Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,6,Mod(107,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([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("225.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.f (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: | \(36.0863594579\) |
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: | \( x^{20} + 19978x^{16} + 11248353x^{12} + 1386043201x^{8} + 1477627450x^{4} + 332150625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{29}\cdot 3^{24}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.8 | ||
Root | \(3.15495 - 3.15495i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.143 |
Dual form | 225.6.f.b.107.8 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.49760 | + | 3.49760i | 0.618294 | + | 0.618294i | 0.945094 | − | 0.326799i | \(-0.105970\pi\) |
−0.326799 | + | 0.945094i | \(0.605970\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 7.53358i | − | 0.235424i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.1207 | + | 24.1207i | −0.186056 | + | 0.186056i | −0.793989 | − | 0.607932i | \(-0.791999\pi\) |
0.607932 | + | 0.793989i | \(0.291999\pi\) | |||||||
\(8\) | 138.273 | − | 138.273i | 0.763856 | − | 0.763856i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 173.562i | 0.432487i | 0.976339 | + | 0.216244i | \(0.0693805\pi\) | ||||
−0.976339 | + | 0.216244i | \(0.930619\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −597.849 | − | 597.849i | −0.981145 | − | 0.981145i | 0.0186808 | − | 0.999825i | \(-0.494053\pi\) |
−0.999825 | + | 0.0186808i | \(0.994053\pi\) | |||||||
\(14\) | −168.729 | −0.230075 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 726.171 | 0.709151 | ||||||||
\(17\) | −734.740 | − | 734.740i | −0.616611 | − | 0.616611i | 0.328050 | − | 0.944661i | \(-0.393609\pi\) |
−0.944661 | + | 0.328050i | \(0.893609\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1622.15i | 1.03088i | 0.856927 | + | 0.515438i | \(0.172371\pi\) | ||||
−0.856927 | + | 0.515438i | \(0.827629\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −607.051 | + | 607.051i | −0.267404 | + | 0.267404i | ||||
\(23\) | 667.211 | − | 667.211i | 0.262993 | − | 0.262993i | −0.563276 | − | 0.826269i | \(-0.690459\pi\) |
0.826269 | + | 0.563276i | \(0.190459\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 4182.07i | − | 1.21327i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 181.715 | + | 181.715i | 0.0438022 | + | 0.0438022i | ||||
\(29\) | −3698.77 | −0.816700 | −0.408350 | − | 0.912825i | \(-0.633896\pi\) | ||||
−0.408350 | + | 0.912825i | \(0.633896\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9560.23 | −1.78675 | −0.893376 | − | 0.449310i | \(-0.851670\pi\) | ||||
−0.893376 | + | 0.449310i | \(0.851670\pi\) | |||||||
\(32\) | −1884.87 | − | 1884.87i | −0.325392 | − | 0.325392i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5139.65i | − | 0.762494i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5758.92 | − | 5758.92i | 0.691571 | − | 0.691571i | −0.271007 | − | 0.962577i | \(-0.587357\pi\) |
0.962577 | + | 0.271007i | \(0.0873565\pi\) | |||||||
\(38\) | −5673.62 | + | 5673.62i | −0.637385 | + | 0.637385i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 16087.5i | − | 1.49462i | −0.664477 | − | 0.747309i | \(-0.731346\pi\) | ||
0.664477 | − | 0.747309i | \(-0.268654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9780.29 | − | 9780.29i | −0.806641 | − | 0.806641i | 0.177483 | − | 0.984124i | \(-0.443205\pi\) |
−0.984124 | + | 0.177483i | \(0.943205\pi\) | |||||||
\(44\) | 1307.54 | 0.101818 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4667.28 | 0.325214 | ||||||||
\(47\) | −11110.0 | − | 11110.0i | −0.733615 | − | 0.733615i | 0.237719 | − | 0.971334i | \(-0.423600\pi\) |
−0.971334 | + | 0.237719i | \(0.923600\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15643.4i | 0.930766i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4503.94 | + | 4503.94i | −0.230985 | + | 0.230985i | ||||
\(53\) | −1013.67 | + | 1013.67i | −0.0495687 | + | 0.0495687i | −0.731457 | − | 0.681888i | \(-0.761159\pi\) |
0.681888 | + | 0.731457i | \(0.261159\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6670.46i | 0.284240i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12936.8 | − | 12936.8i | −0.504961 | − | 0.504961i | ||||
\(59\) | −46524.8 | −1.74002 | −0.870010 | − | 0.493035i | \(-0.835888\pi\) | ||||
−0.870010 | + | 0.493035i | \(0.835888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 52196.0 | 1.79602 | 0.898012 | − | 0.439971i | \(-0.145011\pi\) | ||||
0.898012 | + | 0.439971i | \(0.145011\pi\) | |||||||
\(62\) | −33437.9 | − | 33437.9i | −1.10474 | − | 1.10474i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 36422.5i | − | 1.11153i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31213.8 | − | 31213.8i | 0.849494 | − | 0.849494i | −0.140576 | − | 0.990070i | \(-0.544895\pi\) |
0.990070 | + | 0.140576i | \(0.0448954\pi\) | |||||||
\(68\) | −5535.22 | + | 5535.22i | −0.145165 | + | 0.145165i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 22440.4i | − | 0.528306i | −0.964481 | − | 0.264153i | \(-0.914908\pi\) | ||
0.964481 | − | 0.264153i | \(-0.0850924\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3589.53 | + | 3589.53i | 0.0788371 | + | 0.0788371i | 0.745426 | − | 0.666589i | \(-0.232246\pi\) |
−0.666589 | + | 0.745426i | \(0.732246\pi\) | |||||||
\(74\) | 40284.8 | 0.855189 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12220.6 | 0.242693 | ||||||||
\(77\) | −4186.44 | − | 4186.44i | −0.0804669 | − | 0.0804669i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 17531.6i | − | 0.316049i | −0.987435 | − | 0.158024i | \(-0.949488\pi\) | ||
0.987435 | − | 0.158024i | \(-0.0505125\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 56267.8 | − | 56267.8i | 0.924113 | − | 0.924113i | ||||
\(83\) | −71122.6 | + | 71122.6i | −1.13322 | + | 1.13322i | −0.143576 | + | 0.989639i | \(0.545860\pi\) |
−0.989639 | + | 0.143576i | \(0.954140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 68415.1i | − | 0.997483i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 23998.9 | + | 23998.9i | 0.330358 | + | 0.330358i | ||||
\(89\) | 48621.5 | 0.650659 | 0.325330 | − | 0.945601i | \(-0.394525\pi\) | ||||
0.325330 | + | 0.945601i | \(0.394525\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28841.0 | 0.365096 | ||||||||
\(92\) | −5026.49 | − | 5026.49i | −0.0619149 | − | 0.0619149i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 77716.5i | − | 0.907180i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7908.79 | − | 7908.79i | 0.0853455 | − | 0.0853455i | −0.663145 | − | 0.748491i | \(-0.730779\pi\) |
0.748491 | + | 0.663145i | \(0.230779\pi\) | |||||||
\(98\) | −54714.3 | + | 54714.3i | −0.575487 | + | 0.575487i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 69114.4i | 0.674163i | 0.941475 | + | 0.337082i | \(0.109440\pi\) | ||||
−0.941475 | + | 0.337082i | \(0.890560\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 66208.5 | + | 66208.5i | 0.614923 | + | 0.614923i | 0.944225 | − | 0.329302i | \(-0.106813\pi\) |
−0.329302 | + | 0.944225i | \(0.606813\pi\) | |||||||
\(104\) | −165332. | −1.49891 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7090.84 | −0.0612961 | ||||||||
