Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,6,Mod(17,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.17");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.62302918878\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} + 2 x^{18} - 382 x^{17} + 117610 x^{16} - 661518 x^{15} + 1160778 x^{14} + \cdots + 48\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{14}\cdot 5^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(14.4102 - 9.21685i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.17 |
Dual form | 60.6.i.a.53.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −15.0272 | − | 4.14525i | −0.963996 | − | 0.265918i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 29.4180 | + | 47.5351i | 0.526245 | + | 0.850333i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −98.6056 | − | 98.6056i | −0.760600 | − | 0.760600i | 0.215831 | − | 0.976431i | \(-0.430754\pi\) |
−0.976431 | + | 0.215831i | \(0.930754\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 208.634 | + | 124.583i | 0.858575 | + | 0.512688i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 208.182i | 0.518754i | 0.965776 | + | 0.259377i | \(0.0835172\pi\) | ||||
−0.965776 | + | 0.259377i | \(0.916483\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 823.732 | − | 823.732i | 1.35185 | − | 1.35185i | 0.468251 | − | 0.883596i | \(-0.344884\pi\) |
0.883596 | − | 0.468251i | \(-0.155116\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −245.025 | − | 836.264i | −0.281179 | − | 0.959655i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1335.24 | − | 1335.24i | 1.12056 | − | 1.12056i | 0.128907 | − | 0.991657i | \(-0.458853\pi\) |
0.991657 | − | 0.128907i | \(-0.0411469\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2162.52i | − | 1.37428i | −0.726523 | − | 0.687142i | \(-0.758865\pi\) | ||
0.726523 | − | 0.687142i | \(-0.241135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1073.02 | + | 1890.51i | 0.530958 | + | 0.935472i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2062.09 | + | 2062.09i | 0.812807 | + | 0.812807i | 0.985054 | − | 0.172247i | \(-0.0551028\pi\) |
−0.172247 | + | 0.985054i | \(0.555103\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1394.16 | + | 2796.77i | −0.446133 | + | 0.894967i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2618.75 | − | 2736.98i | −0.691330 | − | 0.722540i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −43.7465 | −0.00965936 | −0.00482968 | − | 0.999988i | \(-0.501537\pi\) | ||||
−0.00482968 | + | 0.999988i | \(0.501537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1056.81 | 0.197511 | 0.0987556 | − | 0.995112i | \(-0.468514\pi\) | ||||
0.0987556 | + | 0.995112i | \(0.468514\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 862.967 | − | 3128.39i | 0.137946 | − | 0.500076i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1786.44 | − | 7588.00i | 0.246501 | − | 1.04703i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2198.97 | + | 2198.97i | 0.264067 | + | 0.264067i | 0.826704 | − | 0.562637i | \(-0.190213\pi\) |
−0.562637 | + | 0.826704i | \(0.690213\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15793.0 | + | 8963.81i | −1.66265 | + | 0.943693i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7326.11i | 0.680635i | 0.940311 | + | 0.340317i | \(0.110534\pi\) | ||||
−0.940311 | + | 0.340317i | \(0.889466\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5654.14 | + | 5654.14i | −0.466332 | + | 0.466332i | −0.900724 | − | 0.434392i | \(-0.856963\pi\) |
0.434392 | + | 0.900724i | \(0.356963\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 215.515 | + | 13582.4i | 0.0158652 | + | 0.999874i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17023.3 | − | 17023.3i | 1.12409 | − | 1.12409i | 0.132966 | − | 0.991121i | \(-0.457550\pi\) |
0.991121 | − | 0.132966i | \(-0.0424500\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2639.11i | 0.157025i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −25599.8 | + | 14530.0i | −1.37820 | + | 0.782240i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −16153.6 | − | 16153.6i | −0.789915 | − | 0.789915i | 0.191565 | − | 0.981480i | \(-0.438644\pi\) |
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9895.94 | + | 6124.29i | −0.441113 | + | 0.272991i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8964.21 | + | 32496.7i | −0.365447 | + | 1.32480i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13460.4 | 0.503417 | 0.251709 | − | 0.967803i | \(-0.419008\pi\) | ||||
0.251709 | + | 0.967803i | \(0.419008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1895.46 | −0.0652213 | −0.0326107 | − | 0.999468i | \(-0.510382\pi\) | ||||
−0.0326107 | + | 0.999468i | \(0.510382\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8287.85 | − | 32857.0i | −0.263082 | − | 1.04298i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 63388.7 | + | 14923.6i | 1.86092 | + | 0.438117i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8179.25 | + | 8179.25i | 0.222601 | + | 0.222601i | 0.809593 | − | 0.586992i | \(-0.199688\pi\) |
−0.586992 | + | 0.809593i | \(0.699688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22439.5 | − | 39535.3i | −0.567402 | − | 0.999682i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10066.0i | 0.236980i | 0.992955 | + | 0.118490i | \(0.0378054\pi\) | ||||
−0.992955 | + | 0.118490i | \(0.962195\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24469.5 | − | 24469.5i | 0.537426 | − | 0.537426i | −0.385346 | − | 0.922772i | \(-0.625918\pi\) |
0.922772 | + | 0.385346i | \(0.125918\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 32543.7 | − | 36248.5i | 0.668058 | − | 0.744109i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20527.9 | − | 20527.9i | 0.394564 | − | 0.394564i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 85638.4i | − | 1.54383i | −0.635723 | − | 0.771917i | \(-0.719298\pi\) | ||
0.635723 | − | 0.771917i | \(-0.280702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 28007.1 | + | 51984.5i | 0.474302 | + | 0.880362i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9108.14 | − | 9108.14i | −0.145122 | − | 0.145122i | 0.630813 | − | 0.775935i | \(-0.282722\pi\) |
−0.775935 | + | 0.630813i | \(0.782722\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 102751. | + | 24190.6i | 1.54254 | + | 0.363162i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 657.388 | + | 181.340i | 0.00931158 | + | 0.00256860i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −34273.4 | −0.458651 | −0.229325 | − | 0.973350i | \(-0.573652\pi\) | ||||
−0.229325 | + | 0.973350i | \(0.573652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −162449. | −2.05643 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15880.9 | − | 4380.74i | −0.190400 | − | 0.0525218i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 102796. | − | 63617.1i | 1.16860 | − | 0.723210i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −997.190 | − | 997.190i | −0.0107609 | − | 0.0107609i | 0.701706 | − | 0.712467i | \(-0.252422\pi\) |
−0.712467 | + | 0.701706i | \(0.752422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25936.0 | + | 43433.8i | −0.265959 | + | 0.445389i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 152435.i | 1.48690i | 0.668793 | + | 0.743449i | \(0.266811\pi\) | ||||
−0.668793 | + | 0.743449i | \(0.733189\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 42872.6 | − | 42872.6i | 0.398187 | − | 0.398187i | −0.479406 | − | 0.877593i | \(-0.659148\pi\) |
0.877593 | + | 0.479406i | \(0.159148\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −58299.5 | + | 106621.i | −0.516049 | + | 0.943778i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −37956.8 | + | 37956.8i | −0.320502 | + | 0.320502i | −0.848959 | − | 0.528458i | \(-0.822770\pi\) |
0.528458 | + | 0.848959i | \(0.322770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 65604.7i | 0.528894i | 0.964400 | + | 0.264447i | \(0.0851894\pi\) | ||||
