Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(81,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.81");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.d (of order \(2\), degree \(1\), 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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{90}\cdot 3^{4}\cdot 5^{12} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 81.10 | ||
Root | \(-2.63430 + 3.01006i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.81 |
Dual form | 160.6.d.a.81.11 |
$q$-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 \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 6.67450i | − 0.428169i | −0.976815 | − | 0.214085i | \(-0.931323\pi\) | ||||
0.976815 | − | 0.214085i | \(-0.0686769\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 25.0000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 38.2812 | 0.295284 | 0.147642 | − | 0.989041i | \(-0.452832\pi\) | ||||
0.147642 | + | 0.989041i | \(0.452832\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 198.451 | 0.816671 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 491.486i | − 1.22470i | −0.790587 | − | 0.612349i | \(-0.790225\pi\) | ||||
0.790587 | − | 0.612349i | \(-0.209775\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 956.299i | 1.56941i | 0.619872 | + | 0.784703i | \(0.287185\pi\) | ||||
−0.619872 | + | 0.784703i | \(0.712815\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −166.863 | −0.191483 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 339.725 | 0.285105 | 0.142553 | − | 0.989787i | \(-0.454469\pi\) | ||||
0.142553 | + | 0.989787i | \(0.454469\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1862.39i | − 1.18355i | −0.806104 | − | 0.591774i | \(-0.798428\pi\) | ||||
0.806104 | − | 0.591774i | \(-0.201572\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 255.508i | − 0.126432i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1991.10 | 0.784825 | 0.392412 | − | 0.919789i | \(-0.371641\pi\) | ||||
0.392412 | + | 0.919789i | \(0.371641\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2946.47i | − 0.777843i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3573.66i | − 0.789076i | −0.918880 | − | 0.394538i | \(-0.870905\pi\) | ||||
0.918880 | − | 0.394538i | \(-0.129095\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7710.17 | −1.44099 | −0.720493 | − | 0.693462i | \(-0.756085\pi\) | ||||
−0.720493 | + | 0.693462i | \(0.756085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3280.42 | −0.524379 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 957.029i | − 0.132055i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2835.87i | − 0.340551i | −0.985397 | − | 0.170275i | \(-0.945534\pi\) | ||||
0.985397 | − | 0.170275i | \(-0.0544657\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6382.82 | 0.671972 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10681.6 | 0.992373 | 0.496187 | − | 0.868216i | \(-0.334733\pi\) | ||||
0.496187 | + | 0.868216i | \(0.334733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 20581.0i | − 1.69744i | −0.528841 | − | 0.848721i | \(-0.677373\pi\) | ||||
0.528841 | − | 0.848721i | \(-0.322627\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 4961.28i | − 0.365226i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 756.983 | 0.0499852 | 0.0249926 | − | 0.999688i | \(-0.492044\pi\) | ||||
0.0249926 | + | 0.999688i | \(0.492044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15341.6 | −0.912807 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 2267.49i | − 0.122073i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 31628.2i | − 1.54662i | −0.634025 | − | 0.773312i | \(-0.718599\pi\) | ||||
0.634025 | − | 0.773312i | \(-0.281401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12287.1 | −0.547702 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12430.5 | −0.506759 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4914.36i | 0.183796i | 0.995768 | + | 0.0918981i | \(0.0292934\pi\) | ||||
−0.995768 | + | 0.0918981i | \(0.970707\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 21422.9i | − 0.737147i | −0.929599 | − | 0.368573i | \(-0.879846\pi\) | ||||
0.929599 | − | 0.368573i | \(-0.120154\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7596.94 | 0.241150 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23907.5 | 0.701860 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6818.32i | − 0.185563i | −0.995687 | − | 0.0927813i | \(-0.970424\pi\) | ||||
0.995687 | − | 0.0927813i | \(-0.0295758\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 13289.6i | − 0.336038i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11134.9 | 0.262143 | 0.131072 | − | 0.991373i | \(-0.458158\pi\) | ||||
0.131072 | + | 0.991373i | \(0.458158\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7305.98 | 0.160462 | 0.0802308 | − | 0.996776i | \(-0.474434\pi\) | ||||
0.0802308 | + | 0.996776i | \(0.474434\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4171.56i | 0.0856339i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 18814.6i | − 0.361634i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23560.4 | 0.424732 | 0.212366 | − | 0.977190i | \(-0.431883\pi\) | ||||
0.212366 | + | 0.977190i | \(0.431883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 28557.4 | 0.483622 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 23708.5i | 0.377754i | 0.982001 | + | 0.188877i | \(0.0604848\pi\) | ||||
−0.982001 | + | 0.188877i | \(0.939515\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 8493.12i | − 0.127503i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −23852.4 | −0.337858 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −125652. | −1.68149 | −0.840746 | − | 0.541429i | \(-0.817883\pi\) | ||||
−0.840746 | + | 0.541429i | \(0.817883\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 36608.2i | 0.463421i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 51461.6i | 0.616986i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −46559.7 | −0.529299 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 126994. | 1.37042 | 0.685212 | − | 0.728344i | \(-0.259710\pi\) | ||||
0.685212 | + | 0.728344i | \(0.259710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 97535.9i | − 1.00018i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 128800.i | 1.25635i | 0.778070 | + | 0.628177i | \(0.216199\pi\) | ||||
−0.778070 | + | 0.628177i | \(0.783801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 70343.6 | 0.653328 | 0.326664 | − | 0.945140i | \(-0.394075\pi\) | ||||
0.326664 | + | 0.945140i | \(0.394075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6387.69 | −0.0565419 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 90073.6i | 0.760568i | 0.924870 | + | 0.380284i | \(0.124174\pi\) | ||||