\(107\) | −84771.5 | − | 84771.5i | −0.715798 | − | 0.715798i | 0.251944 | − | 0.967742i | \(-0.418930\pi\) |
−0.967742 | + | 0.251944i | \(0.918930\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 43319.2i | 0.349232i | 0.984637 | + | 0.174616i | \(0.0558685\pi\) | ||||
−0.984637 | + | 0.174616i | \(0.944132\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17515.7 | + | 17515.7i | −0.131942 | + | 0.131942i | ||||
\(113\) | 97783.2 | − | 97783.2i | 0.720391 | − | 0.720391i | −0.248294 | − | 0.968685i | \(-0.579870\pi\) |
0.968685 | + | 0.248294i | \(0.0798700\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 27865.0i | 0.192271i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −162725. | − | 162725.i | −1.07584 | − | 1.07584i | ||||
\(119\) | 35444.8 | 0.229449 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 130927. | 0.812955 | ||||||||
\(122\) | 182561. | + | 182561.i | 1.11047 | + | 1.11047i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 72022.8i | 0.420645i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −136748. | + | 136748.i | −0.752337 | + | 0.752337i | −0.974915 | − | 0.222578i | \(-0.928553\pi\) |
0.222578 | + | 0.974915i | \(0.428553\pi\) | |||||||
\(128\) | 67075.6 | − | 67075.6i | 0.361859 | − | 0.361859i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8932.22i | − | 0.0454759i | −0.999741 | − | 0.0227379i | \(-0.992762\pi\) | ||
0.999741 | − | 0.0227379i | \(-0.00723834\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −39127.3 | − | 39127.3i | −0.191801 | − | 0.191801i | ||||
\(134\) | 218347. | 1.05047 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −203189. | −0.942004 | ||||||||
\(137\) | −155119. | − | 155119.i | −0.706093 | − | 0.706093i | 0.259618 | − | 0.965711i | \(-0.416403\pi\) |
−0.965711 | + | 0.259618i | \(0.916403\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 148665.i | 0.652636i | 0.945260 | + | 0.326318i | \(0.105808\pi\) | ||||
−0.945260 | + | 0.326318i | \(0.894192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 78487.7 | − | 78487.7i | 0.326649 | − | 0.326649i | ||||
\(143\) | 103764. | − | 103764.i | 0.424332 | − | 0.424332i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 25109.5i | 0.0974890i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −43385.3 | − | 43385.3i | −0.162813 | − | 0.162813i | ||||
\(149\) | −168325. | −0.621130 | −0.310565 | − | 0.950552i | \(-0.600518\pi\) | ||||
−0.310565 | + | 0.950552i | \(0.600518\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −365709. | −1.30525 | −0.652625 | − | 0.757681i | \(-0.726332\pi\) | ||||
−0.652625 | + | 0.757681i | \(0.726332\pi\) | |||||||
\(152\) | 224299. | + | 224299.i | 0.787440 | + | 0.787440i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 29285.0i | − | 0.0995045i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −336039. | + | 336039.i | −1.08803 | + | 1.08803i | −0.0922993 | + | 0.995731i | \(0.529422\pi\) |
−0.995731 | + | 0.0922993i | \(0.970578\pi\) | |||||||
\(158\) | 61318.6 | − | 61318.6i | 0.195411 | − | 0.195411i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32187.2i | 0.0978629i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 425628. | + | 425628.i | 1.25476 | + | 1.25476i | 0.953561 | + | 0.301200i | \(0.0973873\pi\) |
0.301200 | + | 0.953561i | \(0.402613\pi\) | |||||||
\(164\) | −121197. | −0.351869 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −497517. | −1.40132 | ||||||||
\(167\) | 272794. | + | 272794.i | 0.756909 | + | 0.756909i | 0.975759 | − | 0.218849i | \(-0.0702303\pi\) |
−0.218849 | + | 0.975759i | \(0.570230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 343554.i | 0.925290i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −73680.6 | + | 73680.6i | −0.189903 | + | 0.189903i | ||||
\(173\) | 166817. | − | 166817.i | 0.423764 | − | 0.423764i | −0.462733 | − | 0.886498i | \(-0.653131\pi\) |
0.886498 | + | 0.462733i | \(0.153131\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 126036.i | 0.306699i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 170059. | + | 170059.i | 0.402299 | + | 0.402299i | ||||
\(179\) | 651990. | 1.52093 | 0.760463 | − | 0.649381i | \(-0.224972\pi\) | ||||
0.760463 | + | 0.649381i | \(0.224972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 247026. | 0.560461 | 0.280231 | − | 0.959933i | \(-0.409589\pi\) | ||||
0.280231 | + | 0.959933i | \(0.409589\pi\) | |||||||
\(182\) | 100874. | + | 100874.i | 0.225737 | + | 0.225737i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 184514.i | − | 0.401777i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 127523. | − | 127523.i | 0.266676 | − | 0.266676i | ||||
\(188\) | −83697.9 | + | 83697.9i | −0.172711 | + | 0.172711i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 63445.3i | 0.125839i | 0.998019 | + | 0.0629196i | \(0.0200412\pi\) | ||||
−0.998019 | + | 0.0629196i | \(0.979959\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −184478. | − | 184478.i | −0.356493 | − | 0.356493i | 0.506026 | − | 0.862518i | \(-0.331114\pi\) |
−0.862518 | + | 0.506026i | \(0.831114\pi\) | |||||||
\(194\) | 55323.6 | 0.105537 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 117851. | 0.219125 | ||||||||
\(197\) | 153826. | + | 153826.i | 0.282399 | + | 0.282399i | 0.834065 | − | 0.551666i | \(-0.186008\pi\) |
−0.551666 | + | 0.834065i | \(0.686008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 88348.0i | 0.158148i | 0.996869 | + | 0.0790740i | \(0.0251963\pi\) | ||||
−0.996869 | + | 0.0790740i | \(0.974804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −241734. | + | 241734.i | −0.416831 | + | 0.416831i | ||||
\(203\) | 89216.9 | − | 89216.9i | 0.151952 | − | 0.151952i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 463142.i | 0.760407i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −434140. | − | 434140.i | −0.695780 | − | 0.695780i | ||||
\(209\) | −281543. | −0.445840 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 220425. | 0.340843 | 0.170422 | − | 0.985371i | \(-0.445487\pi\) | ||||
0.170422 | + | 0.985371i | \(0.445487\pi\) | |||||||
\(212\) | 7636.57 | + | 7636.57i | 0.0116697 | + | 0.0116697i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 592994.i | − | 0.885147i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 230599. | − | 230599.i | 0.332436 | − | 0.332436i | ||||
\(218\) | −151513. | + | 151513.i | −0.215928 | + | 0.215928i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 878527.i | 1.20997i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 550351. | + | 550351.i | 0.741101 | + | 0.741101i | 0.972790 | − | 0.231689i | \(-0.0744252\pi\) |
−0.231689 | + | 0.972790i | \(0.574425\pi\) | |||||||
\(224\) | 90928.7 | 0.121082 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 684013. | 0.890827 | ||||||||
\(227\) | −32455.5 | − | 32455.5i | −0.0418045 | − | 0.0418045i | 0.685896 | − | 0.727700i | \(-0.259411\pi\) |
−0.727700 | + | 0.685896i | \(0.759411\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 389872.i | 0.491285i | 0.969360 | + | 0.245643i | \(0.0789990\pi\) | ||||
−0.969360 | + | 0.245643i | \(0.921001\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −511439. | + | 511439.i | −0.623841 | + | 0.623841i | ||||
