Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + \cdots - 6400833792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-6.06926\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.06926 | −1.07290 | −0.536452 | − | 0.843931i | \(-0.680236\pi\) | ||||
−0.536452 | + | 0.843931i | \(0.680236\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 4.83596 | 0.151124 | ||||||||
\(5\) | 26.0687 | 0.466331 | 0.233166 | − | 0.972437i | \(-0.425092\pi\) | ||||
0.233166 | + | 0.972437i | \(0.425092\pi\) | |||||||
\(6\) | 54.6234 | 0.619442 | ||||||||
\(7\) | −152.673 | −1.17766 | −0.588828 | − | 0.808258i | \(-0.700411\pi\) | ||||
−0.588828 | + | 0.808258i | \(0.700411\pi\) | |||||||
\(8\) | 164.866 | 0.910763 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −158.218 | −0.500329 | ||||||||
\(11\) | 105.236 | 0.262231 | 0.131115 | − | 0.991367i | \(-0.458144\pi\) | ||||
0.131115 | + | 0.991367i | \(0.458144\pi\) | |||||||
\(12\) | −43.5237 | −0.0872514 | ||||||||
\(13\) | −582.342 | −0.955696 | −0.477848 | − | 0.878443i | \(-0.658583\pi\) | ||||
−0.477848 | + | 0.878443i | \(0.658583\pi\) | |||||||
\(14\) | 926.616 | 1.26351 | ||||||||
\(15\) | −234.618 | −0.269236 | ||||||||
\(16\) | −1155.36 | −1.12829 | ||||||||
\(17\) | −1069.36 | −0.897431 | −0.448715 | − | 0.893675i | \(-0.648118\pi\) | ||||
−0.448715 | + | 0.893675i | \(0.648118\pi\) | |||||||
\(18\) | −491.610 | −0.357635 | ||||||||
\(19\) | 390.786 | 0.248345 | 0.124172 | − | 0.992261i | \(-0.460372\pi\) | ||||
0.124172 | + | 0.992261i | \(0.460372\pi\) | |||||||
\(20\) | 126.067 | 0.0704737 | ||||||||
\(21\) | 1374.06 | 0.679920 | ||||||||
\(22\) | −638.707 | −0.281349 | ||||||||
\(23\) | −400.841 | −0.157998 | −0.0789992 | − | 0.996875i | \(-0.525172\pi\) | ||||
−0.0789992 | + | 0.996875i | \(0.525172\pi\) | |||||||
\(24\) | −1483.79 | −0.525829 | ||||||||
\(25\) | −2445.42 | −0.782535 | ||||||||
\(26\) | 3534.39 | 1.02537 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −738.323 | −0.177972 | ||||||||
\(29\) | −4917.03 | −1.08569 | −0.542847 | − | 0.839831i | \(-0.682654\pi\) | ||||
−0.542847 | + | 0.839831i | \(0.682654\pi\) | |||||||
\(30\) | 1423.96 | 0.288865 | ||||||||
\(31\) | −6824.95 | −1.27554 | −0.637772 | − | 0.770226i | \(-0.720144\pi\) | ||||
−0.637772 | + | 0.770226i | \(0.720144\pi\) | |||||||
\(32\) | 1736.51 | 0.299779 | ||||||||
\(33\) | −947.126 | −0.151399 | ||||||||
\(34\) | 6490.22 | 0.962857 | ||||||||
\(35\) | −3980.00 | −0.549178 | ||||||||
\(36\) | 391.713 | 0.0503746 | ||||||||
\(37\) | 15771.2 | 1.89392 | 0.946960 | − | 0.321352i | \(-0.104137\pi\) | ||||
0.946960 | + | 0.321352i | \(0.104137\pi\) | |||||||
\(38\) | −2371.78 | −0.266450 | ||||||||
\(39\) | 5241.08 | 0.551771 | ||||||||
\(40\) | 4297.83 | 0.424717 | ||||||||
\(41\) | −3504.92 | −0.325625 | −0.162813 | − | 0.986657i | \(-0.552057\pi\) | ||||
−0.162813 | + | 0.986657i | \(0.552057\pi\) | |||||||
\(42\) | −8339.54 | −0.729489 | ||||||||
\(43\) | 10247.6 | 0.845182 | 0.422591 | − | 0.906320i | \(-0.361121\pi\) | ||||
0.422591 | + | 0.906320i | \(0.361121\pi\) | |||||||
\(44\) | 508.919 | 0.0396293 | ||||||||
\(45\) | 2111.56 | 0.155444 | ||||||||
\(46\) | 2432.81 | 0.169517 | ||||||||
\(47\) | 7721.01 | 0.509835 | 0.254917 | − | 0.966963i | \(-0.417952\pi\) | ||||
0.254917 | + | 0.966963i | \(0.417952\pi\) | |||||||
\(48\) | 10398.3 | 0.651416 | ||||||||
\(49\) | 6502.19 | 0.386874 | ||||||||
\(50\) | 14841.9 | 0.839586 | ||||||||
\(51\) | 9624.22 | 0.518132 | ||||||||
\(52\) | −2816.18 | −0.144428 | ||||||||
\(53\) | 17958.4 | 0.878169 | 0.439084 | − | 0.898446i | \(-0.355303\pi\) | ||||
0.439084 | + | 0.898446i | \(0.355303\pi\) | |||||||
\(54\) | 4424.49 | 0.206481 | ||||||||
\(55\) | 2743.37 | 0.122286 | ||||||||
\(56\) | −25170.6 | −1.07257 | ||||||||
\(57\) | −3517.07 | −0.143382 | ||||||||
\(58\) | 29842.7 | 1.16485 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | −1134.61 | −0.0406880 | ||||||||
\(61\) | 45574.7 | 1.56819 | 0.784095 | − | 0.620640i | \(-0.213127\pi\) | ||||
0.784095 | + | 0.620640i | \(0.213127\pi\) | |||||||
\(62\) | 41422.4 | 1.36854 | ||||||||
\(63\) | −12366.6 | −0.392552 | ||||||||
\(64\) | 26432.3 | 0.806651 | ||||||||
\(65\) | −15180.9 | −0.445671 | ||||||||
\(66\) | 5748.36 | 0.162437 | ||||||||
\(67\) | 20668.2 | 0.562490 | 0.281245 | − | 0.959636i | \(-0.409253\pi\) | ||||
0.281245 | + | 0.959636i | \(0.409253\pi\) | |||||||
\(68\) | −5171.38 | −0.135623 | ||||||||
\(69\) | 3607.57 | 0.0912204 | ||||||||
\(70\) | 24155.7 | 0.589215 | ||||||||
\(71\) | −39463.9 | −0.929081 | −0.464541 | − | 0.885552i | \(-0.653781\pi\) | ||||
−0.464541 | + | 0.885552i | \(0.653781\pi\) | |||||||
\(72\) | 13354.1 | 0.303588 | ||||||||
\(73\) | −2618.86 | −0.0575181 | −0.0287590 | − | 0.999586i | \(-0.509156\pi\) | ||||
−0.0287590 | + | 0.999586i | \(0.509156\pi\) | |||||||
\(74\) | −95719.8 | −2.03199 | ||||||||
\(75\) | 22008.8 | 0.451797 | ||||||||
\(76\) | 1889.83 | 0.0375308 | ||||||||
\(77\) | −16066.8 | −0.308818 | ||||||||
\(78\) | −31809.5 | −0.591998 | ||||||||
\(79\) | 5265.20 | 0.0949177 | 0.0474589 | − | 0.998873i | \(-0.484888\pi\) | ||||
0.0474589 | + | 0.998873i | \(0.484888\pi\) | |||||||
\(80\) | −30118.8 | −0.526154 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 21272.3 | 0.349365 | ||||||||
\(83\) | 98001.8 | 1.56149 | 0.780744 | − | 0.624851i | \(-0.214840\pi\) | ||||
0.780744 | + | 0.624851i | \(0.214840\pi\) | |||||||
\(84\) | 6644.91 | 0.102752 | ||||||||
\(85\) | −27876.8 | −0.418500 | ||||||||
\(86\) | −62195.3 | −0.906800 | ||||||||
\(87\) | 44253.3 | 0.626826 | ||||||||
\(88\) | 17349.8 | 0.238830 | ||||||||
\(89\) | 35159.0 | 0.470501 | 0.235251 | − | 0.971935i | \(-0.424409\pi\) | ||||
0.235251 | + | 0.971935i | \(0.424409\pi\) | |||||||
\(90\) | −12815.6 | −0.166776 | ||||||||
\(91\) | 88908.2 | 1.12548 | ||||||||
\(92\) | −1938.45 | −0.0238773 | ||||||||
\(93\) | 61424.5 | 0.736435 | ||||||||
\(94\) | −46860.9 | −0.547004 | ||||||||
\(95\) | 10187.3 | 0.115811 | ||||||||
\(96\) | −15628.6 | −0.173078 | ||||||||
\(97\) | 126268. | 1.36258 | 0.681291 | − | 0.732012i | \(-0.261419\pi\) | ||||
0.681291 | + | 0.732012i | \(0.261419\pi\) | |||||||
\(98\) | −39463.5 | −0.415079 | ||||||||
\(99\) | 8524.14 | 0.0874103 | ||||||||
\(100\) | −11826.0 | −0.118260 | ||||||||
\(101\) | −67402.7 | −0.657467 | −0.328733 | − | 0.944423i | \(-0.606622\pi\) | ||||
−0.328733 | + | 0.944423i | \(0.606622\pi\) | |||||||
\(102\) | −58411.9 | −0.555906 | ||||||||
\(103\) | −122149. | −1.13448 | −0.567240 | − | 0.823553i | \(-0.691989\pi\) | ||||
−0.567240 | + | 0.823553i | \(0.691989\pi\) | |||||||
\(104\) | −96008.2 | −0.870412 | ||||||||
\(105\) | 35820.0 | 0.317068 | ||||||||
\(106\) | −108994. | −0.942191 | ||||||||
\(107\) | 108415. | 0.915444 | 0.457722 | − | 0.889095i | \(-0.348666\pi\) | ||||
0.457722 | + | 0.889095i | \(0.348666\pi\) | |||||||
\(108\) | −3525.42 | −0.0290838 | ||||||||
\(109\) | −135107. | −1.08921 | −0.544604 | − | 0.838694i | \(-0.683320\pi\) | ||||
−0.544604 | + | 0.838694i | \(0.683320\pi\) | |||||||
\(110\) | −16650.2 | −0.131202 | ||||||||
\(111\) | −141941. | −1.09346 | ||||||||
\(112\) | 176393. | 1.32873 | ||||||||
\(113\) | −140109. | −1.03222 | −0.516108 | − | 0.856523i | \(-0.672620\pi\) | ||||