−0.964400 | + | 0.264447i | \(0.914811\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23929.0 | − | 42159.6i | −0.184339 | − | 0.324780i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −162953. | − | 162953.i | −1.20051 | − | 1.20051i | −0.974010 | − | 0.226504i | \(-0.927270\pi\) |
−0.226504 | − | 0.974010i | \(-0.572730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −37359.0 | + | 158684.i | −0.263421 | + | 1.11889i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 274481. | − | 69235.1i | 1.85374 | − | 0.467586i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −263324. | −1.70460 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 117711. | 0.730895 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 30368.6 | − | 110091.i | 0.180993 | − | 0.656129i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −173958. | + | 16003.7i | −0.995795 | + | 0.0916103i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −37081.8 | − | 37081.8i | −0.204010 | − | 0.204010i | 0.597706 | − | 0.801716i | \(-0.296079\pi\) |
−0.801716 | + | 0.597706i | \(0.796079\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 108404. | − | 61528.1i | 0.573548 | − | 0.325536i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 281184.i | 1.43157i | 0.698322 | + | 0.715784i | \(0.253930\pi\) | ||||
−0.698322 | + | 0.715784i | \(0.746070\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −213237. | + | 213237.i | −1.04528 | + | 1.04528i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 53063.9 | − | 204999.i | 0.250591 | − | 0.968093i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 103510. | − | 103510.i | 0.471175 | − | 0.471175i | −0.431120 | − | 0.902295i | \(-0.641881\pi\) |
0.902295 | + | 0.431120i | \(0.141881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 75372.5i | 0.330884i | 0.986220 | + | 0.165442i | \(0.0529051\pi\) | ||||
−0.986220 | + | 0.165442i | \(0.947095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −326379. | + | 185247.i | −1.38253 | + | 0.784699i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 171486. | + | 171486.i | 0.701275 | + | 0.701275i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1286.93 | − | 2079.49i | −0.00508319 | − | 0.00821367i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10939.8 | − | 39658.5i | 0.0417557 | − | 0.151371i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −222865. | −0.822388 | −0.411194 | − | 0.911548i | \(-0.634888\pi\) | ||||
−0.411194 | + | 0.911548i | \(0.634888\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 261656. | 0.933873 | 0.466937 | − | 0.884291i | \(-0.345358\pi\) | ||||
0.466937 | + | 0.884291i | \(0.345358\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 444924. | − | 112228.i | 1.53659 | − | 0.387589i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31089.2 | + | 50235.4i | 0.103939 | + | 0.167950i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −231534. | − | 231534.i | −0.749662 | − | 0.749662i | 0.224754 | − | 0.974416i | \(-0.427842\pi\) |
−0.974416 | + | 0.224754i | \(0.927842\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 175783. | + | 309705.i | 0.551422 | + | 0.971527i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 406666.i | − | 1.23644i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 130361. | − | 130361.i | 0.384308 | − | 0.384308i | −0.488344 | − | 0.872651i | \(-0.662399\pi\) |
0.872651 | + | 0.488344i | \(0.162399\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 174095. | − | 51009.8i | 0.497825 | − | 0.145862i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −302566. | + | 302566.i | −0.839517 | + | 0.839517i | −0.988795 | − | 0.149278i | \(-0.952305\pi\) |
0.149278 | + | 0.988795i | \(0.452305\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 985774.i | − | 2.65498i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 269414. | − | 451175.i | 0.704579 | − | 1.17993i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −27432.5 | − | 27432.5i | −0.0696868 | − | 0.0696868i | 0.671404 | − | 0.741091i | \(-0.265691\pi\) |
−0.741091 | + | 0.671404i | \(0.765691\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 413250. | − | 138305.i | 1.02004 | − | 0.341383i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −202272. | − | 55796.8i | −0.485292 | − | 0.133868i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 699192. | 1.63104 | 0.815518 | − | 0.578731i | \(-0.196452\pi\) | ||||
0.815518 | + | 0.578731i | \(0.196452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 53437.5 | 0.121241 | 0.0606206 | − | 0.998161i | \(-0.480692\pi\) | ||||
0.0606206 | + | 0.998161i | \(0.480692\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28483.4 | + | 7857.15i | 0.0628731 | + | 0.0173435i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −39838.8 | + | 169217.i | −0.0855810 | + | 0.363509i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 277972. | + | 277972.i | 0.581297 | + | 0.581297i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11657.5 | + | 528105.i | −0.0237383 | + | 1.07539i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 199891.i | 0.396470i | 0.980155 | + | 0.198235i | \(0.0635209\pi\) | ||||
−0.980155 | + | 0.198235i | \(0.936479\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −649229. | + | 649229.i | −1.25460 | + | 1.25460i | −0.300962 | + | 0.953636i | \(0.597308\pi\) |
−0.953636 | + | 0.300962i | \(0.902692\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −890692. | − | 487022.i | −1.67742 | − | 0.917196i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 43021.0 | − | 43021.0i | 0.0789796 | − | 0.0789796i | −0.666513 | − | 0.745493i | \(-0.732214\pi\) |
0.745493 | + | 0.666513i | \(0.232214\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 155958.i | 0.279174i | 0.990210 | + | 0.139587i | \(0.0445775\pi\) | ||||
−0.990210 | + | 0.139587i | \(0.955422\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −89006.2 | − | 156816.i | −0.155392 | − | 0.273780i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4313.65 | + | 4313.65i | 0.00734691 | + | 0.00734691i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −348247. | + | 215519.i | −0.578766 | + | 0.358180i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 173320. | + | 687122.i | 0.281139 | + | 1.11457i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 450198. | 0.712915 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23276.7 | 0.0359928 | 0.0179964 | − | 0.999838i | \(-0.494271\pi\) | ||||
0.0179964 | + | 0.999838i | \(0.494271\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 41726.2 | − | 151264.i | 0.0630173 | − | 0.228448i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −435103. | − | 102437.i | −0.641943 | − | 0.151133i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −104207. | − | 104207.i | −0.150227 | − | 0.150227i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −469141. | + | 266276.i | −0.660988 | + | 0.375165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.19976e6i | − | 3.02966i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −710151. | + | 710151.i | −0.956288 | + | 0.956288i | −0.999084 | − | 0.0427958i | \(-0.986374\pi\) |
0.0427958 | + | 0.999084i | \(0.486374\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −639300. | + | 409811.i | −0.841877 | + | 0.539669i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −390981. | + | 390981.i | −0.503606 | + | 0.503606i | −0.912557 | − | 0.408951i | \(-0.865895\pi\) |
0.408951 | + | 0.912557i | \(0.365895\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.01954e6i | 1.28474i | 0.766393 | + | 0.642372i | \(0.222049\pi\) | ||||
−0.766393 | + | 0.642372i | \(0.777951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −393570. | + | 223383.i | −0.485280 | + | 0.275436i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 462104. | + | 462104.i | 0.557635 | + | 0.557635i | 0.928633 | − | 0.370998i | \(-0.120984\pi\) |
−0.370998 | + | 0.928633i | \(0.620984\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.31000e6 | + | 308413.i | 1.54739 | + | 0.364303i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −354993. | + | 1.28691e6i | −0.410534 | + | 1.48825i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.00447e6 | 1.13747 | 0.568737 | − | 0.822519i | \(-0.307432\pi\) | ||||
