Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(31,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.f (of order \(4\), degree \(2\), not 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: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{42} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 95.5 | ||
Root | \(-2.15805 + 1.82834i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.95 |
Dual form | 128.5.f.a.31.5 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 3.91498 | − | 3.91498i | 0.434998 | − | 0.434998i | −0.455327 | − | 0.890324i | \(-0.650477\pi\) |
0.890324 | + | 0.455327i | \(0.150477\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.72348 | + | 4.72348i | −0.188939 | + | 0.188939i | −0.795237 | − | 0.606298i | \(-0.792654\pi\) |
0.606298 | + | 0.795237i | \(0.292654\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −45.3712 | −0.925943 | −0.462971 | − | 0.886373i | \(-0.653217\pi\) | ||||
−0.462971 | + | 0.886373i | \(0.653217\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 50.3458i | 0.621554i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 110.228 | + | 110.228i | 0.910974 | + | 0.910974i | 0.996349 | − | 0.0853752i | \(-0.0272089\pi\) |
−0.0853752 | + | 0.996349i | \(0.527209\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 157.128 | + | 157.128i | 0.929754 | + | 0.929754i | 0.997690 | − | 0.0679357i | \(-0.0216413\pi\) |
−0.0679357 | + | 0.997690i | \(0.521641\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 36.9847i | 0.164376i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −378.592 | −1.31001 | −0.655003 | − | 0.755626i | \(-0.727333\pi\) | ||||
−0.655003 | + | 0.755626i | \(0.727333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 203.127 | − | 203.127i | 0.562680 | − | 0.562680i | −0.367388 | − | 0.930068i | \(-0.619748\pi\) |
0.930068 | + | 0.367388i | \(0.119748\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −177.627 | + | 177.627i | −0.402783 | + | 0.402783i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 740.444 | 1.39971 | 0.699853 | − | 0.714287i | \(-0.253249\pi\) | ||||
0.699853 | + | 0.714287i | \(0.253249\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 580.377i | 0.928604i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 514.217 | + | 514.217i | 0.705372 | + | 0.705372i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −82.6244 | − | 82.6244i | −0.0982455 | − | 0.0982455i | 0.656276 | − | 0.754521i | \(-0.272131\pi\) |
−0.754521 | + | 0.656276i | \(0.772131\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 286.217i | 0.297833i | 0.988850 | + | 0.148916i | \(0.0475785\pi\) | ||||
−0.988850 | + | 0.148916i | \(0.952421\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 863.080 | 0.792543 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 214.310 | − | 214.310i | 0.174947 | − | 0.174947i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1470.39 | + | 1470.39i | −1.07406 | + | 1.07406i | −0.0770352 | + | 0.997028i | \(0.524545\pi\) |
−0.997028 | + | 0.0770352i | \(0.975455\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1230.31 | 0.808882 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1301.21i | 0.774070i | 0.922065 | + | 0.387035i | \(0.126501\pi\) | ||||
−0.922065 | + | 0.387035i | \(0.873499\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −366.979 | − | 366.979i | −0.198474 | − | 0.198474i | 0.600871 | − | 0.799346i | \(-0.294820\pi\) |
−0.799346 | + | 0.600871i | \(0.794820\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −237.808 | − | 237.808i | −0.117436 | − | 0.117436i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 751.307i | 0.340112i | 0.985434 | + | 0.170056i | \(0.0543948\pi\) | ||||
−0.985434 | + | 0.170056i | \(0.945605\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.455 | −0.142630 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1482.18 | + | 1482.18i | −0.569850 | + | 0.569850i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1929.33 | − | 1929.33i | 0.686838 | − | 0.686838i | −0.274693 | − | 0.961532i | \(-0.588576\pi\) |
0.961532 | + | 0.274693i | \(0.0885764\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1041.32 | −0.344238 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1590.48i | − | 0.489529i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1357.57 | − | 1357.57i | −0.389994 | − | 0.389994i | 0.484691 | − | 0.874685i | \(-0.338932\pi\) |
−0.874685 | + | 0.484691i | \(0.838932\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1835.78 | + | 1835.78i | 0.493356 | + | 0.493356i | 0.909362 | − | 0.416006i | \(-0.136570\pi\) |
−0.416006 | + | 0.909362i | \(0.636570\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2284.25i | − | 0.575523i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1484.39 | −0.351334 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2205.02 | − | 2205.02i | 0.491204 | − | 0.491204i | −0.417481 | − | 0.908686i | \(-0.637087\pi\) |
0.908686 | + | 0.417481i | \(0.137087\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2898.83 | − | 2898.83i | 0.608869 | − | 0.608869i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8970.40 | −1.77949 | −0.889744 | − | 0.456460i | \(-0.849117\pi\) | ||||
−0.889744 | + | 0.456460i | \(0.849117\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9350.46i | − | 1.75464i | −0.479909 | − | 0.877318i | \(-0.659330\pi\) | ||
0.479909 | − | 0.877318i | \(-0.340670\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2272.17 | + | 2272.17i | 0.403941 | + | 0.403941i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5001.17 | − | 5001.17i | −0.843509 | − | 0.843509i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2860.08i | − | 0.458273i | −0.973394 | − | 0.229137i | \(-0.926410\pi\) | ||
0.973394 | − | 0.229137i | \(-0.0735903\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −51.7173 | −0.00788253 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1036.63 | + | 1036.63i | −0.150477 | + | 0.150477i | −0.778331 | − | 0.627854i | \(-0.783933\pi\) |
0.627854 | + | 0.778331i | \(0.283933\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1788.27 | − | 1788.27i | 0.247512 | − | 0.247512i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −646.946 | −0.0854731 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5171.06i | 0.652830i | 0.945227 | + | 0.326415i | \(0.105841\pi\) | ||||
−0.945227 | + | 0.326415i | \(0.894159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7129.10 | − | 7129.10i | −0.860899 | − | 0.860899i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1120.54 | + | 1120.54i | 0.129557 | + | 0.129557i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1918.94i | 0.212625i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8539.92 | 0.907633 | 0.453817 | − | 0.891095i | \(-0.350062\pi\) | ||||
0.453817 | + | 0.891095i | \(0.350062\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5549.51 | + | 5549.51i | −0.566219 | + | 0.566219i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −537.642 | + | 537.642i | −0.0527049 | + | 0.0527049i | −0.732968 | − | 0.680263i | \(-0.761866\pi\) |
0.680263 | + | 0.732968i | \(0.261866\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5543.86 | 0.522562 | 0.261281 | − | 0.965263i | \(-0.415855\pi\) | ||||
0.261281 | + | 0.965263i | \(0.415855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1678.04i | − | 0.152203i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2989.60 | − | 2989.60i | −0.261123 | − | 0.261123i | 0.564387 | − | 0.825510i | \(-0.309113\pi\) |
