Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 318 x^{11} + 776 x^{10} + 37929 x^{9} - 75673 x^{8} - 2114192 x^{7} + \cdots + 1037920000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{9}\cdot 5^{6} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-3.62063\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.62063 | 0.640043 | 0.320021 | − | 0.947410i | \(-0.396310\pi\) | ||||
0.320021 | + | 0.947410i | \(0.396310\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −18.8910 | −0.590345 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 32.5857 | 0.369529 | ||||||||
\(7\) | 187.526 | 1.44649 | 0.723245 | − | 0.690592i | \(-0.242650\pi\) | ||||
0.723245 | + | 0.690592i | \(0.242650\pi\) | |||||||
\(8\) | −184.258 | −1.01789 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −170.019 | −0.340836 | ||||||||
\(13\) | −145.247 | −0.238369 | −0.119184 | − | 0.992872i | \(-0.538028\pi\) | ||||
−0.119184 | + | 0.992872i | \(0.538028\pi\) | |||||||
\(14\) | 678.961 | 0.925816 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −62.6149 | −0.0611474 | ||||||||
\(17\) | −1828.13 | −1.53421 | −0.767105 | − | 0.641522i | \(-0.778303\pi\) | ||||
−0.767105 | + | 0.641522i | \(0.778303\pi\) | |||||||
\(18\) | 293.271 | 0.213348 | ||||||||
\(19\) | 1453.94 | 0.923981 | 0.461990 | − | 0.886885i | \(-0.347135\pi\) | ||||
0.461990 | + | 0.886885i | \(0.347135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1687.73 | 0.835131 | ||||||||
\(22\) | −438.096 | −0.192980 | ||||||||
\(23\) | −66.0886 | −0.0260499 | −0.0130250 | − | 0.999915i | \(-0.504146\pi\) | ||||
−0.0130250 | + | 0.999915i | \(0.504146\pi\) | |||||||
\(24\) | −1658.32 | −0.587679 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −525.886 | −0.152566 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −3542.55 | −0.853928 | ||||||||
\(29\) | −2596.02 | −0.573210 | −0.286605 | − | 0.958049i | \(-0.592527\pi\) | ||||
−0.286605 | + | 0.958049i | \(0.592527\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7120.85 | −1.33085 | −0.665423 | − | 0.746467i | \(-0.731749\pi\) | ||||
−0.665423 | + | 0.746467i | \(0.731749\pi\) | |||||||
\(32\) | 5669.54 | 0.978752 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −6618.98 | −0.981960 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1530.17 | −0.196782 | ||||||||
\(37\) | 13727.9 | 1.64854 | 0.824270 | − | 0.566197i | \(-0.191586\pi\) | ||||
0.824270 | + | 0.566197i | \(0.191586\pi\) | |||||||
\(38\) | 5264.18 | 0.591387 | ||||||||
\(39\) | −1307.22 | −0.137622 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1924.14 | 0.178763 | 0.0893815 | − | 0.995997i | \(-0.471511\pi\) | ||||
0.0893815 | + | 0.995997i | \(0.471511\pi\) | |||||||
\(42\) | 6110.65 | 0.534520 | ||||||||
\(43\) | −247.123 | −0.0203818 | −0.0101909 | − | 0.999948i | \(-0.503244\pi\) | ||||
−0.0101909 | + | 0.999948i | \(0.503244\pi\) | |||||||
\(44\) | 2285.82 | 0.177996 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −239.282 | −0.0166731 | ||||||||
\(47\) | −23893.7 | −1.57775 | −0.788877 | − | 0.614551i | \(-0.789337\pi\) | ||||
−0.788877 | + | 0.614551i | \(0.789337\pi\) | |||||||
\(48\) | −563.534 | −0.0353035 | ||||||||
\(49\) | 18358.8 | 1.09233 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16453.2 | −0.885776 | ||||||||
\(52\) | 2743.87 | 0.140720 | ||||||||
\(53\) | −33243.2 | −1.62560 | −0.812798 | − | 0.582545i | \(-0.802057\pi\) | ||||
−0.812798 | + | 0.582545i | \(0.802057\pi\) | |||||||
\(54\) | 2639.44 | 0.123176 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −34553.0 | −1.47237 | ||||||||
\(57\) | 13085.5 | 0.533461 | ||||||||
\(58\) | −9399.23 | −0.366879 | ||||||||
\(59\) | −30883.3 | −1.15503 | −0.577515 | − | 0.816380i | \(-0.695978\pi\) | ||||
−0.577515 | + | 0.816380i | \(0.695978\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −44616.4 | −1.53522 | −0.767609 | − | 0.640918i | \(-0.778554\pi\) | ||||
−0.767609 | + | 0.640918i | \(0.778554\pi\) | |||||||
\(62\) | −25782.0 | −0.851798 | ||||||||
\(63\) | 15189.6 | 0.482163 | ||||||||
\(64\) | 22531.0 | 0.687591 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3942.86 | −0.111417 | ||||||||
\(67\) | 36268.1 | 0.987046 | 0.493523 | − | 0.869733i | \(-0.335709\pi\) | ||||
0.493523 | + | 0.869733i | \(0.335709\pi\) | |||||||
\(68\) | 34535.3 | 0.905713 | ||||||||
\(69\) | −594.797 | −0.0150399 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 21658.8 | 0.509905 | 0.254953 | − | 0.966954i | \(-0.417940\pi\) | ||||
0.254953 | + | 0.966954i | \(0.417940\pi\) | |||||||
\(72\) | −14924.9 | −0.339296 | ||||||||
\(73\) | 74800.2 | 1.64284 | 0.821420 | − | 0.570323i | \(-0.193182\pi\) | ||||
0.821420 | + | 0.570323i | \(0.193182\pi\) | |||||||
\(74\) | 49703.6 | 1.05514 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −27466.5 | −0.545468 | ||||||||
\(77\) | −22690.6 | −0.436133 | ||||||||
\(78\) | −4732.98 | −0.0880842 | ||||||||
\(79\) | 3276.39 | 0.0590648 | 0.0295324 | − | 0.999564i | \(-0.490598\pi\) | ||||
0.0295324 | + | 0.999564i | \(0.490598\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 6966.61 | 0.114416 | ||||||||
\(83\) | −64618.5 | −1.02958 | −0.514792 | − | 0.857315i | \(-0.672131\pi\) | ||||
−0.514792 | + | 0.857315i | \(0.672131\pi\) | |||||||
\(84\) | −31883.0 | −0.493016 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −894.741 | −0.0130452 | ||||||||
\(87\) | −23364.2 | −0.330943 | ||||||||
\(88\) | 22295.2 | 0.306905 | ||||||||
\(89\) | −10036.5 | −0.134309 | −0.0671546 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671546 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27237.6 | −0.344798 | ||||||||
\(92\) | 1248.48 | 0.0153785 | ||||||||
\(93\) | −64087.7 | −0.768364 | ||||||||
\(94\) | −86510.3 | −1.00983 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 51025.8 | 0.565083 | ||||||||
\(97\) | 176913. | 1.90910 | 0.954552 | − | 0.298046i | \(-0.0963349\pi\) | ||||
0.954552 | + | 0.298046i | \(0.0963349\pi\) | |||||||
\(98\) | 66470.6 | 0.699140 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −33318.6 | −0.325000 | −0.162500 | − | 0.986709i | \(-0.551956\pi\) | ||||
−0.162500 | + | 0.986709i | \(0.551956\pi\) | |||||||
\(102\) | −59570.8 | −0.566935 | ||||||||
\(103\) | −168417. | −1.56420 | −0.782101 | − | 0.623152i | \(-0.785852\pi\) | ||||
−0.782101 | + | 0.623152i | \(0.785852\pi\) | |||||||
\(104\) | 26762.9 | 0.242633 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −120361. | −1.04045 | ||||||||
\(107\) | 103640. | 0.875122 | 0.437561 | − | 0.899189i | \(-0.355842\pi\) | ||||
0.437561 | + | 0.899189i | \(0.355842\pi\) | |||||||
\(108\) | −13771.6 | −0.113612 | ||||||||
\(109\) | −163450. | −1.31770 | −0.658852 | − | 0.752273i | \(-0.728958\pi\) | ||||
−0.658852 | + | 0.752273i | \(0.728958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 123551. | 0.951785 | ||||||||
\(112\) | −11741.9 | −0.0884491 | ||||||||
\(113\) | −9079.82 | −0.0668931 | −0.0334465 | − | 0.999441i | \(-0.510648\pi\) | ||||