0.568737 | + | 0.822519i | \(0.307432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.33193e6 | 1.47720 | 0.738600 | − | 0.674144i | \(-0.235487\pi\) | ||||
0.738600 | + | 0.674144i | \(0.235487\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −205379. | − | 897278.i | −0.223121 | − | 0.974791i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −125450. | + | 77637.4i | −0.133523 | + | 0.0826334i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.78134e6 | − | 1.78134e6i | −1.85782 | − | 1.85782i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 99114.4 | + | 174626.i | 0.101307 | + | 0.178488i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 196187.i | − | 0.196556i | −0.995159 | − | 0.0982781i | \(-0.968667\pi\) | ||
0.995159 | − | 0.0982781i | \(-0.0313335\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −429289. | + | 429289.i | −0.421646 | + | 0.421646i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.44378e6 | − | 789445.i | −1.39043 | − | 0.760276i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 946428. | − | 946428.i | 0.893830 | − | 0.893830i | −0.101051 | − | 0.994881i | \(-0.532221\pi\) |
0.994881 | + | 0.101051i | \(0.0322206\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 433660.i | − | 0.401699i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9127.00 | − | 5450.08i | −0.00829329 | − | 0.00495224i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.45489e6 | + | 1.45489e6i | 1.29700 | + | 1.29700i | 0.930364 | + | 0.366637i | \(0.119491\pi\) |
0.366637 | + | 0.930364i | \(0.380509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 292656. | − | 1.24307e6i | 0.256002 | − | 1.08738i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 515033. | + | 142072.i | 0.442137 | + | 0.121964i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.58867e6 | −1.33861 | −0.669303 | − | 0.742989i | \(-0.733407\pi\) | ||||
−0.669303 | + | 0.742989i | \(0.733407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 555550. | 0.459516 | 0.229758 | − | 0.973248i | \(-0.426207\pi\) | ||||
0.229758 | + | 0.973248i | \(0.426207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.44115e6 | + | 673392.i | 1.98239 | + | 0.546842i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −582237. | − | 290240.i | −0.464267 | − | 0.231433i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 124826. | + | 124826.i | 0.0977478 | + | 0.0977478i | 0.754290 | − | 0.656542i | \(-0.227981\pi\) |
−0.656542 | + | 0.754290i | \(0.727981\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 220486. | + | 131660.i | 0.169578 | + | 0.101262i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.16333e6i | 0.878897i | 0.898268 | + | 0.439448i | \(0.144826\pi\) | ||||
−0.898268 | + | 0.439448i | \(0.855174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −646581. | + | 646581.i | −0.479907 | + | 0.479907i | −0.905102 | − | 0.425195i | \(-0.860205\pi\) |
0.425195 | + | 0.905102i | \(0.360205\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.80844e6 | + | 529872.i | −1.31884 | + | 0.386420i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 722396. | − | 722396.i | 0.517691 | − | 0.517691i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 2.14587e6i | − | 1.51133i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10851.4 | + | 19118.6i | 0.00751194 | + | 0.0132350i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −327629. | − | 327629.i | −0.222953 | − | 0.222953i | 0.586788 | − | 0.809741i | \(-0.300392\pi\) |
−0.809741 | + | 0.586788i | \(0.800392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 395978. | + | 639841.i | 0.264921 | + | 0.428072i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 569789. | − | 545177.i | 0.374820 | − | 0.358630i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.39721e6 | 2.19758 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.11506e6 | 0.709385 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 631881. | − | 2.29067e6i | 0.395393 | − | 1.43336i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −55760.5 | − | 90100.7i | −0.0343224 | − | 0.0554598i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −915551. | − | 915551.i | −0.554417 | − | 0.554417i | 0.373296 | − | 0.927712i | \(-0.378228\pi\) |
−0.927712 | + | 0.373296i | \(0.878228\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −821973. | + | 466537.i | −0.489735 | + | 0.277965i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 893599.i | 0.523892i | 0.965083 | + | 0.261946i | \(0.0843642\pi\) | ||||
−0.965083 | + | 0.261946i | \(0.915636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 807590. | − | 807590.i | 0.465940 | − | 0.465940i | −0.434656 | − | 0.900596i | \(-0.643130\pi\) |
0.900596 | + | 0.434656i | \(0.143130\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.31805e6 | − | 1.36055e6i | 0.748437 | − | 0.772571i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −825216. | + | 825216.i | −0.461232 | + | 0.461232i | −0.899059 | − | 0.437827i | \(-0.855748\pi\) |
0.437827 | + | 0.899059i | \(0.355748\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9107.23i | − | 0.00501083i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 727725. | − | 413044.i | 0.394189 | − | 0.223735i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.88748e6 | − | 2.88748e6i | −1.53997 | − | 1.53997i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.15537e6 | + | 3.45221e6i | 0.606755 | + | 1.81296i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 271948. | − | 985855.i | 0.140643 | − | 0.509852i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.35719e6 | −1.70996 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.16978e6 | −1.08854 | −0.544271 | − | 0.838910i | \(-0.683194\pi\) | ||||
−0.544271 | + | 0.838910i | \(0.683194\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 184824. | + | 732732.i | 0.0913374 | + | 0.362105i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −148184. | + | 629418.i | −0.0721422 | + | 0.306427i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.48010e6 | + | 1.48010e6i | 0.709931 | + | 0.709931i | 0.966521 | − | 0.256589i | \(-0.0825987\pi\) |
−0.256589 | + | 0.966521i | \(0.582599\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.77325e6 | + | 3.12422e6i | 0.838052 | + | 1.47653i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 220008.i | 0.102460i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.39703e6 | + | 1.39703e6i | −0.641167 | + | 0.641167i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.21919e6 | − | 2.22971e6i | 0.551470 | − | 1.00856i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.14143e6 | + | 2.14143e6i | −0.954729 | + | 0.954729i | −0.999019 | − | 0.0442899i | \(-0.985897\pi\) |
0.0442899 | + | 0.999019i | \(0.485897\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.13070e6i | − | 0.496917i | −0.968643 | − | 0.248458i | \(-0.920076\pi\) | ||
0.968643 | − | 0.248458i | \(-0.0799239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.41168e6 | − | 97384.3i | −1.91133 | − | 0.0421911i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.65417e6 | + | 1.65417e6i | 0.706550 | + | 0.706550i | 0.965808 | − | 0.259258i | \(-0.0834781\pi\) |
−0.259258 | + | 0.965808i | \(0.583478\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −478489. | + | 296122.i | −0.201512 | + | 0.124710i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.95702e6 | + | 1.09154e6i | 1.64323 | + | 0.453285i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.51467e6 | −1.43929 | −0.719644 | − | 0.694343i | \(-0.755695\pi\) | ||||
−0.719644 | + | 0.694343i | \(0.755695\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.20040e6 | −0.888658 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.76887e6 | − | 487943.i | −0.704579 | − | 0.194358i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.88301e6 | + | 443317.i | 0.739809 | + | 0.174173i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −162338. | − | 162338.i | −0.0629152 | − | 0.0629152i | 0.674949 | − | 0.737864i | \(-0.264166\pi\) |