−0.825510 | + | 0.564387i | \(0.809113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3353.83 | + | 3353.83i | 0.282285 | + | 0.282285i | 0.834020 | − | 0.551734i | \(-0.186034\pi\) |
−0.551734 | + | 0.834020i | \(0.686034\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11513.1i | 0.934431i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3193.81 | −0.250122 | −0.125061 | − | 0.992149i | \(-0.539913\pi\) | ||||
−0.125061 | + | 0.992149i | \(0.539913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3497.48 | + | 3497.48i | −0.264459 | + | 0.264459i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7910.76 | + | 7910.76i | −0.577892 | + | 0.577892i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17177.2 | 1.21299 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9659.34i | 0.659746i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5094.22 | + | 5094.22i | 0.336719 | + | 0.336719i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5693.58 | − | 5693.58i | −0.364389 | − | 0.364389i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 22900.5i | − | 1.41983i | −0.704287 | − | 0.709915i | \(-0.748733\pi\) | ||
0.704287 | − | 0.709915i | \(-0.251267\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2873.43 | −0.172672 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19255.9 | − | 19255.9i | 1.12207 | − | 1.12207i | 0.130644 | − | 0.991429i | \(-0.458296\pi\) |
0.991429 | − | 0.130644i | \(-0.0417045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9216.13 | + | 9216.13i | −0.521009 | + | 0.521009i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4857.79 | −0.266545 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19938.2i | 1.06229i | 0.847280 | + | 0.531147i | \(0.178239\pi\) | ||||
−0.847280 | + | 0.531147i | \(0.821761\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 25175.4 | + | 25175.4i | 1.30301 | + | 1.30301i | 0.926356 | + | 0.376649i | \(0.122924\pi\) |
0.376649 | + | 0.926356i | \(0.377076\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2941.35 | + | 2941.35i | 0.147948 | + | 0.147948i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 34639.8i | 1.69396i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 780.550 | 0.0371249 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1340.70 | + | 1340.70i | −0.0620438 | + | 0.0620438i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3216.99 | − | 3216.99i | 0.144903 | − | 0.144903i | −0.630934 | − | 0.775837i | \(-0.717328\pi\) |
0.775837 | + | 0.630934i | \(0.217328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14770.5 | 0.647802 | 0.323901 | − | 0.946091i | \(-0.395006\pi\) | ||||
0.323901 | + | 0.946091i | \(0.395006\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 19060.5i | − | 0.814239i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1351.94 | − | 1351.94i | −0.0562723 | − | 0.0562723i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18014.6 | + | 18014.6i | 0.730845 | + | 0.730845i | 0.970787 | − | 0.239942i | \(-0.0771284\pi\) |
−0.239942 | + | 0.970787i | \(0.577128\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 15106.6i | − | 0.597547i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33594.8 | −1.29605 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15083.2 | − | 15083.2i | 0.567700 | − | 0.567700i | −0.363784 | − | 0.931483i | \(-0.618515\pi\) |
0.931483 | + | 0.363784i | \(0.118515\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4076.74 | + | 4076.74i | −0.149743 | + | 0.149743i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23733.6 | −0.851001 | −0.425501 | − | 0.904958i | \(-0.639902\pi\) | ||||
−0.425501 | + | 0.904958i | \(0.639902\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20817.7i | 0.728885i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10226.6 | + | 10226.6i | 0.349736 | + | 0.349736i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12072.3 | + | 12072.3i | 0.403363 | + | 0.403363i | 0.879416 | − | 0.476053i | \(-0.157933\pi\) |
−0.476053 | + | 0.879416i | \(0.657933\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 26332.4i | − | 0.859834i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10629.7 | −0.339293 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −28111.5 | + | 28111.5i | −0.877361 | + | 0.877361i | −0.993261 | − | 0.115900i | \(-0.963025\pi\) |
0.115900 | + | 0.993261i | \(0.463025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15906.7 | − | 15906.7i | 0.485539 | − | 0.485539i | −0.421356 | − | 0.906895i | \(-0.638446\pi\) |
0.906895 | + | 0.421356i | \(0.138446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14374.1 | 0.429218 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 13890.8i | − | 0.405866i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −41731.4 | − | 41731.4i | −1.19338 | − | 1.19338i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23330.6 | − | 23330.6i | −0.653134 | − | 0.653134i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 28038.6i | 0.768581i | 0.923212 | + | 0.384290i | \(0.125554\pi\) | ||||
−0.923212 | + | 0.384290i | \(0.874446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 56713.1 | 1.52254 | 0.761270 | − | 0.648436i | \(-0.224576\pi\) | ||||
0.761270 | + | 0.648436i | \(0.224576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5811.35 | + | 5811.35i | −0.152830 | + | 0.152830i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10179.3 | − | 10179.3i | 0.262292 | − | 0.262292i | −0.563692 | − | 0.825985i | \(-0.690620\pi\) |
0.825985 | + | 0.563692i | \(0.190620\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −31787.3 | −0.802689 | −0.401344 | − | 0.915927i | \(-0.631457\pi\) | ||||
−0.401344 | + | 0.915927i | \(0.631457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 17265.2i | − | 0.427346i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3748.77 | + | 3748.77i | 0.0909697 | + | 0.0909697i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6146.25 | − | 6146.25i | −0.146252 | − | 0.146252i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 37278.3i | 0.869992i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 44780.6 | 1.02517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10699.8 | + | 10699.8i | −0.240332 | + | 0.240332i | −0.816988 | − | 0.576655i | \(-0.804358\pi\) |
0.576655 | + | 0.816988i | \(0.304358\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −35118.9 | + | 35118.9i | −0.774073 | + | 0.774073i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3466.84 | 0.0749992 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 12986.0i | − | 0.275776i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −36606.9 | − | 36606.9i | −0.763263 | − | 0.763263i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −59487.5 | − | 59487.5i | −1.21798 | − | 1.21798i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 91700.4i | − | 1.84400i | −0.387187 | − | 0.922001i | \(-0.626553\pi\) | ||
0.387187 | − | 0.922001i | \(-0.373447\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29219.6 | −0.577177 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17499.5 | − | 17499.5i | 0.339605 | − | 0.339605i | −0.516614 | − | 0.856218i | \(-0.672808\pi\) |
0.856218 | + | 0.516614i | \(0.172808\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 63859.8 | − | 63859.8i | 1.21775 | − | 1.21775i | 0.249326 | − | 0.968420i | \(-0.419791\pi\) |
0.968420 | − | 0.249326i | \(-0.0802091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −39159.0 | −0.733850 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 63891.7i | − | 1.17688i | −0.808540 | − | 0.588441i | \(-0.799742\pi\) | ||