−0.516108 | + | 0.856523i | \(0.672620\pi\) | |||||||
\(114\) | 21346.0 | 0.153835 | ||||||||
\(115\) | −10449.4 | −0.0736795 | ||||||||
\(116\) | −23778.6 | −0.164074 | ||||||||
\(117\) | −47169.7 | −0.318565 | ||||||||
\(118\) | −21127.1 | −0.139680 | ||||||||
\(119\) | 163263. | 1.05686 | ||||||||
\(120\) | −38680.5 | −0.245210 | ||||||||
\(121\) | −149976. | −0.931235 | ||||||||
\(122\) | −276605. | −1.68252 | ||||||||
\(123\) | 31544.3 | 0.188000 | ||||||||
\(124\) | −33005.2 | −0.192765 | ||||||||
\(125\) | −145214. | −0.831252 | ||||||||
\(126\) | 75055.9 | 0.421171 | ||||||||
\(127\) | 300303. | 1.65215 | 0.826076 | − | 0.563559i | \(-0.190568\pi\) | ||||
0.826076 | + | 0.563559i | \(0.190568\pi\) | |||||||
\(128\) | −215993. | −1.16524 | ||||||||
\(129\) | −92228.3 | −0.487966 | ||||||||
\(130\) | 92136.8 | 0.478162 | ||||||||
\(131\) | −24226.5 | −0.123342 | −0.0616712 | − | 0.998097i | \(-0.519643\pi\) | ||||
−0.0616712 | + | 0.998097i | \(0.519643\pi\) | |||||||
\(132\) | −4580.27 | −0.0228800 | ||||||||
\(133\) | −59662.7 | −0.292465 | ||||||||
\(134\) | −125441. | −0.603498 | ||||||||
\(135\) | −19004.1 | −0.0897454 | ||||||||
\(136\) | −176300. | −0.817347 | ||||||||
\(137\) | −238971. | −1.08779 | −0.543894 | − | 0.839154i | \(-0.683051\pi\) | ||||
−0.543894 | + | 0.839154i | \(0.683051\pi\) | |||||||
\(138\) | −21895.3 | −0.0978708 | ||||||||
\(139\) | 13346.3 | 0.0585901 | 0.0292951 | − | 0.999571i | \(-0.490674\pi\) | ||||
0.0292951 | + | 0.999571i | \(0.490674\pi\) | |||||||
\(140\) | −19247.1 | −0.0829938 | ||||||||
\(141\) | −69489.1 | −0.294353 | ||||||||
\(142\) | 239517. | 0.996815 | ||||||||
\(143\) | −61283.5 | −0.250613 | ||||||||
\(144\) | −93584.5 | −0.376095 | ||||||||
\(145\) | −128181. | −0.506293 | ||||||||
\(146\) | 15894.5 | 0.0617114 | ||||||||
\(147\) | −58519.7 | −0.223362 | ||||||||
\(148\) | 76269.1 | 0.286216 | ||||||||
\(149\) | 231222. | 0.853225 | 0.426612 | − | 0.904435i | \(-0.359707\pi\) | ||||
0.426612 | + | 0.904435i | \(0.359707\pi\) | |||||||
\(150\) | −133577. | −0.484735 | ||||||||
\(151\) | 444904. | 1.58790 | 0.793951 | − | 0.607981i | \(-0.208020\pi\) | ||||
0.793951 | + | 0.607981i | \(0.208020\pi\) | |||||||
\(152\) | 64427.2 | 0.226183 | ||||||||
\(153\) | −86618.0 | −0.299144 | ||||||||
\(154\) | 97513.6 | 0.331332 | ||||||||
\(155\) | −177918. | −0.594825 | ||||||||
\(156\) | 25345.7 | 0.0833858 | ||||||||
\(157\) | 356448. | 1.15411 | 0.577054 | − | 0.816706i | \(-0.304202\pi\) | ||||
0.577054 | + | 0.816706i | \(0.304202\pi\) | |||||||
\(158\) | −31955.9 | −0.101838 | ||||||||
\(159\) | −161626. | −0.507011 | ||||||||
\(160\) | 45268.5 | 0.139796 | ||||||||
\(161\) | 61197.8 | 0.186068 | ||||||||
\(162\) | −39820.4 | −0.119212 | ||||||||
\(163\) | 110391. | 0.325437 | 0.162718 | − | 0.986673i | \(-0.447974\pi\) | ||||
0.162718 | + | 0.986673i | \(0.447974\pi\) | |||||||
\(164\) | −16949.7 | −0.0492098 | ||||||||
\(165\) | −24690.3 | −0.0706021 | ||||||||
\(166\) | −594799. | −1.67533 | ||||||||
\(167\) | 164938. | 0.457645 | 0.228823 | − | 0.973468i | \(-0.426512\pi\) | ||||
0.228823 | + | 0.973468i | \(0.426512\pi\) | |||||||
\(168\) | 226536. | 0.619246 | ||||||||
\(169\) | −32170.9 | −0.0866457 | ||||||||
\(170\) | 169191. | 0.449010 | ||||||||
\(171\) | 31653.7 | 0.0827816 | ||||||||
\(172\) | 49556.9 | 0.127727 | ||||||||
\(173\) | 432927. | 1.09976 | 0.549881 | − | 0.835243i | \(-0.314673\pi\) | ||||
0.549881 | + | 0.835243i | \(0.314673\pi\) | |||||||
\(174\) | −268585. | −0.672525 | ||||||||
\(175\) | 373351. | 0.921558 | ||||||||
\(176\) | −121586. | −0.295871 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | −213389. | −0.504803 | ||||||||
\(179\) | 331441. | 0.773168 | 0.386584 | − | 0.922254i | \(-0.373655\pi\) | ||||
0.386584 | + | 0.922254i | \(0.373655\pi\) | |||||||
\(180\) | 10211.4 | 0.0234912 | ||||||||
\(181\) | 136830. | 0.310444 | 0.155222 | − | 0.987880i | \(-0.450391\pi\) | ||||
0.155222 | + | 0.987880i | \(0.450391\pi\) | |||||||
\(182\) | −539607. | −1.20753 | ||||||||
\(183\) | −410172. | −0.905395 | ||||||||
\(184\) | −66085.0 | −0.143899 | ||||||||
\(185\) | 411136. | 0.883194 | ||||||||
\(186\) | −372802. | −0.790125 | ||||||||
\(187\) | −112535. | −0.235334 | ||||||||
\(188\) | 37338.5 | 0.0770482 | ||||||||
\(189\) | 111299. | 0.226640 | ||||||||
\(190\) | −61829.3 | −0.124254 | ||||||||
\(191\) | 777758. | 1.54263 | 0.771314 | − | 0.636455i | \(-0.219600\pi\) | ||||
0.771314 | + | 0.636455i | \(0.219600\pi\) | |||||||
\(192\) | −237891. | −0.465720 | ||||||||
\(193\) | −402573. | −0.777949 | −0.388974 | − | 0.921249i | \(-0.627171\pi\) | ||||
−0.388974 | + | 0.921249i | \(0.627171\pi\) | |||||||
\(194\) | −766352. | −1.46192 | ||||||||
\(195\) | 136628. | 0.257308 | ||||||||
\(196\) | 31444.4 | 0.0584659 | ||||||||
\(197\) | −335493. | −0.615910 | −0.307955 | − | 0.951401i | \(-0.599645\pi\) | ||||
−0.307955 | + | 0.951401i | \(0.599645\pi\) | |||||||
\(198\) | −51735.2 | −0.0937828 | ||||||||
\(199\) | 642899. | 1.15083 | 0.575413 | − | 0.817863i | \(-0.304841\pi\) | ||||
0.575413 | + | 0.817863i | \(0.304841\pi\) | |||||||
\(200\) | −403166. | −0.712704 | ||||||||
\(201\) | −186013. | −0.324754 | ||||||||
\(202\) | 409085. | 0.705399 | ||||||||
\(203\) | 750700. | 1.27858 | ||||||||
\(204\) | 46542.4 | 0.0783021 | ||||||||
\(205\) | −91368.7 | −0.151849 | ||||||||
\(206\) | 741354. | 1.21719 | ||||||||
\(207\) | −32468.1 | −0.0526661 | ||||||||
\(208\) | 672817. | 1.07830 | ||||||||
\(209\) | 41124.8 | 0.0651236 | ||||||||
\(210\) | −217401. | −0.340183 | ||||||||
\(211\) | 905267. | 1.39982 | 0.699908 | − | 0.714233i | \(-0.253224\pi\) | ||||
0.699908 | + | 0.714233i | \(0.253224\pi\) | |||||||
\(212\) | 86846.2 | 0.132712 | ||||||||
\(213\) | 355175. | 0.536405 | ||||||||
\(214\) | −658002. | −0.982184 | ||||||||
\(215\) | 267141. | 0.394135 | ||||||||
\(216\) | −120187. | −0.175276 | ||||||||
\(217\) | 1.04199e6 | 1.50215 | ||||||||
\(218\) | 819998. | 1.16861 | ||||||||
\(219\) | 23569.7 | 0.0332081 | ||||||||
\(220\) | 13266.8 | 0.0184804 | ||||||||
\(221\) | 622732. | 0.857671 | ||||||||
\(222\) | 861478. | 1.17317 | ||||||||
\(223\) | −156940. | −0.211335 | −0.105667 | − | 0.994402i | \(-0.533698\pi\) | ||||
−0.105667 | + | 0.994402i | \(0.533698\pi\) | |||||||
\(224\) | −265119. | −0.353037 | ||||||||
\(225\) | −198079. | −0.260845 | ||||||||
\(226\) | 850360. | 1.10747 | ||||||||
\(227\) | 784043. | 1.00989 | 0.504946 | − | 0.863151i | \(-0.331512\pi\) | ||||
0.504946 | + | 0.863151i | \(0.331512\pi\) | |||||||
\(228\) | −17008.4 | −0.0216684 | ||||||||
\(229\) | −664454. | −0.837290 | −0.418645 | − | 0.908150i | \(-0.637495\pi\) | ||||
−0.418645 | + | 0.908150i | \(0.637495\pi\) | |||||||
\(230\) | 63420.2 | 0.0790511 | ||||||||
\(231\) | 144601. | 0.178296 | ||||||||
\(232\) | −810650. | −0.988811 | ||||||||
\(233\) | −984844. | −1.18844 | −0.594220 | − | 0.804302i | \(-0.702539\pi\) | ||||
−0.594220 | + | 0.804302i | \(0.702539\pi\) | |||||||
\(234\) | 286285. | 0.341790 | ||||||||
\(235\) | 201277. | 0.237752 | ||||||||
\(236\) | 16834.0 | 0.0196746 | ||||||||
\(237\) | −47386.8 | −0.0548008 | ||||||||
\(238\) | −990884. | −1.13391 | ||||||||
\(239\) | −1.51318e6 | −1.71355 | −0.856774 | − | 0.515692i | \(-0.827535\pi\) | ||||