−0.0334465 | + | 0.999441i | \(0.510648\pi\) | |||||||
\(114\) | 47377.7 | 0.341438 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 49041.6 | 0.338391 | ||||||||
\(117\) | −11765.0 | −0.0794563 | ||||||||
\(118\) | −111817. | −0.739269 | ||||||||
\(119\) | −342821. | −2.21922 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −161539. | −0.982605 | ||||||||
\(123\) | 17317.3 | 0.103209 | ||||||||
\(124\) | 134520. | 0.785658 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 54995.8 | 0.308605 | ||||||||
\(127\) | −117210. | −0.644845 | −0.322422 | − | 0.946596i | \(-0.604497\pi\) | ||||
−0.322422 | + | 0.946596i | \(0.604497\pi\) | |||||||
\(128\) | −99848.9 | −0.538665 | ||||||||
\(129\) | −2224.11 | −0.0117674 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −120279. | −0.612366 | −0.306183 | − | 0.951973i | \(-0.599052\pi\) | ||||
−0.306183 | + | 0.951973i | \(0.599052\pi\) | |||||||
\(132\) | 20572.3 | 0.102766 | ||||||||
\(133\) | 272651. | 1.33653 | ||||||||
\(134\) | 131313. | 0.631752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 336847. | 1.56166 | ||||||||
\(137\) | −369850. | −1.68354 | −0.841772 | − | 0.539834i | \(-0.818487\pi\) | ||||
−0.841772 | + | 0.539834i | \(0.818487\pi\) | |||||||
\(138\) | −2153.54 | −0.00962620 | ||||||||
\(139\) | −120159. | −0.527498 | −0.263749 | − | 0.964591i | \(-0.584959\pi\) | ||||
−0.263749 | + | 0.964591i | \(0.584959\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −215044. | −0.910917 | ||||||||
\(142\) | 78418.6 | 0.326361 | ||||||||
\(143\) | 17574.9 | 0.0718709 | ||||||||
\(144\) | −5071.81 | −0.0203825 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 270824. | 1.05149 | ||||||||
\(147\) | 165230. | 0.630659 | ||||||||
\(148\) | −259334. | −0.973207 | ||||||||
\(149\) | −526307. | −1.94211 | −0.971055 | − | 0.238856i | \(-0.923227\pi\) | ||||
−0.971055 | + | 0.238856i | \(0.923227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6526.41 | −0.0232934 | −0.0116467 | − | 0.999932i | \(-0.503707\pi\) | ||||
−0.0116467 | + | 0.999932i | \(0.503707\pi\) | |||||||
\(152\) | −267900. | −0.940510 | ||||||||
\(153\) | −148079. | −0.511403 | ||||||||
\(154\) | −82154.2 | −0.279144 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 24694.8 | 0.0812447 | ||||||||
\(157\) | 78920.0 | 0.255528 | 0.127764 | − | 0.991805i | \(-0.459220\pi\) | ||||
0.127764 | + | 0.991805i | \(0.459220\pi\) | |||||||
\(158\) | 11862.6 | 0.0378040 | ||||||||
\(159\) | −299189. | −0.938539 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12393.3 | −0.0376810 | ||||||||
\(162\) | 23754.9 | 0.0711159 | ||||||||
\(163\) | −334420. | −0.985879 | −0.492939 | − | 0.870064i | \(-0.664078\pi\) | ||||
−0.492939 | + | 0.870064i | \(0.664078\pi\) | |||||||
\(164\) | −36349.1 | −0.105532 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −233960. | −0.658978 | ||||||||
\(167\) | −460611. | −1.27804 | −0.639018 | − | 0.769191i | \(-0.720659\pi\) | ||||
−0.639018 | + | 0.769191i | \(0.720659\pi\) | |||||||
\(168\) | −310977. | −0.850071 | ||||||||
\(169\) | −350196. | −0.943180 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 117769. | 0.307994 | ||||||||
\(172\) | 4668.41 | 0.0120323 | ||||||||
\(173\) | 121903. | 0.309671 | 0.154836 | − | 0.987940i | \(-0.450515\pi\) | ||||
0.154836 | + | 0.987940i | \(0.450515\pi\) | |||||||
\(174\) | −84593.1 | −0.211817 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7576.41 | 0.0184366 | ||||||||
\(177\) | −277950. | −0.666857 | ||||||||
\(178\) | −36338.3 | −0.0859637 | ||||||||
\(179\) | 572399. | 1.33526 | 0.667631 | − | 0.744493i | \(-0.267309\pi\) | ||||
0.667631 | + | 0.744493i | \(0.267309\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 46785.9 | 0.106150 | 0.0530749 | − | 0.998591i | \(-0.483098\pi\) | ||||
0.0530749 | + | 0.998591i | \(0.483098\pi\) | |||||||
\(182\) | −98617.1 | −0.220686 | ||||||||
\(183\) | −401548. | −0.886359 | ||||||||
\(184\) | 12177.3 | 0.0265159 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −232038. | −0.491786 | ||||||||
\(187\) | 221204. | 0.462582 | ||||||||
\(188\) | 451378. | 0.931420 | ||||||||
\(189\) | 136706. | 0.278377 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −581929. | −1.15421 | −0.577107 | − | 0.816668i | \(-0.695819\pi\) | ||||
−0.577107 | + | 0.816668i | \(0.695819\pi\) | |||||||
\(192\) | 202779. | 0.396981 | ||||||||
\(193\) | −586600. | −1.13357 | −0.566786 | − | 0.823865i | \(-0.691813\pi\) | ||||
−0.566786 | + | 0.823865i | \(0.691813\pi\) | |||||||
\(194\) | 640535. | 1.22191 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −346818. | −0.644854 | ||||||||
\(197\) | −446858. | −0.820359 | −0.410179 | − | 0.912005i | \(-0.634534\pi\) | ||||
−0.410179 | + | 0.912005i | \(0.634534\pi\) | |||||||
\(198\) | −35485.8 | −0.0643267 | ||||||||
\(199\) | −259397. | −0.464336 | −0.232168 | − | 0.972676i | \(-0.574582\pi\) | ||||
−0.232168 | + | 0.972676i | \(0.574582\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 326413. | 0.569871 | ||||||||
\(202\) | −120634. | −0.208014 | ||||||||
\(203\) | −486821. | −0.829142 | ||||||||
\(204\) | 310818. | 0.522914 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −609776. | −1.00116 | ||||||||
\(207\) | −5353.17 | −0.00868331 | ||||||||
\(208\) | 9094.65 | 0.0145756 | ||||||||
\(209\) | −175927. | −0.278591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 494961. | 0.765358 | 0.382679 | − | 0.923881i | \(-0.375002\pi\) | ||||
0.382679 | + | 0.923881i | \(0.375002\pi\) | |||||||
\(212\) | 627998. | 0.959663 | ||||||||
\(213\) | 194930. | 0.294394 | ||||||||
\(214\) | 375243. | 0.560116 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −134324. | −0.195893 | ||||||||
\(217\) | −1.33534e6 | −1.92505 | ||||||||
\(218\) | −591791. | −0.843387 | ||||||||
\(219\) | 673202. | 0.948495 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 265531. | 0.365708 | ||||||||
\(222\) | 447332. | 0.609183 | ||||||||
\(223\) | −812706. | −1.09439 | −0.547194 | − | 0.837006i | \(-0.684304\pi\) | ||||
−0.547194 | + | 0.837006i | \(0.684304\pi\) | |||||||
\(224\) | 1.06318e6 | 1.41576 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32874.7 | −0.0428144 | ||||||||
\(227\) | 1.25202e6 | 1.61267 | 0.806337 | − | 0.591456i | \(-0.201447\pi\) | ||||
0.806337 | + | 0.591456i | \(0.201447\pi\) | |||||||
\(228\) | −247198. | −0.314926 | ||||||||
\(229\) | −434753. | −0.547841 | −0.273920 | − | 0.961752i | \(-0.588320\pi\) | ||||
−0.273920 | + | 0.961752i | \(0.588320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −204215. | −0.251802 | ||||||||
\(232\) | 478337. | 0.583464 | ||||||||
\(233\) | −453587. | −0.547358 | −0.273679 | − | 0.961821i | \(-0.588241\pi\) | ||||
−0.273679 | + | 0.961821i | \(0.588241\pi\) | |||||||
\(234\) | −42596.8 | −0.0508554 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 583418. | 0.681867 | ||||||||
\(237\) | 29487.6 | 0.0341011 | ||||||||
\(238\) | −1.24123e6 | −1.42040 | ||||||||
\(239\) | 860298. | 0.974214 | 0.487107 | − | 0.873342i | \(-0.338052\pi\) | ||||
