) | 762496. | 0.328005 | ||||||||
\(353\) | 661854. | 0.282700 | 0.141350 | − | 0.989960i | \(-0.454856\pi\) | ||||
0.141350 | + | 0.989960i | \(0.454856\pi\) | |||||||
\(354\) | 160160. | 0.0679275 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.83836e6 | −1.18698 | ||||||||
\(357\) | −1.28870e6 | −0.535159 | ||||||||
\(358\) | 1.18892e6 | 0.490281 | ||||||||
\(359\) | −259320. | −0.106194 | −0.0530970 | − | 0.998589i | \(-0.516909\pi\) | ||||
−0.0530970 | + | 0.998589i | \(0.516909\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.35250e6 | −0.546222 | ||||||||
\(362\) | 214196. | 0.0859093 | ||||||||
\(363\) | −556588. | −0.221701 | ||||||||
\(364\) | −1.53754e6 | −0.608236 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −258416. | −0.100836 | ||||||||
\(367\) | 1.49993e6 | 0.581307 | 0.290653 | − | 0.956828i | \(-0.406127\pi\) | ||||
0.290653 | + | 0.956828i | \(0.406127\pi\) | |||||||
\(368\) | −1.95226e6 | −0.751480 | ||||||||
\(369\) | 2.13335e6 | 0.815634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.57843e6 | 1.72696 | ||||||||
\(372\) | 274176. | 0.102724 | ||||||||
\(373\) | 2.23807e6 | 0.832918 | 0.416459 | − | 0.909154i | \(-0.363271\pi\) | ||||
0.416459 | + | 0.909154i | \(0.363271\pi\) | |||||||
\(374\) | 496688. | 0.183614 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.45056e6 | 0.529135 | ||||||||
\(377\) | 975260. | 0.353400 | ||||||||
\(378\) | −721920. | −0.259872 | ||||||||
\(379\) | 3.15934e6 | 1.12979 | 0.564896 | − | 0.825162i | \(-0.308916\pi\) | ||||
0.564896 | + | 0.825162i | \(0.308916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −282208. | −0.0995994 | ||||||||
\(382\) | −939104. | −0.329272 | ||||||||
\(383\) | −342216. | −0.119207 | −0.0596037 | − | 0.998222i | \(-0.518984\pi\) | ||||
−0.0596037 | + | 0.998222i | \(0.518984\pi\) | |||||||
\(384\) | 744960. | 0.257813 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 105412. | 0.0360099 | ||||||||
\(387\) | −282388. | −0.0958449 | ||||||||
\(388\) | −3.33306e6 | −1.12399 | ||||||||
\(389\) | 88470.0 | 0.0296430 | 0.0148215 | − | 0.999890i | \(-0.495282\pi\) | ||||
0.0148215 | + | 0.999890i | \(0.495282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.99373e6 | −1.65190 | ||||||||
\(392\) | 2.40684e6 | 0.791101 | ||||||||
\(393\) | 305808. | 0.0998775 | ||||||||
\(394\) | 911724. | 0.295885 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −940688. | −0.301445 | ||||||||
\(397\) | 5.45674e6 | 1.73763 | 0.868814 | − | 0.495138i | \(-0.164883\pi\) | ||||
0.868814 | + | 0.495138i | \(0.164883\pi\) | |||||||
\(398\) | −1.73000e6 | −0.547442 | ||||||||
\(399\) | −814080. | −0.255997 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.04680e6 | 1.25676 | 0.628378 | − | 0.777908i | \(-0.283719\pi\) | ||||
0.628378 | + | 0.777908i | \(0.283719\pi\) | |||||||
\(402\) | 487776. | 0.150541 | ||||||||
\(403\) | 700128. | 0.214741 | ||||||||
\(404\) | 2.51714e6 | 0.767281 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.30944e6 | −0.394249 | ||||||||
\(407\) | 26936.0 | 0.00806022 | ||||||||
\(408\) | 805440. | 0.239543 | ||||||||
\(409\) | −2.71207e6 | −0.801664 | −0.400832 | − | 0.916151i | \(-0.631279\pi\) | ||||
−0.400832 | + | 0.916151i | \(0.631279\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 579672. | 0.169269 | ||||||||
\(412\) | −546112. | −0.158503 | ||||||||
\(413\) | 3.84384e6 | 1.10889 | ||||||||
\(414\) | −1.35110e6 | −0.387425 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.47347e6 | 0.417454 | ||||||||
\(417\) | 448880. | 0.126413 | ||||||||
\(418\) | 313760. | 0.0878328 | ||||||||
\(419\) | 3.71746e6 | 1.03445 | 0.517227 | − | 0.855848i | \(-0.326964\pi\) | ||||
0.517227 | + | 0.855848i | \(0.326964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.55250e6 | 0.976853 | 0.488426 | − | 0.872605i | \(-0.337571\pi\) | ||||
0.488426 | + | 0.872605i | \(0.337571\pi\) | |||||||
\(422\) | −2.21130e6 | −0.604460 | ||||||||
\(423\) | −2.74398e6 | −0.745640 | ||||||||
\(424\) | −2.86152e6 | −0.773005 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 261184. | 0.0697305 | ||||||||
\(427\) | −6.20198e6 | −1.64612 | ||||||||
\(428\) | 4.43218e6 | 1.16952 | ||||||||
\(429\) | 169312. | 0.0444165 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.06205e6 | −1.05330 | −0.526650 | − | 0.850082i | \(-0.676552\pi\) | ||||
−0.526650 | + | 0.850082i | \(0.676552\pi\) | |||||||
\(432\) | −1.23328e6 | −0.317945 | ||||||||
\(433\) | −7.26287e6 | −1.86161 | −0.930804 | − | 0.365518i | \(-0.880892\pi\) | ||||
−0.930804 | + | 0.365518i | \(0.880892\pi\) | |||||||
\(434\) | −940032. | −0.239562 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.03124e6 | −0.259803 | ||||||||