0.808540 | − | 0.588441i | \(-0.200258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3548.79 | − | 3548.79i | −0.0642605 | − | 0.0642605i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11197.2 | − | 11197.2i | −0.199348 | − | 0.199348i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12096.4i | 0.211768i | 0.994378 | + | 0.105884i | \(0.0337672\pi\) | ||||
−0.994378 | + | 0.105884i | \(0.966233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27978.6 | 0.481717 | 0.240859 | − | 0.970560i | \(-0.422571\pi\) | ||||
0.240859 | + | 0.970560i | \(0.422571\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −41854.0 | + | 41854.0i | −0.708801 | + | 0.708801i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1617.58 | − | 1617.58i | 0.0269484 | − | 0.0269484i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 63834.2 | 1.04631 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8116.80i | 0.130914i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1996.06 | + | 1996.06i | 0.0316830 | + | 0.0316830i | 0.722771 | − | 0.691088i | \(-0.242868\pi\) |
−0.691088 | + | 0.722771i | \(0.742868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 81617.5 | + | 81617.5i | 1.27509 | + | 1.27509i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 14002.1i | − | 0.215334i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −73510.4 | −1.11297 | −0.556484 | − | 0.830859i | \(-0.687850\pi\) | ||||
−0.556484 | + | 0.830859i | \(0.687850\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 66713.5 | − | 66713.5i | 0.994521 | − | 0.994521i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4159.80 | − | 4159.80i | 0.0610648 | − | 0.0610648i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −68109.3 | −0.984680 | −0.492340 | − | 0.870403i | \(-0.663858\pi\) | ||||
−0.492340 | + | 0.870403i | \(0.663858\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18226.3i | 0.259542i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20244.6 | + | 20244.6i | 0.283980 | + | 0.283980i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15056.1 | + | 15056.1i | 0.208069 | + | 0.208069i | 0.803446 | − | 0.595377i | \(-0.202997\pi\) |
−0.595377 | + | 0.803446i | \(0.702997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 104320.i | 1.42046i | 0.703968 | + | 0.710232i | \(0.251410\pi\) | ||||
−0.703968 | + | 0.710232i | \(0.748590\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −55820.6 | −0.748979 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −63973.7 | + | 63973.7i | −0.845934 | + | 0.845934i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2136.36 | + | 2136.36i | −0.0278430 | + | 0.0278430i | −0.720891 | − | 0.693048i | \(-0.756267\pi\) |
0.693048 | + | 0.720891i | \(0.256267\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14409.8 | −0.185119 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 36783.7i | 0.465846i | 0.972495 | + | 0.232923i | \(0.0748290\pi\) | ||||
−0.972495 | + | 0.232923i | \(0.925171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14172.0 | + | 14172.0i | 0.176953 | + | 0.176953i | 0.790026 | − | 0.613073i | \(-0.210067\pi\) |
−0.613073 | + | 0.790026i | \(0.710067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7512.60 | + | 7512.60i | 0.0924913 | + | 0.0924913i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 59037.5i | − | 0.716744i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 59810.8 | 0.716117 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33433.6 | − | 33433.6i | 0.394819 | − | 0.394819i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −80721.8 | + | 80721.8i | −0.940276 | + | 0.940276i | −0.998314 | − | 0.0580384i | \(-0.981515\pi\) |
0.0580384 | + | 0.998314i | \(0.481515\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12824.9 | 0.147370 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 113362.i | 1.28515i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 116345. | + | 116345.i | 1.30138 | + | 1.30138i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16650.3 | + | 16650.3i | 0.183776 | + | 0.183776i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4209.72i | 0.0458530i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17342.5 | −0.186429 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 113714. | − | 113714.i | 1.20653 | − | 1.20653i | 0.234389 | − | 0.972143i | \(-0.424691\pi\) |
0.972143 | − | 0.234389i | \(-0.0753090\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21704.1 | − | 21704.1i | 0.227313 | − | 0.227313i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 93801.8 | 0.969819 | 0.484909 | − | 0.874564i | \(-0.338853\pi\) | ||||
0.484909 | + | 0.874564i | \(0.338853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9229.52i | 0.0942086i | 0.998890 | + | 0.0471043i | \(0.0149993\pi\) | ||||
−0.998890 | + | 0.0471043i | \(0.985001\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10789.6 | + | 10789.6i | 0.108739 | + | 0.108739i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8447.44 | + | 8447.44i | 0.0840634 | + | 0.0840634i | 0.747888 | − | 0.663825i | \(-0.231068\pi\) |
−0.663825 | + | 0.747888i | \(0.731068\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 18215.0i | − | 0.178998i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23408.5 | −0.227176 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −76902.4 | + | 76902.4i | −0.737114 | + | 0.737114i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −91193.8 | + | 91193.8i | −0.863373 | + | 0.863373i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26260.4 | 0.245587 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 34087.7i | − | 0.314924i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −46092.1 | − | 46092.1i | −0.420698 | − | 0.420698i | 0.464746 | − | 0.885444i | \(-0.346146\pi\) |
−0.885444 | + | 0.464746i | \(0.846146\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −74028.2 | − | 74028.2i | −0.667588 | − | 0.667588i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20830.7i | 0.185616i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 39317.8 | 0.346201 | 0.173101 | − | 0.984904i | \(-0.444621\pi\) | ||||
0.173101 | + | 0.984904i | \(0.444621\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12503.7 | + | 12503.7i | −0.108803 | + | 0.108803i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31549.1 | + | 31549.1i | −0.271318 | + | 0.271318i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 124474. | 1.05801 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 27385.1i | 0.230079i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −67694.0 | − | 67694.0i | −0.562201 | − | 0.562201i | 0.367731 | − | 0.929932i | \(-0.380135\pi\) |
−0.929932 | + | 0.367731i | \(0.880135\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7662.83 | + | 7662.83i | 0.0629127 | + | 0.0629127i | 0.737863 | − | 0.674950i | \(-0.235835\pi\) |
−0.674950 | + | 0.737863i | \(0.735835\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 161596.i | 1.31165i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 70618.0 | 0.566716 | 0.283358 | − | 0.959014i | \(-0.408551\pi\) | ||||
0.283358 | + | 0.959014i | \(0.408551\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 42371.5 | − | 42371.5i | 0.336215 | − | 0.336215i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 67248.3 | − | 67248.3i | 0.527649 | − | 0.527649i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 168144. | 1.30465 | 0.652323 | − | 0.757941i | \(-0.273794\pi\) | ||||
0.652323 | + | 0.757941i | \(0.273794\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 47799.6i | 0.366783i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 37816.1 | + | 37816.1i | 0.286988 | + | 0.286988i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44166.7 | + | 44166.7i | 0.331520 | + | 0.331520i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 82596.4i | − | 0.613238i | −0.951832 | − | 0.306619i | \(-0.900802\pi\) | ||