−0.737864 | + | 0.674949i | \(0.764166\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −912710. | + | 1.52847e6i | −0.348953 | + | 0.584376i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.18567e6i | 1.20162i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.75008e6 | + | 2.75008e6i | −1.02347 | + | 1.02347i | −0.0237481 | + | 0.999718i | \(0.507560\pi\) |
−0.999718 | + | 0.0237481i | \(0.992440\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.68044e6 | + | 480611.i | 0.984303 | + | 0.176488i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36035.4 | + | 36035.4i | −0.0130580 | + | 0.0130580i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.85204e6i | − | 1.01990i | −0.860204 | − | 0.509950i | \(-0.829664\pi\) | ||
0.860204 | − | 0.509950i | \(-0.170336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 403522. | + | 710949.i | 0.142415 | + | 0.250915i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.58384e6 | − | 3.58384e6i | −1.24839 | − | 1.24839i | −0.956429 | − | 0.291964i | \(-0.905691\pi\) |
−0.291964 | − | 0.956429i | \(-0.594309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.57968e6 | + | 371905.i | 0.543148 | + | 0.127874i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.88406e6 | + | 475234.i | −0.639464 | + | 0.161298i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.35177e6 | −1.12305 | −0.561526 | − | 0.827459i | \(-0.689786\pi\) | ||||
−0.561526 | + | 0.827459i | \(0.689786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.50675e6 | 1.82160 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.16558e6 | − | 4.22540e6i | 0.380680 | − | 1.38002i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.07083e6 | − | 2.51931e6i | 1.31277 | − | 0.812435i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 979362. | + | 979362.i | 0.311865 | + | 0.311865i | 0.845632 | − | 0.533767i | \(-0.179224\pi\) |
−0.533767 | + | 0.845632i | \(0.679224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.08827e6 | − | 2.32043e6i | 1.28561 | − | 0.729687i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.32513e6i | − | 0.722082i | −0.932550 | − | 0.361041i | \(-0.882421\pi\) | ||
0.932550 | − | 0.361041i | \(-0.117579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 870526. | − | 870526.i | 0.267005 | − | 0.267005i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.64717e6 | + | 2.86060e6i | −0.499002 | + | 0.866601i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −457785. | + | 457785.i | −0.136986 | + | 0.136986i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.54373e6i | − | 1.04750i | −0.851873 | − | 0.523748i | \(-0.824533\pi\) | ||
0.851873 | − | 0.523748i | \(-0.175467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.98455e6 | + | 1.12639e6i | −0.579504 | + | 0.328917i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.32727e6 | − | 1.32727e6i | −0.382899 | − | 0.382899i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 165013. | − | 700899.i | 0.0470325 | − | 0.199772i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 312438. | − | 1.13264e6i | 0.0879881 | − | 0.318971i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.37590e6 | 0.382869 | 0.191435 | − | 0.981505i | \(-0.438686\pi\) | ||||
0.191435 | + | 0.981505i | \(0.438686\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.61684e6 | −1.26952 | −0.634760 | − | 0.772709i | \(-0.718901\pi\) | ||||
−0.634760 | + | 0.772709i | \(0.718901\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.67246e6 | − | 1.43082e6i | 1.54142 | − | 0.388807i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.87281e6 | + | 5.59590e6i | 0.502947 | + | 1.50279i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 186903. | + | 186903.i | 0.0496073 | + | 0.0496073i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.86610e6 | − | 3.28781e6i | −0.489544 | − | 0.862508i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.92127e6i | 1.53540i | 0.640809 | + | 0.767700i | \(0.278599\pi\) | ||||
−0.640809 | + | 0.767700i | \(0.721401\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.94617e6 | − | 1.94617e6i | 0.498839 | − | 0.498839i | −0.412238 | − | 0.911076i | \(-0.635253\pi\) |
0.911076 | + | 0.412238i | \(0.135253\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10719.0 | + | 36583.6i | 0.00271601 | + | 0.00926966i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.45931e6 | − | 4.45931e6i | 1.11703 | − | 1.11703i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.65182e6i | 1.39967i | 0.714302 | + | 0.699837i | \(0.246744\pi\) | ||||
−0.714302 | + | 0.699837i | \(0.753256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −328789. | + | 550608.i | −0.0805046 | + | 0.134817i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.62907e6 | + | 3.62907e6i | 0.878589 | + | 0.878589i | 0.993389 | − | 0.114800i | \(-0.0366227\pi\) |
−0.114800 | + | 0.993389i | \(0.536623\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00825e6 | − | 1.62919e6i | −0.241363 | − | 0.390006i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.34904e6 | + | 923833.i | 0.792778 | + | 0.218688i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.78413e6 | 1.11992 | 0.559960 | − | 0.828520i | \(-0.310817\pi\) | ||||
0.559960 | + | 0.828520i | \(0.310817\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.52516e6 | −0.353082 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.93196e6 | − | 1.08463e6i | −0.900250 | − | 0.248334i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.77892e6 | − | 7.72202e6i | −1.08218 | − | 1.74865i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.31444e6 | − | 4.31444e6i | −0.966350 | − | 0.966350i | 0.0331021 | − | 0.999452i | \(-0.489461\pi\) |
−0.999452 | + | 0.0331021i | \(0.989461\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.15118e6 | − | 157856.i | −1.58433 | − | 0.0349728i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.42320e6i | 1.18851i | 0.804277 | + | 0.594255i | \(0.202553\pi\) | ||||
−0.804277 | + | 0.594255i | \(0.797447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.73081e6 | − | 3.73081e6i | 0.808818 | − | 0.808818i | −0.175637 | − | 0.984455i | \(-0.556198\pi\) |
0.984455 | + | 0.175637i | \(0.0561985\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −258945. | − | 883771.i | −0.0555360 | − | 0.189543i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.99079e6 | − | 1.99079e6i | 0.422408 | − | 0.422408i | −0.463624 | − | 0.886032i | \(-0.653451\pi\) |
0.886032 | + | 0.463624i | \(0.153451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.61304e6i | − | 0.338620i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.51954e6 | + | 4.43907e6i | 0.523322 | + | 0.922020i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.17709e6 | − | 1.17709e6i | −0.241912 | − | 0.241912i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.04808e6 | + | 3.01491e6i | 1.22994 | + | 0.613113i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.35772e6 | − | 5.38266e6i | −0.273221 | − | 1.08318i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.98299e6 | 0.394896 | 0.197448 | − | 0.980313i | \(-0.436735\pi\) | ||||
0.197448 | + | 0.980313i | \(0.436735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.62271e6 | 0.713956 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.68574e6 | + | 6.11106e6i | −0.328792 | + | 1.19192i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18066.2 | − | 76736.8i | 0.00348748 | − | 0.0148132i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.03480e6 | − | 1.03480e6i | −0.197712 | − | 0.197712i | 0.601307 | − | 0.799018i | \(-0.294647\pi\) |
−0.799018 | + | 0.601307i | \(0.794647\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.49934e6 | + | 1.41858e6i | −0.472665 | + | 0.268277i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.04226e6i | − | 1.31828i | −0.752019 | − | 0.659141i | \(-0.770920\pi\) | ||