\(437\) | −3.15456e6 | −0.790197 | ||||||||
\(438\) | −310192. | −0.0772583 | ||||||||
\(439\) | −5.41028e6 | −1.33986 | −0.669928 | − | 0.742426i | \(-0.733675\pi\) | ||||
−0.669928 | + | 0.742426i | \(0.733675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.55294e6 | −1.11480 | ||||||||
\(442\) | 959816. | 0.233686 | ||||||||
\(443\) | 6.51524e6 | 1.57733 | 0.788663 | − | 0.614826i | \(-0.210774\pi\) | ||||
0.788663 | + | 0.614826i | \(0.210774\pi\) | |||||||
\(444\) | 20384.0 | 0.00490718 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.24315e6 | 0.533976 | ||||||||
\(447\) | 1.61500e6 | 0.382299 | ||||||||
\(448\) | 2.05210e6 | 0.483062 | ||||||||
\(449\) | −509950. | −0.119375 | −0.0596873 | − | 0.998217i | \(-0.519010\pi\) | ||||
−0.0596873 | + | 0.998217i | \(0.519010\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.39090e6 | 0.322000 | ||||||||
\(452\) | 313208. | 0.0721085 | ||||||||
\(453\) | −1.78659e6 | −0.409053 | ||||||||
\(454\) | −46696.0 | −0.0106326 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 508800. | 0.114587 | ||||||||
\(457\) | −1.22084e6 | −0.273444 | −0.136722 | − | 0.990609i | \(-0.543657\pi\) | ||||
−0.136722 | + | 0.990609i | \(0.543657\pi\) | |||||||
\(458\) | 1.19202e6 | 0.265534 | ||||||||
\(459\) | −3.15464e6 | −0.698905 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.07210e6 | −0.892413 | −0.446207 | − | 0.894930i | \(-0.647225\pi\) | ||||
−0.446207 | + | 0.894930i | \(0.647225\pi\) | |||||||
\(462\) | −227328. | −0.0495505 | ||||||||
\(463\) | −2.02294e6 | −0.438561 | −0.219280 | − | 0.975662i | \(-0.570371\pi\) | ||||
−0.219280 | + | 0.975662i | \(0.570371\pi\) | |||||||
\(464\) | −2.23696e6 | −0.482351 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −970668. | −0.207065 | ||||||||
\(467\) | −3.25097e6 | −0.689797 | −0.344898 | − | 0.938640i | \(-0.612087\pi\) | ||||
−0.344898 | + | 0.938640i | \(0.612087\pi\) | |||||||
\(468\) | −1.81782e6 | −0.383650 | ||||||||
\(469\) | 1.17066e7 | 2.45753 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.04903e6 | 0.217890 | ||||||||
\(472\) | −2.40240e6 | −0.496353 | ||||||||
\(473\) | −184112. | −0.0378381 | ||||||||
\(474\) | 266880. | 0.0545595 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.02093e6 | 1.82488 | ||||||||
\(477\) | 5.41304e6 | 1.08929 | ||||||||
\(478\) | 97760.0 | 0.0195700 | ||||||||
\(479\) | −3.27936e6 | −0.653056 | −0.326528 | − | 0.945188i | \(-0.605879\pi\) | ||||
−0.326528 | + | 0.945188i | \(0.605879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52052.0 | 0.0102583 | ||||||||
\(482\) | 221596. | 0.0434455 | ||||||||
\(483\) | 2.28557e6 | 0.445786 | ||||||||
\(484\) | 3.89612e6 | 0.755994 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.29481e6 | −0.248665 | ||||||||
\(487\) | 8.53197e6 | 1.63015 | 0.815074 | − | 0.579357i | \(-0.196696\pi\) | ||||
0.815074 | + | 0.579357i | \(0.196696\pi\) | |||||||
\(488\) | 3.87624e6 | 0.736819 | ||||||||
\(489\) | 618256. | 0.116922 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.51265e6 | 0.283162 | 0.141581 | − | 0.989927i | \(-0.454781\pi\) | ||||
0.141581 | + | 0.989927i | \(0.454781\pi\) | |||||||
\(492\) | 1.05258e6 | 0.196038 | ||||||||
\(493\) | −5.72198e6 | −1.06030 | ||||||||
\(494\) | 606320. | 0.111785 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.60589e6 | −0.293097 | ||||||||
\(497\) | 6.26842e6 | 1.13833 | ||||||||
\(498\) | 133728. | 0.0241629 | ||||||||
\(499\) | −6.49190e6 | −1.16713 | −0.583567 | − | 0.812065i | \(-0.698343\pi\) | ||||
−0.583567 | + | 0.812065i | \(0.698343\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.58669e6 | −0.282421 | ||||||||
\(502\) | 3.28750e6 | 0.582245 | ||||||||
\(503\) | −8.61770e6 | −1.51870 | −0.759349 | − | 0.650684i | \(-0.774482\pi\) | ||||
−0.759349 | + | 0.650684i | \(0.774482\pi\) | |||||||
\(504\) | 5.23008e6 | 0.917132 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −880896. | −0.152950 | ||||||||
\(507\) | −1.15799e6 | −0.200071 | ||||||||
\(508\) | 1.97546e6 | 0.339632 | ||||||||
\(509\) | 2.67323e6 | 0.457343 | 0.228671 | − | 0.973504i | \(-0.426562\pi\) | ||||
0.228671 | + | 0.973504i | \(0.426562\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.44461e6 | −1.26122 | ||||||||
\(512\) | −5.89875e6 | −0.994455 | ||||||||
\(513\) | −1.99280e6 | −0.334326 | ||||||||
\(514\) | 2.61248e6 | 0.436160 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −139328. | −0.0230364 | ||||||||
\(517\) | −1.78902e6 | −0.294367 | ||||||||
\(518\) | −69888.0 | −0.0114440 | ||||||||