0.951832 | − | 0.306619i | \(-0.0991977\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −65510.6 | −0.481126 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −87536.0 | + | 87536.0i | −0.635973 | + | 0.635973i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 76631.0 | − | 76631.0i | 0.550791 | − | 0.550791i | −0.375878 | − | 0.926669i | \(-0.622659\pi\) |
0.926669 | + | 0.375878i | \(0.122659\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −44580.5 | −0.317017 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 25965.3i | − | 0.182688i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −95935.8 | − | 95935.8i | −0.667886 | − | 0.667886i | 0.289340 | − | 0.957226i | \(-0.406564\pi\) |
−0.957226 | + | 0.289340i | \(0.906564\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −89654.8 | − | 89654.8i | −0.617623 | − | 0.617623i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 168708.i | − | 1.15011i | −0.818116 | − | 0.575054i | \(-0.804981\pi\) | ||
0.818116 | − | 0.575054i | \(-0.195019\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 47245.9 | 0.318744 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18475.9 | − | 18475.9i | 0.123362 | − | 0.123362i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −66490.0 | + | 66490.0i | −0.439397 | + | 0.439397i | −0.891809 | − | 0.452412i | \(-0.850564\pi\) |
0.452412 | + | 0.891809i | \(0.350564\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −280326. | −1.83362 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 150773.i | − | 0.976199i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13509.6 | + | 13509.6i | 0.0865859 | + | 0.0865859i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18578.8 | − | 18578.8i | −0.117879 | − | 0.117879i | 0.645706 | − | 0.763586i | \(-0.276563\pi\) |
−0.763586 | + | 0.645706i | \(0.776563\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 72162.0i | 0.453276i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −129108. | −0.802908 | −0.401454 | − | 0.915879i | \(-0.631495\pi\) | ||||
−0.401454 | + | 0.915879i | \(0.631495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −44972.9 | + | 44972.9i | −0.276911 | + | 0.276911i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 244.286 | − | 244.286i | 0.00148932 | − | 0.00148932i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −324156. | −1.95689 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17952.4i | 0.107319i | 0.998559 | + | 0.0536594i | \(0.0170885\pi\) | ||||
−0.998559 | + | 0.0536594i | \(0.982911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 78057.7 | + | 78057.7i | 0.462096 | + | 0.462096i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 61594.5 | + | 61594.5i | 0.361112 | + | 0.361112i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9793.04i | − | 0.0568619i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 197122. | 1.13361 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 56887.3 | − | 56887.3i | 0.324031 | − | 0.324031i | −0.526280 | − | 0.850311i | \(-0.676414\pi\) |
0.850311 | + | 0.526280i | \(0.176414\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 144162. | − | 144162.i | 0.813365 | − | 0.813365i | −0.171772 | − | 0.985137i | \(-0.554949\pi\) |
0.985137 | + | 0.171772i | \(0.0549492\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −37825.2 | −0.211398 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 219726.i | − | 1.21648i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −83291.4 | − | 83291.4i | −0.456819 | − | 0.456819i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 135614. | + | 135614.i | 0.736870 | + | 0.736870i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18641.5i | 0.100352i | 0.998740 | + | 0.0501760i | \(0.0159782\pi\) | ||||
−0.998740 | + | 0.0501760i | \(0.984022\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2193.97 | 0.0117019 | 0.00585094 | − | 0.999983i | \(-0.498138\pi\) | ||||
0.00585094 | + | 0.999983i | \(0.498138\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3055.84 | − | 3055.84i | 0.0161492 | − | 0.0161492i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 150404. | − | 150404.i | 0.787586 | − | 0.787586i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −118115. | −0.612880 | −0.306440 | − | 0.951890i | \(-0.599138\pi\) | ||||
−0.306440 | + | 0.951890i | \(0.599138\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 17241.2i | − | 0.0886523i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37885.8 | + | 37885.8i | 0.193050 | + | 0.193050i | 0.797013 | − | 0.603963i | \(-0.206412\pi\) |
−0.603963 | + | 0.797013i | \(0.706412\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24425.4 | − | 24425.4i | −0.123345 | − | 0.123345i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 25188.9i | − | 0.126065i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −85186.6 | −0.422550 | −0.211275 | − | 0.977427i | \(-0.567762\pi\) | ||||
−0.211275 | + | 0.977427i | \(0.567762\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −143430. | + | 143430.i | −0.705157 | + | 0.705157i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 57826.4 | − | 57826.4i | 0.281793 | − | 0.281793i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 67348.4 | 0.325315 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 96935.7i | 0.464142i | 0.972699 | + | 0.232071i | \(0.0745502\pi\) | ||||
−0.972699 | + | 0.232071i | \(0.925450\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −194678. | − | 194678.i | −0.924042 | − | 0.924042i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −295014. | − | 295014.i | −1.38816 | − | 1.38816i | −0.829176 | − | 0.558988i | \(-0.811190\pi\) |
−0.558988 | − | 0.829176i | \(-0.688810\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 224348.i | − | 1.04655i | −0.852164 | − | 0.523275i | \(-0.824710\pi\) | ||
0.852164 | − | 0.523275i | \(-0.175290\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10585.7 | −0.0489567 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 189556. | − | 189556.i | 0.869168 | − | 0.869168i | −0.123212 | − | 0.992380i | \(-0.539320\pi\) |
0.992380 | + | 0.123212i | \(0.0393196\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −100044. | + | 100044.i | −0.454827 | + | 0.454827i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 141054. | 0.635832 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 80902.6i | − | 0.361610i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 117891. | + | 117891.i | 0.522506 | + | 0.522506i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 97133.7 | + | 97133.7i | 0.426907 | + | 0.426907i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 132796.i | 0.578781i | 0.957211 | + | 0.289390i | \(0.0934526\pi\) | ||||
−0.957211 | + | 0.289390i | \(0.906547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −462081. | −1.99723 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −131523. | + | 131523.i | −0.563778 | + | 0.563778i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −40338.2 | + | 40338.2i | −0.171488 | + | 0.171488i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 283936. | 1.19719 | 0.598595 | − | 0.801052i | \(-0.295726\pi\) | ||||
0.598595 | + | 0.801052i | \(0.295726\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 118101.i | − | 0.493896i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −111725. | − | 111725.i | −0.463435 | − | 0.463435i | 0.436345 | − | 0.899780i | \(-0.356273\pi\) |