−0.856774 | + | 0.515692i | \(0.827535\pi\) | |||||||
\(240\) | 271070. | 0.303775 | ||||||||
\(241\) | 392563. | 0.435378 | 0.217689 | − | 0.976018i | \(-0.430148\pi\) | ||||
0.217689 | + | 0.976018i | \(0.430148\pi\) | |||||||
\(242\) | 910246. | 0.999126 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 220397. | 0.236991 | ||||||||
\(245\) | 169504. | 0.180411 | ||||||||
\(246\) | −191451. | −0.201706 | ||||||||
\(247\) | −227571. | −0.237342 | ||||||||
\(248\) | −1.12520e6 | −1.16172 | ||||||||
\(249\) | −882016. | −0.901526 | ||||||||
\(250\) | 881340. | 0.891853 | ||||||||
\(251\) | −239322. | −0.239772 | −0.119886 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(252\) | −59804.2 | −0.0593240 | ||||||||
\(253\) | −42183.0 | −0.0414320 | ||||||||
\(254\) | −1.82262e6 | −1.77260 | ||||||||
\(255\) | 250891. | 0.241621 | ||||||||
\(256\) | 465084. | 0.443539 | ||||||||
\(257\) | −118296. | −0.111721 | −0.0558607 | − | 0.998439i | \(-0.517790\pi\) | ||||
−0.0558607 | + | 0.998439i | \(0.517790\pi\) | |||||||
\(258\) | 559758. | 0.523541 | ||||||||
\(259\) | −2.40785e6 | −2.23039 | ||||||||
\(260\) | −73414.2 | −0.0673514 | ||||||||
\(261\) | −398279. | −0.361898 | ||||||||
\(262\) | 147037. | 0.132335 | ||||||||
\(263\) | 170441. | 0.151944 | 0.0759722 | − | 0.997110i | \(-0.475794\pi\) | ||||
0.0759722 | + | 0.997110i | \(0.475794\pi\) | |||||||
\(264\) | −156149. | −0.137889 | ||||||||
\(265\) | 468152. | 0.409517 | ||||||||
\(266\) | 362108. | 0.313787 | ||||||||
\(267\) | −316431. | −0.271644 | ||||||||
\(268\) | 99950.4 | 0.0850056 | ||||||||
\(269\) | 1.16647e6 | 0.982867 | 0.491433 | − | 0.870915i | \(-0.336473\pi\) | ||||
0.491433 | + | 0.870915i | \(0.336473\pi\) | |||||||
\(270\) | 115341. | 0.0962883 | ||||||||
\(271\) | 25230.7 | 0.0208692 | 0.0104346 | − | 0.999946i | \(-0.496678\pi\) | ||||
0.0104346 | + | 0.999946i | \(0.496678\pi\) | |||||||
\(272\) | 1.23550e6 | 1.01256 | ||||||||
\(273\) | −800173. | −0.649797 | ||||||||
\(274\) | 1.45038e6 | 1.16709 | ||||||||
\(275\) | −257347. | −0.205205 | ||||||||
\(276\) | 17446.1 | 0.0137856 | ||||||||
\(277\) | −118869. | −0.0930824 | −0.0465412 | − | 0.998916i | \(-0.514820\pi\) | ||||
−0.0465412 | + | 0.998916i | \(0.514820\pi\) | |||||||
\(278\) | −81002.3 | −0.0628616 | ||||||||
\(279\) | −552821. | −0.425181 | ||||||||
\(280\) | −656165. | −0.500171 | ||||||||
\(281\) | −492378. | −0.371991 | −0.185996 | − | 0.982551i | \(-0.559551\pi\) | ||||
−0.185996 | + | 0.982551i | \(0.559551\pi\) | |||||||
\(282\) | 421748. | 0.315813 | ||||||||
\(283\) | 532204. | 0.395014 | 0.197507 | − | 0.980302i | \(-0.436716\pi\) | ||||
0.197507 | + | 0.980302i | \(0.436716\pi\) | |||||||
\(284\) | −190846. | −0.140406 | ||||||||
\(285\) | −91685.5 | −0.0668634 | ||||||||
\(286\) | 371946. | 0.268884 | ||||||||
\(287\) | 535108. | 0.383475 | ||||||||
\(288\) | 140657. | 0.0999265 | ||||||||
\(289\) | −276330. | −0.194618 | ||||||||
\(290\) | 777962. | 0.543204 | ||||||||
\(291\) | −1.13641e6 | −0.786687 | ||||||||
\(292\) | −12664.7 | −0.00869235 | ||||||||
\(293\) | 170024. | 0.115702 | 0.0578510 | − | 0.998325i | \(-0.481575\pi\) | ||||
0.0578510 | + | 0.998325i | \(0.481575\pi\) | |||||||
\(294\) | 355172. | 0.239646 | ||||||||
\(295\) | 90745.1 | 0.0607111 | ||||||||
\(296\) | 2.60014e6 | 1.72491 | ||||||||
\(297\) | −76717.2 | −0.0504663 | ||||||||
\(298\) | −1.40335e6 | −0.915428 | ||||||||
\(299\) | 233427. | 0.150998 | ||||||||
\(300\) | 106434. | 0.0682773 | ||||||||
\(301\) | −1.56453e6 | −0.995334 | ||||||||
\(302\) | −2.70024e6 | −1.70367 | ||||||||
\(303\) | 606624. | 0.379589 | ||||||||
\(304\) | −451500. | −0.280204 | ||||||||
\(305\) | 1.18807e6 | 0.731296 | ||||||||
\(306\) | 525708. | 0.320952 | ||||||||
\(307\) | −118160. | −0.0715522 | −0.0357761 | − | 0.999360i | \(-0.511390\pi\) | ||||
−0.0357761 | + | 0.999360i | \(0.511390\pi\) | |||||||
\(308\) | −77698.4 | −0.0466697 | ||||||||
\(309\) | 1.09934e6 | 0.654992 | ||||||||
\(310\) | 1.07983e6 | 0.638191 | ||||||||
\(311\) | −2.00186e6 | −1.17363 | −0.586816 | − | 0.809720i | \(-0.699619\pi\) | ||||
−0.586816 | + | 0.809720i | \(0.699619\pi\) | |||||||
\(312\) | 864074. | 0.502533 | ||||||||
\(313\) | 3.40535e6 | 1.96472 | 0.982361 | − | 0.186992i | \(-0.0598739\pi\) | ||||
0.982361 | + | 0.186992i | \(0.0598739\pi\) | |||||||
\(314\) | −2.16337e6 | −1.23825 | ||||||||
\(315\) | −322380. | −0.183059 | ||||||||
\(316\) | 25462.3 | 0.0143443 | ||||||||
\(317\) | −394188. | −0.220321 | −0.110160 | − | 0.993914i | \(-0.535136\pi\) | ||||
−0.110160 | + | 0.993914i | \(0.535136\pi\) | |||||||
\(318\) | 980948. | 0.543974 | ||||||||
\(319\) | −517450. | −0.284703 | ||||||||
\(320\) | 689056. | 0.376166 | ||||||||
\(321\) | −975739. | −0.528532 | ||||||||
\(322\) | −371426. | −0.199633 | ||||||||
\(323\) | −417890. | −0.222872 | ||||||||
\(324\) | 31728.7 | 0.0167915 | ||||||||
\(325\) | 1.42407e6 | 0.747866 | ||||||||
\(326\) | −669995. | −0.349162 | ||||||||
\(327\) | 1.21596e6 | 0.628854 | ||||||||
\(328\) | −577841. | −0.296568 | ||||||||
\(329\) | −1.17879e6 | −0.600410 | ||||||||
\(330\) | 149852. | 0.0757493 | ||||||||
\(331\) | −2.27331e6 | −1.14048 | −0.570240 | − | 0.821478i | \(-0.693150\pi\) | ||||
−0.570240 | + | 0.821478i | \(0.693150\pi\) | |||||||
\(332\) | 473933. | 0.235978 | ||||||||
\(333\) | 1.27747e6 | 0.631307 | ||||||||
\(334\) | −1.00105e6 | −0.491010 | ||||||||
\(335\) | 538792. | 0.262307 | ||||||||
\(336\) | −1.58754e6 | −0.767144 | ||||||||
\(337\) | −1.15578e6 | −0.554370 | −0.277185 | − | 0.960817i | \(-0.589402\pi\) | ||||
−0.277185 | + | 0.960817i | \(0.589402\pi\) | |||||||
\(338\) | 195254. | 0.0929626 | ||||||||
\(339\) | 1.26098e6 | 0.595950 | ||||||||
\(340\) | −134811. | −0.0632453 | ||||||||
\(341\) | −718232. | −0.334487 | ||||||||
\(342\) | −192114. | −0.0888167 | ||||||||
\(343\) | 1.57327e6 | 0.722051 | ||||||||
\(344\) | 1.68948e6 | 0.769761 | ||||||||
\(345\) | 94044.6 | 0.0425389 | ||||||||
\(346\) | −2.62755e6 | −1.17994 | ||||||||
\(347\) | 3.28503e6 | 1.46459 | 0.732295 | − | 0.680988i | \(-0.238449\pi\) | ||||
0.732295 | + | 0.680988i | \(0.238449\pi\) | |||||||
\(348\) | 214007. | 0.0947284 | ||||||||
\(349\) | 3.89003e6 | 1.70958 | 0.854790 | − | 0.518974i | \(-0.173686\pi\) | ||||
0.854790 | + | 0.518974i | \(0.173686\pi\) | |||||||
\(350\) | −2.26597e6 | −0.988743 | ||||||||
\(351\) | 424527. | 0.183924 | ||||||||
\(352\) | 182744. | 0.0786114 | ||||||||
\(353\) | −2.80229e6 | −1.19695 | −0.598476 | − | 0.801141i | \(-0.704227\pi\) | ||||
−0.598476 | + | 0.801141i | \(0.704227\pi\) | |||||||
\(354\) | 190144. | 0.0806444 | ||||||||
\(355\) | −1.02877e6 | −0.433259 | ||||||||
\(356\) | 170027. | 0.0711040 | ||||||||
\(357\) | −1.46936e6 | −0.610181 | ||||||||
\(358\) | −2.01160e6 | −0.829536 | ||||||||
\(359\) | 671218. | 0.274870 | 0.137435 | − | 0.990511i | \(-0.456114\pi\) | ||||
0.137435 | + | 0.990511i | \(0.456114\pi\) | |||||||
\(360\) | 348125. | 0.141572 | ||||||||
\(361\) | −2.32339e6 | −0.938325 | ||||||||
\(362\) | −830455. | −0.333077 | ||||||||
\(363\) | 1.34979e6 | 0.537649 | ||||||||
\(364\) | 429957. | 0.170087 | ||||||||
\(365\) | −68270.2 | −0.0268225 | ||||||||
\(366\) | 2.48944e6 | 0.971403 | ||||||||
\(367\) | −642875. | −0.249150 | −0.124575 | − | 0.992210i | \(-0.539757\pi\) | ||||