\(233\) | 737801. | − | 737801.i | 0.890326 | − | 0.890326i | −0.104227 | − | 0.994554i | \(-0.533237\pi\) |
0.994554 | + | 0.104227i | \(0.0332369\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 350498.i | 0.409643i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 123972. | + | 123972.i | 0.141867 | + | 0.141867i | ||||
\(239\) | 367547. | 0.416216 | 0.208108 | − | 0.978106i | \(-0.433269\pi\) | ||||
0.208108 | + | 0.978106i | \(0.433269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.10156e6 | 1.22170 | 0.610850 | − | 0.791747i | \(-0.290828\pi\) | ||||
0.610850 | + | 0.791747i | \(0.290828\pi\) | |||||||
\(242\) | 457931. | + | 457931.i | 0.502645 | + | 0.502645i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 393222.i | − | 0.422828i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 969799. | − | 969799.i | 1.01144 | − | 1.01144i | ||||
\(248\) | −1.32192e6 | + | 1.32192e6i | −1.36482 | + | 1.36482i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.75554e6i | − | 1.75884i | −0.476049 | − | 0.879419i | \(-0.657932\pi\) | ||
0.476049 | − | 0.879419i | \(-0.342068\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 115803. | + | 115803.i | 0.113741 | + | 0.113741i | ||||
\(254\) | −956581. | −0.930331 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −696313. | −0.664056 | ||||||||
\(257\) | −1.38179e6 | − | 1.38179e6i | −1.30500 | − | 1.30500i | −0.924978 | − | 0.380020i | \(-0.875917\pi\) |
−0.380020 | − | 0.924978i | \(-0.624083\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 277818.i | 0.257342i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 31241.3 | − | 31241.3i | 0.0281175 | − | 0.0281175i | ||||
\(263\) | −504029. | + | 504029.i | −0.449330 | + | 0.449330i | −0.895132 | − | 0.445801i | \(-0.852919\pi\) |
0.445801 | + | 0.895132i | \(0.352919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 273703.i | − | 0.237179i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −235152. | − | 235152.i | −0.199992 | − | 0.199992i | ||||
\(269\) | 715977. | 0.603279 | 0.301640 | − | 0.953422i | \(-0.402466\pi\) | ||||
0.301640 | + | 0.953422i | \(0.402466\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.50875e6 | −1.24794 | −0.623969 | − | 0.781449i | \(-0.714481\pi\) | ||||
−0.623969 | + | 0.781449i | \(0.714481\pi\) | |||||||
\(272\) | −533547. | − | 533547.i | −0.437270 | − | 0.437270i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 1.08509e6i | − | 0.873147i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.19043e6 | − | 1.19043e6i | 0.932189 | − | 0.932189i | −0.0656538 | − | 0.997842i | \(-0.520913\pi\) |
0.997842 | + | 0.0656538i | \(0.0209133\pi\) | |||||||
\(278\) | −519970. | + | 519970.i | −0.403521 | + | 0.403521i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.32423e6i | − | 1.00045i | −0.865894 | − | 0.500227i | \(-0.833250\pi\) | ||
0.865894 | − | 0.500227i | \(-0.166750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13034.8 | − | 13034.8i | −0.00967472 | − | 0.00967472i | 0.702253 | − | 0.711928i | \(-0.252178\pi\) |
−0.711928 | + | 0.702253i | \(0.752178\pi\) | |||||||
\(284\) | −169057. | −0.124376 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 725849. | 0.524725 | ||||||||
\(287\) | 388042. | + | 388042.i | 0.278083 | + | 0.278083i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 340172.i | − | 0.239582i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 27042.0 | − | 27042.0i | 0.0185602 | − | 0.0185602i | ||||
\(293\) | 776691. | − | 776691.i | 0.528542 | − | 0.528542i | −0.391596 | − | 0.920137i | \(-0.628077\pi\) |
0.920137 | + | 0.391596i | \(0.128077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 1.59260e6i | − | 1.05652i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −588733. | − | 588733.i | −0.384041 | − | 0.384041i | ||||
\(299\) | −797783. | −0.516068 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 471814. | 0.300161 | ||||||||
\(302\) | −1.27910e6 | − | 1.27910e6i | −0.807028 | − | 0.807028i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.17796e6i | 0.731047i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −397374. | + | 397374.i | −0.240632 | + | 0.240632i | −0.817112 | − | 0.576479i | \(-0.804426\pi\) |
0.576479 | + | 0.817112i | \(0.304426\pi\) | |||||||
\(308\) | −31538.8 | + | 31538.8i | −0.0189439 | + | 0.0189439i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 726100.i | − | 0.425692i | −0.977086 | − | 0.212846i | \(-0.931727\pi\) | ||
0.977086 | − | 0.212846i | \(-0.0682732\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −971529. | − | 971529.i | −0.560525 | − | 0.560525i | 0.368931 | − | 0.929457i | \(-0.379724\pi\) |
−0.929457 | + | 0.368931i | \(0.879724\pi\) | |||||||
\(314\) | −2.35066e6 | −1.34545 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −132076. | −0.0744056 | ||||||||
\(317\) | −1.02045e6 | − | 1.02045e6i | −0.570352 | − | 0.570352i | 0.361875 | − | 0.932227i | \(-0.382137\pi\) |
−0.932227 | + | 0.361875i | \(0.882137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 641967.i | − | 0.353212i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −112578. | + | 112578.i | −0.0605081 | + | 0.0605081i | ||||
\(323\) | 1.19186e6 | − | 1.19186e6i | 0.635649 | − | 0.635649i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.97735e6i | 1.55162i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.22447e6 | − | 2.22447e6i | −1.14167 | − | 1.14167i | ||||
\(329\) | 535960. | 0.272988 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 640294. | 0.321225 | 0.160613 | − | 0.987018i | \(-0.448653\pi\) | ||||
0.160613 | + | 0.987018i | \(0.448653\pi\) | |||||||
\(332\) | 535808. | + | 535808.i | 0.266786 | + | 0.266786i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.90825e6i | 0.935986i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −891757. | + | 891757.i | −0.427732 | + | 0.427732i | −0.887855 | − | 0.460123i | \(-0.847805\pi\) |
0.460123 | + | 0.887855i | \(0.347805\pi\) | |||||||
\(338\) | −1.20161e6 | + | 1.20161e6i | −0.572102 | + | 0.572102i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.65929e6i | − | 0.772747i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −782725. | − | 782725.i | −0.359231 | − | 0.359231i | ||||
\(344\) | −2.70469e6 | −1.23232 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.16692e6 | 0.524022 | ||||||||
\(347\) | −2.35342e6 | − | 2.35342e6i | −1.04924 | − | 1.04924i | −0.998723 | − | 0.0505198i | \(-0.983912\pi\) |
−0.0505198 | − | 0.998723i | \(-0.516088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 781439.i | 0.343425i | 0.985147 | + | 0.171712i | \(0.0549299\pi\) | ||||
−0.985147 | + | 0.171712i | \(0.945070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 327142. | − | 327142.i | 0.140728 | − | 0.140728i | ||||
\(353\) | −1.35451e6 | + | 1.35451e6i | −0.578558 | + | 0.578558i | −0.934506 | − | 0.355948i | \(-0.884158\pi\) |
0.355948 | + | 0.934506i | \(0.384158\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 366294.i | − | 0.153181i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.28040e6 | + | 2.28040e6i | 0.940380 | + | 0.940380i | ||||
\(359\) | 3.10750e6 | 1.27255 | 0.636276 | − | 0.771461i | \(-0.280474\pi\) | ||||