−0.899780 | + | 0.436345i | \(0.856273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31280.9 | + | 31280.9i | 0.128702 | + | 0.128702i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 52426.1i | − | 0.213962i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 406998. | 1.64770 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 61595.1 | − | 61595.1i | 0.247369 | − | 0.247369i | −0.572521 | − | 0.819890i | \(-0.694035\pi\) |
0.819890 | + | 0.572521i | \(0.194035\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −92916.5 | + | 92916.5i | −0.370184 | + | 0.370184i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 70874.1 | 0.280125 | 0.140062 | − | 0.990143i | \(-0.455270\pi\) | ||||
0.140062 | + | 0.990143i | \(0.455270\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5079.09i | − | 0.0199160i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 81500.9 | + | 81500.9i | 0.317064 | + | 0.317064i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 128181. | + | 128181.i | 0.494754 | + | 0.494754i | 0.909800 | − | 0.415046i | \(-0.136235\pi\) |
−0.415046 | + | 0.909800i | \(0.636235\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 424241.i | 1.62469i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 208903. | 0.793797 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26186.3 | + | 26186.3i | −0.0987324 | + | 0.0987324i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −82814.9 | + | 82814.9i | −0.309833 | + | 0.309833i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 94525.3 | 0.350924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 494250.i | 1.82084i | 0.413688 | + | 0.910419i | \(0.364241\pi\) | ||||
−0.413688 | + | 0.910419i | \(0.635759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 179670. | + | 179670.i | 0.656859 | + | 0.656859i | 0.954636 | − | 0.297776i | \(-0.0962450\pi\) |
−0.297776 | + | 0.954636i | \(0.596245\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −103091. | − | 103091.i | −0.374026 | − | 0.374026i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 108360.i | − | 0.390163i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 268417. | 0.959175 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 68347.9 | − | 68347.9i | 0.242402 | − | 0.242402i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −204457. | + | 204457.i | −0.719694 | + | 0.719694i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28242.7 | 0.0986729 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 220112.i | 0.763300i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37748.1 | − | 37748.1i | −0.129932 | − | 0.129932i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −300961. | − | 300961.i | −1.02829 | − | 1.02829i | −0.999588 | − | 0.0287034i | \(-0.990862\pi\) |
−0.0287034 | − | 0.999588i | \(-0.509138\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 124549.i | − | 0.422417i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −31683.6 | −0.106670 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −159057. | + | 159057.i | −0.531591 | + | 0.531591i | −0.921046 | − | 0.389455i | \(-0.872663\pi\) |
0.389455 | + | 0.921046i | \(0.372663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −92423.8 | + | 92423.8i | −0.306647 | + | 0.306647i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33566.6 | −0.110561 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 129765.i | 0.424335i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −54382.0 | − | 54382.0i | −0.176551 | − | 0.176551i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 394524. | + | 394524.i | 1.27164 | + | 1.27164i | 0.945229 | + | 0.326409i | \(0.105839\pi\) |
0.326409 | + | 0.945229i | \(0.394161\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 115326.i | − | 0.369065i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −326755. | −1.03824 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 169317. | − | 169317.i | 0.534177 | − | 0.534177i | −0.387636 | − | 0.921813i | \(-0.626708\pi\) |
0.921813 | + | 0.387636i | \(0.126708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15085.9 | − | 15085.9i | 0.0472579 | − | 0.0472579i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2346.48 | 0.00729877 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 165645.i | 0.511626i | 0.966726 | + | 0.255813i | \(0.0823432\pi\) | ||||
−0.966726 | + | 0.255813i | \(0.917657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 335641. | + | 335641.i | 1.02945 | + | 1.02945i | 0.999553 | + | 0.0298925i | \(0.00951651\pi\) |
0.0298925 | + | 0.999553i | \(0.490483\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 109771. | + | 109771.i | 0.334331 | + | 0.334331i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 429737.i | 1.29977i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −99615.9 | −0.299211 | −0.149605 | − | 0.988746i | \(-0.547800\pi\) | ||||
−0.149605 | + | 0.988746i | \(0.547800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 222031. | − | 222031.i | 0.662301 | − | 0.662301i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 47033.3 | − | 47033.3i | 0.139333 | − | 0.139333i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 425331. | 1.25138 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 74732.7i | − | 0.218373i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45023.9 | − | 45023.9i | −0.130667 | − | 0.130667i | 0.638748 | − | 0.769416i | \(-0.279452\pi\) |
−0.769416 | + | 0.638748i | \(0.779452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 58138.5 | + | 58138.5i | 0.167584 | + | 0.167584i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 79703.6i | − | 0.228193i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −385101. | −1.09513 | −0.547564 | − | 0.836764i | \(-0.684445\pi\) | ||||
−0.547564 | + | 0.836764i | \(0.684445\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −81136.1 | + | 81136.1i | −0.229182 | + | 0.229182i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −124447. | + | 124447.i | −0.349168 | + | 0.349168i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −209331. | −0.583417 | −0.291709 | − | 0.956507i | \(-0.594224\pi\) | ||||
−0.291709 | + | 0.956507i | \(0.594224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 515555.i | − | 1.42734i | −0.700484 | − | 0.713668i | \(-0.747033\pi\) | ||
0.700484 | − | 0.713668i | \(-0.252967\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 111013. | + | 111013.i | 0.305310 | + | 0.305310i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −45625.7 | − | 45625.7i | −0.124652 | − | 0.124652i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30292.7i | 0.0822167i | 0.999155 | + | 0.0411084i | \(0.0130889\pi\) | ||||
−0.999155 | + | 0.0411084i | \(0.986911\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29352.7 | 0.0791432 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −118052. | + | 118052.i | −0.316220 | + | 0.316220i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 99803.4 | − | 99803.4i | 0.265598 | − | 0.265598i | −0.561726 | − | 0.827324i | \(-0.689862\pi\) |
0.827324 | + | 0.561726i | \(0.189862\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −48124.9 | −0.127239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 102196.i | 0.268451i | 0.990951 | + | 0.134226i | \(0.0428547\pi\) | ||||
−0.990951 | + | 0.134226i | \(0.957145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −105904. | − | 105904.i | −0.276395 | − | 0.276395i | 0.555273 | − | 0.831668i | \(-0.312614\pi\) |