0.487107 | + | 0.873342i | \(0.338052\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −374215. | −0.415029 | −0.207515 | − | 0.978232i | \(-0.566537\pi\) | ||||
−0.207515 | + | 0.978232i | \(0.566537\pi\) | |||||||
\(242\) | 53009.6 | 0.0581857 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 842851. | 0.906309 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 62699.4 | 0.0660581 | ||||||||
\(247\) | −211181. | −0.220248 | ||||||||
\(248\) | 1.31207e6 | 1.35465 | ||||||||
\(249\) | −581567. | −0.594431 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.45908e6 | 1.46182 | 0.730912 | − | 0.682472i | \(-0.239095\pi\) | ||||
0.730912 | + | 0.682472i | \(0.239095\pi\) | |||||||
\(252\) | −286947. | −0.284643 | ||||||||
\(253\) | 7996.72 | 0.00785435 | ||||||||
\(254\) | −424374. | −0.412728 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.08251e6 | −1.03236 | ||||||||
\(257\) | 1.04725e6 | 0.989053 | 0.494526 | − | 0.869163i | \(-0.335342\pi\) | ||||
0.494526 | + | 0.869163i | \(0.335342\pi\) | |||||||
\(258\) | −8052.67 | −0.00753166 | ||||||||
\(259\) | 2.57433e6 | 2.38460 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −210278. | −0.191070 | ||||||||
\(262\) | −435485. | −0.391940 | ||||||||
\(263\) | −150062. | −0.133777 | −0.0668885 | − | 0.997760i | \(-0.521307\pi\) | ||||
−0.0668885 | + | 0.997760i | \(0.521307\pi\) | |||||||
\(264\) | 200657. | 0.177192 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 987169. | 0.855436 | ||||||||
\(267\) | −90328.2 | −0.0775435 | ||||||||
\(268\) | −685142. | −0.582698 | ||||||||
\(269\) | −1.45785e6 | −1.22838 | −0.614191 | − | 0.789158i | \(-0.710518\pi\) | ||||
−0.614191 | + | 0.789158i | \(0.710518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 583177. | 0.482367 | 0.241183 | − | 0.970480i | \(-0.422465\pi\) | ||||
0.241183 | + | 0.970480i | \(0.422465\pi\) | |||||||
\(272\) | 114468. | 0.0938129 | ||||||||
\(273\) | −245138. | −0.199069 | ||||||||
\(274\) | −1.33909e6 | −1.07754 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11236.3 | 0.00887876 | ||||||||
\(277\) | −2.35418e6 | −1.84349 | −0.921743 | − | 0.387802i | \(-0.873234\pi\) | ||||
−0.921743 | + | 0.387802i | \(0.873234\pi\) | |||||||
\(278\) | −435053. | −0.337621 | ||||||||
\(279\) | −576789. | −0.443615 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 177355. | 0.133991 | 0.0669957 | − | 0.997753i | \(-0.478659\pi\) | ||||
0.0669957 | + | 0.997753i | \(0.478659\pi\) | |||||||
\(282\) | −778593. | −0.583026 | ||||||||
\(283\) | −114604. | −0.0850616 | −0.0425308 | − | 0.999095i | \(-0.513542\pi\) | ||||
−0.0425308 | + | 0.999095i | \(0.513542\pi\) | |||||||
\(284\) | −409158. | −0.301020 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 63632.2 | 0.0460005 | ||||||||
\(287\) | 360826. | 0.258579 | ||||||||
\(288\) | 459233. | 0.326251 | ||||||||
\(289\) | 1.92220e6 | 1.35380 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.59221e6 | 1.10222 | ||||||||
\(292\) | −1.41305e6 | −0.969843 | ||||||||
\(293\) | 634916. | 0.432063 | 0.216032 | − | 0.976386i | \(-0.430689\pi\) | ||||
0.216032 | + | 0.976386i | \(0.430689\pi\) | |||||||
\(294\) | 598235. | 0.403649 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.52947e6 | −1.67803 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −1.90556e6 | −1.24303 | ||||||||
\(299\) | 9599.18 | 0.00620949 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −46341.9 | −0.0294820 | ||||||||
\(302\) | −23629.7 | −0.0149087 | ||||||||
\(303\) | −299868. | −0.187639 | ||||||||
\(304\) | −91038.5 | −0.0564990 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −536137. | −0.327320 | ||||||||
\(307\) | −1.16348e6 | −0.704555 | −0.352277 | − | 0.935896i | \(-0.614593\pi\) | ||||
−0.352277 | + | 0.935896i | \(0.614593\pi\) | |||||||
\(308\) | 428649. | 0.257469 | ||||||||
\(309\) | −1.51575e6 | −0.903093 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.80571e6 | 1.64491 | 0.822455 | − | 0.568830i | \(-0.192604\pi\) | ||||
0.822455 | + | 0.568830i | \(0.192604\pi\) | |||||||
\(312\) | 240866. | 0.140084 | ||||||||
\(313\) | 799439. | 0.461238 | 0.230619 | − | 0.973044i | \(-0.425925\pi\) | ||||
0.230619 | + | 0.973044i | \(0.425925\pi\) | |||||||
\(314\) | 285740. | 0.163549 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −61894.5 | −0.0348686 | ||||||||
\(317\) | 1.23775e6 | 0.691808 | 0.345904 | − | 0.938270i | \(-0.387572\pi\) | ||||
0.345904 | + | 0.938270i | \(0.387572\pi\) | |||||||
\(318\) | −1.08325e6 | −0.600705 | ||||||||
\(319\) | 314119. | 0.172829 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 932762. | 0.505252 | ||||||||
\(322\) | −44871.5 | −0.0241174 | ||||||||
\(323\) | −2.65799e6 | −1.41758 | ||||||||
\(324\) | −123944. | −0.0655939 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.21081e6 | −0.631005 | ||||||||
\(327\) | −1.47105e6 | −0.760777 | ||||||||
\(328\) | −354538. | −0.181961 | ||||||||
\(329\) | −4.48069e6 | −2.28221 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.27850e6 | 0.641402 | 0.320701 | − | 0.947180i | \(-0.396082\pi\) | ||||
0.320701 | + | 0.947180i | \(0.396082\pi\) | |||||||
\(332\) | 1.22071e6 | 0.607810 | ||||||||
\(333\) | 1.11196e6 | 0.549513 | ||||||||
\(334\) | −1.66770e6 | −0.817998 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −105677. | −0.0510661 | ||||||||
\(337\) | 2.54954e6 | 1.22289 | 0.611446 | − | 0.791286i | \(-0.290588\pi\) | ||||
0.611446 | + | 0.791286i | \(0.290588\pi\) | |||||||
\(338\) | −1.26793e6 | −0.603676 | ||||||||
\(339\) | −81718.4 | −0.0386207 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 861623. | 0.401265 | ||||||||
\(342\) | 426399. | 0.197129 | ||||||||
\(343\) | 291011. | 0.133559 | ||||||||
\(344\) | 45534.3 | 0.0207464 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 441367. | 0.198203 | ||||||||
\(347\) | 2.80363e6 | 1.24996 | 0.624982 | − | 0.780639i | \(-0.285106\pi\) | ||||
0.624982 | + | 0.780639i | \(0.285106\pi\) | |||||||
\(348\) | 441374. | 0.195370 | ||||||||
\(349\) | 1.94021e6 | 0.852678 | 0.426339 | − | 0.904563i | \(-0.359803\pi\) | ||||
0.426339 | + | 0.904563i | \(0.359803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −105885. | −0.0458741 | ||||||||
\(352\) | −686014. | −0.295105 | ||||||||
\(353\) | −2.21823e6 | −0.947478 | −0.473739 | − | 0.880665i | \(-0.657096\pi\) | ||||
−0.473739 | + | 0.880665i | \(0.657096\pi\) | |||||||
\(354\) | −1.00635e6 | −0.426817 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 189599. | 0.0792888 | ||||||||
\(357\) | −3.08539e6 | −1.28127 | ||||||||
\(358\) | 2.07244e6 | 0.854624 | ||||||||
\(359\) | 2.03978e6 | 0.835309 | 0.417655 | − | 0.908606i | \(-0.362852\pi\) | ||||
0.417655 | + | 0.908606i | \(0.362852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −362152. | −0.146259 | ||||||||
\(362\) | 169395. | 0.0679404 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 514546. | 0.203550 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.45386e6 | −0.567307 | ||||||||