−0.924870 | + | 0.380284i | \(0.875826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 176201.i | 1.42051i | 0.703947 | + | 0.710253i | \(0.251419\pi\) | ||||
−0.703947 | + | 0.710253i | \(0.748581\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18928.0 | −0.145813 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5466.04 | −0.0402695 | −0.0201348 | − | 0.999797i | \(-0.506410\pi\) | ||||
−0.0201348 | + | 0.999797i | \(0.506410\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 49777.4i | − 0.350984i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 189779.i | 1.28169i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13005.1 | 0.0841870 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −80507.4 | −0.499888 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 71294.1i | − 0.424904i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −273870. | −1.50673 | −0.753364 | − | 0.657603i | \(-0.771570\pi\) | ||||
−0.753364 | + | 0.657603i | \(0.771570\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −137368. | −0.726793 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 131830.i | 0.671175i | 0.942009 | + | 0.335588i | \(0.108935\pi\) | ||||
−0.942009 | + | 0.335588i | \(0.891065\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 71294.3i | − 0.349483i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −73661.6 | −0.347862 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 385733. | 1.75584 | 0.877922 | − | 0.478804i | \(-0.158929\pi\) | ||||
0.877922 | + | 0.478804i | \(0.158929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 445530.i | 1.95587i | 0.208910 | + | 0.977935i | \(0.433008\pi\) | ||||
−0.208910 | + | 0.977935i | \(0.566992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 5052.48i | − 0.0214021i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 470008. | 1.92205 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −89341.6 | −0.352885 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 102397.i | 0.390836i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 125864.i | − 0.464448i | −0.972662 | − | 0.232224i | \(-0.925400\pi\) | ||||
0.972662 | − | 0.232224i | \(-0.0746003\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 449332. | 1.60371 | 0.801853 | − | 0.597522i | \(-0.203848\pi\) | ||||
0.801853 | + | 0.597522i | \(0.203848\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 67418.8 | 0.232837 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 192754.i | 0.644429i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 475430.i | − 1.53935i | −0.638436 | − | 0.769675i | \(-0.720418\pi\) | ||||
0.638436 | − | 0.769675i | \(-0.279582\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −211102. | −0.662217 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 76221.5 | 0.231746 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 210514.i | 0.620602i | 0.950638 | + | 0.310301i | \(0.100430\pi\) | ||||
−0.950638 | + | 0.310301i | \(0.899570\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 82010.6i | 0.234509i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −366778. | −1.01768 | −0.508842 | − | 0.860860i | \(-0.669926\pi\) | ||||
−0.508842 | + | 0.860860i | \(0.669926\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −543215. | −1.46304 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 369593.i | − 0.966569i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 242252.i | 0.615393i | 0.951485 | + | 0.307697i | \(0.0995582\pi\) | ||||
−0.951485 | + | 0.307697i | \(0.900442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23925.7 | −0.0590568 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32800.9 | 0.0786959 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 587964.i | − 1.37157i | −0.727804 | − | 0.685785i | \(-0.759459\pi\) | ||||
0.727804 | − | 0.685785i | \(-0.240541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 429244.i | − 0.973885i | −0.873434 | − | 0.486942i | \(-0.838112\pi\) | ||||
0.873434 | − | 0.486942i | \(-0.161888\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −142987. | −0.315624 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −70896.7 | −0.152299 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 166970.i | − 0.349168i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 112794.i | − 0.229685i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 271725. | 0.538947 | 0.269473 | − | 0.963008i | \(-0.413150\pi\) | ||||
0.269473 | + | 0.963008i | \(0.413150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 871451. | 1.68403 | 0.842015 | − | 0.539454i | \(-0.181369\pi\) | ||||
0.842015 | + | 0.539454i | \(0.181369\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 159570.i | − 0.300515i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 207994.i | 0.381844i | 0.981605 | + | 0.190922i | \(0.0611477\pi\) | ||||
−0.981605 | + | 0.190922i | \(0.938852\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −669523. | −1.19849 | −0.599243 | − | 0.800567i | \(-0.704532\pi\) | ||||
−0.599243 | + | 0.800567i | \(0.704532\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −45508.9 | −0.0794523 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 136804.i | − 0.233001i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 267039.i | − 0.443803i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 395135. | 0.640944 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −915337. | −1.44949 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 617471.i | − 0.954796i | −0.878687 | − | 0.477398i | \(-0.841580\pi\) | ||||
0.878687 | − | 0.477398i | \(-0.158420\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 74319.6i | − 0.112242i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −514525. | −0.759119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −295154. | −0.425500 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 48763.7i | − 0.0687047i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 324879.i | 0.447446i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 800666. | 1.07817 | 0.539087 | − | 0.842250i | \(-0.318769\pi\) | ||||
0.539087 | + | 0.842250i | \(0.318769\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −124032. | −0.163334 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 936259.i | − 1.20596i | −0.797758 | − | 0.602978i | \(-0.793981\pi\) | ||||
0.797758 | − | 0.602978i | \(-0.206019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 541008.i | − 0.681735i | −0.940111 | − | 0.340867i | \(-0.889279\pi\) | ||||
0.940111 | − | 0.340867i | \(-0.110721\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −125578. | −0.154841 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 550428. | 0.664218 | 0.332109 | − | 0.943241i | \(-0.392240\pi\) | ||||