0.752019 | − | 0.659141i | \(-0.229080\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −58412.0 | + | 58412.0i | −0.0108239 | + | 0.0108239i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.82761e6 | + | 44866.4i | −0.518688 | + | 0.00823016i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 992566. | − | 992566.i | 0.180247 | − | 0.180247i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.72365e6i | 0.669448i | 0.942316 | + | 0.334724i | \(0.108643\pi\) | ||||
−0.942316 | + | 0.334724i | \(0.891357\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.80094e6 | − | 3.29251e6i | 1.03253 | − | 0.586048i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 193077. | + | 193077.i | 0.0340260 | + | 0.0340260i | 0.723915 | − | 0.689889i | \(-0.242341\pi\) |
−0.689889 | + | 0.723915i | \(0.742341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.24600e6 | + | 4.48433e6i | −1.26436 | + | 0.782472i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.08629e6 | + | 1.48134e7i | −0.706007 | + | 2.55939i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.85889e6 | −0.489106 | −0.244553 | − | 0.969636i | \(-0.578641\pi\) | ||||
−0.244553 | + | 0.969636i | \(0.578641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.82567e6 | −0.817533 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.91877e6 | + | 5.66311e6i | −0.992975 | + | 0.950084i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.29918e6 | + | 776726.i | 0.548135 | + | 0.129048i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.54395e6 | + | 3.54395e6i | 0.583124 | + | 0.583124i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 298519. | + | 525949.i | 0.0486468 | + | 0.0857088i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.00713e7i | − | 1.62551i | −0.582604 | − | 0.812756i | \(-0.697966\pi\) | ||
0.582604 | − | 0.812756i | \(-0.302034\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.23772e6 | − | 1.23772e6i | 0.197865 | − | 0.197865i | −0.601219 | − | 0.799084i | \(-0.705318\pi\) |
0.799084 | + | 0.601219i | \(0.205318\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.78329e6 | + | 365310.i | −1.07409 | + | 0.0578447i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.41109e6 | − | 1.41109e6i | 0.221324 | − | 0.221324i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.06805e6i | 0.321309i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.80829e6 | + | 1.67694e6i | 0.432221 | + | 0.258096i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.03475e6 | + | 6.03475e6i | 0.920113 | + | 0.920113i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.92089e6 | − | 687666.i | −0.441195 | − | 0.103871i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.05069e7 | − | 2.89833e6i | −1.57231 | − | 0.433722i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −549415. | −0.0814571 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −900681. | −0.132305 | −0.0661527 | − | 0.997810i | \(-0.521072\pi\) | ||||
−0.0661527 | + | 0.997810i | \(0.521072\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −803017. | − | 221512.i | −0.116876 | − | 0.0322402i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.11852e6 | + | 1.92996e6i | −0.449736 | + | 0.278328i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.60062e6 | + | 1.60062e6i | 0.228729 | + | 0.228729i | 0.812162 | − | 0.583433i | \(-0.198291\pi\) |
−0.583433 | + | 0.812162i | \(0.698291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −395456. | − | 236142.i | −0.0559974 | − | 0.0334382i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 94602.8i | 0.0132747i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.44442e6 | + | 8.44442e6i | −1.17424 | + | 1.17424i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.30011e6 | − | 2.37772e6i | 0.179163 | − | 0.327663i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.32883e6 | + | 1.32883e6i | −0.181481 | + | 0.181481i | −0.792001 | − | 0.610520i | \(-0.790960\pi\) |
0.610520 | + | 0.792001i | \(0.290960\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.31499e6i | 1.26082i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.02488e6 | − | 5.32942e6i | −0.405790 | − | 0.714945i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.12575e6 | − | 2.12575e6i | −0.282645 | − | 0.282645i | 0.551518 | − | 0.834163i | \(-0.314049\pi\) |
−0.834163 | + | 0.551518i | \(0.814049\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.95224e6 | − | 1.25398e7i | 0.389073 | − | 1.65260i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.36431e6 | − | 7.88761e6i | 0.308849 | − | 1.03036i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.15075e7 | 1.49005 | 0.745025 | − | 0.667037i | \(-0.232438\pi\) | ||||
0.745025 | + | 0.667037i | \(0.232438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −281869. | −0.0361790 | −0.0180895 | − | 0.999836i | \(-0.505758\pi\) | ||||
−0.0180895 | + | 0.999836i | \(0.505758\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 828600. | − | 3.00381e6i | 0.105429 | − | 0.382195i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.64207e6 | + | 2.89230e6i | −1.09005 | + | 0.364815i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.50758e6 | + | 8.50758e6i | 1.06382 | + | 1.06382i | 0.997820 | + | 0.0659963i | \(0.0210226\pi\) |
0.0659963 | + | 0.997820i | \(0.478977\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.24473e7 | − | 7.06488e6i | 1.54305 | − | 0.875807i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.79623e6i | 0.220760i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.36289e6 | − | 3.36289e6i | 0.409771 | − | 0.409771i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.13658e7 | + | 1.10107e7i | 1.37312 | + | 1.33023i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.65918e6 | + | 7.65918e6i | −0.917460 | + | 0.917460i | −0.996844 | − | 0.0793840i | \(-0.974705\pi\) |
0.0793840 | + | 0.996844i | \(0.474705\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.28537e6i | − | 0.271437i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −824818. | + | 468152.i | −0.0971380 | + | 0.0551338i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.60064e6 | + | 1.60064e6i | 0.186921 | + | 0.186921i | 0.794363 | − | 0.607443i | \(-0.207805\pi\) |
−0.607443 | + | 0.794363i | \(0.707805\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.74646e6 | − | 1.25171e7i | −0.897038 | − | 1.44948i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 646486. | − | 2.34362e6i | 0.0742375 | − | 0.269123i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.83755e6 | 0.323129 | 0.161565 | − | 0.986862i | \(-0.448346\pi\) | ||||
0.161565 | + | 0.986862i | \(0.448346\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.15589e7 | 1.30536 | 0.652680 | − | 0.757634i | \(-0.273645\pi\) | ||||
0.652680 | + | 0.757634i | \(0.273645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 687470. | + | 2.72546e6i | 0.0769947 | + | 0.305244i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.46283e6 | + | 5.59541e6i | 0.384630 | + | 0.621504i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.80631e6 | − | 7.80631e6i | −0.859952 | − | 0.859952i | 0.131380 | − | 0.991332i | \(-0.458059\pi\) |
−0.991332 | + | 0.131380i | \(0.958059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −46940.9 | − | 82703.2i | −0.00512871 | − | 0.00903606i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2.80453e7i | − | 3.03918i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.92317e6 | − | 8.92317e6i | 0.959109 | − | 0.959109i | −0.0400875 | − | 0.999196i | \(-0.512764\pi\) |
0.999196 | + | 0.0400875i | \(0.0127637\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.12657e6 | − | 1.79508e6i | 0.653175 | − | 0.191380i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.99766e6 | + | 3.99766e6i | −0.422759 | + | 0.422759i | −0.886152 | − | 0.463394i | \(-0.846632\pi\) |
0.463394 | + | 0.886152i | \(0.346632\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.32337e6i | − | 0.348620i | −0.984691 | − | 0.174310i | \(-0.944231\pi\) | ||