\(367\) | −332022. | −0.128677 | −0.0643387 | − | 0.997928i | \(-0.520494\pi\) | ||||
−0.0643387 | + | 0.997928i | \(0.520494\pi\) | |||||||
\(368\) | 4138.13 | 0.00159289 | ||||||||
\(369\) | 155856. | 0.0595877 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.23395e6 | −2.35141 | ||||||||
\(372\) | 1.21068e6 | 0.453600 | ||||||||
\(373\) | 2.34078e6 | 0.871142 | 0.435571 | − | 0.900154i | \(-0.356546\pi\) | ||||
0.435571 | + | 0.900154i | \(0.356546\pi\) | |||||||
\(374\) | 800897. | 0.296072 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.40260e6 | 1.60598 | ||||||||
\(377\) | 377065. | 0.136635 | ||||||||
\(378\) | 494962. | 0.178173 | ||||||||
\(379\) | −2.36625e6 | −0.846179 | −0.423089 | − | 0.906088i | \(-0.639054\pi\) | ||||
−0.423089 | + | 0.906088i | \(0.639054\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.05489e6 | −0.372301 | ||||||||
\(382\) | −2.10695e6 | −0.738747 | ||||||||
\(383\) | −913385. | −0.318168 | −0.159084 | − | 0.987265i | \(-0.550854\pi\) | ||||
−0.159084 | + | 0.987265i | \(0.550854\pi\) | |||||||
\(384\) | −898640. | −0.310998 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.12386e6 | −0.725535 | ||||||||
\(387\) | −20017.0 | −0.00679393 | ||||||||
\(388\) | −3.34206e6 | −1.12703 | ||||||||
\(389\) | −2.01815e6 | −0.676208 | −0.338104 | − | 0.941109i | \(-0.609786\pi\) | ||||
−0.338104 | + | 0.941109i | \(0.609786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 120818. | 0.0399661 | ||||||||
\(392\) | −3.38276e6 | −1.11187 | ||||||||
\(393\) | −1.08251e6 | −0.353549 | ||||||||
\(394\) | −1.61791e6 | −0.525065 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 185151. | 0.0593319 | ||||||||
\(397\) | −919738. | −0.292879 | −0.146439 | − | 0.989220i | \(-0.546781\pi\) | ||||
−0.146439 | + | 0.989220i | \(0.546781\pi\) | |||||||
\(398\) | −939181. | −0.297195 | ||||||||
\(399\) | 2.45386e6 | 0.771646 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.22661e6 | 1.00204 | 0.501020 | − | 0.865436i | \(-0.332958\pi\) | ||||
0.501020 | + | 0.865436i | \(0.332958\pi\) | |||||||
\(402\) | 1.18182e6 | 0.364742 | ||||||||
\(403\) | 1.03428e6 | 0.317232 | ||||||||
\(404\) | 629424. | 0.191862 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.76260e6 | −0.530686 | ||||||||
\(407\) | −1.66107e6 | −0.497053 | ||||||||
\(408\) | 3.03162e6 | 0.901622 | ||||||||
\(409\) | 2.73228e6 | 0.807638 | 0.403819 | − | 0.914839i | \(-0.367682\pi\) | ||||
0.403819 | + | 0.914839i | \(0.367682\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.32865e6 | −0.971994 | ||||||||
\(412\) | 3.18157e6 | 0.923419 | ||||||||
\(413\) | −5.79141e6 | −1.67074 | ||||||||
\(414\) | −19381.9 | −0.00555769 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −823485. | −0.233304 | ||||||||
\(417\) | −1.08143e6 | −0.304551 | ||||||||
\(418\) | −636966. | −0.178310 | ||||||||
\(419\) | 1.74485e6 | 0.485538 | 0.242769 | − | 0.970084i | \(-0.421944\pi\) | ||||
0.242769 | + | 0.970084i | \(0.421944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.54354e6 | −0.974389 | −0.487194 | − | 0.873294i | \(-0.661980\pi\) | ||||
−0.487194 | + | 0.873294i | \(0.661980\pi\) | |||||||
\(422\) | 1.79207e6 | 0.489862 | ||||||||
\(423\) | −1.93539e6 | −0.525918 | ||||||||
\(424\) | 6.12531e6 | 1.65468 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 705768. | 0.188425 | ||||||||
\(427\) | −8.36672e6 | −2.22068 | ||||||||
\(428\) | −1.95787e6 | −0.516624 | ||||||||
\(429\) | 158174. | 0.0414947 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 93351.9 | 0.0242064 | 0.0121032 | − | 0.999927i | \(-0.496147\pi\) | ||||
0.0121032 | + | 0.999927i | \(0.496147\pi\) | |||||||
\(432\) | −45646.3 | −0.0117678 | ||||||||
\(433\) | −4.10096e6 | −1.05115 | −0.525576 | − | 0.850746i | \(-0.676150\pi\) | ||||
−0.525576 | + | 0.850746i | \(0.676150\pi\) | |||||||
\(434\) | −4.83478e6 | −1.23212 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.08773e6 | 0.777900 | ||||||||
\(437\) | −96088.9 | −0.0240696 | ||||||||
\(438\) | 2.43741e6 | 0.607077 | ||||||||
\(439\) | 1.90862e6 | 0.472671 | 0.236335 | − | 0.971672i | \(-0.424054\pi\) | ||||
0.236335 | + | 0.971672i | \(0.424054\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.48707e6 | 0.364111 | ||||||||
\(442\) | 961388. | 0.234069 | ||||||||
\(443\) | 714784. | 0.173048 | 0.0865238 | − | 0.996250i | \(-0.472424\pi\) | ||||
0.0865238 | + | 0.996250i | \(0.472424\pi\) | |||||||
\(444\) | −2.33401e6 | −0.561882 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.94251e6 | −0.700455 | ||||||||
\(447\) | −4.73677e6 | −1.12128 | ||||||||
\(448\) | 4.22513e6 | 0.994593 | ||||||||
\(449\) | −1.96182e6 | −0.459243 | −0.229621 | − | 0.973280i | \(-0.573749\pi\) | ||||
−0.229621 | + | 0.973280i | \(0.573749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −232821. | −0.0538991 | ||||||||
\(452\) | 171527. | 0.0394900 | ||||||||
\(453\) | −58737.7 | −0.0134484 | ||||||||
\(454\) | 4.53310e6 | 1.03218 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.41110e6 | −0.543004 | ||||||||
\(457\) | 8.72831e6 | 1.95497 | 0.977484 | − | 0.211012i | \(-0.0676758\pi\) | ||||
0.977484 | + | 0.211012i | \(0.0676758\pi\) | |||||||
\(458\) | −1.57408e6 | −0.350642 | ||||||||
\(459\) | −1.33271e6 | −0.295259 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.76308e6 | 0.386384 | 0.193192 | − | 0.981161i | \(-0.438116\pi\) | ||||
0.193192 | + | 0.981161i | \(0.438116\pi\) | |||||||
\(462\) | −739388. | −0.161164 | ||||||||
\(463\) | 2.70535e6 | 0.586505 | 0.293252 | − | 0.956035i | \(-0.405262\pi\) | ||||
0.293252 | + | 0.956035i | \(0.405262\pi\) | |||||||
\(464\) | 162550. | 0.0350503 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.64227e6 | −0.350332 | ||||||||
\(467\) | 1.15801e6 | 0.245708 | 0.122854 | − | 0.992425i | \(-0.460795\pi\) | ||||
0.122854 | + | 0.992425i | \(0.460795\pi\) | |||||||
\(468\) | 222254. | 0.0469066 | ||||||||
\(469\) | 6.80119e6 | 1.42775 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 710280. | 0.147529 | ||||||||
\(472\) | 5.69048e6 | 1.17569 | ||||||||
\(473\) | 29901.9 | 0.00614534 | ||||||||
\(474\) | 106763. | 0.0218261 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.47625e6 | 1.31011 | ||||||||
\(477\) | −2.69270e6 | −0.541866 | ||||||||
\(478\) | 3.11482e6 | 0.623538 | ||||||||
\(479\) | 8.60379e6 | 1.71337 | 0.856685 | − | 0.515840i | \(-0.172520\pi\) | ||||
0.856685 | + | 0.515840i | \(0.172520\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.99394e6 | −0.392960 | ||||||||
\(482\) | −1.35489e6 | −0.265637 | ||||||||
\(483\) | −111540. | −0.0217551 | ||||||||
\(484\) | −276584. | −0.0536677 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 213795. | 0.0410588 | ||||||||
\(487\) | −5.23139e6 | −0.999527 | −0.499764 | − | 0.866162i | \(-0.666580\pi\) | ||||
−0.499764 | + | 0.866162i | \(0.666580\pi\) | |||||||
\(488\) | 8.22091e6 | 1.56268 | ||||||||
\(489\) | −3.00978e6 | −0.569197 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.91924e6 | −0.920862 | −0.460431 | − | 0.887695i | \(-0.652305\pi\) | ||||