0.636276 | + | 0.771461i | \(0.280474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −155264. | −0.0627049 | ||||||||
\(362\) | 863997. | + | 863997.i | 0.346530 | + | 0.346530i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 217276.i | − | 0.0859526i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.25930e6 | − | 1.25930e6i | 0.488050 | − | 0.488050i | −0.419640 | − | 0.907690i | \(-0.637844\pi\) |
0.907690 | + | 0.419640i | \(0.137844\pi\) | |||||||
\(368\) | 484509. | − | 484509.i | 0.186502 | − | 0.186502i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 48900.9i | − | 0.0184451i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 731112. | + | 731112.i | 0.272090 | + | 0.272090i | 0.829941 | − | 0.557851i | \(-0.188374\pi\) |
−0.557851 | + | 0.829941i | \(0.688374\pi\) | |||||||
\(374\) | 892049. | 0.329769 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.07241e6 | −1.12075 | ||||||||
\(377\) | 2.21131e6 | + | 2.21131e6i | 0.801301 | + | 0.801301i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.11660e6i | − | 1.47211i | −0.676921 | − | 0.736056i | \(-0.736686\pi\) | ||
0.676921 | − | 0.736056i | \(-0.263314\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −221906. | + | 221906.i | −0.0778057 | + | 0.0778057i | ||||
\(383\) | 998442. | − | 998442.i | 0.347797 | − | 0.347797i | −0.511491 | − | 0.859288i | \(-0.670907\pi\) |
0.859288 | + | 0.511491i | \(0.170907\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.29046e6i | − | 0.440835i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −59581.5 | − | 59581.5i | −0.0200924 | − | 0.0200924i | ||||
\(389\) | 1.81467e6 | 0.608027 | 0.304014 | − | 0.952668i | \(-0.401673\pi\) | ||||
0.304014 | + | 0.952668i | \(0.401673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −980454. | −0.324329 | ||||||||
\(392\) | 2.16305e6 | + | 2.16305e6i | 0.710971 | + | 0.710971i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.07604e6i | 0.349212i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −130258. | + | 130258.i | −0.0414789 | + | 0.0414789i | −0.727542 | − | 0.686063i | \(-0.759337\pi\) |
0.686063 | + | 0.727542i | \(0.259337\pi\) | |||||||
\(398\) | −309006. | + | 309006.i | −0.0977820 | + | 0.0977820i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.71814e6i | 0.533578i | 0.963755 | + | 0.266789i | \(0.0859626\pi\) | ||||
−0.963755 | + | 0.266789i | \(0.914037\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.71557e6 | + | 5.71557e6i | 1.75306 | + | 1.75306i | ||||
\(404\) | 520678. | 0.158714 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 624090. | 0.187902 | ||||||||
\(407\) | 999530. | + | 999530.i | 0.299095 | + | 0.299095i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.89387e6i | − | 0.855402i | −0.903920 | − | 0.427701i | \(-0.859324\pi\) | ||
0.903920 | − | 0.427701i | \(-0.140676\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 498787. | − | 498787.i | 0.144768 | − | 0.144768i | ||||
\(413\) | 1.12221e6 | − | 1.12221e6i | 0.323742 | − | 0.323742i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.25374e6i | 0.638513i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −984726. | − | 984726.i | −0.275661 | − | 0.275661i | ||||
\(419\) | −143217. | −0.0398527 | −0.0199264 | − | 0.999801i | \(-0.506343\pi\) | ||||
−0.0199264 | + | 0.999801i | \(0.506343\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.34045e6 | 0.368592 | 0.184296 | − | 0.982871i | \(-0.440999\pi\) | ||||
0.184296 | + | 0.982871i | \(0.440999\pi\) | |||||||
\(422\) | 770959. | + | 770959.i | 0.210742 | + | 0.210742i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 280326.i | 0.0757267i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.25900e6 | + | 1.25900e6i | −0.334162 | + | 0.334162i | ||||
\(428\) | −638633. | + | 638633.i | −0.168516 | + | 0.168516i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.72542e6i | 1.74392i | 0.489577 | + | 0.871960i | \(0.337151\pi\) | ||||
−0.489577 | + | 0.871960i | \(0.662849\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 493739. | + | 493739.i | 0.126555 | + | 0.126555i | 0.767547 | − | 0.640993i | \(-0.221477\pi\) |
−0.640993 | + | 0.767547i | \(0.721477\pi\) | |||||||
\(434\) | 1.61309e6 | 0.411087 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 326349. | 0.0822178 | ||||||||
\(437\) | 1.08232e6 | + | 1.08232e6i | 0.271113 | + | 0.271113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.03925e6i | 1.74327i | 0.490154 | + | 0.871636i | \(0.336941\pi\) | ||||
−0.490154 | + | 0.871636i | \(0.663059\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.07274e6 | + | 3.07274e6i | −0.748117 | + | 0.748117i | ||||
\(443\) | 1.43616e6 | − | 1.43616e6i | 0.347691 | − | 0.347691i | −0.511558 | − | 0.859249i | \(-0.670931\pi\) |
0.859249 | + | 0.511558i | \(0.170931\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.84981e6i | 0.916437i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 878536. | + | 878536.i | 0.206807 | + | 0.206807i | ||||
\(449\) | 3.63556e6 | 0.851052 | 0.425526 | − | 0.904946i | \(-0.360089\pi\) | ||||
0.425526 | + | 0.904946i | \(0.360089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.79219e6 | 0.646403 | ||||||||
\(452\) | −736657. | − | 736657.i | −0.169597 | − | 0.169597i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 227033.i | − | 0.0516950i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.72616e6 | − | 1.72616e6i | 0.386625 | − | 0.386625i | −0.486857 | − | 0.873482i | \(-0.661857\pi\) |
0.873482 | + | 0.486857i | \(0.161857\pi\) | |||||||
\(458\) | −1.36362e6 | + | 1.36362e6i | −0.303759 | + | 0.303759i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.59109e6i | − | 0.348693i | −0.984684 | − | 0.174347i | \(-0.944219\pi\) | ||
0.984684 | − | 0.174347i | \(-0.0557813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.66635e6 | − | 5.66635e6i | −1.22843 | − | 1.22843i | −0.964557 | − | 0.263874i | \(-0.915000\pi\) |
−0.263874 | − | 0.964557i | \(-0.585000\pi\) | |||||||
\(464\) | −2.68594e6 | −0.579164 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.16106e6 | 1.10097 | ||||||||
\(467\) | 2.14280e6 | + | 2.14280e6i | 0.454662 | + | 0.454662i | 0.896898 | − | 0.442237i | \(-0.145815\pi\) |
−0.442237 | + | 0.896898i | \(0.645815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.50580e6i | 0.316107i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.43310e6 | + | 6.43310e6i | −1.32912 | + | 1.32912i | ||||
\(473\) | 1.69749e6 | − | 1.69749e6i | 0.348862 | − | 0.348862i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 267027.i | − | 0.0540178i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.28553e6 | + | 1.28553e6i | 0.257344 | + | 0.257344i | ||||
\(479\) | −779790. | −0.155288 | −0.0776441 | − | 0.996981i | \(-0.524740\pi\) | ||||
−0.0776441 | + | 0.996981i | \(0.524740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.88593e6 | −1.35706 | ||||||||
\(482\) | 3.85281e6 | + | 3.85281e6i | 0.755370 | + | 0.755370i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 986350.i | − | 0.191389i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.11432e6 | + | 2.11432e6i | −0.403970 | + | 0.403970i | −0.879629 | − | 0.475659i | \(-0.842209\pi\) |
0.475659 | + | 0.879629i | \(0.342209\pi\) | |||||||