\(519\) | 2.29390e6 | 0.373814 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.18500e6 | 0.998264 | 0.499132 | − | 0.866526i | \(-0.333652\pi\) | ||||
0.499132 | + | 0.866526i | \(0.333652\pi\) | |||||||
\(522\) | −1.54814e6 | −0.248676 | ||||||||
\(523\) | 6.89452e6 | 1.10217 | 0.551087 | − | 0.834448i | \(-0.314213\pi\) | ||||
0.551087 | + | 0.834448i | \(0.314213\pi\) | |||||||
\(524\) | −2.14066e6 | −0.340580 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.25667e6 | 0.670820 | ||||||||
\(527\) | −4.10774e6 | −0.644283 | ||||||||
\(528\) | −388352. | −0.0606235 | ||||||||
\(529\) | 2.42023e6 | 0.376026 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.54454e6 | 0.699445 | ||||||||
\(532\) | 5.69856e6 | 0.872943 | ||||||||
\(533\) | 2.68783e6 | 0.409811 | ||||||||
\(534\) | −810960. | −0.123068 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.31664e6 | −1.10002 | ||||||||
\(537\) | −2.37784e6 | −0.355834 | ||||||||
\(538\) | 2.88218e6 | 0.429304 | ||||||||
\(539\) | −2.96844e6 | −0.440104 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 155502. | 0.0228425 | 0.0114212 | − | 0.999935i | \(-0.496364\pi\) | ||||
0.0114212 | + | 0.999935i | \(0.496364\pi\) | |||||||
\(542\) | 186496. | 0.0272691 | ||||||||
\(543\) | −428392. | −0.0623508 | ||||||||
\(544\) | −8.64506e6 | −1.25248 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −439296. | −0.0630631 | ||||||||
\(547\) | −1.26544e7 | −1.80831 | −0.904157 | − | 0.427201i | \(-0.859500\pi\) | ||||
−0.904157 | + | 0.427201i | \(0.859500\pi\) | |||||||
\(548\) | −4.05770e6 | −0.577204 | ||||||||
\(549\) | −7.33255e6 | −1.03830 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.61460e6 | −0.507202 | ||||||||
\(552\) | −1.42848e6 | −0.199538 | ||||||||
\(553\) | 6.40512e6 | 0.890665 | ||||||||
\(554\) | −220596. | −0.0305368 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.14216e6 | −0.431064 | ||||||||
\(557\) | 7.07786e6 | 0.966638 | 0.483319 | − | 0.875444i | \(-0.339431\pi\) | ||||
0.483319 | + | 0.875444i | \(0.339431\pi\) | |||||||
\(558\) | −1.11139e6 | −0.151106 | ||||||||
\(559\) | −355784. | −0.0481567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −993376. | −0.133262 | ||||||||
\(562\) | 384396. | 0.0513379 | ||||||||
\(563\) | −846636. | −0.112571 | −0.0562854 | − | 0.998415i | \(-0.517926\pi\) | ||||
−0.0562854 | + | 0.998415i | \(0.517926\pi\) | |||||||
\(564\) | −1.35386e6 | −0.179215 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −663768. | −0.0870914 | ||||||||
\(567\) | −9.14707e6 | −1.19488 | ||||||||
\(568\) | −3.91776e6 | −0.509527 | ||||||||
\(569\) | 4.96041e6 | 0.642299 | 0.321149 | − | 0.947029i | \(-0.395931\pi\) | ||||
0.321149 | + | 0.947029i | \(0.395931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.96505e6 | 1.15070 | 0.575351 | − | 0.817907i | \(-0.304866\pi\) | ||||
0.575351 | + | 0.817907i | \(0.304866\pi\) | |||||||
\(572\) | −1.18518e6 | −0.151459 | ||||||||
\(573\) | 1.87821e6 | 0.238978 | ||||||||
\(574\) | −3.60883e6 | −0.457180 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.42618e6 | 0.304696 | ||||||||
\(577\) | 2.86080e6 | 0.357724 | 0.178862 | − | 0.983874i | \(-0.442758\pi\) | ||||
0.178862 | + | 0.983874i | \(0.442758\pi\) | |||||||
\(578\) | −2.79165e6 | −0.347570 | ||||||||
\(579\) | −210824. | −0.0261351 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.20947e6 | 0.394451 | ||||||||
\(582\) | −952304. | −0.116538 | ||||||||
\(583\) | 3.52921e6 | 0.430037 | ||||||||
\(584\) | 4.65288e6 | 0.564534 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.38961e6 | 0.528059 | ||||||||
\(587\) | 6.74027e6 | 0.807387 | 0.403694 | − | 0.914894i | \(-0.367726\pi\) | ||||
0.403694 | + | 0.914894i | \(0.367726\pi\) | |||||||
\(588\) | −2.24638e6 | −0.267942 | ||||||||
\(589\) | −2.59488e6 | −0.308197 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.82345e6 | −0.214746 | ||||||||
\(592\) | −119392. | −0.0140014 | ||||||||
\(593\) | 1.78609e6 | 0.208578 | 0.104289 | − | 0.994547i | \(-0.466743\pi\) | ||||
0.104289 | + | 0.994547i | \(0.466743\pi\) | |||||||
\(594\) | −556480. | −0.0647118 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.13050e7 | −1.30363 | ||||||||
\(597\) | 3.46000e6 | 0.397320 | ||||||||
\(598\) | −1.70227e6 | −0.194660 | ||||||||
\(599\) | 4.94620e6 | 0.563254 | 0.281627 | − | 0.959524i | \(-0.409126\pi\) | ||||
0.281627 | + | 0.959524i | \(0.409126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.58100e6 | −0.517337 | −0.258669 | − | 0.965966i | \(-0.583284\pi\) | ||||
−0.258669 | + | 0.965966i | \(0.583284\pi\) | |||||||
\(602\) | 477696. | 0.0537230 | ||||||||
\(603\) | 1.38406e7 | 1.55011 | ||||||||