−0.124575 | + | 0.992210i | \(0.539757\pi\) | |||||||
\(368\) | 463117. | 0.178267 | ||||||||
\(369\) | −283898. | −0.108542 | ||||||||
\(370\) | −2.49529e6 | −0.947582 | ||||||||
\(371\) | −2.74177e6 | −1.03418 | ||||||||
\(372\) | 297047. | 0.111293 | ||||||||
\(373\) | −3.08089e6 | −1.14658 | −0.573290 | − | 0.819352i | \(-0.694333\pi\) | ||||
−0.573290 | + | 0.819352i | \(0.694333\pi\) | |||||||
\(374\) | 683006. | 0.252491 | ||||||||
\(375\) | 1.30692e6 | 0.479923 | ||||||||
\(376\) | 1.27293e6 | 0.464339 | ||||||||
\(377\) | 2.86339e6 | 1.03759 | ||||||||
\(378\) | −675503. | −0.243163 | ||||||||
\(379\) | −2.66225e6 | −0.952030 | −0.476015 | − | 0.879437i | \(-0.657919\pi\) | ||||
−0.476015 | + | 0.879437i | \(0.657919\pi\) | |||||||
\(380\) | 49265.3 | 0.0175018 | ||||||||
\(381\) | −2.70272e6 | −0.953870 | ||||||||
\(382\) | −4.72042e6 | −1.65509 | ||||||||
\(383\) | 944201. | 0.328903 | 0.164451 | − | 0.986385i | \(-0.447415\pi\) | ||||
0.164451 | + | 0.986385i | \(0.447415\pi\) | |||||||
\(384\) | 1.94394e6 | 0.672751 | ||||||||
\(385\) | −418840. | −0.144011 | ||||||||
\(386\) | 2.44332e6 | 0.834664 | ||||||||
\(387\) | 830054. | 0.281727 | ||||||||
\(388\) | 610626. | 0.205919 | ||||||||
\(389\) | −3.17438e6 | −1.06362 | −0.531808 | − | 0.846865i | \(-0.678487\pi\) | ||||
−0.531808 | + | 0.846865i | \(0.678487\pi\) | |||||||
\(390\) | −829232. | −0.276067 | ||||||||
\(391\) | 428643. | 0.141793 | ||||||||
\(392\) | 1.07199e6 | 0.352351 | ||||||||
\(393\) | 218038. | 0.0712118 | ||||||||
\(394\) | 2.03619e6 | 0.660813 | ||||||||
\(395\) | 137257. | 0.0442631 | ||||||||
\(396\) | 41222.4 | 0.0132098 | ||||||||
\(397\) | 3.57862e6 | 1.13957 | 0.569783 | − | 0.821795i | \(-0.307027\pi\) | ||||
0.569783 | + | 0.821795i | \(0.307027\pi\) | |||||||
\(398\) | −3.90192e6 | −1.23473 | ||||||||
\(399\) | 536964. | 0.168855 | ||||||||
\(400\) | 2.82535e6 | 0.882923 | ||||||||
\(401\) | −4.84786e6 | −1.50553 | −0.752764 | − | 0.658290i | \(-0.771280\pi\) | ||||
−0.752764 | + | 0.658290i | \(0.771280\pi\) | |||||||
\(402\) | 1.12896e6 | 0.348430 | ||||||||
\(403\) | 3.97445e6 | 1.21903 | ||||||||
\(404\) | −325957. | −0.0993589 | ||||||||
\(405\) | 171037. | 0.0518146 | ||||||||
\(406\) | −4.55620e6 | −1.37179 | ||||||||
\(407\) | 1.65971e6 | 0.496644 | ||||||||
\(408\) | 1.58670e6 | 0.471895 | ||||||||
\(409\) | −2.38119e6 | −0.703859 | −0.351930 | − | 0.936026i | \(-0.614474\pi\) | ||||
−0.351930 | + | 0.936026i | \(0.614474\pi\) | |||||||
\(410\) | 554541. | 0.162920 | ||||||||
\(411\) | 2.15074e6 | 0.628035 | ||||||||
\(412\) | −590708. | −0.171447 | ||||||||
\(413\) | −531456. | −0.153318 | ||||||||
\(414\) | 197058. | 0.0565057 | ||||||||
\(415\) | 2.55478e6 | 0.728171 | ||||||||
\(416\) | −1.01124e6 | −0.286498 | ||||||||
\(417\) | −120117. | −0.0338270 | ||||||||
\(418\) | −249598. | −0.0698714 | ||||||||
\(419\) | −510637. | −0.142095 | −0.0710473 | − | 0.997473i | \(-0.522634\pi\) | ||||
−0.0710473 | + | 0.997473i | \(0.522634\pi\) | |||||||
\(420\) | 173224. | 0.0479165 | ||||||||
\(421\) | −2.82268e6 | −0.776168 | −0.388084 | − | 0.921624i | \(-0.626863\pi\) | ||||
−0.388084 | + | 0.921624i | \(0.626863\pi\) | |||||||
\(422\) | −5.49431e6 | −1.50187 | ||||||||
\(423\) | 625402. | 0.169945 | ||||||||
\(424\) | 2.96072e6 | 0.799804 | ||||||||
\(425\) | 2.61503e6 | 0.702271 | ||||||||
\(426\) | −2.15565e6 | −0.575512 | ||||||||
\(427\) | −6.95804e6 | −1.84679 | ||||||||
\(428\) | 524293. | 0.138345 | ||||||||
\(429\) | 551551. | 0.144691 | ||||||||
\(430\) | −1.62135e6 | −0.422869 | ||||||||
\(431\) | −2.25262e6 | −0.584111 | −0.292056 | − | 0.956401i | \(-0.594339\pi\) | ||||
−0.292056 | + | 0.956401i | \(0.594339\pi\) | |||||||
\(432\) | 842261. | 0.217139 | ||||||||
\(433\) | −720129. | −0.184582 | −0.0922912 | − | 0.995732i | \(-0.529419\pi\) | ||||
−0.0922912 | + | 0.995732i | \(0.529419\pi\) | |||||||
\(434\) | −6.32410e6 | −1.61166 | ||||||||
\(435\) | 1.15362e6 | 0.292309 | ||||||||
\(436\) | −653371. | −0.164605 | ||||||||
\(437\) | −156643. | −0.0392381 | ||||||||
\(438\) | −143051. | −0.0356291 | ||||||||
\(439\) | 1.48562e6 | 0.367913 | 0.183957 | − | 0.982934i | \(-0.441109\pi\) | ||||
0.183957 | + | 0.982934i | \(0.441109\pi\) | |||||||
\(440\) | 452288. | 0.111374 | ||||||||
\(441\) | 526678. | 0.128958 | ||||||||
\(442\) | −3.77952e6 | −0.920199 | ||||||||
\(443\) | 5.34112e6 | 1.29307 | 0.646536 | − | 0.762884i | \(-0.276217\pi\) | ||||
0.646536 | + | 0.762884i | \(0.276217\pi\) | |||||||
\(444\) | −686422. | −0.165247 | ||||||||
\(445\) | 916548. | 0.219409 | ||||||||
\(446\) | 952508. | 0.226742 | ||||||||
\(447\) | −2.08100e6 | −0.492609 | ||||||||
\(448\) | −4.03552e6 | −0.949957 | ||||||||
\(449\) | −2.91837e6 | −0.683163 | −0.341582 | − | 0.939852i | \(-0.610963\pi\) | ||||
−0.341582 | + | 0.939852i | \(0.610963\pi\) | |||||||
\(450\) | 1.20220e6 | 0.279862 | ||||||||
\(451\) | −368845. | −0.0853890 | ||||||||
\(452\) | −677563. | −0.155992 | ||||||||
\(453\) | −4.00414e6 | −0.916776 | ||||||||
\(454\) | −4.75856e6 | −1.08352 | ||||||||
\(455\) | 2.31772e6 | 0.524847 | ||||||||
\(456\) | −579845. | −0.130587 | ||||||||
\(457\) | 4.95434e6 | 1.10967 | 0.554837 | − | 0.831959i | \(-0.312781\pi\) | ||||
0.554837 | + | 0.831959i | \(0.312781\pi\) | |||||||
\(458\) | 4.03274e6 | 0.898332 | ||||||||
\(459\) | 779562. | 0.172711 | ||||||||
\(460\) | −50532.9 | −0.0111347 | ||||||||
\(461\) | 8.92176e6 | 1.95523 | 0.977616 | − | 0.210396i | \(-0.0674755\pi\) | ||||
0.977616 | + | 0.210396i | \(0.0674755\pi\) | |||||||
\(462\) | −877622. | −0.191295 | ||||||||
\(463\) | −4.66737e6 | −1.01186 | −0.505929 | − | 0.862575i | \(-0.668850\pi\) | ||||
−0.505929 | + | 0.862575i | \(0.668850\pi\) | |||||||
\(464\) | 5.68096e6 | 1.22497 | ||||||||
\(465\) | 1.60126e6 | 0.343423 | ||||||||
\(466\) | 5.97728e6 | 1.27508 | ||||||||
\(467\) | −1.63053e6 | −0.345968 | −0.172984 | − | 0.984925i | \(-0.555341\pi\) | ||||
−0.172984 | + | 0.984925i | \(0.555341\pi\) | |||||||
\(468\) | −228111. | −0.0481428 | ||||||||
\(469\) | −3.15548e6 | −0.662420 | ||||||||
\(470\) | −1.22160e6 | −0.255085 | ||||||||
\(471\) | −3.20803e6 | −0.666325 | ||||||||
\(472\) | 573898. | 0.118571 | ||||||||
\(473\) | 1.07842e6 | 0.221633 | ||||||||
\(474\) | 287603. | 0.0587960 | ||||||||
\(475\) | −955637. | −0.194339 | ||||||||
\(476\) | 789532. | 0.159717 | ||||||||
\(477\) | 1.45463e6 | 0.292723 | ||||||||
\(478\) | 9.18390e6 | 1.83847 | ||||||||
\(479\) | −2.82698e6 | −0.562969 | −0.281484 | − | 0.959566i | \(-0.590827\pi\) | ||||
−0.281484 | + | 0.959566i | \(0.590827\pi\) | |||||||
\(480\) | −407416. | −0.0807115 | ||||||||
\(481\) | −9.18425e6 | −1.81001 | ||||||||
\(482\) | −2.38257e6 | −0.467119 | ||||||||
\(483\) | −550780. | −0.107426 | ||||||||
\(484\) | −725280. | −0.140732 | ||||||||
\(485\) | 3.29163e6 | 0.635414 | ||||||||
\(486\) | 358384. | 0.0688268 | ||||||||
\(487\) | 9.05496e6 | 1.73007 | 0.865036 | − | 0.501710i | \(-0.167296\pi\) | ||||
0.865036 | + | 0.501710i | \(0.167296\pi\) | |||||||
\(488\) | 7.51370e6 | 1.42825 | ||||||||
\(489\) | −993523. | −0.187891 | ||||||||
\(490\) | −1.02876e6 | −0.193564 | ||||||||
\(491\) | 5.23566e6 | 0.980094 | 0.490047 | − | 0.871696i | \(-0.336980\pi\) | ||||