0.332109 | + | 0.943241i | \(0.392240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 18924.6i | − 0.0223541i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 157254.i | − 0.181857i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.17782e6 | −1.33378 | −0.666889 | − | 0.745157i | \(-0.732374\pi\) | ||||
−0.666889 | + | 0.745157i | \(0.732374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 998860. | 1.10780 | 0.553901 | − | 0.832583i | \(-0.313139\pi\) | ||||
0.553901 | + | 0.832583i | \(0.313139\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 906598.i | − 0.984915i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 383539.i | 0.408220i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.78100e6 | 1.85747 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 158243. | 0.161743 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.05232e6i | 1.05430i | 0.849773 | + | 0.527149i | \(0.176739\pi\) | ||||
−0.849773 | + | 0.527149i | \(0.823261\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 978596.i | − 0.961174i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −56687.4 | −0.0545929 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −416435. | −0.393292 | −0.196646 | − | 0.980475i | \(-0.563005\pi\) | ||||
−0.196646 | + | 0.980475i | \(0.563005\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 108560.i | − 0.100559i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 709197.i | − 0.644415i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.05502e6 | 0.940528 | 0.470264 | − | 0.882526i | \(-0.344159\pi\) | ||||
0.470264 | + | 0.882526i | \(0.344159\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −790705. | −0.691672 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 838665.i | 0.719964i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.73328e6i | 1.46045i | 0.683206 | + | 0.730226i | \(0.260585\pi\) | ||||
−0.683206 | + | 0.730226i | \(0.739415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.32031e6 | −1.09208 | −0.546039 | − | 0.837760i | \(-0.683865\pi\) | ||||
−0.546039 | + | 0.837760i | \(0.683865\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 244342. | 0.198423 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 307179.i | 0.244940i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5852.67i | − 0.00458305i | −0.999997 | − | 0.00229153i | \(-0.999271\pi\) | ||||
0.999997 | − | 0.00229153i | \(-0.000729416\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.53009e6 | −1.17681 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.46507e6 | 1.10686 | 0.553432 | − | 0.832895i | \(-0.313318\pi\) | ||||
0.553432 | + | 0.832895i | \(0.313318\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.97541e6i | 1.46619i | 0.680124 | + | 0.733097i | \(0.261926\pi\) | ||||
−0.680124 | + | 0.733097i | \(0.738074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 310763.i | 0.226630i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 408903. | 0.293032 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.30444e6 | −0.918715 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 847623.i | − 0.586774i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.38276e6i | 0.940976i | 0.882406 | + | 0.470488i | \(0.155922\pi\) | ||||
−0.882406 | + | 0.470488i | \(0.844078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 122859. | 0.0821962 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.44815e6 | −0.952623 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.90408e6i | 1.23171i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 787864.i | − 0.501228i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 859675. | 0.537933 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −535573. | −0.329662 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 54523.5i | − 0.0330170i | −0.999864 | − | 0.0165085i | \(-0.994745\pi\) | ||||
0.999864 | − | 0.0165085i | \(-0.00525506\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 469508.i | − 0.279735i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.07373e6 | 0.629499 | 0.314749 | − | 0.949175i | \(-0.398079\pi\) | ||||
0.314749 | + | 0.949175i | \(0.398079\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.70724e6 | 1.56195 | 0.780973 | − | 0.624565i | \(-0.214724\pi\) | ||||
0.780973 | + | 0.624565i | \(0.214724\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 189923.i | − 0.107846i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.52062e6i | 0.849908i | 0.905215 | + | 0.424954i | \(0.139710\pi\) | ||||
−0.905215 | + | 0.424954i | \(0.860290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.75641e6 | −0.966380 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 601196. | 0.325652 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 632699.i | − 0.337436i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 597687.i | − 0.313881i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.17606e6 | 0.608217 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 28978.2 | 0.0147598 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.31163e6i | 1.66139i | 0.556729 | + | 0.830694i | \(0.312056\pi\) | ||||
−0.556729 | + | 0.830694i | \(0.687944\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 562781.i | − 0.278118i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −170458. | −0.0829861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.65162e6 | −1.27185 | −0.635927 | − | 0.771749i | \(-0.719382\pi\) | ||||
−0.635927 | + | 0.771749i | \(0.719382\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36483.1i | 0.0172422i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.78944e6i | 1.76477i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.23068e6 | −0.564821 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −332239. | −0.150281 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.89737e6i | 1.29175i | 0.763441 | + | 0.645877i | \(0.223508\pi\) | ||||
−0.763441 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.23263e6i | − 0.541713i | −0.962620 | − | 0.270856i | \(-0.912693\pi\) | ||||
0.962620 | − | 0.270856i | \(-0.0873068\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.81770e6 | 1.22075 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 145202. | 0.0620207 | 0.0310103 | − | 0.999519i | \(-0.490128\pi\) | ||||
0.0310103 | + | 0.999519i | \(0.490128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 278372.i | − 0.117234i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 86802.3i | − 0.0360463i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.97212e6 | −0.807600 | −0.403800 | − | 0.914847i | \(-0.632311\pi\) | ||||
−0.403800 | + | 0.914847i | \(0.632311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −992386. | −0.400786 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 537347.i | 0.214037i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 182649.i | − 0.0717606i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −371055. | −0.143805 | −0.0719024 | − | 0.997412i | \(-0.522907\pi\) | ||||