\(604\) | 1.25061e7 | 1.39486 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 719184. | 0.0795533 | ||||||||
\(607\) | −7.07999e6 | −0.779940 | −0.389970 | − | 0.920828i | \(-0.627515\pi\) | ||||
−0.389970 | + | 0.920828i | \(0.627515\pi\) | |||||||
\(608\) | −5.46112e6 | −0.599132 | ||||||||
\(609\) | 2.61888e6 | 0.286136 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.45717e6 | −0.374643 | ||||||||
\(612\) | 1.06654e7 | 1.15106 | ||||||||
\(613\) | −5.09609e6 | −0.547754 | −0.273877 | − | 0.961765i | \(-0.588306\pi\) | ||||
−0.273877 | + | 0.961765i | \(0.588306\pi\) | |||||||
\(614\) | −4.75502e6 | −0.509016 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.40992e6 | 0.362070 | ||||||||
\(617\) | 1.30003e7 | 1.37480 | 0.687400 | − | 0.726279i | \(-0.258752\pi\) | ||||
0.687400 | + | 0.726279i | \(0.258752\pi\) | |||||||
\(618\) | −156032. | −0.0164340 | ||||||||
\(619\) | 4.84406e6 | 0.508139 | 0.254070 | − | 0.967186i | \(-0.418231\pi\) | ||||
0.254070 | + | 0.967186i | \(0.418231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.59488e6 | 0.582186 | ||||||||
\(622\) | 4.74610e6 | 0.491882 | ||||||||
\(623\) | −1.94630e7 | −2.00905 | ||||||||
\(624\) | −750464. | −0.0771558 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.85883e6 | −0.291576 | ||||||||
\(627\) | −627520. | −0.0637468 | ||||||||
\(628\) | −7.34322e6 | −0.742998 | ||||||||
\(629\) | −305396. | −0.0307777 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.22775e6 | 0.622670 | 0.311335 | − | 0.950300i | \(-0.399224\pi\) | ||||
0.311335 | + | 0.950300i | \(0.399224\pi\) | |||||||
\(632\) | −4.00320e6 | −0.398671 | ||||||||
\(633\) | 4.42261e6 | 0.438702 | ||||||||
\(634\) | 4.24924e6 | 0.419845 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.67075e6 | 0.261813 | ||||||||
\(637\) | −5.73630e6 | −0.560123 | ||||||||
\(638\) | −1.00936e6 | −0.0981735 | ||||||||
\(639\) | 7.41110e6 | 0.718010 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.53280e6 | 0.147347 | 0.0736734 | − | 0.997282i | \(-0.476528\pi\) | ||||
0.0736734 | + | 0.997282i | \(0.476528\pi\) | |||||||
\(642\) | 1.26634e6 | 0.121258 | ||||||||
\(643\) | 1.74382e7 | 1.66332 | 0.831659 | − | 0.555287i | \(-0.187391\pi\) | ||||
0.831659 | + | 0.555287i | \(0.187391\pi\) | |||||||
\(644\) | −1.59990e7 | −1.52012 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.55736e6 | −0.335387 | ||||||||
\(647\) | 4.25469e6 | 0.399583 | 0.199792 | − | 0.979838i | \(-0.435974\pi\) | ||||
0.199792 | + | 0.979838i | \(0.435974\pi\) | |||||||
\(648\) | 5.71692e6 | 0.534841 | ||||||||
\(649\) | 2.96296e6 | 0.276130 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88006e6 | 0.173868 | ||||||||
\(652\) | −4.32779e6 | −0.398701 | ||||||||
\(653\) | −3.01085e6 | −0.276316 | −0.138158 | − | 0.990410i | \(-0.544118\pi\) | ||||
−0.138158 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(654\) | −294640. | −0.0269369 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.16509e6 | −0.559345 | ||||||||
\(657\) | −8.80170e6 | −0.795524 | ||||||||
\(658\) | 4.64179e6 | 0.417947 | ||||||||
\(659\) | −8.11462e6 | −0.727871 | −0.363936 | − | 0.931424i | \(-0.618567\pi\) | ||||
−0.363936 | + | 0.931424i | \(0.618567\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.47370e6 | 0.220213 | 0.110107 | − | 0.993920i | \(-0.464881\pi\) | ||||
0.110107 | + | 0.993920i | \(0.464881\pi\) | |||||||
\(662\) | −6.19970e6 | −0.549827 | ||||||||
\(663\) | −1.91963e6 | −0.169603 | ||||||||
\(664\) | −2.00592e6 | −0.176560 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −82628.0 | −0.00721841 | ||||||||
\(667\) | 1.01482e7 | 0.883228 | ||||||||
\(668\) | 1.11068e7 | 0.963049 | ||||||||
\(669\) | −4.48630e6 | −0.387546 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.78070e6 | −0.409907 | ||||||||
\(672\) | 3.95674e6 | 0.337998 | ||||||||
\(673\) | −5.77063e6 | −0.491117 | −0.245559 | − | 0.969382i | \(-0.578971\pi\) | ||||
−0.245559 | + | 0.969382i | \(0.578971\pi\) | |||||||
\(674\) | 4.80016e6 | 0.407011 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.10592e6 | 0.682237 | ||||||||
\(677\) | −1.67197e7 | −1.40203 | −0.701014 | − | 0.713147i | \(-0.747269\pi\) | ||||
−0.701014 | + | 0.713147i | \(0.747269\pi\) | |||||||
\(678\) | 89488.0 | 0.00747637 | ||||||||
\(679\) | −2.28553e7 | −1.90245 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 93392.0 | 0.00771688 | ||||||||
\(682\) | −724608. | −0.0596544 | ||||||||
\(683\) | −7.14532e6 | −0.586097 | −0.293049 | − | 0.956098i | \(-0.594670\pi\) | ||||
−0.293049 | + | 0.956098i | \(0.594670\pi\) | |||||||
\(684\) | 6.73736e6 | 0.550617 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.24800e6 | 0.101252 | ||||||||
