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: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 152x^{5} + 358x^{4} + 5771x^{3} - 13444x^{2} - 51316x + 92576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(4.42881\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.42881 | 0.959688 | 0.479844 | − | 0.877354i | \(-0.340693\pi\) | ||||
0.479844 | + | 0.877354i | \(0.340693\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −2.52798 | −0.0789994 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −48.8593 | −0.554076 | ||||||||
\(7\) | −29.0935 | −0.224414 | −0.112207 | − | 0.993685i | \(-0.535792\pi\) | ||||
−0.112207 | + | 0.993685i | \(0.535792\pi\) | |||||||
\(8\) | −187.446 | −1.03550 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 22.7518 | 0.0456103 | ||||||||
\(13\) | −433.055 | −0.710697 | −0.355348 | − | 0.934734i | \(-0.615638\pi\) | ||||
−0.355348 | + | 0.934734i | \(0.615638\pi\) | |||||||
\(14\) | −157.943 | −0.215368 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −936.714 | −0.914760 | ||||||||
\(17\) | 681.634 | 0.572043 | 0.286021 | − | 0.958223i | \(-0.407667\pi\) | ||||
0.286021 | + | 0.958223i | \(0.407667\pi\) | |||||||
\(18\) | 439.734 | 0.319896 | ||||||||
\(19\) | 1400.22 | 0.889844 | 0.444922 | − | 0.895569i | \(-0.353231\pi\) | ||||
0.444922 | + | 0.895569i | \(0.353231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 261.841 | 0.129566 | ||||||||
\(22\) | 656.886 | 0.289357 | ||||||||
\(23\) | 4762.16 | 1.87709 | 0.938543 | − | 0.345164i | \(-0.112177\pi\) | ||||
0.938543 | + | 0.345164i | \(0.112177\pi\) | |||||||
\(24\) | 1687.01 | 0.597848 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2350.97 | −0.682047 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 73.5478 | 0.0177286 | ||||||||
\(29\) | −646.539 | −0.142758 | −0.0713789 | − | 0.997449i | \(-0.522740\pi\) | ||||
−0.0713789 | + | 0.997449i | \(0.522740\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 840.506 | 0.157086 | 0.0785428 | − | 0.996911i | \(-0.474973\pi\) | ||||
0.0785428 | + | 0.996911i | \(0.474973\pi\) | |||||||
\(32\) | 913.026 | 0.157619 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 3700.46 | 0.548983 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −204.767 | −0.0263331 | ||||||||
\(37\) | 7782.45 | 0.934571 | 0.467285 | − | 0.884107i | \(-0.345232\pi\) | ||||
0.467285 | + | 0.884107i | \(0.345232\pi\) | |||||||
\(38\) | 7601.56 | 0.853972 | ||||||||
\(39\) | 3897.49 | 0.410321 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15790.5 | −1.46702 | −0.733510 | − | 0.679679i | \(-0.762119\pi\) | ||||
−0.733510 | + | 0.679679i | \(0.762119\pi\) | |||||||
\(42\) | 1421.49 | 0.124343 | ||||||||
\(43\) | −857.270 | −0.0707044 | −0.0353522 | − | 0.999375i | \(-0.511255\pi\) | ||||
−0.0353522 | + | 0.999375i | \(0.511255\pi\) | |||||||
\(44\) | −305.886 | −0.0238192 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 25852.9 | 1.80142 | ||||||||
\(47\) | −9406.46 | −0.621129 | −0.310564 | − | 0.950552i | \(-0.600518\pi\) | ||||
−0.310564 | + | 0.950552i | \(0.600518\pi\) | |||||||
\(48\) | 8430.42 | 0.528137 | ||||||||
\(49\) | −15960.6 | −0.949638 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6134.70 | −0.330269 | ||||||||
\(52\) | 1094.75 | 0.0561446 | ||||||||
\(53\) | −38888.1 | −1.90163 | −0.950817 | − | 0.309755i | \(-0.899753\pi\) | ||||
−0.950817 | + | 0.309755i | \(0.899753\pi\) | |||||||
\(54\) | −3957.61 | −0.184692 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5453.45 | 0.232382 | ||||||||
\(57\) | −12602.0 | −0.513751 | ||||||||
\(58\) | −3509.94 | −0.137003 | ||||||||
\(59\) | 43344.6 | 1.62108 | 0.810540 | − | 0.585683i | \(-0.199174\pi\) | ||||
0.810540 | + | 0.585683i | \(0.199174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35683.2 | −1.22783 | −0.613917 | − | 0.789371i | \(-0.710407\pi\) | ||||
−0.613917 | + | 0.789371i | \(0.710407\pi\) | |||||||
\(62\) | 4562.95 | 0.150753 | ||||||||
\(63\) | −2356.57 | −0.0748047 | ||||||||
\(64\) | 34931.5 | 1.06602 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5911.98 | −0.167060 | ||||||||
\(67\) | −4283.17 | −0.116568 | −0.0582838 | − | 0.998300i | \(-0.518563\pi\) | ||||
−0.0582838 | + | 0.998300i | \(0.518563\pi\) | |||||||
\(68\) | −1723.16 | −0.0451911 | ||||||||
\(69\) | −42859.4 | −1.08374 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 790.935 | 0.0186207 | 0.00931033 | − | 0.999957i | \(-0.497036\pi\) | ||||
0.00931033 | + | 0.999957i | \(0.497036\pi\) | |||||||
\(72\) | −15183.1 | −0.345168 | ||||||||
\(73\) | 54354.4 | 1.19379 | 0.596894 | − | 0.802320i | \(-0.296401\pi\) | ||||
0.596894 | + | 0.802320i | \(0.296401\pi\) | |||||||
\(74\) | 42249.5 | 0.896896 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3539.74 | −0.0702972 | ||||||||
\(77\) | −3520.31 | −0.0676634 | ||||||||
\(78\) | 21158.8 | 0.393780 | ||||||||
\(79\) | 24658.1 | 0.444521 | 0.222261 | − | 0.974987i | \(-0.428656\pi\) | ||||
0.222261 | + | 0.974987i | \(0.428656\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −85723.6 | −1.40788 | ||||||||
\(83\) | 67785.3 | 1.08004 | 0.540021 | − | 0.841652i | \(-0.318416\pi\) | ||||
0.540021 | + | 0.841652i | \(0.318416\pi\) | |||||||
\(84\) | −661.930 | −0.0102356 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4653.96 | −0.0678542 | ||||||||
\(87\) | 5818.85 | 0.0824212 | ||||||||
\(88\) | −22681.0 | −0.312216 | ||||||||
\(89\) | −43023.8 | −0.575750 | −0.287875 | − | 0.957668i | \(-0.592949\pi\) | ||||