\(488\) | 7.21727e6 | − | 7.21727e6i | 1.37190 | − | 1.37190i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.20117e6i | 0.412049i | 0.978547 | + | 0.206025i | \(0.0660527\pi\) | ||||
−0.978547 | + | 0.206025i | \(0.933947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.71764e6 | + | 2.71764e6i | 0.503586 | + | 0.503586i | ||||
\(494\) | 6.78394e6 | 1.25073 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.94236e6 | −1.26708 | ||||||||
\(497\) | 541279. | + | 541279.i | 0.0982947 | + | 0.0982947i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 287378.i | 0.0516656i | 0.999666 | + | 0.0258328i | \(0.00822375\pi\) | ||||
−0.999666 | + | 0.0258328i | \(0.991776\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.14017e6 | − | 6.14017e6i | 1.08748 | − | 1.08748i | ||||
\(503\) | 734293. | − | 734293.i | 0.129405 | − | 0.129405i | −0.639438 | − | 0.768843i | \(-0.720833\pi\) |
0.768843 | + | 0.639438i | \(0.220833\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 810063.i | 0.140651i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.03020e6 | + | 1.03020e6i | 0.177118 | + | 0.177118i | ||||
\(509\) | −9.29537e6 | −1.59028 | −0.795138 | − | 0.606429i | \(-0.792601\pi\) | ||||
−0.795138 | + | 0.606429i | \(0.792601\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −173164. | −0.0293363 | ||||||||
\(512\) | −4.58184e6 | − | 4.58184e6i | −0.772441 | − | 0.772441i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 9.66591e6i | − | 1.61375i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.92827e6 | − | 1.92827e6i | 0.317279 | − | 0.317279i | ||||
\(518\) | −971697. | + | 971697.i | −0.159113 | + | 0.159113i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4.12354e6i | − | 0.665543i | −0.943008 | − | 0.332771i | \(-0.892016\pi\) | ||
0.943008 | − | 0.332771i | \(-0.107984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.87029e6 | − | 3.87029e6i | −0.618713 | − | 0.618713i | 0.326489 | − | 0.945201i | \(-0.394135\pi\) |
−0.945201 | + | 0.326489i | \(0.894135\pi\) | |||||||
\(524\) | −67291.6 | −0.0107061 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.52578e6 | −0.555637 | ||||||||
\(527\) | 7.02428e6 | + | 7.02428e6i | 1.10173 | + | 1.10173i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.54600e6i | 0.861670i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −294769. | + | 294769.i | −0.0451546 | + | 0.0451546i | ||||
\(533\) | −9.61792e6 | + | 9.61792e6i | −1.46644 | + | 1.46644i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 8.63204e6i | − | 1.29778i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.50420e6 | + | 2.50420e6i | 0.373004 | + | 0.373004i | ||||
\(539\) | −2.71510e6 | −0.402544 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.61255e6 | −1.11825 | −0.559123 | − | 0.829085i | \(-0.688862\pi\) | ||||
−0.559123 | + | 0.829085i | \(0.688862\pi\) | |||||||
\(542\) | −5.27699e6 | − | 5.27699e6i | −0.771593 | − | 0.771593i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.76978e6i | 0.401280i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.10895e6 | + | 8.10895e6i | −1.15877 | + | 1.15877i | −0.174027 | + | 0.984741i | \(0.555678\pi\) |
−0.984741 | + | 0.174027i | \(0.944322\pi\) | |||||||
\(548\) | −1.16860e6 | + | 1.16860e6i | −0.166232 | + | 0.166232i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 5.99996e6i | − | 0.841917i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 422874. | + | 422874.i | 0.0588029 | + | 0.0588029i | ||||
\(554\) | 8.32729e6 | 1.15273 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.11998e6 | 0.153646 | ||||||||
\(557\) | −7.99279e6 | − | 7.99279e6i | −1.09159 | − | 1.09159i | −0.995359 | − | 0.0962338i | \(-0.969320\pi\) |
−0.0962338 | − | 0.995359i | \(-0.530680\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.16943e7i | 1.58286i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.63163e6 | − | 4.63163e6i | 0.618576 | − | 0.618576i | ||||
\(563\) | 4.58626e6 | − | 4.58626e6i | 0.609801 | − | 0.609801i | −0.333093 | − | 0.942894i | \(-0.608092\pi\) |
0.942894 | + | 0.333093i | \(0.108092\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 91181.1i | − | 0.0119637i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.10290e6 | − | 3.10290e6i | −0.403550 | − | 0.403550i | ||||
\(569\) | −3.63459e6 | −0.470624 | −0.235312 | − | 0.971920i | \(-0.575611\pi\) | ||||
−0.235312 | + | 0.971920i | \(0.575611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.08250e6 | 0.395652 | 0.197826 | − | 0.980237i | \(-0.436612\pi\) | ||||
0.197826 | + | 0.980237i | \(0.436612\pi\) | |||||||
\(572\) | −781713. | − | 781713.i | −0.0998982 | − | 0.0998982i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.71443e6i | 0.343874i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.08704e6 | − | 3.08704e6i | 0.386014 | − | 0.386014i | −0.487249 | − | 0.873263i | \(-0.662000\pi\) |
0.873263 | + | 0.487249i | \(0.162000\pi\) | |||||||
\(578\) | 1.18979e6 | − | 1.18979e6i | 0.148132 | − | 0.148132i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 3.43105e6i | − | 0.421684i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −175935. | − | 175935.i | −0.0214378 | − | 0.0214378i | ||||
\(584\) | 992668. | 0.120440 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.43311e6 | 0.653589 | ||||||||
\(587\) | −635529. | − | 635529.i | −0.0761272 | − | 0.0761272i | 0.668018 | − | 0.744145i | \(-0.267143\pi\) |
−0.744145 | + | 0.668018i | \(0.767143\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.55081e7i | − | 1.84192i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.18196e6 | − | 4.18196e6i | 0.490428 | − | 0.490428i | ||||
\(593\) | −4.12654e6 | + | 4.12654e6i | −0.481892 | + | 0.481892i | −0.905735 | − | 0.423843i | \(-0.860681\pi\) |
0.423843 | + | 0.905735i | \(0.360681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.26809e6i | 0.146229i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.79033e6 | − | 2.79033e6i | −0.319082 | − | 0.319082i | ||||
\(599\) | −9.76542e6 | −1.11205 | −0.556025 | − | 0.831166i | \(-0.687674\pi\) | ||||
−0.556025 | + | 0.831166i | \(0.687674\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.09854e7 | 1.24059 | 0.620297 | − | 0.784367i | \(-0.287012\pi\) | ||||
0.620297 | + | 0.784367i | \(0.287012\pi\) | |||||||
\(602\) | 1.65022e6 | + | 1.65022e6i | 0.185588 | + | 0.185588i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.75510e6i | 0.307287i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.19843e6 | + | 3.19843e6i | −0.352343 | + | 0.352343i | −0.860981 | − | 0.508638i | \(-0.830149\pi\) |
0.508638 | + | 0.860981i | \(0.330149\pi\) | |||||||
\(608\) | 3.05754e6 | − | 3.05754e6i | 0.335438 | − | 0.335438i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.32842e7i | 1.43957i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.58934e6 | − | 7.58934e6i | −0.815742 | − | 0.815742i | 0.169746 | − | 0.985488i | \(-0.445705\pi\) |
−0.985488 | + | 0.169746i | \(0.945705\pi\) | |||||||
\(614\) | −2.77971e6 | −0.297563 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.15774e6 | −0.122930 | ||||||||
\(617\) | −7.77526e6 | − | 7.77526e6i | −0.822247 | − | 0.822247i | 0.164183 | − | 0.986430i | \(-0.447501\pi\) |