0.984691 | − | 0.174310i | \(-0.0557694\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 243787. | − | 1.10440e7i | 0.0253677 | − | 1.14920i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.37955e6 | + | 3.37955e6i | 0.348850 | + | 0.348850i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.87823e6 | − | 7.79832e6i | −0.601931 | − | 0.798548i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.76522e6 | − | 1.86618e6i | −0.687247 | − | 0.189577i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.87229e6 | 0.591808 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.99889e6 | 0.999720 | 0.499860 | − | 0.866106i | \(-0.333385\pi\) | ||||
0.499860 | + | 0.866106i | \(0.333385\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −349784. | − | 96487.9i | −0.0346969 | − | 0.00957114i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 671814. | − | 2.85356e6i | 0.0661172 | − | 0.280836i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.17392e6 | + | 2.17392e6i | 0.212273 | + | 0.212273i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.25406e6 | + | 2.10011e6i | −0.121497 | + | 0.203465i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.75514e7i | 1.68720i | 0.536975 | + | 0.843598i | \(0.319567\pi\) | ||||
−0.536975 | + | 0.843598i | \(0.680433\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.09211e6 | − | 3.09211e6i | 0.294936 | − | 0.294936i | −0.544090 | − | 0.839027i | \(-0.683125\pi\) |
0.839027 | + | 0.544090i | \(0.183125\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.11376e6 | + | 3.34295e6i | 0.578641 | + | 0.316396i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.72315e6 | + | 9.72315e6i | −0.913159 | + | 0.913159i | −0.996519 | − | 0.0833606i | \(-0.973435\pi\) |
0.0833606 | + | 0.996519i | \(0.473435\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.80221e6i | 0.261149i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.13398e6 | + | 1.99791e6i | 0.104870 | + | 0.184766i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 985787. | + | 985787.i | 0.0904691 | + | 0.0904691i | 0.750893 | − | 0.660424i | \(-0.229623\pi\) |
−0.660424 | + | 0.750893i | \(0.729623\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.33661e7 | + | 8.27185e6i | −1.21731 | + | 0.753355i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.15367e6 | − | 2.05668e6i | 0.736953 | − | 0.185889i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 804495. | 0.0721622 | 0.0360811 | − | 0.999349i | \(-0.488513\pi\) | ||||
0.0360811 | + | 0.999349i | \(0.488513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.24195e7 | −1.10561 | −0.552803 | − | 0.833312i | \(-0.686442\pi\) | ||||
−0.552803 | + | 0.833312i | \(0.686442\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.11855e6 | + | 3.30562e7i | −0.805642 | + | 2.92058i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.64092e7 | − | 3.86323e6i | −1.43891 | − | 0.338763i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −90209.0 | − | 90209.0i | −0.00785119 | − | 0.00785119i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.36153e7 | − | 7.72783e6i | 1.17615 | − | 0.667563i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 394600.i | − | 0.0338338i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.41526e6 | + | 5.41526e6i | −0.460873 | + | 0.460873i | −0.898942 | − | 0.438068i | \(-0.855663\pi\) |
0.438068 | + | 0.898942i | \(0.355663\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.13057e7 | − | 3.50826e6i | 0.955074 | − | 0.296369i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.26339e6 | + | 3.26339e6i | −0.273651 | + | 0.273651i | −0.830568 | − | 0.556917i | \(-0.811984\pi\) |
0.556917 | + | 0.830568i | \(0.311984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 196657.i | 0.0163695i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.49606e6 | − | 4.25463e6i | 0.619392 | − | 0.351556i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.56392e6 | − | 1.56392e6i | −0.128281 | − | 0.128281i | 0.640051 | − | 0.768332i | \(-0.278913\pi\) |
−0.768332 | + | 0.640051i | \(0.778913\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.96543e6 | + | 1.87530e6i | 0.648609 | + | 0.152702i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.22626e6 | − | 1.53209e7i | 0.341637 | − | 1.23849i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.66125e7 | −2.13569 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.53262e6 | −0.281450 | −0.140725 | − | 0.990049i | \(-0.544943\pi\) | ||||
−0.140725 | + | 0.990049i | \(0.544943\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.84024e6 | − | 1.72538e6i | 0.541051 | − | 0.136475i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.58284e6 | + | 2.21731e6i | −0.281362 | + | 0.174126i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.78211e6 | + | 9.78211e6i | 0.762695 | + | 0.762695i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.02859e6 | − | 8.85967e6i | −0.389272 | − | 0.685843i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.42784e6i | 0.494049i | 0.969009 | + | 0.247024i | \(0.0794528\pi\) | ||||
−0.969009 | + | 0.247024i | \(0.920547\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.75531e6 | − | 4.75531e6i | 0.362903 | − | 0.362903i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.84071e7 | − | 1.00649e7i | −1.39480 | − | 0.762666i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.50309e7 | − | 1.50309e7i | 1.13093 | − | 1.13093i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.88206e7i | 1.40610i | 0.711138 | + | 0.703052i | \(0.248180\pi\) | ||||
−0.711138 | + | 0.703052i | \(0.751820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.06691e7 | − | 1.78671e7i | 0.791505 | − | 1.32550i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.17923e6 | + | 2.17923e6i | 0.160538 | + | 0.160538i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.10683e6 | + | 1.31964e7i | −0.227275 | + | 0.965360i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.50944e7 | − | 4.16378e6i | −1.09652 | − | 0.302475i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.88543e7 | −1.36015 | −0.680077 | − | 0.733141i | \(-0.738054\pi\) | ||||
−0.680077 | + | 0.733141i | \(0.738054\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.45495e6 | −0.605721 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.00152e7 | − | 5.52120e6i | −1.42402 | − | 0.392815i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 60989.8 | − | 122349.i | 0.00430936 | − | 0.00864481i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.11465e7 | + | 1.11465e7i | 0.782170 | + | 0.782170i | 0.980197 | − | 0.198027i | \(-0.0634533\pi\) |
−0.198027 | + | 0.980197i | \(0.563453\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −633172. | + | 1.43349e7i | −0.0441269 | + | 0.999026i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.50993e7i | 1.04511i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.56320e7 | − | 1.56320e7i | 1.07462 | − | 1.07462i | 0.0776406 | − | 0.996981i | \(-0.475261\pi\) |
0.996981 | − | 0.0776406i | \(-0.0247387\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.20700e6 | − | 646649.i | 0.150690 | − | 0.0441520i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.70277e6 | + | 1.70277e6i | −0.115475 | + | 0.115475i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.95334e7i | 1.31573i | 0.753136 | + | 0.657865i | \(0.228540\pi\) | ||||
−0.753136 | + | 0.657865i | \(0.771460\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.93844e7 | + | 3.41526e7i | 1.29690 | + | 2.28496i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.17441e7 | − | 1.17441e7i | −0.780453 | − | 0.780453i | 0.199454 | − | 0.979907i | \(-0.436083\pi\) |
−0.979907 | + | 0.199454i | \(0.936083\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.55624e6 | − | 1.05939e7i | −0.432777 | − | 0.699303i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −765545. | − | 3.03499e6i | −0.0501960 | − | 0.199001i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.48550e6 | 0.487547 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.69135e7 | −1.74128 | −0.870642 | − | 0.491917i | \(-0.836296\pi\) | ||||