−0.831668 | + | 0.555273i | \(0.812614\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 380749. | + | 380749.i | 0.987314 | + | 0.987314i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 234617.i | − | 0.604483i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −308949. | −0.790909 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 175315. | − | 175315.i | 0.445948 | − | 0.445948i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 556679. | − | 556679.i | 1.40703 | − | 1.40703i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −692480. | −1.73920 | −0.869598 | − | 0.493760i | \(-0.835622\pi\) | ||||
−0.869598 | + | 0.493760i | \(0.835622\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 83779.3i | 0.209088i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 108170. | + | 108170.i | 0.268262 | + | 0.268262i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −53809.4 | − | 53809.4i | −0.132611 | − | 0.132611i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 451622.i | − | 1.10605i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49519.0 | 0.120519 | 0.0602595 | − | 0.998183i | \(-0.480807\pi\) | ||||
0.0602595 | + | 0.998183i | \(0.480807\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −165494. | + | 165494.i | −0.400276 | + | 0.400276i | −0.878330 | − | 0.478054i | \(-0.841342\pi\) |
0.478054 | + | 0.878330i | \(0.341342\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13572.6 | − | 13572.6i | 0.0326245 | − | 0.0326245i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 666565. | 1.59233 | 0.796166 | − | 0.605078i | \(-0.206858\pi\) | ||||
0.796166 | + | 0.605078i | \(0.206858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 299284.i | − | 0.710548i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −50840.0 | − | 50840.0i | −0.119962 | − | 0.119962i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −461118. | − | 461118.i | −1.08140 | − | 1.08140i | −0.996379 | − | 0.0850198i | \(-0.972905\pi\) |
−0.0850198 | − | 0.996379i | \(-0.527095\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 181910.i | 0.424008i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 470757. | 1.09060 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 326883. | − | 326883.i | 0.752698 | − | 0.752698i | −0.222284 | − | 0.974982i | \(-0.571351\pi\) |
0.974982 | + | 0.222284i | \(0.0713511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −549615. | + | 549615.i | −1.25793 | + | 1.25793i | −0.305848 | + | 0.952080i | \(0.598940\pi\) |
−0.952080 | + | 0.305848i | \(0.901060\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −465785. | −1.05964 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 87064.5i | − | 0.196878i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −61178.8 | − | 61178.8i | −0.137515 | − | 0.137515i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −359005. | − | 359005.i | −0.802137 | − | 0.802137i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 404708.i | 0.898869i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 191664. | 0.423166 | 0.211583 | − | 0.977360i | \(-0.432138\pi\) | ||||
0.211583 | + | 0.977360i | \(0.432138\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −298440. | + | 298440.i | −0.655012 | + | 0.655012i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 544201. | − | 544201.i | 1.18736 | − | 1.18736i | 0.209564 | − | 0.977795i | \(-0.432796\pi\) |
0.977795 | − | 0.209564i | \(-0.0672043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −387466. | −0.840416 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 137020.i | − | 0.295455i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −570769. | − | 570769.i | −1.22354 | − | 1.22354i | −0.966364 | − | 0.257179i | \(-0.917207\pi\) |
−0.257179 | − | 0.966364i | \(-0.582793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −94177.8 | − | 94177.8i | −0.200709 | − | 0.200709i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 500020.i | − | 1.05943i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 606305. | 1.27718 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −333477. | + | 333477.i | −0.698409 | + | 0.698409i | −0.964067 | − | 0.265658i | \(-0.914411\pi\) |
0.265658 | + | 0.964067i | \(0.414411\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 251788. | − | 251788.i | 0.524286 | − | 0.524286i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −237831. | −0.492378 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 492628.i | − | 1.01404i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −250135. | − | 250135.i | −0.511941 | − | 0.511941i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31503.2 | − | 31503.2i | −0.0641089 | − | 0.0641089i | 0.674325 | − | 0.738434i | \(-0.264435\pi\) |
−0.738434 | + | 0.674325i | \(0.764435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 597354.i | 1.20871i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27786.9 | −0.0559064 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24393.5 | − | 24393.5i | 0.0488017 | − | 0.0488017i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −609708. | + | 609708.i | −1.21291 | + | 1.21291i | −0.242847 | + | 0.970064i | \(0.578081\pi\) |
−0.970064 | + | 0.242847i | \(0.921919\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 143993. | 0.284841 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 211928.i | 0.416878i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −163621. | − | 163621.i | −0.320056 | − | 0.320056i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47357.2 | + | 47357.2i | 0.0921187 | + | 0.0921187i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 720908.i | − | 1.39451i | −0.716823 | − | 0.697256i | \(-0.754404\pi\) | ||
0.716823 | − | 0.697256i | \(-0.245596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −251531. | −0.483862 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 109536. | − | 109536.i | 0.209546 | − | 0.209546i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 47953.4 | − | 47953.4i | 0.0912311 | − | 0.0912311i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 279904. | 0.529591 | 0.264796 | − | 0.964305i | \(-0.414696\pi\) | ||||
0.264796 | + | 0.964305i | \(0.414696\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 323526.i | 0.608772i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 138935. | + | 138935.i | 0.260003 | + | 0.260003i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 266306. | + | 266306.i | 0.495648 | + | 0.495648i | 0.910080 | − | 0.414432i | \(-0.136020\pi\) |
−0.414432 | + | 0.910080i | \(0.636020\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 12665.6i | − | 0.0234450i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 486108. | 0.894948 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −594958. | + | 594958.i | −1.08943 | + | 1.08943i | −0.0938378 | + | 0.995587i | \(0.529914\pi\) |
−0.995587 | + | 0.0938378i | \(0.970086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 249910. | − | 249910.i | 0.455142 | − | 0.455142i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −289367. | −0.524170 | −0.262085 | − | 0.965045i | \(-0.584410\pi\) | ||||
−0.262085 | + | 0.965045i | \(0.584410\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30390.8i | 0.0547557i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −52190.2 | − | 52190.2i | −0.0935293 | − | 0.0935293i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 135642. | + | 135642.i | 0.241785 | + | 0.241785i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 935795.i | 1.65921i | 0.558352 | + | 0.829604i | \(0.311434\pi\) | ||||