−0.986430 | + | 0.164183i | \(0.947501\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8.12168e6i | − | 0.851960i | −0.904733 | − | 0.425980i | \(-0.859929\pi\) | ||
0.904733 | − | 0.425980i | \(-0.140071\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.53961e6 | − | 2.53961e6i | 0.263203 | − | 0.263203i | ||||
\(623\) | −1.17278e6 | + | 1.17278e6i | −0.121059 | + | 0.121059i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 6.79604e6i | − | 0.693139i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.53158e6 | + | 2.53158e6i | 0.256149 | + | 0.256149i | ||||
\(629\) | −8.46262e6 | −0.852860 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.96100e6 | 0.695983 | 0.347991 | − | 0.937498i | \(-0.386864\pi\) | ||||
0.347991 | + | 0.937498i | \(0.386864\pi\) | |||||||
\(632\) | −2.42414e6 | − | 2.42414e6i | −0.241416 | − | 0.241416i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 7.13824e6i | − | 0.705291i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.35238e6 | − | 9.35238e6i | 0.913216 | − | 0.913216i | ||||
\(638\) | 2.24534e6 | − | 2.24534e6i | 0.218389 | − | 0.218389i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 2.95734e6i | − | 0.284286i | −0.989846 | − | 0.142143i | \(-0.954601\pi\) | ||
0.989846 | − | 0.142143i | \(-0.0453993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.84906e6 | − | 6.84906e6i | −0.653287 | − | 0.653287i | 0.300496 | − | 0.953783i | \(-0.402848\pi\) |
−0.953783 | + | 0.300496i | \(0.902848\pi\) | |||||||
\(644\) | 242485. | 0.0230393 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.33728e6 | 0.786037 | ||||||||
\(647\) | −7.70791e6 | − | 7.70791e6i | −0.723896 | − | 0.723896i | 0.245501 | − | 0.969396i | \(-0.421048\pi\) |
−0.969396 | + | 0.245501i | \(0.921048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.07493e6i | − | 0.752536i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.20650e6 | − | 3.20650e6i | 0.295401 | − | 0.295401i | ||||
\(653\) | −1.24415e7 | + | 1.24415e7i | −1.14180 | + | 1.14180i | −0.153682 | + | 0.988120i | \(0.549113\pi\) |
−0.988120 | + | 0.153682i | \(0.950887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.16823e7i | − | 1.05991i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.87457e6 | + | 1.87457e6i | 0.168787 | + | 0.168787i | ||||
\(659\) | 2.14806e7 | 1.92679 | 0.963393 | − | 0.268092i | \(-0.0863933\pi\) | ||||
0.963393 | + | 0.268092i | \(0.0863933\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.56548e6 | 0.673493 | 0.336746 | − | 0.941595i | \(-0.390673\pi\) | ||||
0.336746 | + | 0.941595i | \(0.390673\pi\) | |||||||
\(662\) | 2.23949e6 | + | 2.23949e6i | 0.198612 | + | 0.198612i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.96686e7i | 1.73123i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.46786e6 | + | 2.46786e6i | −0.214786 | + | 0.214786i | ||||
\(668\) | 2.05512e6 | − | 2.05512e6i | 0.178195 | − | 0.178195i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.05924e6i | 0.776757i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.45146e7 | + | 1.45146e7i | 1.23529 | + | 1.23529i | 0.961906 | + | 0.273381i | \(0.0881420\pi\) |
0.273381 | + | 0.961906i | \(0.411858\pi\) | |||||||
\(674\) | −6.23802e6 | −0.528929 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.58819e6 | 0.217836 | ||||||||
\(677\) | 6.19483e6 | + | 6.19483e6i | 0.519467 | + | 0.519467i | 0.917410 | − | 0.397943i | \(-0.130276\pi\) |
−0.397943 | + | 0.917410i | \(0.630276\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 381531.i | 0.0317581i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.80355e6 | − | 5.80355e6i | 0.477785 | − | 0.477785i | ||||
\(683\) | −1.43009e7 | + | 1.43009e7i | −1.17303 | + | 1.17303i | −0.191550 | + | 0.981483i | \(0.561351\pi\) |
−0.981483 | + | 0.191550i | \(0.938649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 5.47532e6i | − | 0.444221i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.10216e6 | − | 7.10216e6i | −0.572031 | − | 0.572031i | ||||
\(689\) | 1.21204e6 | 0.0972682 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.62663e6 | −0.129596 | −0.0647982 | − | 0.997898i | \(-0.520640\pi\) | ||||
−0.0647982 | + | 0.997898i | \(0.520640\pi\) | |||||||
\(692\) | −1.25673e6 | − | 1.25673e6i | −0.0997644 | − | 0.0997644i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1.64627e7i | − | 1.29748i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.18202e7 | + | 1.18202e7i | −0.921597 | + | 0.921597i | ||||
\(698\) | −2.73316e6 | + | 2.73316e6i | −0.212337 | + | 0.212337i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.74205e6i | 0.287617i | 0.989606 | + | 0.143809i | \(0.0459350\pi\) | ||||
−0.989606 | + | 0.143809i | \(0.954065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.34182e6 | + | 9.34182e6i | 0.712924 | + | 0.712924i | ||||
\(704\) | 6.32157e6 | 0.480721 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.47510e6 | −0.715438 | ||||||||
\(707\) | −1.66709e6 | − | 1.66709e6i | −0.125432 | − | 0.125432i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 288785.i | − | 0.0215754i | −0.999942 | − | 0.0107877i | \(-0.996566\pi\) | ||
0.999942 | − | 0.0107877i | \(-0.00343389\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.72303e6 | − | 6.72303e6i | 0.497010 | − | 0.497010i | ||||
\(713\) | −6.37870e6 | + | 6.37870e6i | −0.469903 | + | 0.469903i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 4.91181e6i | − | 0.358063i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.08688e7 | + | 1.08688e7i | 0.786812 | + | 0.786812i | ||||
\(719\) | −2.55140e7 | −1.84059 | −0.920294 | − | 0.391228i | \(-0.872050\pi\) | ||||
−0.920294 | + | 0.391228i | \(0.872050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.19399e6 | −0.228821 | ||||||||
\(722\) | −543050. | − | 543050.i | −0.0387701 | − | 0.0387701i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 1.86099e6i | − | 0.131946i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.35802e7 | − | 1.35802e7i | 0.952949 | − | 0.952949i | −0.0459929 | − | 0.998942i | \(-0.514645\pi\) |
0.998942 | + | 0.0459929i | \(0.0146452\pi\) | |||||||
\(728\) | 3.98793e6 | − | 3.98793e6i | 0.278881 | − | 0.278881i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.43719e7i | 0.994768i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.25323e6 | − | 9.25323e6i | −0.636111 | − | 0.636111i | 0.313483 | − | 0.949594i | \(-0.398504\pi\) |
−0.949594 | + | 0.313483i | \(0.898504\pi\) | |||||||
\(734\) | 8.80907e6 | 0.603517 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.51521e6 | −0.171151 | ||||||||
\(737\) | 5.41754e6 | + | 5.41754e6i | 0.367395 | + | 0.367395i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.43488e7i | − | 0.966503i | −0.875482 | − | 0.483251i | \(-0.839456\pi\) | ||
0.875482 | − | 0.483251i | \(-0.160544\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 171036. | − | 171036.i | 0.0114045 | − | 0.0114045i | ||||
\(743\) | 1.33920e7 | − | 1.33920e7i | 0.889966 | − | 0.889966i | −0.104553 | − | 0.994519i | \(-0.533341\pi\) |
0.994519 | + | 0.104553i | \(0.0333413\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.11428e6i | 0.336463i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −960704. | − | 960704.i | −0.0627821 | − | 0.0627821i | ||||