−0.460431 | + | 0.887695i | \(0.652305\pi\) | |||||||
\(492\) | −327142. | −0.0609288 | ||||||||
\(493\) | 4.74587e6 | 0.879424 | ||||||||
\(494\) | −764608. | −0.140968 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 445872. | 0.0813777 | ||||||||
\(497\) | 4.06159e6 | 0.737572 | ||||||||
\(498\) | −2.10564e6 | −0.380461 | ||||||||
\(499\) | 255957. | 0.0460167 | 0.0230083 | − | 0.999735i | \(-0.492676\pi\) | ||||
0.0230083 | + | 0.999735i | \(0.492676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.14550e6 | −0.737875 | ||||||||
\(502\) | 5.28279e6 | 0.935630 | ||||||||
\(503\) | −3.39889e6 | −0.598987 | −0.299493 | − | 0.954098i | \(-0.596818\pi\) | ||||
−0.299493 | + | 0.954098i | \(0.596818\pi\) | |||||||
\(504\) | −2.79879e6 | −0.490789 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 28953.1 | 0.00502712 | ||||||||
\(507\) | −3.15177e6 | −0.544545 | ||||||||
\(508\) | 2.21422e6 | 0.380681 | ||||||||
\(509\) | 1.51733e6 | 0.259588 | 0.129794 | − | 0.991541i | \(-0.458568\pi\) | ||||
0.129794 | + | 0.991541i | \(0.458568\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.40269e7 | 2.37635 | ||||||||
\(512\) | −724191. | −0.122089 | ||||||||
\(513\) | 1.05992e6 | 0.177820 | ||||||||
\(514\) | 3.79172e6 | 0.633036 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 42015.7 | 0.00694684 | ||||||||
\(517\) | 2.89114e6 | 0.475711 | ||||||||
\(518\) | 9.32069e6 | 1.52624 | ||||||||
\(519\) | 1.09713e6 | 0.178789 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.98003e6 | 0.965181 | 0.482591 | − | 0.875846i | \(-0.339696\pi\) | ||||
0.482591 | + | 0.875846i | \(0.339696\pi\) | |||||||
\(522\) | −761338. | −0.122293 | ||||||||
\(523\) | 6.02099e6 | 0.962528 | 0.481264 | − | 0.876576i | \(-0.340178\pi\) | ||||
0.481264 | + | 0.876576i | \(0.340178\pi\) | |||||||
\(524\) | 2.27219e6 | 0.361507 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −543319. | −0.0856230 | ||||||||
\(527\) | 1.30178e7 | 2.04180 | ||||||||
\(528\) | 68187.7 | 0.0106444 | ||||||||
\(529\) | −6.43198e6 | −0.999321 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.50155e6 | −0.385010 | ||||||||
\(532\) | −5.15067e6 | −0.789014 | ||||||||
\(533\) | −279476. | −0.0426115 | ||||||||
\(534\) | −327045. | −0.0496312 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.68267e6 | −1.00470 | ||||||||
\(537\) | 5.15159e6 | 0.770913 | ||||||||
\(538\) | −5.27835e6 | −0.786217 | ||||||||
\(539\) | −2.22142e6 | −0.329351 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.42013e6 | 1.23687 | 0.618437 | − | 0.785834i | \(-0.287766\pi\) | ||||
0.618437 | + | 0.785834i | \(0.287766\pi\) | |||||||
\(542\) | 2.11147e6 | 0.308735 | ||||||||
\(543\) | 421074. | 0.0612856 | ||||||||
\(544\) | −1.03647e7 | −1.50161 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −887554. | −0.127413 | ||||||||
\(547\) | 3.91280e6 | 0.559138 | 0.279569 | − | 0.960126i | \(-0.409808\pi\) | ||||
0.279569 | + | 0.960126i | \(0.409808\pi\) | |||||||
\(548\) | 6.98686e6 | 0.993872 | ||||||||
\(549\) | −3.61393e6 | −0.511739 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.77447e6 | −0.529635 | ||||||||
\(552\) | 109596. | 0.0153090 | ||||||||
\(553\) | 614408. | 0.0854366 | ||||||||
\(554\) | −8.52360e6 | −1.17991 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.26994e6 | 0.311406 | ||||||||
\(557\) | −6.89573e6 | −0.941765 | −0.470882 | − | 0.882196i | \(-0.656064\pi\) | ||||
−0.470882 | + | 0.882196i | \(0.656064\pi\) | |||||||
\(558\) | −2.08834e6 | −0.283933 | ||||||||
\(559\) | 35893.9 | 0.00485838 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.99083e6 | 0.267072 | ||||||||
\(562\) | 642135. | 0.0857602 | ||||||||
\(563\) | 6.25769e6 | 0.832038 | 0.416019 | − | 0.909356i | \(-0.363425\pi\) | ||||
0.416019 | + | 0.909356i | \(0.363425\pi\) | |||||||
\(564\) | 4.06240e6 | 0.537755 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −414938. | −0.0544431 | ||||||||
\(567\) | 1.23036e6 | 0.160721 | ||||||||
\(568\) | −3.99081e6 | −0.519027 | ||||||||
\(569\) | −4.10333e6 | −0.531320 | −0.265660 | − | 0.964067i | \(-0.585590\pi\) | ||||
−0.265660 | + | 0.964067i | \(0.585590\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.32616e7 | −1.70218 | −0.851092 | − | 0.525017i | \(-0.824059\pi\) | ||||
−0.851092 | + | 0.525017i | \(0.824059\pi\) | |||||||
\(572\) | −332008. | −0.0424286 | ||||||||
\(573\) | −5.23736e6 | −0.666386 | ||||||||
\(574\) | 1.30642e6 | 0.165502 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.82501e6 | 0.229197 | ||||||||
\(577\) | −4.22991e6 | −0.528923 | −0.264461 | − | 0.964396i | \(-0.585194\pi\) | ||||
−0.264461 | + | 0.964396i | \(0.585194\pi\) | |||||||
\(578\) | 6.95958e6 | 0.866490 | ||||||||
\(579\) | −5.27940e6 | −0.654468 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.21176e7 | −1.48928 | ||||||||
\(582\) | 5.76481e6 | 0.705469 | ||||||||
\(583\) | 4.02242e6 | 0.490136 | ||||||||
\(584\) | −1.37825e7 | −1.67223 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.29880e6 | 0.276539 | ||||||||
\(587\) | 3.48400e6 | 0.417333 | 0.208666 | − | 0.977987i | \(-0.433088\pi\) | ||||
0.208666 | + | 0.977987i | \(0.433088\pi\) | |||||||
\(588\) | −3.12136e6 | −0.372306 | ||||||||
\(589\) | −1.03533e7 | −1.22968 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.02172e6 | −0.473634 | ||||||||
\(592\) | −859571. | −0.100804 | ||||||||
\(593\) | 1.44723e7 | 1.69006 | 0.845028 | − | 0.534722i | \(-0.179584\pi\) | ||||
0.845028 | + | 0.534722i | \(0.179584\pi\) | |||||||
\(594\) | −319372. | −0.0371391 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.94250e6 | 1.14652 | ||||||||
\(597\) | −2.33457e6 | −0.268085 | ||||||||
\(598\) | 34755.1 | 0.00397434 | ||||||||
\(599\) | −2.29915e6 | −0.261819 | −0.130909 | − | 0.991394i | \(-0.541790\pi\) | ||||
−0.130909 | + | 0.991394i | \(0.541790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.18751e6 | 0.359969 | 0.179984 | − | 0.983669i | \(-0.442395\pi\) | ||||
0.179984 | + | 0.983669i | \(0.442395\pi\) | |||||||
\(602\) | −167787. | −0.0188698 | ||||||||
\(603\) | 2.93771e6 | 0.329015 | ||||||||
\(604\) | 123291. | 0.0137511 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.08571e6 | −0.120097 | ||||||||
\(607\) | −3.06556e6 | −0.337706 | −0.168853 | − | 0.985641i | \(-0.554006\pi\) | ||||
−0.168853 | + | 0.985641i | \(0.554006\pi\) | |||||||
\(608\) | 8.24318e6 | 0.904348 | ||||||||
\(609\) | −4.38139e6 | −0.478705 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.47050e6 | 0.376087 | ||||||||
\(612\) | 2.79736e6 | 0.301904 | ||||||||
\(613\) | −3.64199e6 | −0.391460 | −0.195730 | − | 0.980658i | \(-0.562708\pi\) | ||||
−0.195730 | + | 0.980658i | \(0.562708\pi\) | |||||||
\(614\) | −4.21255e6 | −0.450945 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.18091e6 | 0.443935 | ||||||||
\(617\) | 6.08176e6 | 0.643156 | 0.321578 | − | 0.946883i | \(-0.395787\pi\) | ||||
0.321578 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(618\) | −5.48798e6 | −0.578018 | ||||||||