0.490047 | + | 0.871696i | \(0.336980\pi\) | |||||||
\(492\) | 152547. | 0.0284113 | ||||||||
\(493\) | 5.25807e6 | 0.974336 | ||||||||
\(494\) | 1.38119e6 | 0.254645 | ||||||||
\(495\) | 222213. | 0.0407621 | ||||||||
\(496\) | 7.88530e6 | 1.43918 | ||||||||
\(497\) | 6.02508e6 | 1.09414 | ||||||||
\(498\) | 5.35319e6 | 0.967251 | ||||||||
\(499\) | 6.52056e6 | 1.17229 | 0.586143 | − | 0.810208i | \(-0.300646\pi\) | ||||
0.586143 | + | 0.810208i | \(0.300646\pi\) | |||||||
\(500\) | −702248. | −0.125622 | ||||||||
\(501\) | −1.48444e6 | −0.264222 | ||||||||
\(502\) | 1.45251e6 | 0.257252 | ||||||||
\(503\) | 8.90079e6 | 1.56859 | 0.784294 | − | 0.620390i | \(-0.213026\pi\) | ||||
0.784294 | + | 0.620390i | \(0.213026\pi\) | |||||||
\(504\) | −2.03882e6 | −0.357522 | ||||||||
\(505\) | −1.75710e6 | −0.306597 | ||||||||
\(506\) | 256020. | 0.0444526 | ||||||||
\(507\) | 289539. | 0.0500249 | ||||||||
\(508\) | 1.45225e6 | 0.249679 | ||||||||
\(509\) | 4.51848e6 | 0.773033 | 0.386516 | − | 0.922283i | \(-0.373678\pi\) | ||||
0.386516 | + | 0.922283i | \(0.373678\pi\) | |||||||
\(510\) | −1.52272e6 | −0.259236 | ||||||||
\(511\) | 399830. | 0.0677365 | ||||||||
\(512\) | 4.08906e6 | 0.689364 | ||||||||
\(513\) | −284883. | −0.0477940 | ||||||||
\(514\) | 717968. | 0.119866 | ||||||||
\(515\) | −3.18426e6 | −0.529043 | ||||||||
\(516\) | −446012. | −0.0737433 | ||||||||
\(517\) | 812530. | 0.133694 | ||||||||
\(518\) | 1.46139e7 | 2.39299 | ||||||||
\(519\) | −3.89634e6 | −0.634948 | ||||||||
\(520\) | −2.50281e6 | −0.405900 | ||||||||
\(521\) | −3.74138e6 | −0.603862 | −0.301931 | − | 0.953330i | \(-0.597631\pi\) | ||||
−0.301931 | + | 0.953330i | \(0.597631\pi\) | |||||||
\(522\) | 2.41726e6 | 0.388282 | ||||||||
\(523\) | −1.64299e6 | −0.262653 | −0.131326 | − | 0.991339i | \(-0.541924\pi\) | ||||
−0.131326 | + | 0.991339i | \(0.541924\pi\) | |||||||
\(524\) | −117158. | −0.0186400 | ||||||||
\(525\) | −3.36016e6 | −0.532062 | ||||||||
\(526\) | −1.03445e6 | −0.163022 | ||||||||
\(527\) | 7.29831e6 | 1.14471 | ||||||||
\(528\) | 1.09428e6 | 0.170821 | ||||||||
\(529\) | −6.27567e6 | −0.975037 | ||||||||
\(530\) | −2.84134e6 | −0.439373 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | −288526. | −0.0441984 | ||||||||
\(533\) | 2.04106e6 | 0.311199 | ||||||||
\(534\) | 1.92050e6 | 0.291448 | ||||||||
\(535\) | 2.82625e6 | 0.426900 | ||||||||
\(536\) | 3.40747e6 | 0.512295 | ||||||||
\(537\) | −2.98297e6 | −0.446389 | ||||||||
\(538\) | −7.07964e6 | −1.05452 | ||||||||
\(539\) | 684267. | 0.101450 | ||||||||
\(540\) | −91903.0 | −0.0135627 | ||||||||
\(541\) | 896593. | 0.131705 | 0.0658525 | − | 0.997829i | \(-0.479023\pi\) | ||||
0.0658525 | + | 0.997829i | \(0.479023\pi\) | |||||||
\(542\) | −153132. | −0.0223907 | ||||||||
\(543\) | −1.23147e6 | −0.179235 | ||||||||
\(544\) | −1.85695e6 | −0.269031 | ||||||||
\(545\) | −3.52205e6 | −0.507931 | ||||||||
\(546\) | 4.85646e6 | 0.697170 | ||||||||
\(547\) | −3.23932e6 | −0.462898 | −0.231449 | − | 0.972847i | \(-0.574347\pi\) | ||||
−0.231449 | + | 0.972847i | \(0.574347\pi\) | |||||||
\(548\) | −1.15566e6 | −0.164391 | ||||||||
\(549\) | 3.69155e6 | 0.522730 | ||||||||
\(550\) | 1.56191e6 | 0.220165 | ||||||||
\(551\) | −1.92151e6 | −0.269627 | ||||||||
\(552\) | 594765. | 0.0830802 | ||||||||
\(553\) | −803857. | −0.111780 | ||||||||
\(554\) | 721445. | 0.0998685 | ||||||||
\(555\) | −3.70022e6 | −0.509912 | ||||||||
\(556\) | 64542.3 | 0.00885436 | ||||||||
\(557\) | −1.14366e6 | −0.156192 | −0.0780958 | − | 0.996946i | \(-0.524884\pi\) | ||||
−0.0780958 | + | 0.996946i | \(0.524884\pi\) | |||||||
\(558\) | 3.35522e6 | 0.456179 | ||||||||
\(559\) | −5.96760e6 | −0.807737 | ||||||||
\(560\) | 4.59835e6 | 0.619629 | ||||||||
\(561\) | 1.01282e6 | 0.135870 | ||||||||
\(562\) | 2.98837e6 | 0.399111 | ||||||||
\(563\) | 3.50782e6 | 0.466408 | 0.233204 | − | 0.972428i | \(-0.425079\pi\) | ||||
0.233204 | + | 0.972428i | \(0.425079\pi\) | |||||||
\(564\) | −336047. | −0.0444838 | ||||||||
\(565\) | −3.65247e6 | −0.481354 | ||||||||
\(566\) | −3.23009e6 | −0.423812 | ||||||||
\(567\) | −1.00169e6 | −0.130851 | ||||||||
\(568\) | −6.50624e6 | −0.846173 | ||||||||
\(569\) | 2.53909e6 | 0.328774 | 0.164387 | − | 0.986396i | \(-0.447435\pi\) | ||||
0.164387 | + | 0.986396i | \(0.447435\pi\) | |||||||
\(570\) | 556464. | 0.0717381 | ||||||||
\(571\) | 1.08743e7 | 1.39576 | 0.697882 | − | 0.716212i | \(-0.254126\pi\) | ||||
0.697882 | + | 0.716212i | \(0.254126\pi\) | |||||||
\(572\) | −296365. | −0.0378736 | ||||||||
\(573\) | −6.99983e6 | −0.890637 | ||||||||
\(574\) | −3.24771e6 | −0.411432 | ||||||||
\(575\) | 980226. | 0.123639 | ||||||||
\(576\) | 2.14102e6 | 0.268884 | ||||||||
\(577\) | −207945. | −0.0260021 | −0.0130011 | − | 0.999915i | \(-0.504138\pi\) | ||||
−0.0130011 | + | 0.999915i | \(0.504138\pi\) | |||||||
\(578\) | 1.67712e6 | 0.208807 | ||||||||
\(579\) | 3.62315e6 | 0.449149 | ||||||||
\(580\) | −619876. | −0.0765130 | ||||||||
\(581\) | −1.49623e7 | −1.83890 | ||||||||
\(582\) | 6.89717e6 | 0.844040 | ||||||||
\(583\) | 1.88987e6 | 0.230283 | ||||||||
\(584\) | −431759. | −0.0523853 | ||||||||
\(585\) | −1.22965e6 | −0.148557 | ||||||||
\(586\) | −1.03192e6 | −0.124137 | ||||||||
\(587\) | −1.05248e7 | −1.26071 | −0.630357 | − | 0.776305i | \(-0.717092\pi\) | ||||
−0.630357 | + | 0.776305i | \(0.717092\pi\) | |||||||
\(588\) | −282999. | −0.0337553 | ||||||||
\(589\) | −2.66709e6 | −0.316774 | ||||||||
\(590\) | −550756. | −0.0651372 | ||||||||
\(591\) | 3.01943e6 | 0.355596 | ||||||||
\(592\) | −1.82215e7 | −2.13688 | ||||||||
\(593\) | −1.40794e7 | −1.64418 | −0.822089 | − | 0.569359i | \(-0.807191\pi\) | ||||
−0.822089 | + | 0.569359i | \(0.807191\pi\) | |||||||
\(594\) | 465617. | 0.0541456 | ||||||||
\(595\) | 4.25604e6 | 0.492849 | ||||||||
\(596\) | 1.11818e6 | 0.128943 | ||||||||
\(597\) | −5.78609e6 | −0.664430 | ||||||||
\(598\) | −1.41673e6 | −0.162007 | ||||||||
\(599\) | −7.81286e6 | −0.889699 | −0.444849 | − | 0.895605i | \(-0.646743\pi\) | ||||
−0.444849 | + | 0.895605i | \(0.646743\pi\) | |||||||
\(600\) | 3.62850e6 | 0.411480 | ||||||||
\(601\) | 1.10899e7 | 1.25239 | 0.626196 | − | 0.779666i | \(-0.284611\pi\) | ||||
0.626196 | + | 0.779666i | \(0.284611\pi\) | |||||||
\(602\) | 9.49557e6 | 1.06790 | ||||||||
\(603\) | 1.67412e6 | 0.187497 | ||||||||
\(604\) | 2.15154e6 | 0.239970 | ||||||||
\(605\) | −3.90969e6 | −0.434264 | ||||||||
\(606\) | −3.68176e6 | −0.407262 | ||||||||
\(607\) | 729204. | 0.0803299 | 0.0401649 | − | 0.999193i | \(-0.487212\pi\) | ||||
0.0401649 | + | 0.999193i | \(0.487212\pi\) | |||||||
\(608\) | 678603. | 0.0744486 | ||||||||
\(609\) | −6.75630e6 | −0.738186 | ||||||||
\(610\) | −7.21072e6 | −0.784611 | ||||||||
\(611\) | −4.49627e6 | −0.487247 | ||||||||
\(612\) | −418881. | −0.0452077 | ||||||||
\(613\) | 1.53130e7 | 1.64593 | 0.822963 | − | 0.568096i | \(-0.192320\pi\) | ||||
0.822963 | + | 0.568096i | \(0.192320\pi\) | |||||||
\(614\) | 717142. | 0.0767687 | ||||||||
\(615\) | 822318. | 0.0876702 | ||||||||
\(616\) | −2.64886e6 | −0.281260 | ||||||||
\(617\) | 2.52522e6 | 0.267046 | 0.133523 | − | 0.991046i | \(-0.457371\pi\) | ||||
0.133523 | + | 0.991046i | \(0.457371\pi\) | |||||||
\(618\) | −6.67219e6 | −0.702744 | ||||||||