−0.0719024 | + | 0.997412i | \(0.522907\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.11977e6 | 0.810443 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.21076e6i | − 0.456694i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 586109.i | − 0.218125i | −0.994035 | − | 0.109063i | \(-0.965215\pi\) | ||||
0.994035 | − | 0.109063i | \(-0.0347849\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 104289. | 0.0382966 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.41749e6 | 1.23838 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.93721e6i | − 0.692752i | −0.938096 | − | 0.346376i | \(-0.887412\pi\) | ||||
0.938096 | − | 0.346376i | \(-0.112588\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.82794e6i | 0.645135i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 162691. | 0.0566716 | 0.0283358 | − | 0.999598i | \(-0.490979\pi\) | ||||
0.0283358 | + | 0.999598i | \(0.490979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −470366. | −0.161728 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4.08432e6i | − 1.38625i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.24326e6i | 0.751633i | 0.926694 | + | 0.375817i | \(0.122638\pi\) | ||||
−0.926694 | + | 0.375817i | \(0.877362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 676425. | 0.223758 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 879899. | 0.287377 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 589010.i | − 0.189946i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.64851e6i | 0.524947i | 0.964939 | + | 0.262474i | \(0.0845383\pi\) | ||||
−0.964939 | + | 0.262474i | \(0.915462\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −475854. | −0.149638 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.96862e6 | −0.921921 | −0.460960 | − | 0.887421i | \(-0.652495\pi\) | ||||
−0.460960 | + | 0.887421i | \(0.652495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 7.37323e6i | − 2.26149i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 713936.i | − 0.216283i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.39379e6 | −0.417072 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.21238e6 | −0.653962 | −0.326981 | − | 0.945031i | \(-0.606031\pi\) | ||||
−0.326981 | + | 0.945031i | \(0.606031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.57458e6i | − 0.751799i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 188127.i | 0.0542721i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 592713. | 0.168937 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.97369e6 | 0.837444 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.61133e6i | 0.726653i | 0.931662 | + | 0.363327i | \(0.118359\pi\) | ||||
−0.931662 | + | 0.363327i | \(0.881641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 3.16116e6i | − 0.869242i | −0.900614 | − | 0.434621i | \(-0.856882\pi\) | ||||
0.900614 | − | 0.434621i | \(-0.143118\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 150224. | 0.0408214 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −212328. | −0.0570210 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 820094.i | − 0.217668i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3.13707e6i | − 0.822963i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.00949e6 | −0.261764 | −0.130882 | − | 0.991398i | \(-0.541781\pi\) | ||||
−0.130882 | + | 0.991398i | \(0.541781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 741789. | 0.190134 | 0.0950672 | − | 0.995471i | \(-0.469693\pi\) | ||||
0.0950672 | + | 0.995471i | \(0.469693\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 596310.i | 0.151095i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.70819e6i | − 0.928878i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.40195e6 | 1.09014 | 0.545071 | − | 0.838390i | \(-0.316503\pi\) | ||||
0.545071 | + | 0.838390i | \(0.316503\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.04455e6 | −0.745463 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.17840e6i | 1.73788i | 0.494922 | + | 0.868938i | \(0.335197\pi\) | ||||
−0.494922 | + | 0.868938i | \(0.664803\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.14130e6i | 0.751986i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −840082. | −0.198863 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.08371e6 | 0.253686 | 0.126843 | − | 0.991923i | \(-0.459516\pi\) | ||||
0.126843 | + | 0.991923i | \(0.459516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 5.24984e6i | − 1.21536i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 2.99906e6i | − 0.686658i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 915206. | 0.207248 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.76573e6 | 0.395487 | 0.197744 | − | 0.980254i | \(-0.436639\pi\) | ||||
0.197744 | + | 0.980254i | \(0.436639\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.00099e6i | − 0.221767i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 7.82078e6i | − 1.71395i | −0.515359 | − | 0.856975i | \(-0.672341\pi\) | ||||
0.515359 | − | 0.856975i | \(-0.327659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.93389e6 | −0.852844 | −0.426422 | − | 0.904524i | \(-0.640226\pi\) | ||||
−0.426422 | + | 0.904524i | \(0.640226\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.28654e6 | 0.275925 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.58189e6i | 0.335648i | 0.985817 | + | 0.167824i | \(0.0536740\pi\) | ||||
−0.985817 | + | 0.167824i | \(0.946326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 261013.i | − 0.0547937i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.17326e6 | −0.659102 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.01153e7 | −2.07886 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.16399e6i | 0.236710i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 6.27665e6i | − 1.26308i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.28209e6 | 1.05188 | 0.525941 | − | 0.850521i | \(-0.323713\pi\) | ||||
0.525941 | + | 0.850521i | \(0.323713\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.71194e6 | 0.534463 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 508740.i | − 0.0992266i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 3.17486e6i | − 0.612872i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.18631e6 | −1.18198 | −0.590989 | − | 0.806680i | \(-0.701262\pi\) | ||||
−0.590989 | + | 0.806680i | \(0.701262\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.40508e6 | 0.265723 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.31222e6i | 1.55601i | 0.628256 | + | 0.778007i | \(0.283769\pi\) | ||||