\(619\) | 1.33232e7 | 1.39759 | 0.698796 | − | 0.715321i | \(-0.253719\pi\) | ||||
0.698796 | + | 0.715321i | \(0.253719\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −48178.6 | −0.00501331 | ||||||||
\(622\) | 1.01584e7 | 1.05281 | ||||||||
\(623\) | −1.88210e6 | −0.194277 | ||||||||
\(624\) | 81851.8 | 0.00841525 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.89447e6 | 0.295212 | ||||||||
\(627\) | −1.58334e6 | −0.160844 | ||||||||
\(628\) | −1.49088e6 | −0.150850 | ||||||||
\(629\) | −2.50964e7 | −2.52921 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.16585e7 | 1.16565 | 0.582825 | − | 0.812598i | \(-0.301947\pi\) | ||||
0.582825 | + | 0.812598i | \(0.301947\pi\) | |||||||
\(632\) | −603701. | −0.0601214 | ||||||||
\(633\) | 4.45465e6 | 0.441880 | ||||||||
\(634\) | 4.48144e6 | 0.442787 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.65198e6 | 0.554062 | ||||||||
\(637\) | −2.66657e6 | −0.260378 | ||||||||
\(638\) | 1.13731e6 | 0.110618 | ||||||||
\(639\) | 1.75437e6 | 0.169968 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.08123e7 | −1.03937 | −0.519687 | − | 0.854357i | \(-0.673951\pi\) | ||||
−0.519687 | + | 0.854357i | \(0.673951\pi\) | |||||||
\(642\) | 3.37718e6 | 0.323383 | ||||||||
\(643\) | −2.10439e6 | −0.200723 | −0.100362 | − | 0.994951i | \(-0.532000\pi\) | ||||
−0.100362 | + | 0.994951i | \(0.532000\pi\) | |||||||
\(644\) | 234122. | 0.0222448 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.62361e6 | −0.907312 | ||||||||
\(647\) | −8.68332e6 | −0.815502 | −0.407751 | − | 0.913093i | \(-0.633687\pi\) | ||||
−0.407751 | + | 0.913093i | \(0.633687\pi\) | |||||||
\(648\) | −1.20891e6 | −0.113099 | ||||||||
\(649\) | 3.73688e6 | 0.348255 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.20181e7 | −1.11143 | ||||||||
\(652\) | 6.31755e6 | 0.582009 | ||||||||
\(653\) | 1.33057e7 | 1.22111 | 0.610555 | − | 0.791974i | \(-0.290946\pi\) | ||||
0.610555 | + | 0.791974i | \(0.290946\pi\) | |||||||
\(654\) | −5.32611e6 | −0.486930 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −120480. | −0.0109309 | ||||||||
\(657\) | 6.05881e6 | 0.547614 | ||||||||
\(658\) | −1.62229e7 | −1.46071 | ||||||||
\(659\) | 9.70036e6 | 0.870111 | 0.435055 | − | 0.900404i | \(-0.356729\pi\) | ||||
0.435055 | + | 0.900404i | \(0.356729\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.12502e7 | 1.89173 | 0.945864 | − | 0.324562i | \(-0.105217\pi\) | ||||
0.945864 | + | 0.324562i | \(0.105217\pi\) | |||||||
\(662\) | 4.62897e6 | 0.410525 | ||||||||
\(663\) | 2.38978e6 | 0.211141 | ||||||||
\(664\) | 1.19065e7 | 1.04800 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.02599e6 | 0.351712 | ||||||||
\(667\) | 171567. | 0.0149321 | ||||||||
\(668\) | 8.70143e6 | 0.754483 | ||||||||
\(669\) | −7.31435e6 | −0.631845 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.39859e6 | 0.462886 | ||||||||
\(672\) | 9.56865e6 | 0.817387 | ||||||||
\(673\) | 5.24543e6 | 0.446420 | 0.223210 | − | 0.974770i | \(-0.428346\pi\) | ||||
0.223210 | + | 0.974770i | \(0.428346\pi\) | |||||||
\(674\) | 9.23095e6 | 0.782703 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.61557e6 | 0.556802 | ||||||||
\(677\) | −2.18502e7 | −1.83225 | −0.916124 | − | 0.400894i | \(-0.868700\pi\) | ||||
−0.916124 | + | 0.400894i | \(0.868700\pi\) | |||||||
\(678\) | −295872. | −0.0247189 | ||||||||
\(679\) | 3.31756e7 | 2.76150 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.12682e7 | 0.931078 | ||||||||
\(682\) | 3.11962e6 | 0.256827 | ||||||||
\(683\) | −1.61102e7 | −1.32145 | −0.660724 | − | 0.750629i | \(-0.729750\pi\) | ||||
−0.660724 | + | 0.750629i | \(0.729750\pi\) | |||||||
\(684\) | −2.22478e6 | −0.181823 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.05364e6 | 0.0854836 | ||||||||
\(687\) | −3.91278e6 | −0.316296 | ||||||||
\(688\) | 15473.6 | 0.00124629 | ||||||||
\(689\) | 4.82848e6 | 0.387492 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.06476e6 | 0.323847 | 0.161923 | − | 0.986803i | \(-0.448230\pi\) | ||||
0.161923 | + | 0.986803i | \(0.448230\pi\) | |||||||
\(692\) | −2.30288e6 | −0.182813 | ||||||||
\(693\) | −1.83794e6 | −0.145378 | ||||||||
\(694\) | 1.01509e7 | 0.800030 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.30503e6 | 0.336863 | ||||||||
\(697\) | −3.51758e6 | −0.274260 | ||||||||
\(698\) | 7.02478e6 | 0.545751 | ||||||||
\(699\) | −4.08229e6 | −0.316017 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.76410e6 | −0.289312 | −0.144656 | − | 0.989482i | \(-0.546207\pi\) | ||||
−0.144656 | + | 0.989482i | \(0.546207\pi\) | |||||||
\(702\) | −383371. | −0.0293614 | ||||||||
\(703\) | 1.99596e7 | 1.52322 | ||||||||
\(704\) | −2.72625e6 | −0.207316 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.03138e6 | −0.606427 | ||||||||
\(707\) | −6.24810e6 | −0.470110 | ||||||||
\(708\) | 5.25076e6 | 0.393676 | ||||||||
\(709\) | 8.48557e6 | 0.633965 | 0.316982 | − | 0.948431i | \(-0.397330\pi\) | ||||
0.316982 | + | 0.948431i | \(0.397330\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 265388. | 0.0196883 | ||||||||
\(712\) | 1.84930e6 | 0.136712 | ||||||||
\(713\) | 470607. | 0.0346684 | ||||||||
\(714\) | −1.11711e7 | −0.820066 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.08132e7 | −0.788265 | ||||||||
\(717\) | 7.74268e6 | 0.562462 | ||||||||
\(718\) | 7.38529e6 | 0.534634 | ||||||||
\(719\) | −5.44794e6 | −0.393016 | −0.196508 | − | 0.980502i | \(-0.562960\pi\) | ||||
−0.196508 | + | 0.980502i | \(0.562960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.15825e7 | −2.26260 | ||||||||
\(722\) | −1.31122e6 | −0.0936121 | ||||||||
\(723\) | −3.36794e6 | −0.239617 | ||||||||
\(724\) | −883835. | −0.0626650 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 477087. | 0.0335935 | ||||||||
\(727\) | 1.52365e7 | 1.06918 | 0.534589 | − | 0.845112i | \(-0.320467\pi\) | ||||
0.534589 | + | 0.845112i | \(0.320467\pi\) | |||||||
\(728\) | 5.01873e6 | 0.350966 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 451773. | 0.0312699 | ||||||||
\(732\) | 7.58566e6 | 0.523258 | ||||||||
\(733\) | 2.32268e7 | 1.59673 | 0.798363 | − | 0.602177i | \(-0.205700\pi\) | ||||
0.798363 | + | 0.602177i | \(0.205700\pi\) | |||||||
\(734\) | −1.20213e6 | −0.0823590 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −374692. | −0.0254964 | ||||||||
\(737\) | −4.38844e6 | −0.297606 | ||||||||
\(738\) | 564295. | 0.0381387 | ||||||||
\(739\) | −8.86078e6 | −0.596844 | −0.298422 | − | 0.954434i | \(-0.596460\pi\) | ||||
−0.298422 | + | 0.954434i | \(0.596460\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.90063e6 | −0.127160 | ||||||||
\(742\) | −2.25708e7 | −1.50500 | ||||||||
\(743\) | 1.16363e7 | 0.773289 | 0.386644 | − | 0.922229i | \(-0.373634\pi\) | ||||
0.386644 | + | 0.922229i | \(0.373634\pi\) | |||||||
\(744\) | 1.18086e7 | 0.782109 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.47511e6 | 0.557568 | ||||||||
\(747\) | −5.23410e6 | −0.343195 | ||||||||
\(748\) | −4.17877e6 | −0.273083 | ||||||||