−0.870642 | + | 0.491917i | \(0.836296\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −813246. | + | 2.94815e6i | −0.0522679 | + | 0.189479i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.69739e6 | + | 1.24378e7i | 0.491446 | + | 0.794104i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.60633e7 | − | 1.60633e7i | −1.01882 | − | 1.01882i | −0.999820 | − | 0.0189969i | \(-0.993953\pi\) |
−0.0189969 | − | 0.999820i | \(-0.506047\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.23052e6 | − | 4.67150e6i | 0.518589 | − | 0.294342i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.77544e7i | − | 1.11133i | −0.831405 | − | 0.555666i | \(-0.812463\pi\) | ||
0.831405 | − | 0.555666i | \(-0.187537\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.46899e6 | − | 6.46899e6i | 0.402277 | − | 0.402277i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.84235e7 | + | 1.78480e7i | 1.13820 | + | 1.10264i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.10878e7 | − | 1.10878e7i | 0.680543 | − | 0.680543i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.66161e7i | 1.01324i | 0.862168 | + | 0.506622i | \(0.169106\pi\) | ||||
−0.862168 | + | 0.506622i | \(0.830894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.81454e7 | + | 1.02990e7i | −1.09933 | + | 0.623962i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.59367e6 | − | 4.59367e6i | −0.276510 | − | 0.276510i | 0.555204 | − | 0.831714i | \(-0.312640\pi\) |
−0.831714 | + | 0.555204i | \(0.812640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.47336e6 | + | 2.95565e6i | −0.0881162 | + | 0.176766i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.79763e6 | + | 6.51670e6i | −0.106819 | + | 0.387236i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.58429e7 | 0.935386 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.09556e6 | −0.122934 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 114561. | + | 119733.i | 0.00667780 | + | 0.00697927i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.19472e6 | − | 1.78172e7i | 0.242957 | − | 1.03197i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −272451. | − | 272451.i | −0.0156802 | − | 0.0156802i | 0.699223 | − | 0.714903i | \(-0.253529\pi\) |
−0.714903 | + | 0.699223i | \(0.753529\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.58320e7 | − | 2.78938e7i | −0.905407 | − | 1.59520i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.21362e7i | 1.82622i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.56135e6 | + | 1.56135e6i | −0.0881692 | + | 0.0881692i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.55065e6 | + | 1.74667e7i | −0.535939 | + | 0.980153i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.98982e6 | + | 3.98982e6i | −0.222489 | + | 0.222489i | −0.809546 | − | 0.587057i | \(-0.800286\pi\) |
0.587057 | + | 0.809546i | \(0.300286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.54604e7i | − | 2.51922i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.15058e6 | − | 4.26989e6i | −0.393786 | − | 0.235145i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.09412e6 | + | 5.09412e6i | 0.278792 | + | 0.278792i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.93309e7 | − | 1.19633e7i | 1.05139 | − | 0.650671i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.38733e7 | + | 6.58544e6i | 1.29041 | + | 0.355960i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.49611e7 | 0.803699 | 0.401849 | − | 0.915706i | \(-0.368368\pi\) | ||||
0.401849 | + | 0.915706i | \(0.368368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.03434e7 | 1.61999 | 0.809995 | − | 0.586436i | \(-0.199470\pi\) | ||||
0.809995 | + | 0.586436i | \(0.199470\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.34837e6 | − | 2.30290e6i | −0.442971 | − | 0.122194i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.00317e7 | + | 2.36176e6i | 0.529029 | + | 0.124550i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.22272e7 | + | 1.22272e7i | 0.640873 | + | 0.640873i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.38923e7 | − | 2.02384e7i | −1.76560 | − | 1.05431i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.30832e6i | − | 0.119519i | −0.998213 | − | 0.0597597i | \(-0.980967\pi\) | ||
0.998213 | − | 0.0597597i | \(-0.0190334\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.08400e7 | − | 2.08400e7i | 1.07250 | − | 1.07250i | 0.0753457 | − | 0.997157i | \(-0.475994\pi\) |
0.997157 | − | 0.0753457i | \(-0.0240060\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.54628e6 | + | 6.77501e6i | 0.386009 | + | 0.346557i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.14260e7 | − | 2.14260e7i | 1.08937 | − | 1.08937i | 0.0937807 | − | 0.995593i | \(-0.470105\pi\) |
0.995593 | − | 0.0937807i | \(-0.0298953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.19636e6i | − | 0.414223i | −0.978317 | − | 0.207112i | \(-0.933594\pi\) | ||
0.978317 | − | 0.207112i | \(-0.0664064\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.35835e6 | − | 2.39323e6i | −0.0682355 | − | 0.120221i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.52385e6 | + | 3.52385e6i | 0.175956 | + | 0.175956i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.32834e7 | − | 5.48162e6i | −1.15566 | − | 0.272077i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.76752e6 | − | 2.89246e6i | −0.136545 | − | 0.142710i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.49281e7 | −1.22260 | −0.611299 | − | 0.791400i | \(-0.709353\pi\) | ||||
−0.611299 | + | 0.791400i | \(0.709353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.05092e7 | −0.999907 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.82231e6 | − | 1.74816e7i | 0.233715 | − | 0.847253i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.68588e7 | − | 2.89995e7i | 2.25761 | − | 1.39717i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.16070e7 | − | 1.16070e7i | −0.555918 | − | 0.555918i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.23965e7 | − | 7.03606e6i | 0.590244 | − | 0.335012i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.06891e6i | 0.429271i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.43432e6 | − | 3.43432e6i | 0.161610 | − | 0.161610i | −0.621669 | − | 0.783280i | \(-0.713545\pi\) |
0.783280 | + | 0.621669i | \(0.213545\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.93723e7 | − | 466057.i | 1.37411 | − | 0.0218034i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.20442e7 | + | 1.20442e7i | −0.560177 | + | 0.560177i | −0.929358 | − | 0.369181i | \(-0.879638\pi\) |
0.369181 | + | 0.929358i | \(0.379638\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.05636e6i | 0.280046i | 0.990148 | + | 0.140023i | \(0.0447176\pi\) | ||||
−0.990148 | + | 0.140023i | \(0.955282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.38501e7 | + | 7.86107e6i | −0.636715 | + | 0.361388i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.49696e6 | + | 3.49696e6i | 0.159832 | + | 0.159832i | 0.782492 | − | 0.622660i | \(-0.213948\pi\) |
−0.622660 | + | 0.782492i | \(0.713948\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 496997. | − | 2.11102e6i | 0.0225847 | − | 0.0959293i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.89517e6 | + | 3.22464e7i | −0.401889 | + | 1.45691i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.78284e7 | 0.800870 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.34750e7 | 0.601844 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −83814.4 | − | 332280.i | −0.00372206 | − | 0.0147560i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.87313e7 | + | 1.55752e7i | 0.827080 | + | 0.687723i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.20703e7 | + | 1.20703e7i | 0.529929 | + | 0.529929i | 0.920551 | − | 0.390622i | \(-0.127740\pi\) |
−0.390622 | + | 0.920551i | \(0.627740\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.56525e6 | + | 6.28146e6i | 0.155639 | + | 0.274213i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.00926e6i | − | 0.0438092i | −0.999760 | − | 0.0219046i | \(-0.993027\pi\) | ||