−0.628256 | + | 0.778007i | \(0.716231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.21406e6i | − 0.224970i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.43840e6 | −0.447292 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 426255. | 0.0774068 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 9.46854e6i | − 1.70228i | −0.524936 | − | 0.851142i | \(-0.675911\pi\) | ||||
0.524936 | − | 0.851142i | \(-0.324089\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.44806e6i | 0.435741i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.15769e6 | 1.26140 | 0.630700 | − | 0.776027i | \(-0.282768\pi\) | ||||
0.630700 | + | 0.776027i | \(0.282768\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.22000e6 | 0.561859 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.62569e6i | 0.626427i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.08667e6i | 0.185910i | 0.995670 | + | 0.0929551i | \(0.0296313\pi\) | ||||
−0.995670 | + | 0.0929551i | \(0.970369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 279681. | 0.0473817 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.48746e6 | −0.920614 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1.75859e6i | − 0.292177i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 372046.i | − 0.0612168i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.61691e6 | 0.263493 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.39810e6 | 0.709856 | 0.354928 | − | 0.934894i | \(-0.384505\pi\) | ||||
0.354928 | + | 0.934894i | \(0.384505\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.66013e6i | − 0.265392i | −0.991157 | − | 0.132696i | \(-0.957637\pi\) | ||||
0.991157 | − | 0.132696i | \(-0.0423634\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 159692.i | 0.0252863i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.61934e6 | −0.410833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.47188e6 | −0.384050 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 975259.i | 0.150101i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.02148e7i | 1.55744i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.25184e6 | 0.340136 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.92436e6 | −0.587264 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.54016e6i | 1.11791i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.71821e6i | 0.986872i | 0.869782 | + | 0.493436i | \(0.164259\pi\) | ||||
−0.869782 | + | 0.493436i | \(0.835741\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.86499e6 | −0.416988 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.40503e6 | 0.635270 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 6.46880e6i | − 0.924391i | −0.886778 | − | 0.462195i | \(-0.847062\pi\) | ||||
0.886778 | − | 0.462195i | \(-0.152938\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4.25140e6i | − 0.602006i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.65554e6 | −0.933909 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 901919. | 0.125416 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 473200.i | 0.0652097i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.40656e7i | 1.92097i | 0.278325 | + | 0.960487i | \(0.410221\pi\) | ||||
−0.278325 | + | 0.960487i | \(0.589779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.96816e7 | 2.66398 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.11444e6 | −0.149503 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.70453e6i | 0.891451i | 0.895170 | + | 0.445726i | \(0.147054\pi\) | ||||
−0.895170 | + | 0.445726i | \(0.852946\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 136651.i | 0.0180091i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.09321e6 | 0.142806 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.42220e6 | 1.09055 | 0.545274 | − | 0.838258i | \(-0.316426\pi\) | ||||
0.545274 | + | 0.838258i | \(0.316426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 5.62974e6i | − 0.722600i | −0.932450 | − | 0.361300i | \(-0.882333\pi\) | ||||
0.932450 | − | 0.361300i | \(-0.117667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.81363e6i | − 0.230760i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.24444e6 | −0.156965 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.49266e6 | 0.811864 | 0.405932 | − | 0.913903i | \(-0.366947\pi\) | ||||
0.405932 | + | 0.913903i | \(0.366947\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 5.81650e6i | − 0.721050i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 907590.i | 0.111545i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.55448e7 | −1.89415 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.74446e6 | 0.573189 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.45770e6i | 0.414183i | 0.978322 | + | 0.207091i | \(0.0663997\pi\) | ||||
−0.978322 | + | 0.207091i | \(0.933600\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.43593e7i | 1.70548i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.38826e6 | 0.163494 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.86898e6 | −0.451815 | −0.225907 | − | 0.974149i | \(-0.572535\pi\) | ||||
−0.225907 | + | 0.974149i | \(0.572535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 325127.i | − 0.0376496i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.46873e6i | 0.513155i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.06771e6 | 0.690967 | 0.345484 | − | 0.938425i | \(-0.387715\pi\) | ||||
0.345484 | + | 0.938425i | \(0.387715\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.05369e6 | −0.683651 | −0.341825 | − | 0.939764i | \(-0.611045\pi\) | ||||
−0.341825 | + | 0.939764i | \(0.611045\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.35310e6i | − 0.151544i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.01268e6i | 0.223557i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.04959e6 | −0.335946 | −0.167973 | − | 0.985792i | \(-0.553722\pi\) | ||||
−0.167973 | + | 0.985792i | \(0.553722\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −913098. | −0.0997641 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 723902.i | 0.0784471i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.56693e6i | 0.813333i | 0.913577 | + | 0.406667i | \(0.133309\pi\) | ||||
−0.913577 | + | 0.406667i | \(0.866691\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.78235e6 | −0.190023 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.31124e6 | −0.667424 | −0.333712 | − | 0.942675i | \(-0.608301\pi\) | ||||
−0.333712 | + | 0.942675i | \(0.608301\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.15260e7i | 1.20907i | 0.796578 | + | 0.604536i | \(0.206641\pi\) | ||||
−0.796578 | + | 0.604536i | \(0.793359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 5.86670e6i | − 0.610470i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.81011e6 | −0.496518 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.10942e6i | 0.620627i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 963416.i | − 0.0970928i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.69301e6 | −0.369238 | −0.184619 | − | 0.982810i | \(-0.559105\pi\) | ||||