−0.287875 | + | 0.957668i | \(0.592949\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12599.1 | 0.159490 | ||||||||
\(92\) | −12038.6 | −0.148289 | ||||||||
\(93\) | −7564.55 | −0.0906934 | ||||||||
\(94\) | −51065.9 | −0.596090 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8217.24 | −0.0910013 | ||||||||
\(97\) | −77298.9 | −0.834150 | −0.417075 | − | 0.908872i | \(-0.636945\pi\) | ||||
−0.417075 | + | 0.908872i | \(0.636945\pi\) | |||||||
\(98\) | −86647.0 | −0.911356 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −76235.3 | −0.743623 | −0.371811 | − | 0.928308i | \(-0.621263\pi\) | ||||
−0.371811 | + | 0.928308i | \(0.621263\pi\) | |||||||
\(102\) | −33304.2 | −0.316955 | ||||||||
\(103\) | 10863.8 | 0.100899 | 0.0504495 | − | 0.998727i | \(-0.483935\pi\) | ||||
0.0504495 | + | 0.998727i | \(0.483935\pi\) | |||||||
\(104\) | 81174.3 | 0.735928 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −211116. | −1.82497 | ||||||||
\(107\) | −68622.7 | −0.579440 | −0.289720 | − | 0.957111i | \(-0.593562\pi\) | ||||
−0.289720 | + | 0.957111i | \(0.593562\pi\) | |||||||
\(108\) | 1842.90 | 0.0152034 | ||||||||
\(109\) | −105784. | −0.852813 | −0.426406 | − | 0.904532i | \(-0.640221\pi\) | ||||
−0.426406 | + | 0.904532i | \(0.640221\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −70042.1 | −0.539575 | ||||||||
\(112\) | 27252.3 | 0.205285 | ||||||||
\(113\) | −102154. | −0.752594 | −0.376297 | − | 0.926499i | \(-0.622803\pi\) | ||||
−0.376297 | + | 0.926499i | \(0.622803\pi\) | |||||||
\(114\) | −68414.0 | −0.493041 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1634.44 | 0.0112778 | ||||||||
\(117\) | −35077.4 | −0.236899 | ||||||||
\(118\) | 235309. | 1.55573 | ||||||||
\(119\) | −19831.1 | −0.128375 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −193718. | −1.17834 | ||||||||
\(123\) | 142114. | 0.846984 | ||||||||
\(124\) | −2124.78 | −0.0124097 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12793.4 | −0.0717892 | ||||||||
\(127\) | −302945. | −1.66669 | −0.833345 | − | 0.552754i | \(-0.813577\pi\) | ||||
−0.833345 | + | 0.552754i | \(0.813577\pi\) | |||||||
\(128\) | 160420. | 0.865432 | ||||||||
\(129\) | 7715.43 | 0.0408212 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −327544. | −1.66760 | −0.833800 | − | 0.552067i | \(-0.813839\pi\) | ||||
−0.833800 | + | 0.552067i | \(0.813839\pi\) | |||||||
\(132\) | 2752.97 | 0.0137520 | ||||||||
\(133\) | −40737.4 | −0.199694 | ||||||||
\(134\) | −23252.5 | −0.111869 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −127769. | −0.592352 | ||||||||
\(137\) | 411208. | 1.87180 | 0.935902 | − | 0.352259i | \(-0.114586\pi\) | ||||
0.935902 | + | 0.352259i | \(0.114586\pi\) | |||||||
\(138\) | −232676. | −1.04005 | ||||||||
\(139\) | 384656. | 1.68863 | 0.844317 | − | 0.535843i | \(-0.180006\pi\) | ||||
0.844317 | + | 0.535843i | \(0.180006\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 84658.2 | 0.358609 | ||||||||
\(142\) | 4293.84 | 0.0178700 | ||||||||
\(143\) | −52399.6 | −0.214283 | ||||||||
\(144\) | −75873.8 | −0.304920 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 295080. | 1.14566 | ||||||||
\(147\) | 143645. | 0.548274 | ||||||||
\(148\) | −19673.9 | −0.0738306 | ||||||||
\(149\) | −61538.1 | −0.227080 | −0.113540 | − | 0.993533i | \(-0.536219\pi\) | ||||
−0.113540 | + | 0.993533i | \(0.536219\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −337615. | −1.20498 | −0.602489 | − | 0.798127i | \(-0.705824\pi\) | ||||
−0.602489 | + | 0.798127i | \(0.705824\pi\) | |||||||
\(152\) | −262466. | −0.921435 | ||||||||
\(153\) | 55212.3 | 0.190681 | ||||||||
\(154\) | −19111.1 | −0.0649358 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9852.79 | −0.0324151 | ||||||||
\(157\) | −455250. | −1.47401 | −0.737006 | − | 0.675887i | \(-0.763761\pi\) | ||||
−0.737006 | + | 0.675887i | \(0.763761\pi\) | |||||||
\(158\) | 133864. | 0.426602 | ||||||||
\(159\) | 349993. | 1.09791 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −138548. | −0.421245 | ||||||||
\(162\) | 35618.4 | 0.106632 | ||||||||
\(163\) | 36402.3 | 0.107315 | 0.0536575 | − | 0.998559i | \(-0.482912\pi\) | ||||
0.0536575 | + | 0.998559i | \(0.482912\pi\) | |||||||
\(164\) | 39918.1 | 0.115894 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 367994. | 1.03650 | ||||||||
\(167\) | −261013. | −0.724220 | −0.362110 | − | 0.932135i | \(-0.617944\pi\) | ||||
−0.362110 | + | 0.932135i | \(0.617944\pi\) | |||||||
\(168\) | −49081.1 | −0.134166 | ||||||||
\(169\) | −183757. | −0.494910 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 113418. | 0.296615 | ||||||||
\(172\) | 2167.16 | 0.00558561 | ||||||||
\(173\) | −61304.1 | −0.155731 | −0.0778653 | − | 0.996964i | \(-0.524810\pi\) | ||||
−0.0778653 | + | 0.996964i | \(0.524810\pi\) | |||||||
\(174\) | 31589.5 | 0.0790986 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −113342. | −0.275810 | ||||||||
\(177\) | −390101. | −0.935931 | ||||||||
\(178\) | −233568. | −0.552540 | ||||||||
\(179\) | −766914. | −1.78902 | −0.894508 | − | 0.447052i | \(-0.852474\pi\) | ||||
−0.894508 | + | 0.447052i | \(0.852474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 116461. | 0.264231 | 0.132115 | − | 0.991234i | \(-0.457823\pi\) | ||||
0.132115 | + | 0.991234i | \(0.457823\pi\) | |||||||
\(182\) | 68397.9 | 0.153061 | ||||||||
\(183\) | 321149. | 0.708890 | ||||||||
\(184\) | −892647. | −1.94373 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −41066.5 | −0.0870374 | ||||||||