\(749\) | 4.08949e6 | 0.266357 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.51119e7 | −0.977729 | −0.488865 | − | 0.872360i | \(-0.662589\pi\) | ||||
−0.488865 | + | 0.872360i | \(0.662589\pi\) | |||||||
\(752\) | −8.06774e6 | − | 8.06774e6i | −0.520244 | − | 0.520244i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.54685e7i | 0.990880i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.61045e7 | + | 1.61045e7i | −1.02143 | + | 1.02143i | −0.0216614 | + | 0.999765i | \(0.506896\pi\) |
−0.999765 | + | 0.0216614i | \(0.993104\pi\) | |||||||
\(758\) | 1.43982e7 | − | 1.43982e7i | 0.910198 | − | 0.910198i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.01897e7i | − | 1.26377i | −0.775061 | − | 0.631886i | \(-0.782281\pi\) | ||
0.775061 | − | 0.631886i | \(-0.217719\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.04489e6 | − | 1.04489e6i | −0.0649769 | − | 0.0649769i | ||||
\(764\) | 477970. | 0.0296256 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.98430e6 | 0.430082 | ||||||||
\(767\) | 2.78148e7 | + | 2.78148e7i | 1.70721 | + | 1.70721i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.14899e6i | 0.374963i | 0.982268 | + | 0.187481i | \(0.0600324\pi\) | ||||
−0.982268 | + | 0.187481i | \(0.939968\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.38978e6 | + | 1.38978e6i | −0.0839270 | + | 0.0839270i | ||||
\(773\) | 5.16075e6 | − | 5.16075e6i | 0.310645 | − | 0.310645i | −0.534515 | − | 0.845159i | \(-0.679506\pi\) |
0.845159 | + | 0.534515i | \(0.179506\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 2.18714e6i | − | 0.130383i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.34698e6 | + | 6.34698e6i | 0.375940 | + | 0.375940i | ||||
\(779\) | 2.60964e7 | 1.54076 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.89481e6 | 0.228486 | ||||||||
\(782\) | −3.42924e6 | − | 3.42924e6i | −0.200530 | − | 0.200530i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.13598e7i | 0.660054i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.01433e7 | + | 2.01433e7i | −1.15929 | + | 1.15929i | −0.174666 | + | 0.984628i | \(0.555884\pi\) |
−0.984628 | + | 0.174666i | \(0.944116\pi\) | |||||||
\(788\) | 1.15886e6 | − | 1.15886e6i | 0.0664836 | − | 0.0664836i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.71719e6i | 0.268066i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.12053e7 | − | 3.12053e7i | −1.76216 | − | 1.76216i | ||||
\(794\) | −911180. | −0.0512924 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 665576. | 0.0372319 | ||||||||
\(797\) | −1.26474e7 | − | 1.26474e7i | −0.705268 | − | 0.705268i | 0.260269 | − | 0.965536i | \(-0.416189\pi\) |
−0.965536 | + | 0.260269i | \(0.916189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.63259e7i | 0.904711i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.00937e6 | + | 6.00937e6i | −0.329908 | + | 0.329908i | ||||
\(803\) | −623006. | + | 623006.i | −0.0340960 | + | 0.0340960i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.99816e7i | 2.16782i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.55663e6 | + | 9.55663e6i | 0.514963 | + | 0.514963i | ||||
\(809\) | −2.22055e7 | −1.19286 | −0.596428 | − | 0.802666i | \(-0.703414\pi\) | ||||
−0.596428 | + | 0.802666i | \(0.703414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.63199e7 | −0.871297 | −0.435648 | − | 0.900117i | \(-0.643481\pi\) | ||||
−0.435648 | + | 0.900117i | \(0.643481\pi\) | |||||||
\(812\) | −672123. | − | 672123.i | −0.0357733 | − | 0.0357733i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.99191e6i | 0.369858i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.58651e7 | − | 1.58651e7i | 0.831547 | − | 0.831547i | ||||
\(818\) | 1.01216e7 | − | 1.01216e7i | 0.528890 | − | 0.528890i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.30178e7i | − | 0.674030i | −0.941499 | − | 0.337015i | \(-0.890583\pi\) | ||
0.941499 | − | 0.337015i | \(-0.109417\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.21922e6 | − | 1.21922e6i | −0.0627457 | − | 0.0627457i | 0.675038 | − | 0.737783i | \(-0.264127\pi\) |
−0.737783 | + | 0.675038i | \(0.764127\pi\) | |||||||
\(824\) | 1.83097e7 | 0.939425 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.85008e6 | 0.400335 | ||||||||
\(827\) | 1.43495e7 | + | 1.43495e7i | 0.729578 | + | 0.729578i | 0.970536 | − | 0.240957i | \(-0.0774614\pi\) |
−0.240957 | + | 0.970536i | \(0.577461\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.26744e7i | 0.640530i | 0.947328 | + | 0.320265i | \(0.103772\pi\) | ||||
−0.947328 | + | 0.320265i | \(0.896228\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.17752e7 | + | 2.17752e7i | −1.09057 | + | 1.09057i | ||||
\(833\) | 1.14938e7 | − | 1.14938e7i | 0.573921 | − | 0.573921i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.12103e6i | 0.104962i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −500914. | − | 500914.i | −0.0246407 | − | 0.0246407i | ||||
\(839\) | −2.29844e7 | −1.12727 | −0.563636 | − | 0.826023i | \(-0.690598\pi\) | ||||
−0.563636 | + | 0.826023i | \(0.690598\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.83023e6 | −0.333001 | ||||||||
\(842\) | 4.68837e6 | + | 4.68837e6i | 0.227898 | + | 0.227898i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 1.66059e6i | − | 0.0802428i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.15805e6 | + | 3.15805e6i | −0.151255 | + | 0.151255i | ||||
\(848\) | −736099. | + | 736099.i | −0.0351517 | + | 0.0351517i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 7.68483e6i | − | 0.363756i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.90959e6 | + | 7.90959e6i | 0.372204 | + | 0.372204i | 0.868280 | − | 0.496075i | \(-0.165226\pi\) |
−0.496075 | + | 0.868280i | \(0.665226\pi\) | |||||||
\(854\) | −8.80697e6 | −0.413221 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.34432e7 | −1.09353 | ||||||||
\(857\) | −4.10620e6 | − | 4.10620e6i | −0.190980 | − | 0.190980i | 0.605139 | − | 0.796120i | \(-0.293117\pi\) |
−0.796120 | + | 0.605139i | \(0.793117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 8.04118e6i | − | 0.371824i | −0.982566 | − | 0.185912i | \(-0.940476\pi\) | ||
0.982566 | − | 0.185912i | \(-0.0595239\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.35228e7 | + | 2.35228e7i | −1.07826 | + | 1.07826i | ||||
\(863\) | 7.70658e6 | − | 7.70658e6i | 0.352237 | − | 0.352237i | −0.508704 | − | 0.860941i | \(-0.669875\pi\) |
0.860941 | + | 0.508704i | \(0.169875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.45380e6i | 0.156496i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.73724e6 | − | 1.73724e6i | −0.0782636 | − | 0.0782636i | ||||
\(869\) | 3.04282e6 | 0.136687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.73223e7 | −1.66695 | ||||||||
\(872\) | 5.98986e6 | + | 5.98986e6i | 0.266763 | + | 0.266763i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.57101e6i | 0.335255i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.59846e7 | − | 2.59846e7i | 1.14082 | − | 1.14082i | 0.152521 | − | 0.988300i | \(-0.451261\pi\) |
0.988300 | − | 0.152521i | \(-0.0487393\pi\) | |||||||
\(878\) | −2.46205e7 | + | 2.46205e7i | −1.07786 | + | 1.07786i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.62840e7i | 1.14091i | 0.821329 | + | 0.570455i | \(0.193233\pi\) | ||||