0.999760 | − | 0.0219046i | \(-0.00697301\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.57912e7 | + | 2.57912e7i | −1.11319 | + | 1.11319i | −0.120473 | + | 0.992717i | \(0.538441\pi\) |
−0.992717 | + | 0.120473i | \(0.961559\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.29814e6 | − | 1.12565e7i | −0.141550 | − | 0.483107i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.69796e7 | + | 1.69796e7i | −0.724634 | + | 0.724634i | −0.969545 | − | 0.244912i | \(-0.921241\pi\) |
0.244912 | + | 0.969545i | \(0.421241\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.31294e6i | 0.310340i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.08222e7 | + | 5.83056e6i | −0.456691 | + | 0.246046i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.68133e7 | − | 3.68133e7i | −1.54481 | − | 1.54481i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.05688e7 | + | 3.32361e7i | 0.858325 | + | 1.38692i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.10506e7 | − | 1.40823e7i | −2.11846 | − | 0.584376i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46231.7 | −0.00190783 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.31379e7 | −1.77030 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.67562e7 | − | 4.62220e6i | −0.683844 | − | 0.188638i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.57202e6 | + | 2.54016e6i | 0.0638025 | + | 0.103095i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.37950e7 | + | 1.37950e7i | 0.556804 | + | 0.556804i | 0.928396 | − | 0.371592i | \(-0.121188\pi\) |
−0.371592 | + | 0.928396i | \(0.621188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.89908e7 | + | 3.18031e7i | −0.762314 | + | 1.27661i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.68392e7i | − | 1.47067i | −0.677706 | − | 0.735333i | \(-0.737026\pi\) | ||
0.677706 | − | 0.735333i | \(-0.262974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.89615e6 | − | 1.89615e6i | 0.0752828 | − | 0.0752828i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 464435. | + | 1.58510e6i | 0.0183388 | + | 0.0625900i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.77263e7 | − | 2.77263e7i | 1.08885 | − | 1.08885i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.23698e7i | 0.483139i | 0.970383 | + | 0.241570i | \(0.0776622\pi\) | ||||
−0.970383 | + | 0.241570i | \(0.922338\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.96298e6 | + | 1.75534e7i | 0.387026 | + | 0.681885i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.29170e6 | + | 8.29170e6i | 0.320361 | + | 0.320361i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.21572e6 | + | 3.08428e6i | −0.354140 | + | 0.118522i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.42859e7 | − | 3.60347e6i | 0.546018 | − | 0.137728i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.20679e6 | 0.0838921 | 0.0419460 | − | 0.999120i | \(-0.486644\pi\) | ||||
0.0419460 | + | 0.999120i | \(0.486644\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.70714e6 | 0.215796 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.70419e6 | − | 1.34283e7i | 0.139312 | − | 0.505029i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.03605e6 | + | 2.13908e7i | −0.188391 | + | 0.800200i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.22429e6 | + | 4.22429e6i | 0.157183 | + | 0.157183i | 0.781317 | − | 0.624134i | \(-0.214548\pi\) |
−0.624134 | + | 0.781317i | \(0.714548\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.54835e7 | + | 8.78816e6i | −0.573066 | + | 0.325262i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.76967e7i | 1.01966i | 0.860276 | + | 0.509828i | \(0.170291\pi\) | ||||
−0.860276 | + | 0.509828i | \(0.829709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.51071e7 | + | 1.51071e7i | −0.553224 | + | 0.553224i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.54464e7 | + | 1.49816e7i | −0.926931 | + | 0.545732i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.30040e7 | − | 2.30040e7i | 0.833544 | − | 0.833544i | −0.154456 | − | 0.988000i | \(-0.549363\pi\) |
0.988000 | + | 0.154456i | \(0.0493625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.03127e7i | − | 1.45304i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.58214e7 | − | 8.97996e6i | 0.567276 | − | 0.321976i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.18544e7 | − | 1.18544e7i | −0.422814 | − | 0.422814i | 0.463358 | − | 0.886171i | \(-0.346645\pi\) |
−0.886171 | + | 0.463358i | \(0.846645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.50184e6 | + | 5.88039e6i | −0.337131 | + | 0.208640i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −37751.8 | + | 136856.i | −0.00133247 | + | 0.00483042i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.04134e7 | −0.716751 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.75123e7 | −0.960989 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.26478e7 | + | 3.19029e6i | −0.439492 | + | 0.110857i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.99602e7 | − | 1.17621e7i | −1.72705 | − | 0.406601i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.67798e7 | + | 1.67798e7i | 0.577059 | + | 0.577059i | 0.934092 | − | 0.357033i | \(-0.116212\pi\) |
−0.357033 | + | 0.934092i | \(0.616212\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.14215e7 | + | 5.53602e7i | 1.07502 | + | 1.89403i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.14564e7i | 0.730312i | 0.930946 | + | 0.365156i | \(0.118984\pi\) | ||||
−0.930946 | + | 0.365156i | \(0.881016\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.43215e6 | − | 7.43215e6i | 0.251670 | − | 0.251670i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.05173e6 | − | 5.66663e7i | −0.102810 | − | 1.90903i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.04251e6 | + | 8.04251e6i | −0.269560 | + | 0.269560i | −0.828923 | − | 0.559363i | \(-0.811046\pi\) |
0.559363 | + | 0.828923i | \(0.311046\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 7.13510e6i | − | 0.237927i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.17324e6 | + | 1.36874e7i | −0.271158 | + | 0.454095i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.43763e7 | + | 2.43763e7i | 0.804607 | + | 0.804607i | 0.983812 | − | 0.179205i | \(-0.0573524\pi\) |
−0.179205 | + | 0.983812i | \(0.557352\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.31060e6 | + | 779415.i | 0.108722 | + | 0.0255963i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.04492e7 | + | 1.39164e7i | 1.64839 | + | 0.454709i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.33186e7 | −0.758076 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.20983e7 | 1.68515 | 0.842576 | − | 0.538578i | \(-0.181038\pi\) | ||||
0.842576 | + | 0.538578i | \(0.181038\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.26057e7 | + | 8.99427e6i | 1.04935 | + | 0.289463i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.41348e6 | + | 4.58797e6i | −0.237391 | + | 0.146914i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.69329e6 | + | 2.69329e6i | 0.0858114 | + | 0.0858114i | 0.748710 | − | 0.662898i | \(-0.230674\pi\) |
−0.662898 | + | 0.748710i | \(0.730674\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 259969. | − | 1.17771e7i | 0.00824153 | − | 0.373356i |
(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 | 60.6.i.a.17.1 | ✓ | 20 | |
3.2 | odd | 2 | inner | 60.6.i.a.17.6 | yes | 20 | |
5.2 | odd | 4 | 300.6.i.d.293.5 | 20 | |||
5.3 | odd | 4 | inner | 60.6.i.a.53.6 | yes | 20 | |
5.4 | even | 2 | 300.6.i.d.257.10 | 20 | |||
15.2 | even | 4 | 300.6.i.d.293.10 | 20 | |||
15.8 | even | 4 | inner | 60.6.i.a.53.1 | yes | 20 | |
15.14 | odd | 2 | 300.6.i.d.257.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.6.i.a.17.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
60.6.i.a.17.6 | yes | 20 | 3.2 | odd | 2 | inner | |
60.6.i.a.53.1 | yes | 20 | 15.8 | even | 4 | inner | |
60.6.i.a.53.6 | yes | 20 | 5.3 | odd | 4 | inner | |
300.6.i.d.257.5 | 20 | 15.14 | odd | 2 | |||
300.6.i.d.257.10 | 20 | 5.4 | even | 2 | |||
300.6.i.d.293.5 | 20 | 5.2 | odd | 4 | |||
300.6.i.d.293.10 | 20 | 15.2 | even | 4 |