\(187\) | 82477.7 | 0.172477 | ||||||||
\(188\) | 23779.4 | 0.0490688 | ||||||||
\(189\) | 21209.1 | 0.0431885 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −814613. | −1.61573 | −0.807863 | − | 0.589370i | \(-0.799376\pi\) | ||||
−0.807863 | + | 0.589370i | \(0.799376\pi\) | |||||||
\(192\) | −314383. | −0.615470 | ||||||||
\(193\) | −81825.1 | −0.158122 | −0.0790612 | − | 0.996870i | \(-0.525192\pi\) | ||||
−0.0790612 | + | 0.996870i | \(0.525192\pi\) | |||||||
\(194\) | −419641. | −0.800523 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 40348.0 | 0.0750209 | ||||||||
\(197\) | −421809. | −0.774372 | −0.387186 | − | 0.922002i | \(-0.626553\pi\) | ||||
−0.387186 | + | 0.922002i | \(0.626553\pi\) | |||||||
\(198\) | 53207.8 | 0.0964522 | ||||||||
\(199\) | 294642. | 0.527426 | 0.263713 | − | 0.964601i | \(-0.415053\pi\) | ||||
0.263713 | + | 0.964601i | \(0.415053\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 38548.5 | 0.0673003 | ||||||||
\(202\) | −413867. | −0.713646 | ||||||||
\(203\) | 18810.1 | 0.0320369 | ||||||||
\(204\) | 15508.4 | 0.0260911 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 58977.3 | 0.0968316 | ||||||||
\(207\) | 385735. | 0.625695 | ||||||||
\(208\) | 405648. | 0.650117 | ||||||||
\(209\) | 169427. | 0.268298 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 792181. | 1.22495 | 0.612475 | − | 0.790490i | \(-0.290174\pi\) | ||||
0.612475 | + | 0.790490i | \(0.290174\pi\) | |||||||
\(212\) | 98308.3 | 0.150228 | ||||||||
\(213\) | −7118.42 | −0.0107506 | ||||||||
\(214\) | −372540. | −0.556081 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 136648. | 0.199283 | ||||||||
\(217\) | −24453.2 | −0.0352523 | ||||||||
\(218\) | −574282. | −0.818434 | ||||||||
\(219\) | −489189. | −0.689234 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −295185. | −0.406549 | ||||||||
\(222\) | −380245. | −0.517823 | ||||||||
\(223\) | 130498. | 0.175728 | 0.0878638 | − | 0.996132i | \(-0.471996\pi\) | ||||
0.0878638 | + | 0.996132i | \(0.471996\pi\) | |||||||
\(224\) | −26563.1 | −0.0353719 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −554577. | −0.722255 | ||||||||
\(227\) | −615550. | −0.792864 | −0.396432 | − | 0.918064i | \(-0.629752\pi\) | ||||
−0.396432 | + | 0.918064i | \(0.629752\pi\) | |||||||
\(228\) | 31857.7 | 0.0405861 | ||||||||
\(229\) | −698301. | −0.879942 | −0.439971 | − | 0.898012i | \(-0.645011\pi\) | ||||
−0.439971 | + | 0.898012i | \(0.645011\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31682.8 | 0.0390655 | ||||||||
\(232\) | 121191. | 0.147826 | ||||||||
\(233\) | −630539. | −0.760890 | −0.380445 | − | 0.924803i | \(-0.624229\pi\) | ||||
−0.380445 | + | 0.924803i | \(0.624229\pi\) | |||||||
\(234\) | −190429. | −0.227349 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −109574. | −0.128064 | ||||||||
\(237\) | −221923. | −0.256644 | ||||||||
\(238\) | −107659. | −0.123200 | ||||||||
\(239\) | −880589. | −0.997191 | −0.498595 | − | 0.866835i | \(-0.666151\pi\) | ||||
−0.498595 | + | 0.866835i | \(0.666151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −97283.2 | −0.107894 | −0.0539468 | − | 0.998544i | \(-0.517180\pi\) | ||||
−0.0539468 | + | 0.998544i | \(0.517180\pi\) | |||||||
\(242\) | 79483.3 | 0.0872443 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 90206.6 | 0.0969982 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 771513. | 0.812840 | ||||||||
\(247\) | −606374. | −0.632409 | ||||||||
\(248\) | −157549. | −0.162663 | ||||||||
\(249\) | −610068. | −0.623562 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −35093.6 | −0.0351595 | −0.0175798 | − | 0.999845i | \(-0.505596\pi\) | ||||
−0.0175798 | + | 0.999845i | \(0.505596\pi\) | |||||||
\(252\) | 5957.37 | 0.00590953 | ||||||||
\(253\) | 576221. | 0.565962 | ||||||||
\(254\) | −1.64463e6 | −1.59950 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −246919. | −0.235480 | ||||||||
\(257\) | 1.45297e6 | 1.37222 | 0.686111 | − | 0.727497i | \(-0.259317\pi\) | ||||
0.686111 | + | 0.727497i | \(0.259317\pi\) | |||||||
\(258\) | 41885.7 | 0.0391756 | ||||||||
\(259\) | −226419. | −0.209731 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −52369.7 | −0.0475859 | ||||||||
\(262\) | −1.77818e6 | −1.60037 | ||||||||
\(263\) | 1.67823e6 | 1.49610 | 0.748051 | − | 0.663642i | \(-0.230990\pi\) | ||||
0.748051 | + | 0.663642i | \(0.230990\pi\) | |||||||
\(264\) | 204129. | 0.180258 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −221156. | −0.191643 | ||||||||
\(267\) | 387215. | 0.332410 | ||||||||
\(268\) | 10827.8 | 0.00920878 | ||||||||
\(269\) | −2.08881e6 | −1.76002 | −0.880010 | − | 0.474955i | \(-0.842464\pi\) | ||||
−0.880010 | + | 0.474955i | \(0.842464\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −59165.0 | −0.0489375 | −0.0244687 | − | 0.999701i | \(-0.507789\pi\) | ||||
−0.0244687 | + | 0.999701i | \(0.507789\pi\) | |||||||
\(272\) | −638496. | −0.523282 | ||||||||
\(273\) | −113392. | −0.0920818 | ||||||||
\(274\) | 2.23237e6 | 1.79635 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 108348. | 0.0856145 | ||||||||
\(277\) | 1.37762e6 | 1.07877 | 0.539387 | − | 0.842058i | \(-0.318656\pi\) | ||||
0.539387 | + | 0.842058i | \(0.318656\pi\) | |||||||
\(278\) | 2.08823e6 | 1.62056 | ||||||||
\(279\) | 68081.0 | 0.0523619 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 348215. | 0.263077 | 0.131538 | − | 0.991311i | \(-0.458008\pi\) | ||||