−0.821329 | + | 0.570455i | \(0.806767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.82514e7 | + | 2.82514e7i | 1.21938 | + | 1.21938i | 0.967850 | + | 0.251530i | \(0.0809336\pi\) |
0.251530 | + | 0.967850i | \(0.419066\pi\) | |||||||
\(884\) | 6.61845e6 | 0.284856 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.00462e7 | 0.429951 | ||||||||
\(887\) | 3.11073e7 | + | 3.11073e7i | 1.32756 | + | 1.32756i | 0.907496 | + | 0.420061i | \(0.137991\pi\) |
0.420061 | + | 0.907496i | \(0.362009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.59692e6i | − | 0.279954i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.14611e6 | − | 4.14611e6i | 0.174473 | − | 0.174473i | ||||
\(893\) | 1.80220e7 | − | 1.80220e7i | 0.756266 | − | 0.756266i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.23582e6i | 0.134652i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.27158e7 | + | 1.27158e7i | 0.526201 | + | 0.526201i | ||||
\(899\) | 3.53611e7 | 1.45924 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.48957e6 | 0.0611292 | ||||||||
\(902\) | 9.76595e6 | + | 9.76595e6i | 0.399667 | + | 0.399667i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.70415e7i | − | 1.10055i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.56307e7 | + | 1.56307e7i | −0.630900 | + | 0.630900i | −0.948294 | − | 0.317393i | \(-0.897192\pi\) |
0.317393 | + | 0.948294i | \(0.397192\pi\) | |||||||
\(908\) | −244506. | + | 244506.i | −0.00984181 | + | 0.00984181i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.64166e7i | − | 0.655371i | −0.944787 | − | 0.327685i | \(-0.893731\pi\) | ||
0.944787 | − | 0.327685i | \(-0.106269\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.23442e7 | − | 1.23442e7i | −0.490101 | − | 0.490101i | ||||
\(914\) | 1.20748e7 | 0.478096 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.93713e6 | 0.115661 | ||||||||
\(917\) | 215451. | + | 215451.i | 0.00846108 | + | 0.00846108i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 6.26477e6i | − | 0.244690i | −0.992488 | − | 0.122345i | \(-0.960959\pi\) | ||
0.992488 | − | 0.122345i | \(-0.0390414\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.56501e6 | − | 5.56501e6i | 0.215595 | − | 0.215595i | ||||
\(923\) | −1.34160e7 | + | 1.34160e7i | −0.518345 | + | 0.518345i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 3.96372e7i | − | 1.51906i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.97171e6 | + | 6.97171e6i | 0.265748 | + | 0.265748i | ||||
\(929\) | 2.18132e7 | 0.829241 | 0.414620 | − | 0.909995i | \(-0.363914\pi\) | ||||
0.414620 | + | 0.909995i | \(0.363914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.53759e7 | −0.959504 | ||||||||
\(932\) | −5.55828e6 | − | 5.55828e6i | −0.209604 | − | 0.209604i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.49893e7i | 0.562230i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.22575e7 | − | 1.22575e7i | 0.456093 | − | 0.456093i | −0.441277 | − | 0.897371i | \(-0.645475\pi\) |
0.897371 | + | 0.441277i | \(0.145475\pi\) | |||||||
\(938\) | −5.26668e6 | + | 5.26668e6i | −0.195447 | + | 0.195447i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.86115e7i | 0.685183i | 0.939484 | + | 0.342592i | \(0.111305\pi\) | ||||
−0.939484 | + | 0.342592i | \(0.888695\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.07338e7 | − | 1.07338e7i | −0.393074 | − | 0.393074i | ||||
\(944\) | −3.37849e7 | −1.23394 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.18743e7 | 0.431399 | ||||||||
\(947\) | −1.15031e7 | − | 1.15031e7i | −0.416811 | − | 0.416811i | 0.467292 | − | 0.884103i | \(-0.345230\pi\) |
−0.884103 | + | 0.467292i | \(0.845230\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.29199e6i | − | 0.154701i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.90105e6 | − | 4.90105e6i | 0.175266 | − | 0.175266i | ||||
\(953\) | −2.82233e7 | + | 2.82233e7i | −1.00664 | + | 1.00664i | −0.00666540 | + | 0.999978i | \(0.502122\pi\) |
−0.999978 | + | 0.00666540i | \(0.997878\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 2.76895e6i | − | 0.0979873i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.72739e6 | − | 2.72739e6i | −0.0960138 | − | 0.0960138i | ||||
\(959\) | 7.48313e6 | 0.262746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.27689e7 | 2.19248 | ||||||||
\(962\) | −2.40842e7 | − | 2.40842e7i | −0.839064 | − | 0.839064i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 8.29866e6i | − | 0.287618i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.24829e7 | − | 2.24829e7i | 0.773191 | − | 0.773191i | −0.205472 | − | 0.978663i | \(-0.565873\pi\) |
0.978663 | + | 0.205472i | \(0.0658729\pi\) | |||||||
\(968\) | 1.81037e7 | − | 1.81037e7i | 0.620980 | − | 0.620980i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.49863e7i | 1.19083i | 0.803418 | + | 0.595416i | \(0.203013\pi\) | ||||
−0.803418 | + | 0.595416i | \(0.796987\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.58590e6 | − | 3.58590e6i | −0.121427 | − | 0.121427i | ||||
\(974\) | −1.47901e7 | −0.499545 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.79032e7 | 1.27365 | ||||||||
\(977\) | −1.51625e7 | − | 1.51625e7i | −0.508200 | − | 0.508200i | 0.405774 | − | 0.913974i | \(-0.367002\pi\) |
−0.913974 | + | 0.405774i | \(0.867002\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.43886e6i | 0.281402i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.69880e6 | + | 7.69880e6i | −0.254768 | + | 0.254768i | ||||
\(983\) | 1.33195e7 | − | 1.33195e7i | 0.439648 | − | 0.439648i | −0.452245 | − | 0.891894i | \(-0.649377\pi\) |
0.891894 | + | 0.452245i | \(0.149377\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.90104e7i | 0.622729i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.30606e6 | − | 7.30606e6i | −0.238117 | − | 0.238117i | ||||
\(989\) | −1.30510e7 | −0.424282 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.61948e6 | 0.181766 | 0.0908829 | − | 0.995862i | \(-0.471031\pi\) | ||||
0.0908829 | + | 0.995862i | \(0.471031\pi\) | |||||||
\(992\) | 1.80198e7 | + | 1.80198e7i | 0.581394 | + | 0.581394i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.78635e6i | 0.121550i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.08932e6 | + | 7.08932e6i | −0.225874 | + | 0.225874i | −0.810967 | − | 0.585092i | \(-0.801058\pi\) |
0.585092 | + | 0.810967i | \(0.301058\pi\) | |||||||
\(998\) | −1.00513e6 | + | 1.00513e6i | −0.0319446 | + | 0.0319446i | ||||
\(999\) | 0 | 0 |
(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 | 225.6.f.b.143.8 | 20 | ||
3.2 | odd | 2 | inner | 225.6.f.b.143.3 | 20 | ||
5.2 | odd | 4 | inner | 225.6.f.b.107.3 | 20 | ||
5.3 | odd | 4 | 45.6.f.a.17.8 | yes | 20 | ||
5.4 | even | 2 | 45.6.f.a.8.3 | ✓ | 20 | ||
15.2 | even | 4 | inner | 225.6.f.b.107.8 | 20 | ||
15.8 | even | 4 | 45.6.f.a.17.3 | yes | 20 | ||
15.14 | odd | 2 | 45.6.f.a.8.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.6.f.a.8.3 | ✓ | 20 | 5.4 | even | 2 | ||
45.6.f.a.8.8 | yes | 20 | 15.14 | odd | 2 | ||
45.6.f.a.17.3 | yes | 20 | 15.8 | even | 4 | ||
45.6.f.a.17.8 | yes | 20 | 5.3 | odd | 4 | ||
225.6.f.b.107.3 | 20 | 5.2 | odd | 4 | inner | ||
225.6.f.b.107.8 | 20 | 15.2 | even | 4 | inner | ||
225.6.f.b.143.3 | 20 | 3.2 | odd | 2 | inner | ||
225.6.f.b.143.8 | 20 | 1.1 | even | 1 | trivial |