\(687\) | −2.38404e6 | −0.192718 | ||||||||
\(688\) | 816064. | 0.0657284 | ||||||||
\(689\) | 6.81996e6 | 0.547310 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.78395e6 | −0.699833 | −0.349917 | − | 0.936781i | \(-0.613790\pi\) | ||||
−0.349917 | + | 0.936781i | \(0.613790\pi\) | |||||||
\(692\) | −1.60573e7 | −1.27470 | ||||||||
\(693\) | −6.45043e6 | −0.510218 | ||||||||
\(694\) | 3.55482e6 | 0.280169 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.63680e6 | −0.128077 | ||||||||
\(697\) | −1.57698e7 | −1.22955 | ||||||||
\(698\) | 4.29610e6 | 0.333761 | ||||||||
\(699\) | 1.94134e6 | 0.150282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.60141e7 | −1.23086 | −0.615428 | − | 0.788193i | \(-0.711017\pi\) | ||||
−0.615428 | + | 0.788193i | \(0.711017\pi\) | |||||||
\(702\) | −1.07536e6 | −0.0823590 | ||||||||
\(703\) | −192920. | −0.0147228 | ||||||||
\(704\) | 1.58182e6 | 0.120289 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.32371e6 | −0.0999495 | ||||||||
\(707\) | 1.72604e7 | 1.29868 | ||||||||
\(708\) | 2.24224e6 | 0.168112 | ||||||||
\(709\) | −1.91354e7 | −1.42962 | −0.714811 | − | 0.699318i | \(-0.753487\pi\) | ||||
−0.714811 | + | 0.699318i | \(0.753487\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.57272e6 | 0.561795 | ||||||||
\(712\) | 1.21644e7 | 0.899271 | ||||||||
\(713\) | 7.28525e6 | 0.536686 | ||||||||
\(714\) | 2.57741e6 | 0.189207 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.66449e7 | 1.21338 | ||||||||
\(717\) | −195520. | −0.0142034 | ||||||||
\(718\) | 518640. | 0.0375452 | ||||||||
\(719\) | 1.02934e7 | 0.742566 | 0.371283 | − | 0.928520i | \(-0.378918\pi\) | ||||
0.371283 | + | 0.928520i | \(0.378918\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.74477e6 | −0.268279 | ||||||||
\(722\) | 2.70500e6 | 0.193119 | ||||||||
\(723\) | −443192. | −0.0315316 | ||||||||
\(724\) | 2.99874e6 | 0.212615 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.11318e6 | 0.0783831 | ||||||||
\(727\) | 1.93264e7 | 1.35618 | 0.678088 | − | 0.734981i | \(-0.262809\pi\) | ||||
0.678088 | + | 0.734981i | \(0.262809\pi\) | |||||||
\(728\) | 6.58944e6 | 0.460808 | ||||||||
\(729\) | −8.98715e6 | −0.626330 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.08743e6 | 0.144484 | ||||||||
\(732\) | −3.61782e6 | −0.249557 | ||||||||
\(733\) | −5.26197e6 | −0.361733 | −0.180866 | − | 0.983508i | \(-0.557890\pi\) | ||||
−0.180866 | + | 0.983508i | \(0.557890\pi\) | |||||||
\(734\) | −2.99986e6 | −0.205523 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.53324e7 | 1.04331 | ||||||||
\(737\) | 9.02386e6 | 0.611961 | ||||||||
\(738\) | −4.26669e6 | −0.288370 | ||||||||
\(739\) | 2.82944e7 | 1.90585 | 0.952927 | − | 0.303199i | \(-0.0980548\pi\) | ||||
0.952927 | + | 0.303199i | \(0.0980548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.21264e6 | −0.0811309 | ||||||||
\(742\) | −9.15686e6 | −0.610572 | ||||||||
\(743\) | −2.09863e7 | −1.39464 | −0.697321 | − | 0.716759i | \(-0.745625\pi\) | ||||
−0.697321 | + | 0.716759i | \(0.745625\pi\) | |||||||
\(744\) | −1.17504e6 | −0.0778252 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.47615e6 | −0.294481 | ||||||||
\(747\) | 3.79453e6 | 0.248804 | ||||||||
\(748\) | 6.95363e6 | 0.454420 | ||||||||
\(749\) | 3.03921e7 | 1.97950 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.89668e7 | −1.22714 | −0.613572 | − | 0.789639i | \(-0.710268\pi\) | ||||
−0.613572 | + | 0.789639i | \(0.710268\pi\) | |||||||
\(752\) | 7.92973e6 | 0.511345 | ||||||||
\(753\) | −6.57499e6 | −0.422579 | ||||||||
\(754\) | −1.95052e6 | −0.124946 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.01069e7 | −0.643151 | ||||||||
\(757\) | 1.08257e7 | 0.686617 | 0.343309 | − | 0.939223i | \(-0.388452\pi\) | ||||
0.343309 | + | 0.939223i | \(0.388452\pi\) | |||||||
\(758\) | −6.31868e6 | −0.399442 | ||||||||
\(759\) | 1.76179e6 | 0.111007 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.90534e7 | 1.19264 | 0.596322 | − | 0.802745i | \(-0.296628\pi\) | ||||
0.596322 | + | 0.802745i | \(0.296628\pi\) | |||||||
\(762\) | 564416. | 0.0352137 | ||||||||
\(763\) | −7.07136e6 | −0.439736 | ||||||||
\(764\) | −1.31475e7 | −0.814908 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 684432. | 0.0421462 | ||||||||
\(767\) | 5.72572e6 | 0.351432 | ||||||||
\(768\) | −121856. | −0.00745494 | ||||||||
\(769\) | −1.57826e7 | −0.962415 | −0.481208 | − | 0.876607i | \(-0.659802\pi\) | ||||
−0.481208 | + | 0.876607i | \(0.659802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.22497e6 | −0.316554 | ||||||||
\(772\) | 1.47577e6 | 0.0891199 | ||||||||