\(619\) | 6.17194e6 | 0.647433 | 0.323717 | − | 0.946154i | \(-0.395068\pi\) | ||||
0.323717 | + | 0.946154i | \(0.395068\pi\) | |||||||
\(620\) | −860402. | −0.0898923 | ||||||||
\(621\) | 292213. | 0.0304068 | ||||||||
\(622\) | 1.21498e7 | 1.25920 | ||||||||
\(623\) | −5.36784e6 | −0.554089 | ||||||||
\(624\) | −6.05535e6 | −0.622555 | ||||||||
\(625\) | 3.85642e6 | 0.394897 | ||||||||
\(626\) | −2.06680e7 | −2.10796 | ||||||||
\(627\) | −370124. | −0.0375991 | ||||||||
\(628\) | 1.72377e6 | 0.174413 | ||||||||
\(629\) | −1.68651e7 | −1.69966 | ||||||||
\(630\) | 1.95661e6 | 0.196405 | ||||||||
\(631\) | 8.46974e6 | 0.846831 | 0.423416 | − | 0.905936i | \(-0.360831\pi\) | ||||
0.423416 | + | 0.905936i | \(0.360831\pi\) | |||||||
\(632\) | 868051. | 0.0864475 | ||||||||
\(633\) | −8.14741e6 | −0.808184 | ||||||||
\(634\) | 2.39243e6 | 0.236383 | ||||||||
\(635\) | 7.82850e6 | 0.770449 | ||||||||
\(636\) | −781615. | −0.0766214 | ||||||||
\(637\) | −3.78650e6 | −0.369734 | ||||||||
\(638\) | 3.14054e6 | 0.305459 | ||||||||
\(639\) | −3.19657e6 | −0.309694 | ||||||||
\(640\) | −5.63066e6 | −0.543387 | ||||||||
\(641\) | 2.80019e6 | 0.269180 | 0.134590 | − | 0.990901i | \(-0.457028\pi\) | ||||
0.134590 | + | 0.990901i | \(0.457028\pi\) | |||||||
\(642\) | 5.92202e6 | 0.567064 | ||||||||
\(643\) | −2.94663e6 | −0.281059 | −0.140530 | − | 0.990076i | \(-0.544880\pi\) | ||||
−0.140530 | + | 0.990076i | \(0.544880\pi\) | |||||||
\(644\) | 295950. | 0.0281193 | ||||||||
\(645\) | −2.40427e6 | −0.227554 | ||||||||
\(646\) | 2.53629e6 | 0.239121 | ||||||||
\(647\) | 247037. | 0.0232007 | 0.0116003 | − | 0.999933i | \(-0.496307\pi\) | ||||
0.0116003 | + | 0.999933i | \(0.496307\pi\) | |||||||
\(648\) | 1.08168e6 | 0.101196 | ||||||||
\(649\) | 366327. | 0.0341395 | ||||||||
\(650\) | −8.64307e6 | −0.802388 | ||||||||
\(651\) | −9.37790e6 | −0.867267 | ||||||||
\(652\) | 533849. | 0.0491812 | ||||||||
\(653\) | 4.06721e6 | 0.373262 | 0.186631 | − | 0.982430i | \(-0.440243\pi\) | ||||
0.186631 | + | 0.982430i | \(0.440243\pi\) | |||||||
\(654\) | −7.37998e6 | −0.674700 | ||||||||
\(655\) | −631553. | −0.0575184 | ||||||||
\(656\) | 4.04946e6 | 0.367398 | ||||||||
\(657\) | −212127. | −0.0191727 | ||||||||
\(658\) | 7.15441e6 | 0.644183 | ||||||||
\(659\) | −1.80835e7 | −1.62207 | −0.811034 | − | 0.584998i | \(-0.801095\pi\) | ||||
−0.811034 | + | 0.584998i | \(0.801095\pi\) | |||||||
\(660\) | −119402. | −0.0106697 | ||||||||
\(661\) | 5.40254e6 | 0.480944 | 0.240472 | − | 0.970656i | \(-0.422698\pi\) | ||||
0.240472 | + | 0.970656i | \(0.422698\pi\) | |||||||
\(662\) | 1.37973e7 | 1.22363 | ||||||||
\(663\) | −5.60459e6 | −0.495176 | ||||||||
\(664\) | 1.61571e7 | 1.42215 | ||||||||
\(665\) | −1.55533e6 | −0.136385 | ||||||||
\(666\) | −7.75331e6 | −0.677332 | ||||||||
\(667\) | 1.97095e6 | 0.171538 | ||||||||
\(668\) | 797633. | 0.0691611 | ||||||||
\(669\) | 1.41246e6 | 0.122014 | ||||||||
\(670\) | −3.27007e6 | −0.281430 | ||||||||
\(671\) | 4.79611e6 | 0.411228 | ||||||||
\(672\) | 2.38607e6 | 0.203826 | ||||||||
\(673\) | −1.78587e7 | −1.51989 | −0.759946 | − | 0.649986i | \(-0.774775\pi\) | ||||
−0.759946 | + | 0.649986i | \(0.774775\pi\) | |||||||
\(674\) | 7.01472e6 | 0.594786 | ||||||||
\(675\) | 1.78271e6 | 0.150599 | ||||||||
\(676\) | −155577. | −0.0130942 | ||||||||
\(677\) | −1.84660e7 | −1.54846 | −0.774231 | − | 0.632903i | \(-0.781863\pi\) | ||||
−0.774231 | + | 0.632903i | \(0.781863\pi\) | |||||||
\(678\) | −7.65324e6 | −0.639398 | ||||||||
\(679\) | −1.92777e7 | −1.60465 | ||||||||
\(680\) | −4.59592e6 | −0.381154 | ||||||||
\(681\) | −7.05639e6 | −0.583062 | ||||||||
\(682\) | 4.35914e6 | 0.358872 | ||||||||
\(683\) | −1.20352e7 | −0.987193 | −0.493596 | − | 0.869691i | \(-0.664318\pi\) | ||||
−0.493596 | + | 0.869691i | \(0.664318\pi\) | |||||||
\(684\) | 153076. | 0.0125103 | ||||||||
\(685\) | −6.22967e6 | −0.507270 | ||||||||
\(686\) | −9.54859e6 | −0.774692 | ||||||||
\(687\) | 5.98008e6 | 0.483410 | ||||||||
\(688\) | −1.18397e7 | −0.953607 | ||||||||
\(689\) | −1.04579e7 | −0.839262 | ||||||||
\(690\) | −570782. | −0.0456402 | ||||||||
\(691\) | 9.13181e6 | 0.727548 | 0.363774 | − | 0.931487i | \(-0.381488\pi\) | ||||
0.363774 | + | 0.931487i | \(0.381488\pi\) | |||||||
\(692\) | 2.09362e6 | 0.166200 | ||||||||
\(693\) | −1.30141e6 | −0.102939 | ||||||||
\(694\) | −1.99377e7 | −1.57136 | ||||||||
\(695\) | 347921. | 0.0273224 | ||||||||
\(696\) | 7.29585e6 | 0.570890 | ||||||||
\(697\) | 3.74801e6 | 0.292226 | ||||||||
\(698\) | −2.36096e7 | −1.83422 | ||||||||
\(699\) | 8.86359e6 | 0.686146 | ||||||||
\(700\) | 1.80551e6 | 0.139269 | ||||||||
\(701\) | −1.78286e7 | −1.37032 | −0.685160 | − | 0.728393i | \(-0.740268\pi\) | ||||
−0.685160 | + | 0.728393i | \(0.740268\pi\) | |||||||
\(702\) | −2.57657e6 | −0.197333 | ||||||||
\(703\) | 6.16318e6 | 0.470345 | ||||||||
\(704\) | 2.78164e6 | 0.211529 | ||||||||
\(705\) | −1.81149e6 | −0.137266 | ||||||||
\(706\) | 1.70079e7 | 1.28422 | ||||||||
\(707\) | 1.02906e7 | 0.774270 | ||||||||
\(708\) | −151506. | −0.0113592 | ||||||||
\(709\) | 1.63081e7 | 1.21839 | 0.609197 | − | 0.793019i | \(-0.291492\pi\) | ||||
0.609197 | + | 0.793019i | \(0.291492\pi\) | |||||||
\(710\) | 6.24388e6 | 0.464846 | ||||||||
\(711\) | 426481. | 0.0316392 | ||||||||
\(712\) | 5.79651e6 | 0.428515 | ||||||||
\(713\) | 2.73572e6 | 0.201534 | ||||||||
\(714\) | 8.91796e6 | 0.654666 | ||||||||
\(715\) | −1.59758e6 | −0.116869 | ||||||||
\(716\) | 1.60284e6 | 0.116844 | ||||||||
\(717\) | 1.36186e7 | 0.989317 | ||||||||
\(718\) | −4.07380e6 | −0.294909 | ||||||||
\(719\) | −2.01650e7 | −1.45471 | −0.727356 | − | 0.686261i | \(-0.759251\pi\) | ||||
−0.727356 | + | 0.686261i | \(0.759251\pi\) | |||||||
\(720\) | −2.43963e6 | −0.175385 | ||||||||
\(721\) | 1.86489e7 | 1.33603 | ||||||||
\(722\) | 1.41012e7 | 1.00673 | ||||||||
\(723\) | −3.53306e6 | −0.251366 | ||||||||
\(724\) | 661703. | 0.0469155 | ||||||||
\(725\) | 1.20242e7 | 0.849595 | ||||||||
\(726\) | −8.19221e6 | −0.576846 | ||||||||
\(727\) | −2.39725e7 | −1.68220 | −0.841098 | − | 0.540883i | \(-0.818090\pi\) | ||||
−0.841098 | + | 0.540883i | \(0.818090\pi\) | |||||||
\(728\) | 1.46579e7 | 1.02505 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 414350. | 0.0287779 | ||||||||
\(731\) | −1.09583e7 | −0.758492 | ||||||||
\(732\) | −1.98358e6 | −0.136827 | ||||||||
\(733\) | 872995. | 0.0600139 | 0.0300069 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300069 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(734\) | 3.90178e6 | 0.267315 | ||||||||
\(735\) | −1.52553e6 | −0.104161 | ||||||||
\(736\) | −696064. | −0.0473647 | ||||||||
\(737\) | 2.17504e6 | 0.147502 | ||||||||
\(738\) | 1.72305e6 | 0.116455 | ||||||||
\(739\) | 1.39258e7 | 0.938015 | 0.469007 | − | 0.883194i | \(-0.344612\pi\) | ||||
0.469007 | + | 0.883194i | \(0.344612\pi\) | |||||||
\(740\) | 1.98824e6 | 0.133472 | ||||||||
\(741\) | 2.04814e6 | 0.137029 | ||||||||
\(742\) | 1.66405e7 | 1.10958 | ||||||||
\(743\) | −2.00248e7 | −1.33075 | −0.665374 | − | 0.746510i | \(-0.731728\pi\) | ||||
−0.665374 | + | 0.746510i | \(0.731728\pi\) | |||||||
\(744\) | 1.01268e7 | 0.670718 | ||||||||
\(745\) | 6.02766e6 | 0.397885 | ||||||||