−0.184619 | + | 0.982810i | \(0.559105\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.12131e6 | −0.408814 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.84675e6i | 0.673829i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.46711e7i | − 1.43257i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.20972e6 | 0.214085 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.48129e6 | −0.623040 | −0.311520 | − | 0.950240i | \(-0.600838\pi\) | ||||
−0.311520 | + | 0.950240i | \(0.600838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.12433e7i | 1.07243i | 0.844082 | + | 0.536214i | \(0.180146\pi\) | ||||
−0.844082 | + | 0.536214i | \(0.819854\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.43419e6i | 0.325032i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.65936e6 | 0.813252 | 0.406626 | − | 0.913595i | \(-0.366705\pi\) | ||||
0.406626 | + | 0.913595i | \(0.366705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.41534e6 | 0.225095 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.97001e6i | 0.182186i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.20375e6i | − 0.110473i | −0.998473 | − | 0.0552363i | \(-0.982409\pi\) | ||||
0.998473 | − | 0.0552363i | \(-0.0175912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.29575e6 | 0.300159 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.44988e6 | 0.131044 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.18525e6i | 0.285713i | 0.989743 | + | 0.142856i | \(0.0456287\pi\) | ||||
−0.989743 | + | 0.142856i | \(0.954371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.59534e6i | 0.320064i | 0.987112 | + | 0.160032i | \(0.0511597\pi\) | ||||
−0.987112 | + | 0.160032i | \(0.948840\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.16840e6 | 0.191583 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.78236e6 | −0.156293 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.11551e6i | − 0.619286i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 5.34404e6i | − 0.461641i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.05291e7 | −0.902783 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.21823e6 | −0.444105 | −0.222053 | − | 0.975035i | \(-0.571276\pi\) | ||||
−0.222053 | + | 0.975035i | \(0.571276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.84154e6i | 0.155569i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.86028e6i | − 0.155994i | −0.996954 | − | 0.0779969i | \(-0.975148\pi\) | ||||
0.996954 | − | 0.0779969i | \(-0.0248524\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.86149e6 | 0.404664 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.24906e6 | −0.516353 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.83940e7i | − 1.50877i | −0.656431 | − | 0.754386i | \(-0.727935\pi\) | ||||
0.656431 | − | 0.754386i | \(-0.272065\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 9.64334e6i | − 0.785237i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.61096e6 | −0.291898 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.02460e7 | 2.42728 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.52732e6i | 0.759059i | 0.925180 | + | 0.379530i | \(0.123914\pi\) | ||||
−0.925180 | + | 0.379530i | \(0.876086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3.73379e6i | − 0.295336i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.11382e7 | 0.874692 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.62879e6 | 0.282931 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 3.67383e6i | − 0.284398i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.81247e6i | 0.754194i | 0.926174 | + | 0.377097i | \(0.123078\pi\) | ||||
−0.926174 | + | 0.377097i | \(0.876922\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.28149e6 | −0.403058 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −126312. | −0.00957132 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.93061e6i | 0.370981i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.65549e7i | − 1.23683i | −0.785851 | − | 0.618415i | \(-0.787775\pi\) | ||||
0.785851 | − | 0.618415i | \(-0.212225\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.67558e6 | 0.346866 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.53517e7 | −1.13092 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.17502e7i | − 0.859567i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.86134e6i | 0.571083i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.40579e7 | −1.01414 | −0.507070 | − | 0.861905i | \(-0.669271\pi\) | ||||
−0.507070 | + | 0.861905i | \(0.669271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.69283e6 | 0.192917 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.66689e6i | − 0.474327i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.23354e6i | 0.157815i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.78648e6 | 0.125361 | 0.0626806 | − | 0.998034i | \(-0.480035\pi\) | ||||
0.0626806 | + | 0.998034i | \(0.480035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 888368. | 0.0619119 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 6.99187e6i | − 0.483950i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.59012e7i | − 1.09313i | −0.837418 | − | 0.546563i | \(-0.815936\pi\) | ||||
0.837418 | − | 0.546563i | \(-0.184064\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.55993e6 | 0.174787 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.35111e6 | −0.227258 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 5.89659e6i | − 0.397182i | −0.980082 | − | 0.198591i | \(-0.936363\pi\) | ||||
0.980082 | − | 0.198591i | \(-0.0636366\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.18873e7i | − 0.795311i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.21545e6 | 0.147228 | 0.0736139 | − | 0.997287i | \(-0.476547\pi\) | ||||
0.0736139 | + | 0.997287i | \(0.476547\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.14661e6 | −0.207708 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.70498e6i | 0.308501i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.44812e6i | 0.224583i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.69953e7 | 1.09959 | 0.549793 | − | 0.835301i | \(-0.314706\pi\) | ||||
0.549793 | + | 0.835301i | \(0.314706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.02370e6 | 0.451418 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.12333e7i | − 0.717199i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.05028e6i | 0.320314i | 0.987092 | + | 0.160157i | \(0.0512001\pi\) | ||||
−0.987092 | + | 0.160157i | \(0.948800\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.53164e6 | −0.411545 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.21656e7 | 0.761506 | 0.380753 | − | 0.924677i | \(-0.375665\pi\) | ||||