\(773\) | 2.44049e7 | 1.46902 | 0.734510 | − | 0.678598i | \(-0.237412\pi\) | ||||
0.734510 | + | 0.678598i | \(0.237412\pi\) | |||||||
\(774\) | 564776. | 0.0338863 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.42846e7 | 0.851555 | ||||||||
\(777\) | 139776. | 0.00830577 | ||||||||
\(778\) | −176940. | −0.0104804 | ||||||||
\(779\) | −9.96188e6 | −0.588163 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.83190e6 | 0.283459 | ||||||||
\(782\) | 9.98746e6 | 0.584034 | ||||||||
\(783\) | 6.41080e6 | 0.373687 | ||||||||
\(784\) | 1.31574e7 | 0.764504 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −611616. | −0.0353120 | ||||||||
\(787\) | −3.37607e7 | −1.94301 | −0.971505 | − | 0.237019i | \(-0.923830\pi\) | ||||
−0.971505 | + | 0.237019i | \(0.923830\pi\) | |||||||
\(788\) | 1.27641e7 | 0.732278 | ||||||||
\(789\) | −8.51334e6 | −0.486864 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.14771e6 | 0.122049 | ||||||||
\(792\) | 4.03152e6 | 0.228379 | ||||||||
\(793\) | −9.23837e6 | −0.521690 | ||||||||
\(794\) | −1.09135e7 | −0.614344 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.42200e7 | −1.35485 | ||||||||
\(797\) | −2.19885e7 | −1.22617 | −0.613083 | − | 0.790019i | \(-0.710071\pi\) | ||||
−0.613083 | + | 0.790019i | \(0.710071\pi\) | |||||||
\(798\) | 1.62816e6 | 0.0905086 | ||||||||
\(799\) | 2.02837e7 | 1.12403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.30110e7 | −1.26723 | ||||||||
\(802\) | −8.09360e6 | −0.444330 | ||||||||
\(803\) | −5.73855e6 | −0.314061 | ||||||||
\(804\) | 6.82886e6 | 0.372570 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.40026e6 | −0.0759224 | ||||||||
\(807\) | −5.76436e6 | −0.311578 | ||||||||
\(808\) | −1.07878e7 | −0.581303 | ||||||||
\(809\) | −2.93597e7 | −1.57717 | −0.788587 | − | 0.614923i | \(-0.789187\pi\) | ||||
−0.788587 | + | 0.614923i | \(0.789187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.17703e7 | 1.69617 | 0.848083 | − | 0.529863i | \(-0.177757\pi\) | ||||
0.848083 | + | 0.529863i | \(0.177757\pi\) | |||||||
\(812\) | −1.83322e7 | −0.975716 | ||||||||
\(813\) | −372992. | −0.0197912 | ||||||||
\(814\) | −53872.0 | −0.00284972 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.40307e6 | 0.231489 | ||||||||
\(817\) | 1.31864e6 | 0.0691148 | ||||||||
\(818\) | 5.42414e6 | 0.283431 | ||||||||
\(819\) | −1.24650e7 | −0.649357 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.71430e6 | −0.140540 | −0.0702699 | − | 0.997528i | \(-0.522386\pi\) | ||||
−0.0702699 | + | 0.997528i | \(0.522386\pi\) | |||||||
\(822\) | −1.15934e6 | −0.0598457 | ||||||||
\(823\) | 1.25866e7 | 0.647753 | 0.323877 | − | 0.946099i | \(-0.395014\pi\) | ||||
0.323877 | + | 0.946099i | \(0.395014\pi\) | |||||||
\(824\) | 2.34048e6 | 0.120084 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.68768e6 | −0.392053 | ||||||||
\(827\) | 8.72355e6 | 0.443537 | 0.221768 | − | 0.975099i | \(-0.428817\pi\) | ||||
0.221768 | + | 0.975099i | \(0.428817\pi\) | |||||||
\(828\) | −1.89155e7 | −0.958829 | ||||||||
\(829\) | −1.06178e7 | −0.536597 | −0.268299 | − | 0.963336i | \(-0.586461\pi\) | ||||
−0.268299 | + | 0.963336i | \(0.586461\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 441192. | 0.0221628 | ||||||||
\(832\) | 3.05677e6 | 0.153093 | ||||||||
\(833\) | 3.36556e7 | 1.68053 | ||||||||
\(834\) | −897760. | −0.0446936 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.39264e6 | 0.217375 | ||||||||
\(837\) | 4.60224e6 | 0.227068 | ||||||||
\(838\) | −7.43492e6 | −0.365735 | ||||||||
\(839\) | 1.67765e7 | 0.822805 | 0.411403 | − | 0.911454i | \(-0.365039\pi\) | ||||
0.411403 | + | 0.911454i | \(0.365039\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.88305e6 | −0.433084 | ||||||||
\(842\) | −7.10500e6 | −0.345370 | ||||||||
\(843\) | −768792. | −0.0372597 | ||||||||
\(844\) | −3.09583e7 | −1.49596 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.48795e6 | 0.263624 | ||||||||
\(847\) | 2.67162e7 | 1.27958 | ||||||||
\(848\) | −1.56430e7 | −0.747016 | ||||||||
\(849\) | 1.32754e6 | 0.0632087 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 541632. | 0.0256378 | ||||||||
\(852\) | 3.65658e6 | 0.172574 | ||||||||
\(853\) | 2.20186e7 | 1.03613 | 0.518067 | − | 0.855340i | \(-0.326652\pi\) | ||||
0.518067 | + | 0.855340i | \(0.326652\pi\) | |||||||
\(854\) | 1.24040e7 | 0.581991 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.89950e7 | −0.886045 | ||||||||
\(857\) | −3.16676e7 | −1.47287 | −0.736434 | − | 0.676510i | \(-0.763492\pi\) | ||||
−0.736434 | + | 0.676510i | \(0.763492\pi\) | |||||||
\(858\) | −338624. | −0.0157036 | ||||||||