−0.558352 | + | 0.829604i | \(0.688566\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15629.1 | 0.0275641 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −69768.4 | + | 69768.4i | −0.122395 | + | 0.122395i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 626956. | − | 626956.i | 1.09407 | − | 1.09407i | 0.0989818 | − | 0.995089i | \(-0.468441\pi\) |
0.995089 | − | 0.0989818i | \(-0.0315586\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 639062. | 1.10933 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 253505.i | − | 0.437741i | −0.975754 | − | 0.218871i | \(-0.929763\pi\) | ||
0.975754 | − | 0.218871i | \(-0.0702372\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −152167. | − | 152167.i | −0.261380 | − | 0.261380i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 90032.1 | + | 90032.1i | 0.153842 | + | 0.153842i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 426625.i | − | 0.725197i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −740462. | −1.25213 | −0.626066 | − | 0.779770i | \(-0.715336\pi\) | ||||
−0.626066 | + | 0.779770i | \(0.715336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −287792. | + | 287792.i | −0.484138 | + | 0.484138i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −422057. | + | 422057.i | −0.706337 | + | 0.706337i | −0.965763 | − | 0.259426i | \(-0.916467\pi\) |
0.259426 | + | 0.965763i | \(0.416467\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −166114. | −0.276569 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 522364.i | − | 0.865229i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 264312. | + | 264312.i | 0.435553 | + | 0.435553i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −988787. | − | 988787.i | −1.62107 | − | 1.62107i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 84973.7i | − | 0.138599i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −170183. | −0.276171 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 658152. | − | 658152.i | 1.06262 | − | 1.06262i | 0.0647134 | − | 0.997904i | \(-0.479387\pi\) |
0.997904 | − | 0.0647134i | \(-0.0206133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −266647. | + | 266647.i | −0.428334 | + | 0.428334i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 144907. | 0.231599 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 576906.i | 0.917400i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 71355.7 | + | 71355.7i | 0.112900 | + | 0.112900i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 573702. | + | 573702.i | 0.903171 | + | 0.903171i | 0.995709 | − | 0.0925382i | \(-0.0294980\pi\) |
−0.0925382 | + | 0.995709i | \(0.529498\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 284439.i | − | 0.445549i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −260342. | −0.405769 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.03068e6 | − | 1.03068e6i | 1.59843 | − | 1.59843i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 158685. | − | 158685.i | 0.244874 | − | 0.244874i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 117889. | 0.181019 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 297398.i | 0.454402i | 0.973848 | + | 0.227201i | \(0.0729575\pi\) | ||||
−0.973848 | + | 0.227201i | \(0.927043\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 481203. | + | 481203.i | 0.731621 | + | 0.731621i | 0.970941 | − | 0.239320i | \(-0.0769243\pi\) |
−0.239320 | + | 0.970941i | \(0.576924\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 408412. | + | 408412.i | 0.617899 | + | 0.617899i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 142491.i | 0.214522i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −149087. | −0.223355 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 358921. | − | 358921.i | 0.535095 | − | 0.535095i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −506859. | + | 506859.i | −0.751971 | + | 0.751971i | −0.974847 | − | 0.222876i | \(-0.928456\pi\) |
0.222876 | + | 0.974847i | \(0.428456\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −401221. | −0.592357 | −0.296179 | − | 0.955133i | \(-0.595712\pi\) | ||||
−0.296179 | + | 0.955133i | \(0.595712\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 500912.i | 0.735959i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 410169. | + | 410169.i | 0.599725 | + | 0.599725i | 0.940239 | − | 0.340515i | \(-0.110601\pi\) |
−0.340515 | + | 0.940239i | \(0.610601\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 328989. | + | 328989.i | 0.478710 | + | 0.478710i | 0.904719 | − | 0.426009i | \(-0.140081\pi\) |
−0.426009 | + | 0.904719i | \(0.640081\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16727.6i | 0.0242233i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 129651. | 0.186846 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 112105. | − | 112105.i | 0.160788 | − | 0.160788i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −147178. | + | 147178.i | −0.210083 | + | 0.210083i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 114596. | 0.162797 | 0.0813985 | − | 0.996682i | \(-0.474061\pi\) | ||||
0.0813985 | + | 0.996682i | \(0.474061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 693627.i | − | 0.980696i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 144007. | + | 144007.i | 0.202642 | + | 0.202642i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −98332.0 | − | 98332.0i | −0.137715 | − | 0.137715i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 438256.i | − | 0.610887i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 110966. | 0.153949 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.08874e6 | + | 1.08874e6i | −1.50337 | + | 1.50337i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −79602.6 | + | 79602.6i | −0.109403 | + | 0.109403i | −0.759689 | − | 0.650286i | \(-0.774649\pi\) |
0.650286 | + | 0.759689i | \(0.274649\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −96610.5 | −0.132158 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 556304.i | 0.757444i | 0.925510 | + | 0.378722i | \(0.123636\pi\) | ||||
−0.925510 | + | 0.378722i | \(0.876364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 825505. | + | 825505.i | 1.11875 | + | 1.11875i | 0.991925 | + | 0.126825i | \(0.0404788\pi\) |
0.126825 | + | 0.991925i | \(0.459521\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −231131. | − | 231131.i | −0.311782 | − | 0.311782i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 800580.i | 1.07494i | 0.843284 | + | 0.537469i | \(0.180619\pi\) | ||||
−0.843284 | + | 0.537469i | \(0.819381\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −114046. | −0.152422 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 234158. | − | 234158.i | 0.311509 | − | 0.311509i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 315261. | − | 315261.i | 0.417475 | − | 0.417475i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 692941. | 0.913398 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 429949.i | 0.564143i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 258325. | + | 258325.i | 0.337403 | + | 0.337403i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 684224. | + | 684224.i | 0.889609 | + | 0.889609i | 0.994485 | − | 0.104876i | \(-0.0334445\pi\) |
−0.104876 | + | 0.994485i | \(0.533445\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 632048.i | 0.818036i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −995272. | −1.28230 | −0.641150 | − | 0.767415i | \(-0.721542\pi\) | ||||
−0.641150 | + | 0.767415i | \(0.721542\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 67491.2 | − | 67491.2i | 0.0865617 | − | 0.0865617i | −0.662500 | − | 0.749062i | \(-0.730505\pi\) |