\(746\) | 1.86988e7 | 1.23017 | ||||||||
\(747\) | 7.93815e6 | 0.520496 | ||||||||
\(748\) | −544216. | −0.0355646 | ||||||||
\(749\) | −1.65522e7 | −1.07808 | ||||||||
\(750\) | −7.93206e6 | −0.514912 | ||||||||
\(751\) | 1.08500e7 | 0.701986 | 0.350993 | − | 0.936378i | \(-0.385844\pi\) | ||||
0.350993 | + | 0.936378i | \(0.385844\pi\) | |||||||
\(752\) | −8.92058e6 | −0.575239 | ||||||||
\(753\) | 2.15390e6 | 0.138432 | ||||||||
\(754\) | −1.73787e7 | −1.11324 | ||||||||
\(755\) | 1.15981e7 | 0.740488 | ||||||||
\(756\) | 538238. | 0.0342507 | ||||||||
\(757\) | 2.29213e7 | 1.45378 | 0.726892 | − | 0.686751i | \(-0.240964\pi\) | ||||
0.726892 | + | 0.686751i | \(0.240964\pi\) | |||||||
\(758\) | 1.61579e7 | 1.02144 | ||||||||
\(759\) | 379647. | 0.0239208 | ||||||||
\(760\) | 1.67953e6 | 0.105476 | ||||||||
\(761\) | 1.09281e7 | 0.684042 | 0.342021 | − | 0.939692i | \(-0.388889\pi\) | ||||
0.342021 | + | 0.939692i | \(0.388889\pi\) | |||||||
\(762\) | 1.64035e7 | 1.02341 | ||||||||
\(763\) | 2.06272e7 | 1.28271 | ||||||||
\(764\) | 3.76121e6 | 0.233128 | ||||||||
\(765\) | −2.25802e6 | −0.139500 | ||||||||
\(766\) | −5.73061e6 | −0.352881 | ||||||||
\(767\) | −2.02713e6 | −0.124421 | ||||||||
\(768\) | −4.18576e6 | −0.256077 | ||||||||
\(769\) | −1.73650e7 | −1.05891 | −0.529453 | − | 0.848339i | \(-0.677603\pi\) | ||||
−0.529453 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(770\) | 2.54205e6 | 0.154510 | ||||||||
\(771\) | 1.06466e6 | 0.0645024 | ||||||||
\(772\) | −1.94683e6 | −0.117567 | ||||||||
\(773\) | −1.45083e7 | −0.873308 | −0.436654 | − | 0.899629i | \(-0.643837\pi\) | ||||
−0.436654 | + | 0.899629i | \(0.643837\pi\) | |||||||
\(774\) | −5.03782e6 | −0.302267 | ||||||||
\(775\) | 1.66899e7 | 0.998158 | ||||||||
\(776\) | 2.08172e7 | 1.24099 | ||||||||
\(777\) | 2.16707e7 | 1.28771 | ||||||||
\(778\) | 1.92662e7 | 1.14116 | ||||||||
\(779\) | −1.36967e6 | −0.0808674 | ||||||||
\(780\) | 660728. | 0.0388854 | ||||||||
\(781\) | −4.15303e6 | −0.243634 | ||||||||
\(782\) | −2.60155e6 | −0.152130 | ||||||||
\(783\) | 3.58451e6 | 0.208942 | ||||||||
\(784\) | −7.51240e6 | −0.436504 | ||||||||
\(785\) | 9.29213e6 | 0.538197 | ||||||||
\(786\) | −1.32333e6 | −0.0764034 | ||||||||
\(787\) | 1.28648e6 | 0.0740401 | 0.0370200 | − | 0.999315i | \(-0.488213\pi\) | ||||
0.0370200 | + | 0.999315i | \(0.488213\pi\) | |||||||
\(788\) | −1.62243e6 | −0.0930787 | ||||||||
\(789\) | −1.53397e6 | −0.0877252 | ||||||||
\(790\) | −833049. | −0.0474900 | ||||||||
\(791\) | 2.13910e7 | 1.21560 | ||||||||
\(792\) | 1.40534e6 | 0.0796100 | ||||||||
\(793\) | −2.65400e7 | −1.49871 | ||||||||
\(794\) | −2.17196e7 | −1.22265 | ||||||||
\(795\) | −4.21337e6 | −0.236435 | ||||||||
\(796\) | 3.10903e6 | 0.173917 | ||||||||
\(797\) | 1.58057e6 | 0.0881389 | 0.0440694 | − | 0.999028i | \(-0.485968\pi\) | ||||
0.0440694 | + | 0.999028i | \(0.485968\pi\) | |||||||
\(798\) | −3.25898e6 | −0.181165 | ||||||||
\(799\) | −8.25653e6 | −0.457541 | ||||||||
\(800\) | −4.24650e6 | −0.234588 | ||||||||
\(801\) | 2.84788e6 | 0.156834 | ||||||||
\(802\) | 2.94229e7 | 1.61529 | ||||||||
\(803\) | −275599. | −0.0150830 | ||||||||
\(804\) | −899554. | −0.0490780 | ||||||||
\(805\) | 1.59535e6 | 0.0867692 | ||||||||
\(806\) | −2.41220e7 | −1.30790 | ||||||||
\(807\) | −1.04983e7 | −0.567458 | ||||||||
\(808\) | −1.11124e7 | −0.598796 | ||||||||
\(809\) | −7.43750e6 | −0.399536 | −0.199768 | − | 0.979843i | \(-0.564019\pi\) | ||||
−0.199768 | + | 0.979843i | \(0.564019\pi\) | |||||||
\(810\) | −1.03807e6 | −0.0555921 | ||||||||
\(811\) | 2.65806e7 | 1.41910 | 0.709551 | − | 0.704654i | \(-0.248898\pi\) | ||||
0.709551 | + | 0.704654i | \(0.248898\pi\) | |||||||
\(812\) | 3.63036e6 | 0.193223 | ||||||||
\(813\) | −227077. | −0.0120489 | ||||||||
\(814\) | −1.00732e7 | −0.532852 | ||||||||
\(815\) | 2.87776e6 | 0.151761 | ||||||||
\(816\) | −1.11195e7 | −0.584601 | ||||||||
\(817\) | 4.00461e6 | 0.209897 | ||||||||
\(818\) | 1.44521e7 | 0.755174 | ||||||||
\(819\) | 7.20156e6 | 0.375160 | ||||||||
\(820\) | −441855. | −0.0229480 | ||||||||
\(821\) | −1.67822e7 | −0.868942 | −0.434471 | − | 0.900686i | \(-0.643065\pi\) | ||||
−0.434471 | + | 0.900686i | \(0.643065\pi\) | |||||||
\(822\) | −1.30534e7 | −0.673822 | ||||||||
\(823\) | 1.25067e7 | 0.643642 | 0.321821 | − | 0.946801i | \(-0.395705\pi\) | ||||
0.321821 | + | 0.946801i | \(0.395705\pi\) | |||||||
\(824\) | −2.01382e7 | −1.03324 | ||||||||
\(825\) | 2.31612e6 | 0.118475 | ||||||||
\(826\) | 3.22555e6 | 0.164495 | ||||||||
\(827\) | 2.95809e7 | 1.50400 | 0.752000 | − | 0.659163i | \(-0.229089\pi\) | ||||
0.752000 | + | 0.659163i | \(0.229089\pi\) | |||||||
\(828\) | −157015. | −0.00795911 | ||||||||
\(829\) | 2.33450e7 | 1.17980 | 0.589898 | − | 0.807478i | \(-0.299168\pi\) | ||||
0.589898 | + | 0.807478i | \(0.299168\pi\) | |||||||
\(830\) | −1.55056e7 | −0.781257 | ||||||||
\(831\) | 1.06982e6 | 0.0537411 | ||||||||
\(832\) | −1.53927e7 | −0.770913 | ||||||||
\(833\) | −6.95317e6 | −0.347193 | ||||||||
\(834\) | 729021. | 0.0362932 | ||||||||
\(835\) | 4.29971e6 | 0.213414 | ||||||||
\(836\) | 198878. | 0.00984173 | ||||||||
\(837\) | 4.97539e6 | 0.245478 | ||||||||
\(838\) | 3.09919e6 | 0.152454 | ||||||||
\(839\) | −2.47748e7 | −1.21508 | −0.607541 | − | 0.794289i | \(-0.707844\pi\) | ||||
−0.607541 | + | 0.794289i | \(0.707844\pi\) | |||||||
\(840\) | 5.90549e6 | 0.288774 | ||||||||
\(841\) | 3.66603e6 | 0.178733 | ||||||||
\(842\) | 1.71316e7 | 0.832754 | ||||||||
\(843\) | 4.43140e6 | 0.214769 | ||||||||
\(844\) | 4.37784e6 | 0.211545 | ||||||||
\(845\) | −838655. | −0.0404056 | ||||||||
\(846\) | −3.79573e6 | −0.182335 | ||||||||
\(847\) | 2.28974e7 | 1.09667 | ||||||||
\(848\) | −2.07485e7 | −0.990825 | ||||||||
\(849\) | −4.78984e6 | −0.228061 | ||||||||
\(850\) | −1.58713e7 | −0.753470 | ||||||||
\(851\) | −6.32176e6 | −0.299236 | ||||||||
\(852\) | 1.71761e6 | 0.0810636 | ||||||||
\(853\) | −7.94099e6 | −0.373682 | −0.186841 | − | 0.982390i | \(-0.559825\pi\) | ||||
−0.186841 | + | 0.982390i | \(0.559825\pi\) | |||||||
\(854\) | 4.22302e7 | 1.98143 | ||||||||
\(855\) | 825170. | 0.0386036 | ||||||||
\(856\) | 1.78740e7 | 0.833752 | ||||||||
\(857\) | 2.65740e7 | 1.23596 | 0.617981 | − | 0.786193i | \(-0.287951\pi\) | ||||
0.617981 | + | 0.786193i | \(0.287951\pi\) | |||||||
\(858\) | −3.34751e6 | −0.155240 | ||||||||
\(859\) | −2.41374e7 | −1.11611 | −0.558057 | − | 0.829803i | \(-0.688453\pi\) | ||||
−0.558057 | + | 0.829803i | \(0.688453\pi\) | |||||||
\(860\) | 1.29188e6 | 0.0595631 | ||||||||
\(861\) | −4.81597e6 | −0.221399 | ||||||||
\(862\) | 1.36718e7 | 0.626696 | ||||||||
\(863\) | 2.16716e7 | 0.990522 | 0.495261 | − | 0.868744i | \(-0.335072\pi\) | ||||
0.495261 | + | 0.868744i | \(0.335072\pi\) | |||||||
\(864\) | −1.26591e6 | −0.0576926 | ||||||||
\(865\) | 1.12858e7 | 0.512853 | ||||||||
\(866\) | 4.37065e6 | 0.198039 | ||||||||
\(867\) | 2.48697e6 | 0.112363 | ||||||||
\(868\) | 5.03902e6 | 0.227011 | ||||||||
\(869\) | 554090. | 0.0248903 | ||||||||
\(870\) | −7.00165e6 | −0.313619 | ||||||||
\(871\) | −1.20359e7 | −0.537569 | ||||||||
\(872\) | −2.22745e7 | −0.992009 | ||||||||
\(873\) | 1.02277e7 | 0.454194 | ||||||||
\(874\) | 950708. | 0.0420987 | ||||||||
\(875\) | 2.21703e7 | 0.978929 | ||||||||