\(859\) | 1.58064e7 | 0.730886 | 0.365443 | − | 0.930834i | \(-0.380918\pi\) | ||||
0.365443 | + | 0.930834i | \(0.380918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.21766e6 | 0.331809 | ||||||||
\(862\) | 8.12410e6 | 0.372398 | ||||||||
\(863\) | 1.44287e7 | 0.659476 | 0.329738 | − | 0.944072i | \(-0.393040\pi\) | ||||
0.329738 | + | 0.944072i | \(0.393040\pi\) | |||||||
\(864\) | 9.68576e6 | 0.441417 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.45257e7 | 0.658178 | ||||||||
\(867\) | 5.58331e6 | 0.252257 | ||||||||
\(868\) | −1.31604e7 | −0.592886 | ||||||||
\(869\) | 4.93728e6 | 0.221788 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.74380e7 | 0.778845 | ||||||||
\(872\) | 4.41960e6 | 0.196830 | ||||||||
\(873\) | −2.70216e7 | −1.19999 | ||||||||
\(874\) | 6.30912e6 | 0.279377 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.34269e6 | −0.191205 | ||||||||
\(877\) | −247902. | −0.0108838 | −0.00544191 | − | 0.999985i | \(-0.501732\pi\) | ||||
−0.00544191 | + | 0.999985i | \(0.501732\pi\) | |||||||
\(878\) | 1.08206e7 | 0.473711 | ||||||||
\(879\) | −8.77922e6 | −0.383252 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.10268e7 | 1.78085 | 0.890426 | − | 0.455128i | \(-0.150406\pi\) | ||||
0.890426 | + | 0.455128i | \(0.150406\pi\) | |||||||
\(882\) | 9.10588e6 | 0.394140 | ||||||||
\(883\) | −4.18015e7 | −1.80422 | −0.902112 | − | 0.431503i | \(-0.857984\pi\) | ||||
−0.902112 | + | 0.431503i | \(0.857984\pi\) | |||||||
\(884\) | 1.34374e7 | 0.578343 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.30305e7 | −0.557669 | ||||||||
\(887\) | 2.10476e7 | 0.898241 | 0.449120 | − | 0.893471i | \(-0.351737\pi\) | ||||
0.449120 | + | 0.893471i | \(0.351737\pi\) | |||||||
\(888\) | −87360.0 | −0.00371775 | ||||||||
\(889\) | 1.35460e7 | 0.574852 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.05087e6 | −0.297542 | ||||||||
\(892\) | 3.14041e7 | 1.32152 | ||||||||
\(893\) | 1.28133e7 | 0.537690 | ||||||||
\(894\) | −3.23000e6 | −0.135163 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.57581e7 | −1.48800 | ||||||||
\(897\) | 3.40454e6 | 0.141279 | ||||||||
\(898\) | 1.01990e6 | 0.0422053 | ||||||||
\(899\) | 8.34768e6 | 0.344482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00136e7 | −1.64208 | ||||||||
\(902\) | −2.78181e6 | −0.113844 | ||||||||
\(903\) | −955392. | −0.0389908 | ||||||||
\(904\) | −1.34232e6 | −0.0546305 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.57318e6 | 0.144622 | ||||||||
\(907\) | −7.48309e6 | −0.302039 | −0.151019 | − | 0.988531i | \(-0.548256\pi\) | ||||
−0.151019 | + | 0.988531i | \(0.548256\pi\) | |||||||
\(908\) | −653744. | −0.0263144 | ||||||||
\(909\) | 2.04068e7 | 0.819155 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.63165e6 | −0.264744 | −0.132372 | − | 0.991200i | \(-0.542259\pi\) | ||||
−0.132372 | + | 0.991200i | \(0.542259\pi\) | |||||||
\(912\) | 2.78144e6 | 0.110734 | ||||||||
\(913\) | 2.47397e6 | 0.0982239 | ||||||||
\(914\) | 2.44168e6 | 0.0966772 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.66883e7 | 0.657163 | ||||||||
\(917\) | −1.46788e7 | −0.576457 | ||||||||
\(918\) | 6.30928e6 | 0.247100 | ||||||||
\(919\) | −1.68976e7 | −0.659990 | −0.329995 | − | 0.943983i | \(-0.607047\pi\) | ||||
−0.329995 | + | 0.943983i | \(0.607047\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.51003e6 | 0.369431 | ||||||||
\(922\) | 8.14420e6 | 0.315516 | ||||||||
\(923\) | 9.33733e6 | 0.360760 | ||||||||
\(924\) | −3.18259e6 | −0.122631 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.04587e6 | 0.155055 | ||||||||
\(927\) | −4.42741e6 | −0.169219 | ||||||||
\(928\) | 1.75683e7 | 0.669669 | ||||||||
\(929\) | −1.28653e7 | −0.489081 | −0.244541 | − | 0.969639i | \(-0.578637\pi\) | ||||
−0.244541 | + | 0.969639i | \(0.578637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.12604e7 | 0.803892 | ||||||||
\(932\) | −1.35894e7 | −0.512459 | ||||||||
\(933\) | −9.49219e6 | −0.356995 | ||||||||
\(934\) | 6.50194e6 | 0.243880 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.79064e6 | 0.290659 | ||||||||
\(937\) | −1.06887e7 | −0.397718 | −0.198859 | − | 0.980028i | \(-0.563724\pi\) | ||||
−0.198859 | + | 0.980028i | \(0.563724\pi\) | |||||||
\(938\) | −2.34132e7 | −0.868870 | ||||||||
\(939\) | 5.71766e6 | 0.211619 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.82455e7 | 1.03986 | 0.519930 | − | 0.854209i | \(-0.325958\pi\) | ||||
0.519930 | + | 0.854209i | \(0.325958\pi\) | |||||||
\(942\) | −2.09806e6 | −0.0770356 | ||||||||
\(943\) | 2.79684e7 | 1.02421 | ||||||||
\(944\) | −1.31331e7 | −0.479665 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 368224. | 0.0133778 | ||||||||