\(749\) | 1.94352e7 | 1.26586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.39412e7 | −0.901989 | −0.450995 | − | 0.892527i | \(-0.648931\pi\) | ||||
−0.450995 | + | 0.892527i | \(0.648931\pi\) | |||||||
\(752\) | 1.49610e6 | 0.0964756 | ||||||||
\(753\) | 1.31317e7 | 0.843984 | ||||||||
\(754\) | 1.36521e6 | 0.0874524 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.58252e6 | −0.164339 | ||||||||
\(757\) | −1.50634e7 | −0.955394 | −0.477697 | − | 0.878525i | \(-0.658528\pi\) | ||||
−0.477697 | + | 0.878525i | \(0.658528\pi\) | |||||||
\(758\) | −8.56730e6 | −0.541591 | ||||||||
\(759\) | 71970.4 | 0.00453471 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.92157e7 | 1.20280 | 0.601402 | − | 0.798947i | \(-0.294609\pi\) | ||||
0.601402 | + | 0.798947i | \(0.294609\pi\) | |||||||
\(762\) | −3.81936e6 | −0.238289 | ||||||||
\(763\) | −3.06510e7 | −1.90605 | ||||||||
\(764\) | 1.09932e7 | 0.681385 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.30703e6 | −0.203641 | ||||||||
\(767\) | 4.48571e6 | 0.275323 | ||||||||
\(768\) | −9.74256e6 | −0.596033 | ||||||||
\(769\) | 7.66150e6 | 0.467195 | 0.233597 | − | 0.972333i | \(-0.424950\pi\) | ||||
0.233597 | + | 0.972333i | \(0.424950\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.42529e6 | 0.571030 | ||||||||
\(772\) | 1.10815e7 | 0.669199 | ||||||||
\(773\) | −4.99696e6 | −0.300786 | −0.150393 | − | 0.988626i | \(-0.548054\pi\) | ||||
−0.150393 | + | 0.988626i | \(0.548054\pi\) | |||||||
\(774\) | −72474.0 | −0.00434840 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.25975e7 | −1.94326 | ||||||||
\(777\) | 2.31690e7 | 1.37675 | ||||||||
\(778\) | −7.30699e6 | −0.432802 | ||||||||
\(779\) | 2.79759e6 | 0.165174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.62072e6 | −0.153742 | ||||||||
\(782\) | 437439. | 0.0255800 | ||||||||
\(783\) | −1.89250e6 | −0.110314 | ||||||||
\(784\) | −1.14954e6 | −0.0667933 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.91936e6 | −0.226287 | ||||||||
\(787\) | −1.52048e7 | −0.875073 | −0.437537 | − | 0.899201i | \(-0.644149\pi\) | ||||
−0.437537 | + | 0.899201i | \(0.644149\pi\) | |||||||
\(788\) | 8.44161e6 | 0.484295 | ||||||||
\(789\) | −1.35056e6 | −0.0772361 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.70270e6 | −0.0967601 | ||||||||
\(792\) | 1.80591e6 | 0.102302 | ||||||||
\(793\) | 6.48041e6 | 0.365948 | ||||||||
\(794\) | −3.33003e6 | −0.187455 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.90028e6 | 0.274119 | ||||||||
\(797\) | 1.71869e6 | 0.0958411 | 0.0479205 | − | 0.998851i | \(-0.484741\pi\) | ||||
0.0479205 | + | 0.998851i | \(0.484741\pi\) | |||||||
\(798\) | 8.88452e6 | 0.493886 | ||||||||
\(799\) | 4.36808e7 | 2.42061 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −812954. | −0.0447698 | ||||||||
\(802\) | 1.16823e7 | 0.641348 | ||||||||
\(803\) | −9.05082e6 | −0.495335 | ||||||||
\(804\) | −6.16628e6 | −0.336421 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.74476e6 | 0.203042 | ||||||||
\(807\) | −1.31207e7 | −0.709207 | ||||||||
\(808\) | 6.13921e6 | 0.330814 | ||||||||
\(809\) | −2.42828e7 | −1.30445 | −0.652226 | − | 0.758025i | \(-0.726165\pi\) | ||||
−0.652226 | + | 0.758025i | \(0.726165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.20685e7 | 1.17820 | 0.589101 | − | 0.808059i | \(-0.299482\pi\) | ||||
0.589101 | + | 0.808059i | \(0.299482\pi\) | |||||||
\(812\) | 9.19655e6 | 0.489480 | ||||||||
\(813\) | 5.24859e6 | 0.278494 | ||||||||
\(814\) | −6.01413e6 | −0.318135 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.03021e6 | 0.0541629 | ||||||||
\(817\) | −359302. | −0.0188324 | ||||||||
\(818\) | 9.89257e6 | 0.516923 | ||||||||
\(819\) | −2.20624e6 | −0.114933 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.07673e7 | 1.07528 | 0.537640 | − | 0.843175i | \(-0.319316\pi\) | ||||
0.537640 | + | 0.843175i | \(0.319316\pi\) | |||||||
\(822\) | −1.20518e7 | −0.622118 | ||||||||
\(823\) | 1.75590e7 | 0.903650 | 0.451825 | − | 0.892107i | \(-0.350773\pi\) | ||||
0.451825 | + | 0.892107i | \(0.350773\pi\) | |||||||
\(824\) | 3.10321e7 | 1.59218 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.09685e7 | −1.06935 | ||||||||
\(827\) | 807814. | 0.0410722 | 0.0205361 | − | 0.999789i | \(-0.493463\pi\) | ||||
0.0205361 | + | 0.999789i | \(0.493463\pi\) | |||||||
\(828\) | 101127. | 0.00512615 | ||||||||
\(829\) | −6.29584e6 | −0.318176 | −0.159088 | − | 0.987264i | \(-0.550855\pi\) | ||||
−0.159088 | + | 0.987264i | \(0.550855\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.11876e7 | −1.06434 | ||||||||
\(832\) | −3.27256e6 | −0.163900 | ||||||||
\(833\) | −3.35624e7 | −1.67587 | ||||||||
\(834\) | −3.91547e6 | −0.194926 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.32344e6 | 0.164465 | ||||||||
\(837\) | −5.19110e6 | −0.256121 | ||||||||
\(838\) | 6.31745e6 | 0.310765 | ||||||||
\(839\) | −1.62539e7 | −0.797173 | −0.398587 | − | 0.917131i | \(-0.630499\pi\) | ||||
−0.398587 | + | 0.917131i | \(0.630499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.37718e7 | −0.671431 | ||||||||
\(842\) | −1.28298e7 | −0.623651 | ||||||||
\(843\) | 1.59619e6 | 0.0773599 | ||||||||
\(844\) | −9.35032e6 | −0.451825 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.00734e6 | −0.336610 | ||||||||
\(847\) | 2.74556e6 | 0.131499 | ||||||||
\(848\) | 2.08152e6 | 0.0994010 | ||||||||
\(849\) | −1.03144e6 | −0.0491103 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −907256. | −0.0429444 | ||||||||
\(852\) | −3.68242e6 | −0.173794 | ||||||||
\(853\) | −3.26091e7 | −1.53450 | −0.767248 | − | 0.641350i | \(-0.778375\pi\) | ||||
−0.767248 | + | 0.641350i | \(0.778375\pi\) | |||||||
\(854\) | −3.02928e7 | −1.42133 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.90965e7 | −0.890777 | ||||||||
\(857\) | −1.10056e7 | −0.511872 | −0.255936 | − | 0.966694i | \(-0.582384\pi\) | ||||
−0.255936 | + | 0.966694i | \(0.582384\pi\) | |||||||
\(858\) | 572690. | 0.0265584 | ||||||||
\(859\) | 5.98862e6 | 0.276914 | 0.138457 | − | 0.990368i | \(-0.455786\pi\) | ||||
0.138457 | + | 0.990368i | \(0.455786\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.24743e6 | 0.149291 | ||||||||
\(862\) | 337993. | 0.0154931 | ||||||||
\(863\) | −2.17360e7 | −0.993465 | −0.496733 | − | 0.867904i | \(-0.665467\pi\) | ||||
−0.496733 | + | 0.867904i | \(0.665467\pi\) | |||||||
\(864\) | 4.13309e6 | 0.188361 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.48481e7 | −0.672783 | ||||||||
\(867\) | 1.72998e7 | 0.781616 | ||||||||
\(868\) | 2.52260e7 | 1.13645 | ||||||||
\(869\) | −396444. | −0.0178087 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.26784e6 | −0.235281 | ||||||||
\(872\) | 3.01168e7 | 1.34128 | ||||||||
\(873\) | 1.43299e7 | 0.636368 | ||||||||
\(874\) | −347902. | −0.0154056 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.27175e7 | −0.559939 | ||||||||
\(877\) | −2.33923e7 | −1.02701 | −0.513504 | − | 0.858087i | \(-0.671653\pi\) | ||||