0.131538 | + | 0.991311i | \(0.458008\pi\) | |||||||
\(282\) | 459593. | 0.344153 | ||||||||
\(283\) | 1.38544e6 | 1.02831 | 0.514154 | − | 0.857698i | \(-0.328106\pi\) | ||||
0.514154 | + | 0.857698i | \(0.328106\pi\) | |||||||
\(284\) | −1999.47 | −0.00147102 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −284468. | −0.205645 | ||||||||
\(287\) | 459400. | 0.329220 | ||||||||
\(288\) | 73955.1 | 0.0525396 | ||||||||
\(289\) | −955233. | −0.672767 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 695690. | 0.481597 | ||||||||
\(292\) | −137407. | −0.0943086 | ||||||||
\(293\) | 1.41063e6 | 0.959937 | 0.479969 | − | 0.877286i | \(-0.340648\pi\) | ||||
0.479969 | + | 0.877286i | \(0.340648\pi\) | |||||||
\(294\) | 779823. | 0.526172 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.45879e6 | −0.967750 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −334079. | −0.217926 | ||||||||
\(299\) | −2.06227e6 | −1.33404 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24941.0 | 0.0158671 | ||||||||
\(302\) | −1.83285e6 | −1.15640 | ||||||||
\(303\) | 686118. | 0.429331 | ||||||||
\(304\) | −1.31161e6 | −0.813993 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 299737. | 0.182994 | ||||||||
\(307\) | 1.99536e6 | 1.20830 | 0.604150 | − | 0.796871i | \(-0.293513\pi\) | ||||
0.604150 | + | 0.796871i | \(0.293513\pi\) | |||||||
\(308\) | 8899.28 | 0.00534537 | ||||||||
\(309\) | −97773.8 | −0.0582541 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.98713e6 | −1.16500 | −0.582500 | − | 0.812831i | \(-0.697925\pi\) | ||||
−0.582500 | + | 0.812831i | \(0.697925\pi\) | |||||||
\(312\) | −730569. | −0.424888 | ||||||||
\(313\) | 737295. | 0.425383 | 0.212692 | − | 0.977119i | \(-0.431777\pi\) | ||||
0.212692 | + | 0.977119i | \(0.431777\pi\) | |||||||
\(314\) | −2.47147e6 | −1.41459 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −62335.3 | −0.0351169 | ||||||||
\(317\) | 2.58321e6 | 1.44382 | 0.721908 | − | 0.691989i | \(-0.243266\pi\) | ||||
0.721908 | + | 0.691989i | \(0.243266\pi\) | |||||||
\(318\) | 1.90004e6 | 1.05365 | ||||||||
\(319\) | −78231.2 | −0.0430431 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 617604. | 0.334540 | ||||||||
\(322\) | −752149. | −0.404263 | ||||||||
\(323\) | 954440. | 0.509029 | ||||||||
\(324\) | −16586.1 | −0.00877772 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 197621. | 0.102989 | ||||||||
\(327\) | 952056. | 0.492372 | ||||||||
\(328\) | 2.95986e6 | 1.51910 | ||||||||
\(329\) | 273667. | 0.139390 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −263417. | −0.132152 | −0.0660759 | − | 0.997815i | \(-0.521048\pi\) | ||||
−0.0660759 | + | 0.997815i | \(0.521048\pi\) | |||||||
\(332\) | −171360. | −0.0853227 | ||||||||
\(333\) | 630379. | 0.311524 | ||||||||
\(334\) | −1.41699e6 | −0.695025 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −245270. | −0.118521 | ||||||||
\(337\) | −1.74494e6 | −0.836963 | −0.418482 | − | 0.908225i | \(-0.637438\pi\) | ||||
−0.418482 | + | 0.908225i | \(0.637438\pi\) | |||||||
\(338\) | −997581. | −0.474959 | ||||||||
\(339\) | 919389. | 0.434510 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 101701. | 0.0473631 | ||||||||
\(342\) | 615726. | 0.284657 | ||||||||
\(343\) | 953322. | 0.437527 | ||||||||
\(344\) | 160692. | 0.0732146 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −332808. | −0.149453 | ||||||||
\(347\) | 3.21441e6 | 1.43310 | 0.716551 | − | 0.697535i | \(-0.245720\pi\) | ||||
0.716551 | + | 0.697535i | \(0.245720\pi\) | |||||||
\(348\) | −14709.9 | −0.00651123 | ||||||||
\(349\) | 287220. | 0.126227 | 0.0631133 | − | 0.998006i | \(-0.479897\pi\) | ||||
0.0631133 | + | 0.998006i | \(0.479897\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 315697. | 0.136774 | ||||||||
\(352\) | 110476. | 0.0475239 | ||||||||
\(353\) | −1.23752e6 | −0.528587 | −0.264293 | − | 0.964442i | \(-0.585139\pi\) | ||||
−0.264293 | + | 0.964442i | \(0.585139\pi\) | |||||||
\(354\) | −2.11779e6 | −0.898202 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 108763. | 0.0454839 | ||||||||
\(357\) | 178480. | 0.0741171 | ||||||||
\(358\) | −4.16344e6 | −1.71690 | ||||||||
\(359\) | 4.49015e6 | 1.83876 | 0.919379 | − | 0.393373i | \(-0.128692\pi\) | ||||
0.919379 | + | 0.393373i | \(0.128692\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −515470. | −0.208178 | ||||||||
\(362\) | 632245. | 0.253579 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −31850.2 | −0.0125997 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.74346e6 | 0.680313 | ||||||||
\(367\) | −2.56230e6 | −0.993035 | −0.496517 | − | 0.868027i | \(-0.665388\pi\) | ||||
−0.496517 | + | 0.868027i | \(0.665388\pi\) | |||||||
\(368\) | −4.46078e6 | −1.71708 | ||||||||
\(369\) | −1.27903e6 | −0.489007 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.13139e6 | 0.426754 | ||||||||
\(372\) | 19123.1 | 0.00716473 | ||||||||
\(373\) | 1.44404e6 | 0.537411 | 0.268706 | − | 0.963222i | \(-0.413404\pi\) | ||||
0.268706 | + | 0.963222i | \(0.413404\pi\) | |||||||
\(374\) | 447756. | 0.165524 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.76320e6 | 0.643181 | ||||||||
\(377\) | 279987. | 0.101457 | ||||||||
\(378\) | 115140. | 0.0414475 | ||||||||
\(379\) | −3.07135e6 | −1.09833 | −0.549163 | − | 0.835715i | \(-0.685053\pi\) | ||||
−0.549163 | + | 0.835715i | \(0.685053\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.72651e6 | 0.962263 | ||||||||
\(382\) | −4.42238e6 | −1.55059 | ||||||||