\(876\) | 113982. | 0.00501853 | ||||||||
\(877\) | 760211. | 0.0333761 | 0.0166880 | − | 0.999861i | \(-0.494688\pi\) | ||||
0.0166880 | + | 0.999861i | \(0.494688\pi\) | |||||||
\(878\) | −9.01660e6 | −0.394736 | ||||||||
\(879\) | −1.53022e6 | −0.0668006 | ||||||||
\(880\) | −3.16959e6 | −0.137974 | ||||||||
\(881\) | 2.14521e7 | 0.931171 | 0.465585 | − | 0.885003i | \(-0.345844\pi\) | ||||
0.465585 | + | 0.885003i | \(0.345844\pi\) | |||||||
\(882\) | −3.19655e6 | −0.138360 | ||||||||
\(883\) | 2.44065e7 | 1.05343 | 0.526713 | − | 0.850043i | \(-0.323424\pi\) | ||||
0.526713 | + | 0.850043i | \(0.323424\pi\) | |||||||
\(884\) | 3.01151e6 | 0.129614 | ||||||||
\(885\) | −816706. | −0.0350516 | ||||||||
\(886\) | −3.24166e7 | −1.38734 | ||||||||
\(887\) | −3.14967e7 | −1.34417 | −0.672087 | − | 0.740472i | \(-0.734602\pi\) | ||||
−0.672087 | + | 0.740472i | \(0.734602\pi\) | |||||||
\(888\) | −2.34012e7 | −0.995878 | ||||||||
\(889\) | −4.58482e7 | −1.94567 | ||||||||
\(890\) | −5.56277e6 | −0.235405 | ||||||||
\(891\) | 690455. | 0.0291368 | ||||||||
\(892\) | −758954. | −0.0319377 | ||||||||
\(893\) | 3.01726e6 | 0.126615 | ||||||||
\(894\) | 1.26301e7 | 0.528523 | ||||||||
\(895\) | 8.64024e6 | 0.360552 | ||||||||
\(896\) | 3.29764e7 | 1.37225 | ||||||||
\(897\) | −2.10084e6 | −0.0871790 | ||||||||
\(898\) | 1.77124e7 | 0.732969 | ||||||||
\(899\) | 3.35585e7 | 1.38485 | ||||||||
\(900\) | −957904. | −0.0394199 | ||||||||
\(901\) | −1.92040e7 | −0.788096 | ||||||||
\(902\) | 2.23861e6 | 0.0916143 | ||||||||
\(903\) | 1.40808e7 | 0.574656 | ||||||||
\(904\) | −2.30992e7 | −0.940104 | ||||||||
\(905\) | 3.56697e6 | 0.144770 | ||||||||
\(906\) | 2.43022e7 | 0.983613 | ||||||||
\(907\) | 1.45980e7 | 0.589215 | 0.294608 | − | 0.955618i | \(-0.404811\pi\) | ||||
0.294608 | + | 0.955618i | \(0.404811\pi\) | |||||||
\(908\) | 3.79160e6 | 0.152619 | ||||||||
\(909\) | −5.45962e6 | −0.219156 | ||||||||
\(910\) | −1.40669e7 | −0.563110 | ||||||||
\(911\) | −4.38637e7 | −1.75109 | −0.875546 | − | 0.483135i | \(-0.839498\pi\) | ||||
−0.875546 | + | 0.483135i | \(0.839498\pi\) | |||||||
\(912\) | 4.06350e6 | 0.161776 | ||||||||
\(913\) | 1.03133e7 | 0.409470 | ||||||||
\(914\) | −3.00692e7 | −1.19057 | ||||||||
\(915\) | −1.06926e7 | −0.422214 | ||||||||
\(916\) | −3.21327e6 | −0.126534 | ||||||||
\(917\) | 3.69874e6 | 0.145255 | ||||||||
\(918\) | −4.73137e6 | −0.185302 | ||||||||
\(919\) | 7.90937e6 | 0.308925 | 0.154463 | − | 0.987999i | \(-0.450635\pi\) | ||||
0.154463 | + | 0.987999i | \(0.450635\pi\) | |||||||
\(920\) | −1.72275e6 | −0.0671046 | ||||||||
\(921\) | 1.06344e6 | 0.0413107 | ||||||||
\(922\) | −5.41485e7 | −2.09778 | ||||||||
\(923\) | 2.29815e7 | 0.887919 | ||||||||
\(924\) | 699285. | 0.0269448 | ||||||||
\(925\) | −3.85674e7 | −1.48206 | ||||||||
\(926\) | 2.83275e7 | 1.08563 | ||||||||
\(927\) | −9.89407e6 | −0.378160 | ||||||||
\(928\) | −8.53846e6 | −0.325469 | ||||||||
\(929\) | −2.76806e7 | −1.05229 | −0.526146 | − | 0.850394i | \(-0.676364\pi\) | ||||
−0.526146 | + | 0.850394i | \(0.676364\pi\) | |||||||
\(930\) | −9.71845e6 | −0.368460 | ||||||||
\(931\) | 2.54097e6 | 0.0960782 | ||||||||
\(932\) | −4.76267e6 | −0.179602 | ||||||||
\(933\) | 1.80167e7 | 0.677597 | ||||||||
\(934\) | 9.89610e6 | 0.371190 | ||||||||
\(935\) | −2.93365e6 | −0.109744 | ||||||||
\(936\) | −7.77666e6 | −0.290137 | ||||||||
\(937\) | −5.16566e6 | −0.192211 | −0.0961053 | − | 0.995371i | \(-0.530639\pi\) | ||||
−0.0961053 | + | 0.995371i | \(0.530639\pi\) | |||||||
\(938\) | 1.91514e7 | 0.710713 | ||||||||
\(939\) | −3.06482e7 | −1.13433 | ||||||||
\(940\) | 973367. | 0.0359300 | ||||||||
\(941\) | −2.70233e7 | −0.994865 | −0.497433 | − | 0.867503i | \(-0.665724\pi\) | ||||
−0.497433 | + | 0.867503i | \(0.665724\pi\) | |||||||
\(942\) | 1.94704e7 | 0.714903 | ||||||||
\(943\) | 1.40492e6 | 0.0514483 | ||||||||
\(944\) | −4.02182e6 | −0.146890 | ||||||||
\(945\) | 2.90142e6 | 0.105689 | ||||||||
\(946\) | −6.54520e6 | −0.237791 | ||||||||
\(947\) | −2.07792e7 | −0.752930 | −0.376465 | − | 0.926431i | \(-0.622860\pi\) | ||||
−0.376465 | + | 0.926431i | \(0.622860\pi\) | |||||||
\(948\) | −229161. | −0.00828170 | ||||||||
\(949\) | 1.52507e6 | 0.0549698 | ||||||||
\(950\) | 5.80001e6 | 0.208507 | ||||||||
\(951\) | 3.54769e6 | 0.127202 | ||||||||
\(952\) | 2.69164e7 | 0.962553 | ||||||||
\(953\) | 4.60122e7 | 1.64112 | 0.820560 | − | 0.571560i | \(-0.193661\pi\) | ||||
0.820560 | + | 0.571560i | \(0.193661\pi\) | |||||||
\(954\) | −8.82854e6 | −0.314064 | ||||||||
\(955\) | 2.02751e7 | 0.719375 | ||||||||
\(956\) | −7.31769e6 | −0.258958 | ||||||||
\(957\) | 4.65705e6 | 0.164373 | ||||||||
\(958\) | 1.71577e7 | 0.604012 | ||||||||
\(959\) | 3.64846e7 | 1.28104 | ||||||||
\(960\) | −6.20151e6 | −0.217180 | ||||||||
\(961\) | 1.79508e7 | 0.627010 | ||||||||
\(962\) | 5.57417e7 | 1.94197 | ||||||||
\(963\) | 8.78165e6 | 0.305148 | ||||||||
\(964\) | 1.89842e6 | 0.0657960 | ||||||||
\(965\) | −1.04945e7 | −0.362782 | ||||||||
\(966\) | 3.34283e6 | 0.115258 | ||||||||
\(967\) | 3.55492e7 | 1.22254 | 0.611271 | − | 0.791422i | \(-0.290659\pi\) | ||||
0.611271 | + | 0.791422i | \(0.290659\pi\) | |||||||
\(968\) | −2.47260e7 | −0.848134 | ||||||||
\(969\) | 3.76101e6 | 0.128675 | ||||||||
\(970\) | −1.99778e7 | −0.681739 | ||||||||
\(971\) | 2.58132e7 | 0.878606 | 0.439303 | − | 0.898339i | \(-0.355225\pi\) | ||||
0.439303 | + | 0.898339i | \(0.355225\pi\) | |||||||
\(972\) | −285559. | −0.00969460 | ||||||||
\(973\) | −2.03763e6 | −0.0689990 | ||||||||
\(974\) | −5.49569e7 | −1.85620 | ||||||||
\(975\) | −1.28167e7 | −0.431780 | ||||||||
\(976\) | −5.26553e7 | −1.76937 | ||||||||
\(977\) | 2.97056e7 | 0.995641 | 0.497820 | − | 0.867280i | \(-0.334134\pi\) | ||||
0.497820 | + | 0.867280i | \(0.334134\pi\) | |||||||
\(978\) | 6.02995e6 | 0.201589 | ||||||||
\(979\) | 3.70000e6 | 0.123380 | ||||||||
\(980\) | 819714. | 0.0272645 | ||||||||
\(981\) | −1.09436e7 | −0.363069 | ||||||||
\(982\) | −3.17766e7 | −1.05155 | ||||||||
\(983\) | 3.72568e7 | 1.22976 | 0.614882 | − | 0.788619i | \(-0.289204\pi\) | ||||
0.614882 | + | 0.788619i | \(0.289204\pi\) | |||||||
\(984\) | 5.20057e6 | 0.171223 | ||||||||
\(985\) | −8.74586e6 | −0.287218 | ||||||||
\(986\) | −3.19126e7 | −1.04537 | ||||||||
\(987\) | 1.06091e7 | 0.346647 | ||||||||
\(988\) | −1.10052e6 | −0.0358680 | ||||||||
\(989\) | −4.10765e6 | −0.133537 | ||||||||
\(990\) | −1.34867e6 | −0.0437339 | ||||||||
\(991\) | 5.24786e7 | 1.69745 | 0.848727 | − | 0.528831i | \(-0.177370\pi\) | ||||
0.848727 | + | 0.528831i | \(0.177370\pi\) | |||||||
\(992\) | −1.18516e7 | −0.382382 | ||||||||
\(993\) | 2.04598e7 | 0.658457 | ||||||||
\(994\) | −3.65678e7 | −1.17391 | ||||||||
\(995\) | 1.67595e7 | 0.536666 | ||||||||
\(996\) | −4.26540e6 | −0.136242 | ||||||||
\(997\) | 1.26015e7 | 0.401500 | 0.200750 | − | 0.979643i | \(-0.435662\pi\) | ||||
0.200750 | + | 0.979643i | \(0.435662\pi\) | |||||||
\(998\) | −3.95750e7 | −1.25775 | ||||||||
\(999\) | −1.14972e7 | −0.364485 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.6.a.d.1.5 | ✓ | 13 | |
3.2 | odd | 2 | 531.6.a.e.1.9 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.d.1.5 | ✓ | 13 | 1.1 | even | 1 | trivial | |
531.6.a.e.1.9 | 13 | 3.2 | odd | 2 |