0.380753 | + | 0.924677i | \(0.375665\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.74519e6i | 0.419453i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.68547e6i | − 0.104128i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.69960e6 | −0.288451 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.61059e6 | −0.159193 | −0.0795964 | − | 0.996827i | \(-0.525363\pi\) | ||||
−0.0795964 | + | 0.996827i | \(0.525363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.77950e6i | 0.168396i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.34970e7i | − 0.812434i | −0.913777 | − | 0.406217i | \(-0.866848\pi\) | ||||
0.913777 | − | 0.406217i | \(-0.133152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.81886e6 | 0.288197 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −724586. | −0.0430564 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.98932e7i | − 1.17452i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 5.47263e6i | − 0.321047i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.05297e7 | −0.613777 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.18857e7 | −0.688418 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.13703e6i | − 0.122991i | −0.998107 | − | 0.0614956i | \(-0.980413\pi\) | ||||
0.998107 | − | 0.0614956i | \(-0.0195870\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 7.04174e6i | − 0.402705i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −209246. | −0.0118909 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.04867e7 | 1.15688 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.27756e6i | 0.296153i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.73479e7i | − 1.52503i | −0.646969 | − | 0.762516i | \(-0.723964\pi\) | ||||
0.646969 | − | 0.762516i | \(-0.276036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 257166. | 0.0142510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.49358e7 | −1.37323 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.59078e6i | − 0.196517i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.90554e6i | − 0.103640i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.15688e7 | 0.625321 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.30041e6 | 0.499609 | 0.249805 | − | 0.968296i | \(-0.419634\pi\) | ||||
0.249805 | + | 0.968296i | \(0.419634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 9.39914e6i | − 0.501806i | −0.968012 | − | 0.250903i | \(-0.919272\pi\) | ||||
0.968012 | − | 0.250903i | \(-0.0807275\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.81242e6i | 0.467594i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.26286e6 | 0.277542 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.83298e7 | −2.00900 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.26494e6i | 0.378462i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.40799e7i | 0.729024i | 0.931199 | + | 0.364512i | \(0.118764\pi\) | ||||
−0.931199 | + | 0.364512i | \(0.881236\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.71740e7 | −1.39847 | −0.699236 | − | 0.714891i | \(-0.746476\pi\) | ||||
−0.699236 | + | 0.714891i | \(0.746476\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.05026e6 | 0.104876 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.74963e7i | − 1.90645i | −0.302264 | − | 0.953224i | \(-0.597743\pi\) | ||||
0.302264 | − | 0.953224i | \(-0.402257\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.94820e7i | 0.984572i | 0.870433 | + | 0.492286i | \(0.163839\pi\) | ||||
−0.870433 | + | 0.492286i | \(0.836161\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39063.7 | −0.00196232 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.21191e6 | −0.260246 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.16946e6i | 0.455122i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.27178e7i | 1.12086i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.75705e7 | −1.35220 | −0.676099 | − | 0.736811i | \(-0.736331\pi\) | ||||
−0.676099 | + | 0.736811i | \(0.736331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.74008e6 | 0.377359 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 9.77864e6i | − 0.473925i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.35804e7i | 0.654290i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.08192e6 | −0.147609 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.31849e7 | 0.627780 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 5.64649e6i | − 0.267273i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.21852e7i | 0.573403i | 0.958020 | + | 0.286701i | \(0.0925588\pi\) | ||||
−0.958020 | + | 0.286701i | \(0.907441\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.23982e6 | −0.432263 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.11095e6 | 0.144691 | 0.0723455 | − | 0.997380i | \(-0.476952\pi\) | ||||
0.0723455 | + | 0.997380i | \(0.476952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.87955e6i | 0.179390i | 0.995969 | + | 0.0896951i | \(0.0285893\pi\) | ||||
−0.995969 | + | 0.0896951i | \(0.971411\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 2.72922e6i | − 0.125467i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.14946e7 | 1.89655 | 0.948275 | − | 0.317451i | \(-0.102827\pi\) | ||||
0.948275 | + | 0.317451i | \(0.102827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.05631e6 | 0.275212 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.70651e6i | 0.393366i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.15796e7i | − 0.520168i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.52036e6 | 0.291223 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.52022e7 | 1.11919 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 598143.i | 0.0264110i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.44099e6i | 0.107168i | 0.998563 | + | 0.0535842i | \(0.0170646\pi\) | ||||
−0.998563 | + | 0.0535842i | \(0.982935\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.22925e6 | 0.402897 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.29196e7 | 0.560801 | 0.280400 | − | 0.959883i | \(-0.409533\pi\) | ||||
0.280400 | + | 0.959883i | \(0.409533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.07860e7i | 0.465540i | 0.972532 | + | 0.232770i | \(0.0747789\pi\) | ||||
−0.972532 | + | 0.232770i | \(0.925221\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 820022.i | − 0.0351939i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.36076e7 | 1.43426 | 0.717132 | − | 0.696938i | \(-0.245455\pi\) | ||||