−0.513504 | + | 0.858087i | \(0.671653\pi\) | |||||||
\(878\) | 6.91041e6 | 0.302529 | ||||||||
\(879\) | 5.71425e6 | 0.249452 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.31413e6 | 0.404299 | 0.202149 | − | 0.979355i | \(-0.435207\pi\) | ||||
0.202149 | + | 0.979355i | \(0.435207\pi\) | |||||||
\(882\) | 5.38412e6 | 0.233047 | ||||||||
\(883\) | −9.33127e6 | −0.402753 | −0.201377 | − | 0.979514i | \(-0.564542\pi\) | ||||
−0.201377 | + | 0.979514i | \(0.564542\pi\) | |||||||
\(884\) | −5.01615e6 | −0.215894 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.58797e6 | 0.110758 | ||||||||
\(887\) | 9.36515e6 | 0.399674 | 0.199837 | − | 0.979829i | \(-0.435959\pi\) | ||||
0.199837 | + | 0.979829i | \(0.435959\pi\) | |||||||
\(888\) | −2.27652e7 | −0.968811 | ||||||||
\(889\) | −2.19799e7 | −0.932762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | 1.53529e7 | 0.646067 | ||||||||
\(893\) | −3.47401e7 | −1.45781 | ||||||||
\(894\) | −1.71501e7 | −0.717666 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.87242e7 | −0.779173 | ||||||||
\(897\) | 86392.6 | 0.00358505 | ||||||||
\(898\) | −7.10300e6 | −0.293935 | ||||||||
\(899\) | 1.84859e7 | 0.762853 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.07728e7 | 2.49401 | ||||||||
\(902\) | −842959. | −0.0344977 | ||||||||
\(903\) | −417077. | −0.0170215 | ||||||||
\(904\) | 1.67303e6 | 0.0680897 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −212667. | −0.00860757 | ||||||||
\(907\) | 4.47639e7 | 1.80680 | 0.903398 | − | 0.428802i | \(-0.141064\pi\) | ||||
0.903398 | + | 0.428802i | \(0.141064\pi\) | |||||||
\(908\) | −2.36520e7 | −0.952034 | ||||||||
\(909\) | −2.69881e6 | −0.108333 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.58451e6 | −0.302783 | −0.151392 | − | 0.988474i | \(-0.548375\pi\) | ||||
−0.151392 | + | 0.988474i | \(0.548375\pi\) | |||||||
\(912\) | −819346. | −0.0326197 | ||||||||
\(913\) | 7.81884e6 | 0.310431 | ||||||||
\(914\) | 3.16020e7 | 1.25126 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.21295e6 | 0.323415 | ||||||||
\(917\) | −2.25554e7 | −0.885781 | ||||||||
\(918\) | −4.82524e6 | −0.188978 | ||||||||
\(919\) | 4.51373e7 | 1.76298 | 0.881488 | − | 0.472206i | \(-0.156542\pi\) | ||||
0.881488 | + | 0.472206i | \(0.156542\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.04714e7 | −0.406775 | ||||||||
\(922\) | 6.38345e6 | 0.247302 | ||||||||
\(923\) | −3.14589e6 | −0.121545 | ||||||||
\(924\) | 3.85784e6 | 0.148650 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.79508e6 | 0.375388 | ||||||||
\(927\) | −1.36418e7 | −0.521401 | ||||||||
\(928\) | −1.47182e7 | −0.561030 | ||||||||
\(929\) | 2.10501e6 | 0.0800231 | 0.0400115 | − | 0.999199i | \(-0.487261\pi\) | ||||
0.0400115 | + | 0.999199i | \(0.487261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.66927e7 | 1.00930 | ||||||||
\(932\) | 8.56874e6 | 0.323130 | ||||||||
\(933\) | 2.52514e7 | 0.949690 | ||||||||
\(934\) | 4.19271e6 | 0.157263 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.16780e6 | 0.0808777 | ||||||||
\(937\) | −1.16498e7 | −0.433481 | −0.216740 | − | 0.976229i | \(-0.569542\pi\) | ||||
−0.216740 | + | 0.976229i | \(0.569542\pi\) | |||||||
\(938\) | 2.46246e7 | 0.913823 | ||||||||
\(939\) | 7.19495e6 | 0.266296 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.26754e6 | 0.304370 | 0.152185 | − | 0.988352i | \(-0.451369\pi\) | ||||
0.152185 | + | 0.988352i | \(0.451369\pi\) | |||||||
\(942\) | 2.57166e6 | 0.0944249 | ||||||||
\(943\) | −127164. | −0.00465676 | ||||||||
\(944\) | 1.93375e6 | 0.0706271 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 108264. | 0.00393328 | ||||||||
\(947\) | −1.00789e7 | −0.365205 | −0.182602 | − | 0.983187i | \(-0.558452\pi\) | ||||
−0.182602 | + | 0.983187i | \(0.558452\pi\) | |||||||
\(948\) | −557051. | −0.0201314 | ||||||||
\(949\) | −1.08645e7 | −0.391602 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.11398e7 | 0.399416 | ||||||||
\(952\) | 6.31674e7 | 2.25892 | ||||||||
\(953\) | −4.14245e7 | −1.47749 | −0.738747 | − | 0.673983i | \(-0.764582\pi\) | ||||
−0.738747 | + | 0.673983i | \(0.764582\pi\) | |||||||
\(954\) | −9.74926e6 | −0.346817 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.62519e7 | −0.575122 | ||||||||
\(957\) | 2.82707e6 | 0.0997830 | ||||||||
\(958\) | 3.11511e7 | 1.09663 | ||||||||
\(959\) | −6.93564e7 | −2.43523 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.20774e7 | 0.771149 | ||||||||
\(962\) | −7.21931e6 | −0.251512 | ||||||||
\(963\) | 8.39485e6 | 0.291707 | ||||||||
\(964\) | 7.06932e6 | 0.245011 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −403844. | −0.0139242 | ||||||||
\(967\) | −2.26789e7 | −0.779930 | −0.389965 | − | 0.920830i | \(-0.627513\pi\) | ||||
−0.389965 | + | 0.920830i | \(0.627513\pi\) | |||||||
\(968\) | −2.69772e6 | −0.0925354 | ||||||||
\(969\) | −2.39219e7 | −0.818441 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.89929e7 | −0.986833 | −0.493416 | − | 0.869793i | \(-0.664252\pi\) | ||||
−0.493416 | + | 0.869793i | \(0.664252\pi\) | |||||||
\(972\) | −1.11550e6 | −0.0378707 | ||||||||
\(973\) | −2.25330e7 | −0.763020 | ||||||||
\(974\) | −1.89409e7 | −0.639740 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.79365e6 | 0.0938746 | ||||||||
\(977\) | −5.72118e7 | −1.91756 | −0.958781 | − | 0.284146i | \(-0.908290\pi\) | ||||
−0.958781 | + | 0.284146i | \(0.908290\pi\) | |||||||
\(978\) | −1.08973e7 | −0.364311 | ||||||||
\(979\) | 1.21441e6 | 0.0404958 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.32394e7 | −0.439235 | ||||||||
\(982\) | −1.78108e7 | −0.589391 | ||||||||
\(983\) | 8.82345e6 | 0.291242 | 0.145621 | − | 0.989340i | \(-0.453482\pi\) | ||||
0.145621 | + | 0.989340i | \(0.453482\pi\) | |||||||
\(984\) | −3.19084e6 | −0.105055 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.71830e7 | 0.562869 | ||||||||
\(987\) | −4.03262e7 | −1.31763 | ||||||||
\(988\) | 3.98943e6 | 0.130022 | ||||||||
\(989\) | 16332.0 | 0.000530944 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.55123e7 | 1.47213 | 0.736063 | − | 0.676913i | \(-0.236683\pi\) | ||||
0.736063 | + | 0.676913i | \(0.236683\pi\) | |||||||
\(992\) | −4.03719e7 | −1.30257 | ||||||||
\(993\) | 1.15065e7 | 0.370314 | ||||||||
\(994\) | 1.47055e7 | 0.472078 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.09864e7 | 0.350919 | ||||||||
\(997\) | −4.74409e7 | −1.51152 | −0.755762 | − | 0.654847i | \(-0.772733\pi\) | ||||
−0.755762 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(998\) | 926725. | 0.0294527 | ||||||||
\(999\) | 1.00076e7 | 0.317262 |
(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 | 825.6.a.w.1.9 | 13 | ||
5.2 | odd | 4 | 165.6.c.a.34.16 | yes | 26 | ||
5.3 | odd | 4 | 165.6.c.a.34.11 | ✓ | 26 | ||
5.4 | even | 2 | 825.6.a.x.1.5 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.a.34.11 | ✓ | 26 | 5.3 | odd | 4 | ||
165.6.c.a.34.16 | yes | 26 | 5.2 | odd | 4 | ||
825.6.a.w.1.9 | 13 | 1.1 | even | 1 | trivial | ||
825.6.a.x.1.5 | 13 | 5.4 | even | 2 |