0.749062 | + | 0.662500i | \(0.230505\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 50209.3 | − | 50209.3i | 0.0641058 | − | 0.0641058i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −180136. | −0.228957 | −0.114479 | − | 0.993426i | \(-0.536520\pi\) | ||||
−0.114479 | + | 0.993426i | \(0.536520\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.03902e6i | 1.31468i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5700.68 | − | 5700.68i | −0.00718078 | − | 0.00718078i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 152611. | + | 152611.i | 0.191374 | + | 0.191374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 265569.i | − | 0.331536i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 910976. | 1.13220 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23648.5 | − | 23648.5i | 0.0292607 | − | 0.0292607i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −730428. | + | 730428.i | −0.899763 | + | 0.899763i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 130371. | 0.159884 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 150271.i | 0.183475i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −893550. | − | 893550.i | −1.08619 | − | 1.08619i | −0.995917 | − | 0.0902686i | \(-0.971227\pi\) |
−0.0902686 | − | 0.995917i | \(-0.528773\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27068.1 | − | 27068.1i | −0.0327589 | − | 0.0327589i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 638798.i | − | 0.769709i | −0.922977 | − | 0.384855i | \(-0.874252\pi\) | ||
0.922977 | − | 0.384855i | \(-0.125748\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −228532. | −0.274160 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −67895.7 | + | 67895.7i | −0.0810961 | + | 0.0810961i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −873663. | + | 873663.i | −1.03898 | + | 1.03898i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.28409e6 | 1.52043 | 0.760213 | − | 0.649674i | \(-0.225095\pi\) | ||||
0.760213 | + | 0.649674i | \(0.225095\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 890380.i | − | 1.04968i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.40950e6 | − | 1.40950e6i | −1.65449 | − | 1.65449i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −853383. | − | 853383.i | −0.997380 | − | 0.997380i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 279110.i | 0.324800i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 198494. | 0.229994 | 0.114997 | − | 0.993366i | \(-0.463314\pi\) | ||||
0.114997 | + | 0.993366i | \(0.463314\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −69562.0 | + | 69562.0i | −0.0802551 | + | 0.0802551i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 367232. | − | 367232.i | 0.421869 | − | 0.421869i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 394235. | 0.450953 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 389175.i | 0.443267i | 0.975130 | + | 0.221634i | \(0.0711389\pi\) | ||||
−0.975130 | + | 0.221634i | \(0.928861\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36133.4 | + | 36133.4i | 0.0409805 | + | 0.0409805i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 481044. | + | 481044.i | 0.543257 | + | 0.543257i | 0.924482 | − | 0.381225i | \(-0.124498\pi\) |
−0.381225 | + | 0.924482i | \(0.624498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 963474.i | 1.08347i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 220404. | 0.246806 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −399574. | + | 399574.i | −0.445551 | + | 0.445551i | −0.893872 | − | 0.448321i | \(-0.852022\pi\) |
0.448321 | + | 0.893872i | \(0.352022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.46922e6 | − | 1.46922e6i | 1.63138 | − | 1.63138i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 66143.2 | 0.0731348 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.26137e6i | − | 1.38885i | −0.719564 | − | 0.694427i | \(-0.755658\pi\) | ||
0.719564 | − | 0.694427i | \(-0.244342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −132440. | − | 132440.i | −0.145215 | − | 0.145215i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −71311.5 | − | 71311.5i | −0.0778638 | − | 0.0778638i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 904620.i | − | 0.983624i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 841601. | 0.911296 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 150514. | − | 150514.i | 0.162302 | − | 0.162302i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −267883. | + | 267883.i | −0.287668 | + | 0.287668i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.50478e6 | −1.60924 | −0.804619 | − | 0.593791i | \(-0.797630\pi\) | ||||
−0.804619 | + | 0.593791i | \(0.797630\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 602143.i | 0.641286i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 818605. | + | 818605.i | 0.868233 | + | 0.868233i | 0.992277 | − | 0.124044i | \(-0.0395864\pi\) |
−0.124044 | + | 0.992277i | \(0.539586\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.14224e6 | − | 1.14224e6i | −1.20651 | − | 1.20651i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 714044.i | 0.751131i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 753210. | 0.789091 | 0.394545 | − | 0.918876i | \(-0.370902\pi\) | ||||
0.394545 | + | 0.918876i | \(0.370902\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −569995. | + | 569995.i | −0.594711 | + | 0.594711i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −168852. | + | 168852.i | −0.175456 | + | 0.175456i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 460098. | 0.476149 | 0.238075 | − | 0.971247i | \(-0.423484\pi\) | ||||
0.238075 | + | 0.971247i | \(0.423484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 96163.6i | 0.0991147i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −133453. | − | 133453.i | −0.136991 | − | 0.136991i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −271727. | − | 271727.i | −0.277806 | − | 0.277806i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.16135e6i | − | 1.18254i | −0.806472 | − | 0.591272i | \(-0.798626\pi\) | ||
0.806472 | − | 0.591272i | \(-0.201374\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −360899. | −0.366005 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 150147. | − | 150147.i | 0.151659 | − | 0.151659i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −271712. | + | 271712.i | −0.273349 | + | 0.273349i | −0.830447 | − | 0.557098i | \(-0.811915\pi\) |
0.557098 | + | 0.830447i | \(0.311915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.51220e6 | −1.51523 |
(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 | 128.5.f.a.95.5 | 14 | ||
4.3 | odd | 2 | 128.5.f.b.95.3 | 14 | |||
8.3 | odd | 2 | 16.5.f.a.3.4 | ✓ | 14 | ||
8.5 | even | 2 | 64.5.f.a.47.3 | 14 | |||
16.3 | odd | 4 | 64.5.f.a.15.3 | 14 | |||
16.5 | even | 4 | 128.5.f.b.31.3 | 14 | |||
16.11 | odd | 4 | inner | 128.5.f.a.31.5 | 14 | ||
16.13 | even | 4 | 16.5.f.a.11.4 | yes | 14 | ||
24.5 | odd | 2 | 576.5.m.a.559.3 | 14 | |||
24.11 | even | 2 | 144.5.m.a.19.4 | 14 | |||
48.29 | odd | 4 | 144.5.m.a.91.4 | 14 | |||
48.35 | even | 4 | 576.5.m.a.271.3 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.4 | ✓ | 14 | 8.3 | odd | 2 | ||
16.5.f.a.11.4 | yes | 14 | 16.13 | even | 4 | ||
64.5.f.a.15.3 | 14 | 16.3 | odd | 4 | |||
64.5.f.a.47.3 | 14 | 8.5 | even | 2 | |||
128.5.f.a.31.5 | 14 | 16.11 | odd | 4 | inner | ||
128.5.f.a.95.5 | 14 | 1.1 | even | 1 | trivial | ||
128.5.f.b.31.3 | 14 | 16.5 | even | 4 | |||
128.5.f.b.95.3 | 14 | 4.3 | odd | 2 | |||
144.5.m.a.19.4 | 14 | 24.11 | even | 2 | |||
144.5.m.a.91.4 | 14 | 48.29 | odd | 4 | |||
576.5.m.a.271.3 | 14 | 48.35 | even | 4 | |||
576.5.m.a.559.3 | 14 | 24.5 | odd | 2 |