0.717132 | + | 0.696938i | \(0.245455\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.04841e7 | −0.444913 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 1.40356e7i | − 0.592292i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.40979e6i | − 0.0591599i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.46991e7 | −0.613384 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.27088e7 | 0.527380 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.75536e7i | 1.13705i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.07449e7i | − 0.440951i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.25860e6 | −0.214610 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.07311e7 | −0.435534 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.51579e7i | 1.01545i | 0.861520 | + | 0.507723i | \(0.169513\pi\) | ||||
−0.861520 | + | 0.507723i | \(0.830487\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.55605e7i | 1.02603i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.38933e7 | −1.35306 | −0.676531 | − | 0.736414i | \(-0.736518\pi\) | ||||
−0.676531 | + | 0.736414i | \(0.736518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.16524e7 | 0.462635 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.57468e6i | 0.141151i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.04660e6i | 0.198187i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.09549e7 | −1.20904 | −0.604519 | − | 0.796590i | \(-0.706635\pi\) | ||||
−0.604519 | + | 0.796590i | \(0.706635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −363917. | −0.0141369 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.06483e7i | 0.411409i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.77242e6i | 0.0681102i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.39598e7 | 0.533554 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.44068e7 | −1.68815 | −0.844074 | − | 0.536227i | \(-0.819849\pi\) | ||||
−0.844074 | + | 0.536227i | \(0.819849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.85719e7i | 1.08035i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 7.16663e6i | − 0.269532i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.17425e6 | −0.156153 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.56682e7 | −0.955094 | −0.477547 | − | 0.878606i | \(-0.658474\pi\) | ||||
−0.477547 | + | 0.878606i | \(0.658474\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.80695e7i | − 0.668777i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 5.12276e6i | − 0.188595i | −0.995544 | − | 0.0942975i | \(-0.969940\pi\) | ||||
0.995544 | − | 0.0942975i | \(-0.0300605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.12680e7 | 0.778839 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.81985e6 | −0.102718 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.50587e7i | 0.545650i | 0.962064 | + | 0.272825i | \(0.0879580\pi\) | ||||
−0.962064 | + | 0.272825i | \(0.912042\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.98670e6i | 0.251829i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.01494e7 | 0.363905 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.86811e6 | −0.280633 | −0.140316 | − | 0.990107i | \(-0.544812\pi\) | ||||
−0.140316 | + | 0.990107i | \(0.544812\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 6.79312e6i | − 0.241024i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.17231e7i | 0.413774i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.47663e7 | 0.518473 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.08176e7 | 1.07644 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.78752e7i | 0.621134i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 2.17863e7i | − 0.753121i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.04818e7 | 1.04827 | 0.524137 | − | 0.851634i | \(-0.324388\pi\) | ||||
0.524137 | + | 0.851634i | \(0.324388\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.22295e6 | −0.144480 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.94765e7i | 1.00329i | 0.865073 | + | 0.501647i | \(0.167272\pi\) | ||||
−0.865073 | + | 0.501647i | \(0.832728\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.70554e7i | 0.577537i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.98926e6 | −0.134394 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.24171e7 | 1.08652 | 0.543260 | − | 0.839565i | \(-0.317190\pi\) | ||||
0.543260 | + | 0.839565i | \(0.317190\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.17563e7i | 2.05932i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.49673e7i | 1.16009i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.21680e7 | 0.401640 | 0.200820 | − | 0.979628i | \(-0.435639\pi\) | ||||
0.200820 | + | 0.979628i | \(0.435639\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.19985e6 | 0.170766 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 193415.i | − 0.00631971i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 4.09787e7i | − 1.33219i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.84802e7 | 0.597754 | 0.298877 | − | 0.954292i | \(-0.403388\pi\) | ||||
0.298877 | + | 0.954292i | \(0.403388\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.21034e7 | 0.711356 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.67381e7i | 0.535979i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.96954e7i | − 0.627519i | −0.949503 | − | 0.313759i | \(-0.898411\pi\) | ||||
0.949503 | − | 0.313759i | \(-0.101589\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.35579e6 | −0.264895 |
(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 | 160.6.d.a.81.10 | 20 | ||
4.3 | odd | 2 | 40.6.d.a.21.1 | ✓ | 20 | ||
5.2 | odd | 4 | 800.6.f.b.49.12 | 20 | |||
5.3 | odd | 4 | 800.6.f.c.49.9 | 20 | |||
5.4 | even | 2 | 800.6.d.c.401.11 | 20 | |||
8.3 | odd | 2 | 40.6.d.a.21.2 | yes | 20 | ||
8.5 | even | 2 | inner | 160.6.d.a.81.11 | 20 | ||
12.11 | even | 2 | 360.6.k.b.181.20 | 20 | |||
20.3 | even | 4 | 200.6.f.b.149.10 | 20 | |||
20.7 | even | 4 | 200.6.f.c.149.11 | 20 | |||
20.19 | odd | 2 | 200.6.d.b.101.20 | 20 | |||
24.11 | even | 2 | 360.6.k.b.181.19 | 20 | |||
40.3 | even | 4 | 200.6.f.c.149.12 | 20 | |||
40.13 | odd | 4 | 800.6.f.b.49.11 | 20 | |||
40.19 | odd | 2 | 200.6.d.b.101.19 | 20 | |||
40.27 | even | 4 | 200.6.f.b.149.9 | 20 | |||
40.29 | even | 2 | 800.6.d.c.401.10 | 20 | |||
40.37 | odd | 4 | 800.6.f.c.49.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.d.a.21.1 | ✓ | 20 | 4.3 | odd | 2 | ||
40.6.d.a.21.2 | yes | 20 | 8.3 | odd | 2 | ||
160.6.d.a.81.10 | 20 | 1.1 | even | 1 | trivial | ||
160.6.d.a.81.11 | 20 | 8.5 | even | 2 | inner | ||
200.6.d.b.101.19 | 20 | 40.19 | odd | 2 | |||
200.6.d.b.101.20 | 20 | 20.19 | odd | 2 | |||
200.6.f.b.149.9 | 20 | 40.27 | even | 4 | |||
200.6.f.b.149.10 | 20 | 20.3 | even | 4 | |||
200.6.f.c.149.11 | 20 | 20.7 | even | 4 | |||
200.6.f.c.149.12 | 20 | 40.3 | even | 4 | |||
360.6.k.b.181.19 | 20 | 24.11 | even | 2 | |||
360.6.k.b.181.20 | 20 | 12.11 | even | 2 | |||
800.6.d.c.401.10 | 20 | 40.29 | even | 2 | |||
800.6.d.c.401.11 | 20 | 5.4 | even | 2 | |||
800.6.f.b.49.11 | 20 | 40.13 | odd | 4 | |||
800.6.f.b.49.12 | 20 | 5.2 | odd | 4 | |||
800.6.f.c.49.9 | 20 | 5.3 | odd | 4 | |||
800.6.f.c.49.10 | 20 | 40.37 | odd | 4 |