\(383\) | −490553. | −0.170879 | −0.0854395 | − | 0.996343i | \(-0.527229\pi\) | ||||
−0.0854395 | + | 0.996343i | \(0.527229\pi\) | |||||||
\(384\) | −1.44378e6 | −0.499657 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −444213. | −0.151748 | ||||||||
\(387\) | −69438.9 | −0.0235681 | ||||||||
\(388\) | 195410. | 0.0658974 | ||||||||
\(389\) | −2.10754e6 | −0.706157 | −0.353079 | − | 0.935594i | \(-0.614865\pi\) | ||||
−0.353079 | + | 0.935594i | \(0.614865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.24604e6 | 1.07377 | ||||||||
\(392\) | 2.99174e6 | 0.983353 | ||||||||
\(393\) | 2.94790e6 | 0.962789 | ||||||||
\(394\) | −2.28992e6 | −0.743156 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −24776.8 | −0.00793974 | ||||||||
\(397\) | −1.76935e6 | −0.563425 | −0.281713 | − | 0.959499i | \(-0.590902\pi\) | ||||
−0.281713 | + | 0.959499i | \(0.590902\pi\) | |||||||
\(398\) | 1.59956e6 | 0.506164 | ||||||||
\(399\) | 366637. | 0.115293 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.75581e6 | −0.855831 | −0.427916 | − | 0.903819i | \(-0.640752\pi\) | ||||
−0.427916 | + | 0.903819i | \(0.640752\pi\) | |||||||
\(402\) | 209273. | 0.0645873 | ||||||||
\(403\) | −363985. | −0.111640 | ||||||||
\(404\) | 192722. | 0.0587458 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 102116. | 0.0307454 | ||||||||
\(407\) | 941677. | 0.281784 | ||||||||
\(408\) | 1.14993e6 | 0.341995 | ||||||||
\(409\) | 2.37262e6 | 0.701326 | 0.350663 | − | 0.936502i | \(-0.385956\pi\) | ||||
0.350663 | + | 0.936502i | \(0.385956\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.70088e6 | −1.08069 | ||||||||
\(412\) | −27463.4 | −0.00797097 | ||||||||
\(413\) | −1.26104e6 | −0.363793 | ||||||||
\(414\) | 2.09408e6 | 0.600472 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −395390. | −0.112019 | ||||||||
\(417\) | −3.46191e6 | −0.974934 | ||||||||
\(418\) | 919789. | 0.257482 | ||||||||
\(419\) | −1.55244e6 | −0.431996 | −0.215998 | − | 0.976394i | \(-0.569300\pi\) | ||||
−0.215998 | + | 0.976394i | \(0.569300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.71814e6 | −0.472446 | −0.236223 | − | 0.971699i | \(-0.575910\pi\) | ||||
−0.236223 | + | 0.971699i | \(0.575910\pi\) | |||||||
\(422\) | 4.30061e6 | 1.17557 | ||||||||
\(423\) | −761923. | −0.207043 | ||||||||
\(424\) | 7.28941e6 | 1.96915 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −38644.6 | −0.0103173 | ||||||||
\(427\) | 1.03815e6 | 0.275543 | ||||||||
\(428\) | 173477. | 0.0457754 | ||||||||
\(429\) | 471596. | 0.123716 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.93876e6 | −0.762029 | −0.381015 | − | 0.924569i | \(-0.624425\pi\) | ||||
−0.381015 | + | 0.924569i | \(0.624425\pi\) | |||||||
\(432\) | 682864. | 0.176046 | ||||||||
\(433\) | 6.64391e6 | 1.70296 | 0.851480 | − | 0.524388i | \(-0.175706\pi\) | ||||
0.851480 | + | 0.524388i | \(0.175706\pi\) | |||||||
\(434\) | −132752. | −0.0338312 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 267420. | 0.0673717 | ||||||||
\(437\) | 6.66809e6 | 1.67031 | ||||||||
\(438\) | −2.65572e6 | −0.661449 | ||||||||
\(439\) | 1.90964e6 | 0.472922 | 0.236461 | − | 0.971641i | \(-0.424012\pi\) | ||||
0.236461 | + | 0.971641i | \(0.424012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.29281e6 | −0.316546 | ||||||||
\(442\) | −1.60250e6 | −0.390160 | ||||||||
\(443\) | −4.69600e6 | −1.13689 | −0.568445 | − | 0.822721i | \(-0.692455\pi\) | ||||
−0.568445 | + | 0.822721i | \(0.692455\pi\) | |||||||
\(444\) | 177065. | 0.0426261 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 708447. | 0.168644 | ||||||||
\(447\) | 553843. | 0.131105 | ||||||||
\(448\) | −1.01628e6 | −0.239231 | ||||||||
\(449\) | 4.56839e6 | 1.06942 | 0.534708 | − | 0.845037i | \(-0.320421\pi\) | ||||
0.534708 | + | 0.845037i | \(0.320421\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.91065e6 | −0.442323 | ||||||||
\(452\) | 258244. | 0.0594545 | ||||||||
\(453\) | 3.03853e6 | 0.695694 | ||||||||
\(454\) | −3.34171e6 | −0.760902 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.36220e6 | 0.531991 | ||||||||
\(457\) | 3.14110e6 | 0.703545 | 0.351772 | − | 0.936086i | \(-0.385579\pi\) | ||||
0.351772 | + | 0.936086i | \(0.385579\pi\) | |||||||
\(458\) | −3.79095e6 | −0.844470 | ||||||||
\(459\) | −496911. | −0.110090 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.26633e6 | 0.277521 | 0.138760 | − | 0.990326i | \(-0.455688\pi\) | ||||
0.138760 | + | 0.990326i | \(0.455688\pi\) | |||||||
\(462\) | 172000. | 0.0374907 | ||||||||
\(463\) | −1.84439e6 | −0.399852 | −0.199926 | − | 0.979811i | \(-0.564070\pi\) | ||||
−0.199926 | + | 0.979811i | \(0.564070\pi\) | |||||||
\(464\) | 605622. | 0.130589 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.42308e6 | −0.730217 | ||||||||
\(467\) | −3.10954e6 | −0.659787 | −0.329894 | − | 0.944018i | \(-0.607013\pi\) | ||||
−0.329894 | + | 0.944018i | \(0.607013\pi\) | |||||||
\(468\) | 88675.1 | 0.0187149 | ||||||||
\(469\) | 124612. | 0.0261594 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.09725e6 | 0.851021 | ||||||||
\(472\) | −8.12476e6 | −1.67863 | ||||||||
\(473\) | −103730. | −0.0213182 | ||||||||
\(474\) | −1.20478e6 | −0.246299 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 50132.6 | 0.0101415 | ||||||||
\(477\) | −3.14993e6 | −0.633878 | ||||||||
\(478\) | −4.78055e6 | −0.956992 | ||||||||
\(479\) | −2.08110e6 | −0.414433 | −0.207216 | − | 0.978295i | \(-0.566440\pi\) | ||||