\(947\) | 1.70892e7 | 0.619222 | 0.309611 | − | 0.950863i | \(-0.399801\pi\) | ||||
0.309611 | + | 0.950863i | \(0.399801\pi\) | |||||||
\(948\) | 3.73632e6 | 0.135028 | ||||||||
\(949\) | −1.10894e7 | −0.399706 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.49849e6 | −0.304713 | ||||||||
\(952\) | −3.86611e7 | −1.38255 | ||||||||
\(953\) | −2.22259e7 | −0.792735 | −0.396367 | − | 0.918092i | \(-0.629729\pi\) | ||||
−0.396367 | + | 0.918092i | \(0.629729\pi\) | |||||||
\(954\) | −1.08261e7 | −0.385124 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.36864e6 | 0.0484333 | ||||||||
\(957\) | 2.01872e6 | 0.0712519 | ||||||||
\(958\) | 6.55872e6 | 0.230890 | ||||||||
\(959\) | −2.78243e7 | −0.976961 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.26364e7 | −0.790678 | ||||||||
\(962\) | −104104. | −0.00362685 | ||||||||
\(963\) | 3.59323e7 | 1.24859 | ||||||||
\(964\) | 3.10234e6 | 0.107522 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.57114e6 | −0.157609 | ||||||||
\(967\) | −2.41551e7 | −0.830696 | −0.415348 | − | 0.909663i | \(-0.636340\pi\) | ||||
−0.415348 | + | 0.909663i | \(0.636340\pi\) | |||||||
\(968\) | −1.66976e7 | −0.572752 | ||||||||
\(969\) | 7.11472e6 | 0.243416 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.48313e7 | −1.86630 | −0.933149 | − | 0.359491i | \(-0.882950\pi\) | ||||
−0.933149 | + | 0.359491i | \(0.882950\pi\) | |||||||
\(972\) | −1.81273e7 | −0.615415 | ||||||||
\(973\) | −2.15462e7 | −0.729608 | ||||||||
\(974\) | −1.70639e7 | −0.576344 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.11901e7 | 0.712047 | ||||||||
\(977\) | 1.56612e7 | 0.524915 | 0.262457 | − | 0.964944i | \(-0.415467\pi\) | ||||
0.262457 | + | 0.964944i | \(0.415467\pi\) | |||||||
\(978\) | −1.23651e6 | −0.0413382 | ||||||||
\(979\) | −1.50028e7 | −0.500281 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.36041e6 | −0.277367 | ||||||||
\(982\) | −3.02530e6 | −0.100113 | ||||||||
\(983\) | 1.63420e7 | 0.539412 | 0.269706 | − | 0.962943i | \(-0.413073\pi\) | ||||
0.269706 | + | 0.962943i | \(0.413073\pi\) | |||||||
\(984\) | −4.51104e6 | −0.148521 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.14440e7 | 0.374873 | ||||||||
\(987\) | −9.28358e6 | −0.303335 | ||||||||
\(988\) | 8.48848e6 | 0.276654 | ||||||||
\(989\) | −3.70214e6 | −0.120355 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.37576e7 | 0.444997 | 0.222498 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222498 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(992\) | 1.26121e7 | 0.406919 | ||||||||
\(993\) | 1.23994e7 | 0.399050 | ||||||||
\(994\) | −1.25368e7 | −0.402459 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.87219e6 | 0.0598001 | ||||||||
\(997\) | 1.29097e7 | 0.411320 | 0.205660 | − | 0.978624i | \(-0.434066\pi\) | ||||
0.205660 | + | 0.978624i | \(0.434066\pi\) | |||||||
\(998\) | 1.29838e7 | 0.412644 | ||||||||
\(999\) | 342160. | 0.0108471 |
(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 | 25.6.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 225.6.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 400.6.a.g.1.1 | 1 | |||
5.2 | odd | 4 | 25.6.b.a.24.1 | 2 | |||
5.3 | odd | 4 | 25.6.b.a.24.2 | 2 | |||
5.4 | even | 2 | 5.6.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 225.6.b.e.199.2 | 2 | |||
15.8 | even | 4 | 225.6.b.e.199.1 | 2 | |||
15.14 | odd | 2 | 45.6.a.b.1.1 | 1 | |||
20.3 | even | 4 | 400.6.c.j.49.1 | 2 | |||
20.7 | even | 4 | 400.6.c.j.49.2 | 2 | |||
20.19 | odd | 2 | 80.6.a.e.1.1 | 1 | |||
35.34 | odd | 2 | 245.6.a.b.1.1 | 1 | |||
40.19 | odd | 2 | 320.6.a.g.1.1 | 1 | |||
40.29 | even | 2 | 320.6.a.j.1.1 | 1 | |||
55.54 | odd | 2 | 605.6.a.a.1.1 | 1 | |||
60.59 | even | 2 | 720.6.a.a.1.1 | 1 | |||
65.64 | even | 2 | 845.6.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.6.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
25.6.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
25.6.b.a.24.1 | 2 | 5.2 | odd | 4 | |||
25.6.b.a.24.2 | 2 | 5.3 | odd | 4 | |||
45.6.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
80.6.a.e.1.1 | 1 | 20.19 | odd | 2 | |||
225.6.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
225.6.b.e.199.1 | 2 | 15.8 | even | 4 | |||
225.6.b.e.199.2 | 2 | 15.2 | even | 4 | |||
245.6.a.b.1.1 | 1 | 35.34 | odd | 2 | |||
320.6.a.g.1.1 | 1 | 40.19 | odd | 2 | |||
320.6.a.j.1.1 | 1 | 40.29 | even | 2 | |||
400.6.a.g.1.1 | 1 | 4.3 | odd | 2 | |||
400.6.c.j.49.1 | 2 | 20.3 | even | 4 | |||
400.6.c.j.49.2 | 2 | 20.7 | even | 4 | |||
605.6.a.a.1.1 | 1 | 55.54 | odd | 2 | |||
720.6.a.a.1.1 | 1 | 60.59 | even | 2 | |||
845.6.a.b.1.1 | 1 | 65.64 | even | 2 |