−0.207216 | + | 0.978295i | \(0.566440\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.37023e6 | −0.664196 | ||||||||
\(482\) | −528132. | −0.103544 | ||||||||
\(483\) | 1.24693e6 | 0.243206 | ||||||||
\(484\) | −37012.2 | −0.00718177 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −320566. | −0.0615640 | ||||||||
\(487\) | −4.11669e6 | −0.786549 | −0.393274 | − | 0.919421i | \(-0.628658\pi\) | ||||
−0.393274 | + | 0.919421i | \(0.628658\pi\) | |||||||
\(488\) | 6.68868e6 | 1.27142 | ||||||||
\(489\) | −327621. | −0.0619583 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.82019e6 | −1.65110 | −0.825552 | − | 0.564326i | \(-0.809136\pi\) | ||||
−0.825552 | + | 0.564326i | \(0.809136\pi\) | |||||||
\(492\) | −359263. | −0.0669113 | ||||||||
\(493\) | −440703. | −0.0816636 | ||||||||
\(494\) | −3.29189e6 | −0.606915 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −787313. | −0.143696 | ||||||||
\(497\) | −23011.1 | −0.00417874 | ||||||||
\(498\) | −3.31194e6 | −0.598425 | ||||||||
\(499\) | 6.69775e6 | 1.20414 | 0.602071 | − | 0.798442i | \(-0.294342\pi\) | ||||
0.602071 | + | 0.798442i | \(0.294342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.34911e6 | 0.418129 | ||||||||
\(502\) | −190516. | −0.0337422 | ||||||||
\(503\) | −3.07340e6 | −0.541626 | −0.270813 | − | 0.962632i | \(-0.587293\pi\) | ||||
−0.270813 | + | 0.962632i | \(0.587293\pi\) | |||||||
\(504\) | 441730. | 0.0774605 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.12820e6 | 0.543147 | ||||||||
\(507\) | 1.65381e6 | 0.285737 | ||||||||
\(508\) | 765840. | 0.131668 | ||||||||
\(509\) | −1.01798e6 | −0.174158 | −0.0870789 | − | 0.996201i | \(-0.527753\pi\) | ||||
−0.0870789 | + | 0.996201i | \(0.527753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.58136e6 | −0.267903 | ||||||||
\(512\) | −6.47391e6 | −1.09142 | ||||||||
\(513\) | −1.02076e6 | −0.171250 | ||||||||
\(514\) | 7.88791e6 | 1.31690 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −19504.5 | −0.00322485 | ||||||||
\(517\) | −1.13818e6 | −0.187277 | ||||||||
\(518\) | −1.22918e6 | −0.201276 | ||||||||
\(519\) | 551737. | 0.0899112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.06152e6 | −0.171331 | −0.0856653 | − | 0.996324i | \(-0.527302\pi\) | ||||
−0.0856653 | + | 0.996324i | \(0.527302\pi\) | |||||||
\(522\) | −284305. | −0.0456676 | ||||||||
\(523\) | −5.52884e6 | −0.883852 | −0.441926 | − | 0.897051i | \(-0.645705\pi\) | ||||
−0.441926 | + | 0.897051i | \(0.645705\pi\) | |||||||
\(524\) | 828026. | 0.131739 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.11077e6 | 1.43579 | ||||||||
\(527\) | 572917. | 0.0898597 | ||||||||
\(528\) | 1.02008e6 | 0.159239 | ||||||||
\(529\) | 1.62418e7 | 2.52345 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.51091e6 | 0.540360 | ||||||||
\(532\) | 102983. | 0.0157757 | ||||||||
\(533\) | 6.83814e6 | 1.04261 | ||||||||
\(534\) | 2.10212e6 | 0.319009 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 802862. | 0.120706 | ||||||||
\(537\) | 6.90223e6 | 1.03289 | ||||||||
\(538\) | −1.13397e7 | −1.68907 | ||||||||
\(539\) | −1.93123e6 | −0.286327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.20998e6 | 0.324634 | 0.162317 | − | 0.986739i | \(-0.448103\pi\) | ||||
0.162317 | + | 0.986739i | \(0.448103\pi\) | |||||||
\(542\) | −321196. | −0.0469647 | ||||||||
\(543\) | −1.04815e6 | −0.152554 | ||||||||
\(544\) | 622349. | 0.0901648 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −615581. | −0.0883698 | ||||||||
\(547\) | −3.95818e6 | −0.565624 | −0.282812 | − | 0.959175i | \(-0.591267\pi\) | ||||
−0.282812 | + | 0.959175i | \(0.591267\pi\) | |||||||
\(548\) | −1.03953e6 | −0.147872 | ||||||||
\(549\) | −2.89034e6 | −0.409278 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −905300. | −0.127032 | ||||||||
\(552\) | 8.03382e6 | 1.12221 | ||||||||
\(553\) | −717391. | −0.0997569 | ||||||||
\(554\) | 7.47885e6 | 1.03529 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −972404. | −0.133401 | ||||||||
\(557\) | −2.04981e6 | −0.279947 | −0.139974 | − | 0.990155i | \(-0.544702\pi\) | ||||
−0.139974 | + | 0.990155i | \(0.544702\pi\) | |||||||
\(558\) | 369599. | 0.0502511 | ||||||||
\(559\) | 371245. | 0.0502494 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −742299. | −0.0995799 | ||||||||
\(562\) | 1.89040e6 | 0.252471 | ||||||||
\(563\) | −2.43373e6 | −0.323595 | −0.161798 | − | 0.986824i | \(-0.551729\pi\) | ||||
−0.161798 | + | 0.986824i | \(0.551729\pi\) | |||||||
\(564\) | −214014. | −0.0283299 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.52132e6 | 0.986854 | ||||||||
\(567\) | −190882. | −0.0249349 | ||||||||
\(568\) | −148258. | −0.0192817 | ||||||||
\(569\) | −2.17438e6 | −0.281549 | −0.140775 | − | 0.990042i | \(-0.544959\pi\) | ||||
−0.140775 | + | 0.990042i | \(0.544959\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.30560e6 | −1.19441 | −0.597206 | − | 0.802088i | \(-0.703722\pi\) | ||||
−0.597206 | + | 0.802088i | \(0.703722\pi\) | |||||||
\(572\) | 132465. | 0.0169282 | ||||||||
\(573\) | 7.33152e6 | 0.932840 | ||||||||
\(574\) | 2.49400e6 | 0.315949 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.82945e6 | 0.355342 | ||||||||
\(577\) | −1.43013e7 | −1.78828 | −0.894138 | − | 0.447791i | \(-0.852211\pi\) | ||||
−0.894138 | + | 0.447791i | \(0.852211\pi\) | |||||||
\(578\) | −5.18578e6 | −0.645646 | ||||||||
\(579\) | 736426. | 0.0912920 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.97211e6 | −0.242377 | ||||||||
\(582\) | 3.77677e6 | 0.462182 | ||||||||
\(583\) | −4.70546e6 | −0.573364 | ||||||||
\(584\) | −1.01885e7 | −1.23617 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.65803e6 | 0.921240 | ||||||||
\(587\) | 1.27072e7 | 1.52214 | 0.761068 | − | 0.648672i | \(-0.224675\pi\) | ||||
0.761068 | + | 0.648672i | \(0.224675\pi\) | |||||||
\(588\) | −363132. | −0.0433133 | ||||||||
\(589\) | 1.17690e6 | 0.139782 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.79628e6 | 0.447084 | ||||||||
\(592\) | −7.28993e6 | −0.854908 | ||||||||
\(593\) | −1.24734e7 | −1.45662 | −0.728311 | − | 0.685246i | \(-0.759695\pi\) | ||||
−0.728311 | + | 0.685246i | \(0.759695\pi\) | |||||||
\(594\) | −478870. | −0.0556867 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 155567. | 0.0179392 | ||||||||
\(597\) | −2.65178e6 | −0.304510 | ||||||||
\(598\) | −1.11957e7 | −1.28026 | ||||||||
\(599\) | −2.89494e6 | −0.329665 | −0.164832 | − | 0.986322i | \(-0.552708\pi\) | ||||
−0.164832 | + | 0.986322i | \(0.552708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.26362e7 | −1.42702 | −0.713508 | − | 0.700647i | \(-0.752895\pi\) | ||||
−0.713508 | + | 0.700647i | \(0.752895\pi\) | |||||||
\(602\) | 135400. | 0.0152274 | ||||||||
\(603\) | −346936. | −0.0388559 | ||||||||
\(604\) | 853484. | 0.0951925 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.72481e6 | 0.412024 | ||||||||
\(607\) | 4.63540e6 | 0.510641 | 0.255320 | − | 0.966857i | \(-0.417819\pi\) | ||||
0.255320 | + | 0.966857i | \(0.417819\pi\) | |||||||
\(608\) | 1.27844e6 | 0.140256 | ||||||||
\(609\) | −169291. | −0.0184965 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.07351e6 | 0.441434 | ||||||||
\(612\) | −139576. | −0.0150637 | ||||||||
\(613\) | −1.22937e6 | −0.132139 | −0.0660696 | − | 0.997815i | \(-0.521046\pi\) | ||||
−0.0660696 | + | 0.997815i | \(0.521046\pi\) | |||||||
\(614\) | 1.08324e7 | 1.15959 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 659868. | 0.0700657 | ||||||||
\(617\) | 2.09847e6 | 0.221917 | 0.110959 | − | 0.993825i | \(-0.464608\pi\) | ||||
0.110959 | + | 0.993825i | \(0.464608\pi\) | |||||||
\(618\) | −530796. | −0.0559057 | ||||||||
\(619\) | 4.56327e6 | 0.478684 | 0.239342 | − | 0.970935i | \(-0.423068\pi\) | ||||
0.239342 | + | 0.970935i | \(0.423068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.47161e6 | −0.361245 | ||||||||
\(622\) | −1.07878e7 | −1.11804 | ||||||||
\(623\) | 1.25171e6 | 0.129207 | ||||||||
\(624\) | −3.65083e6 | −0.375345 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.00264e6 | 0.408235 | ||||||||
\(627\) | −1.52484e6 | −0.154902 | ||||||||
\(628\) | 1.15086e6 | 0.116446 | ||||||||
\(629\) | 5.30478e6 | 0.534615 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.71323e6 | 0.471243 | 0.235622 | − | 0.971845i | \(-0.424287\pi\) | ||||
0.235622 | + | 0.971845i | \(0.424287\pi\) | |||||||
\(632\) | −4.62207e6 | −0.460303 | ||||||||
\(633\) | −7.12963e6 | −0.707225 | ||||||||
\(634\) | 1.40238e7 | 1.38561 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −884775. | −0.0867341 | ||||||||
\(637\) | 6.91180e6 | 0.674905 | ||||||||
\(638\) | −424703. | −0.0413079 | ||||||||
\(639\) | 64065.8 | 0.00620689 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.81979e6 | −0.367193 | −0.183597 | − | 0.983002i | \(-0.558774\pi\) | ||||
−0.183597 | + | 0.983002i | \(0.558774\pi\) | |||||||
\(642\) | 3.35286e6 | 0.321054 | ||||||||
\(643\) | −1.69452e7 | −1.61629 | −0.808143 | − | 0.588986i | \(-0.799527\pi\) | ||||
−0.808143 | + | 0.588986i | \(0.799527\pi\) | |||||||
\(644\) | 350246. | 0.0332781 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.18148e6 | 0.488509 | ||||||||
\(647\) | 9.06068e6 | 0.850942 | 0.425471 | − | 0.904972i | \(-0.360108\pi\) | ||||
0.425471 | + | 0.904972i | \(0.360108\pi\) | |||||||
\(648\) | −1.22983e6 | −0.115056 | ||||||||
\(649\) | 5.24469e6 | 0.488774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 220079. | 0.0203529 | ||||||||
\(652\) | −92024.4 | −0.00847782 | ||||||||
\(653\) | −1.19377e7 | −1.09556 | −0.547781 | − | 0.836622i | \(-0.684527\pi\) | ||||
−0.547781 | + | 0.836622i | \(0.684527\pi\) | |||||||
\(654\) | 5.16853e6 | 0.472523 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.47912e7 | 1.34197 | ||||||||
\(657\) | 4.40270e6 | 0.397929 | ||||||||
\(658\) | 1.48569e6 | 0.133771 | ||||||||
\(659\) | 1.37103e7 | 1.22979 | 0.614897 | − | 0.788607i | \(-0.289197\pi\) | ||||
0.614897 | + | 0.788607i | \(0.289197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −249304. | −0.0221935 | −0.0110967 | − | 0.999938i | \(-0.503532\pi\) | ||||
−0.0110967 | + | 0.999938i | \(0.503532\pi\) | |||||||
\(662\) | −1.43004e6 | −0.126824 | ||||||||
\(663\) | 2.65666e6 | 0.234721 | ||||||||
\(664\) | −1.27061e7 | −1.11839 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.42221e6 | 0.298965 | ||||||||
\(667\) | −3.07892e6 | −0.267968 | ||||||||
\(668\) | 659835. | 0.0572130 | ||||||||
\(669\) | −1.17448e6 | −0.101456 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.31767e6 | −0.370206 | ||||||||
\(672\) | 239068. | 0.0204220 | ||||||||
\(673\) | −1.03766e7 | −0.883116 | −0.441558 | − | 0.897233i | \(-0.645574\pi\) | ||||
−0.441558 | + | 0.897233i | \(0.645574\pi\) | |||||||
\(674\) | −9.47297e6 | −0.803223 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 464534. | 0.0390976 | ||||||||
\(677\) | 2.08995e7 | 1.75253 | 0.876263 | − | 0.481834i | \(-0.160029\pi\) | ||||
0.876263 | + | 0.481834i | \(0.160029\pi\) | |||||||
\(678\) | 4.99119e6 | 0.416994 | ||||||||
\(679\) | 2.24889e6 | 0.187195 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.53995e6 | 0.457760 | ||||||||
\(682\) | 552117. | 0.0454538 | ||||||||
\(683\) | 1.51871e7 | 1.24573 | 0.622864 | − | 0.782330i | \(-0.285969\pi\) | ||||
0.622864 | + | 0.782330i | \(0.285969\pi\) | |||||||
\(684\) | −286719. | −0.0234324 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.17541e6 | 0.419889 | ||||||||
\(687\) | 6.28471e6 | 0.508035 | ||||||||
\(688\) | 803017. | 0.0646776 | ||||||||
\(689\) | 1.68407e7 | 1.35148 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.73343e7 | −1.38105 | −0.690527 | − | 0.723307i | \(-0.742621\pi\) | ||||
−0.690527 | + | 0.723307i | \(0.742621\pi\) | |||||||
\(692\) | 154976. | 0.0123026 | ||||||||
\(693\) | −285145. | −0.0225545 | ||||||||
\(694\) | 1.74504e7 | 1.37533 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.09072e6 | −0.0853474 | ||||||||
\(697\) | −1.07633e7 | −0.839198 | ||||||||
\(698\) | 1.55926e6 | 0.121138 | ||||||||
\(699\) | 5.67485e6 | 0.439300 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.14097e6 | −0.548861 | −0.274430 | − | 0.961607i | \(-0.588489\pi\) | ||||
−0.274430 | + | 0.961607i | \(0.588489\pi\) | |||||||
\(702\) | 1.71386e6 | 0.131260 | ||||||||
\(703\) | 1.08972e7 | 0.831622 | ||||||||
\(704\) | 4.22671e6 | 0.321419 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.71828e6 | −0.507278 | ||||||||
\(707\) | 2.21795e6 | 0.166880 | ||||||||
\(708\) | 986168. | 0.0739380 | ||||||||
\(709\) | 2.01962e7 | 1.50887 | 0.754437 | − | 0.656372i | \(-0.227910\pi\) | ||||
0.754437 | + | 0.656372i | \(0.227910\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.99731e6 | 0.148174 | ||||||||
\(712\) | 8.06465e6 | 0.596191 | ||||||||
\(713\) | 4.00262e6 | 0.294863 | ||||||||
\(714\) | 968933. | 0.0711293 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.93875e6 | 0.141331 | ||||||||
\(717\) | 7.92530e6 | 0.575728 | ||||||||
\(718\) | 2.43762e7 | 1.76463 | ||||||||
\(719\) | 1.32950e6 | 0.0959106 | 0.0479553 | − | 0.998849i | \(-0.484729\pi\) | ||||
0.0479553 | + | 0.998849i | \(0.484729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −316064. | −0.0226432 | ||||||||
\(722\) | −2.79839e6 | −0.199786 | ||||||||
\(723\) | 875549. | 0.0622924 | ||||||||
\(724\) | −294411. | −0.0208741 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −715349. | −0.0503705 | ||||||||
\(727\) | 1.28863e7 | 0.904256 | 0.452128 | − | 0.891953i | \(-0.350665\pi\) | ||||
0.452128 | + | 0.891953i | \(0.350665\pi\) | |||||||
\(728\) | −2.36164e6 | −0.165153 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −584344. | −0.0404460 | ||||||||
\(732\) | −811859. | −0.0560019 | ||||||||
\(733\) | −1.88150e7 | −1.29344 | −0.646718 | − | 0.762729i | \(-0.723859\pi\) | ||||
−0.646718 | + | 0.762729i | \(0.723859\pi\) | |||||||
\(734\) | −1.39102e7 | −0.953003 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.34797e6 | 0.295864 | ||||||||
\(737\) | −518263. | −0.0351465 | ||||||||
\(738\) | −6.94361e6 | −0.469294 | ||||||||
\(739\) | 3.60917e6 | 0.243106 | 0.121553 | − | 0.992585i | \(-0.461213\pi\) | ||||
0.121553 | + | 0.992585i | \(0.461213\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.45736e6 | 0.365121 | ||||||||
\(742\) | 6.14210e6 | 0.409550 | ||||||||
\(743\) | 9.49631e6 | 0.631078 | 0.315539 | − | 0.948913i | \(-0.397815\pi\) | ||||
0.315539 | + | 0.948913i | \(0.397815\pi\) | |||||||
\(744\) | 1.41794e6 | 0.0939133 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.83941e6 | 0.515747 | ||||||||
\(747\) | 5.49061e6 | 0.360014 | ||||||||
\(748\) | −208502. | −0.0136256 | ||||||||
\(749\) | 1.99647e6 | 0.130035 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.77857e7 | −1.79772 | −0.898858 | − | 0.438241i | \(-0.855602\pi\) | ||||
−0.898858 | + | 0.438241i | \(0.855602\pi\) | |||||||
\(752\) | 8.81116e6 | 0.568184 | ||||||||
\(753\) | 315842. | 0.0202994 | ||||||||
\(754\) | 1.52000e6 | 0.0973675 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −53616.3 | −0.00341187 | ||||||||
\(757\) | 1.28586e7 | 0.815557 | 0.407778 | − | 0.913081i | \(-0.366304\pi\) | ||||
0.407778 | + | 0.913081i | \(0.366304\pi\) | |||||||
\(758\) | −1.66738e7 | −1.05405 | ||||||||
\(759\) | −5.18599e6 | −0.326759 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.18383e7 | 1.36696 | 0.683481 | − | 0.729968i | \(-0.260465\pi\) | ||||
0.683481 | + | 0.729968i | \(0.260465\pi\) | |||||||
\(762\) | 1.48017e7 | 0.923472 | ||||||||
\(763\) | 3.07762e6 | 0.191383 | ||||||||
\(764\) | 2.05933e6 | 0.127642 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.66312e6 | −0.163991 | ||||||||
\(767\) | −1.87706e7 | −1.15210 | ||||||||
\(768\) | 2.22227e6 | 0.135955 | ||||||||
\(769\) | −2.24376e7 | −1.36824 | −0.684119 | − | 0.729371i | \(-0.739813\pi\) | ||||
−0.684119 | + | 0.729371i | \(0.739813\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.30767e7 | −0.792252 | ||||||||
\(772\) | 206852. | 0.0124916 | ||||||||
\(773\) | 2.89760e7 | 1.74417 | 0.872085 | − | 0.489354i | \(-0.162767\pi\) | ||||
0.872085 | + | 0.489354i | \(0.162767\pi\) | |||||||
\(774\) | −376971. | −0.0226181 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.44894e7 | 0.863764 | ||||||||
\(777\) | 2.03777e6 | 0.121088 | ||||||||
\(778\) | −1.14414e7 | −0.677690 | ||||||||
\(779\) | −2.21102e7 | −1.30542 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 95703.2 | 0.00561434 | ||||||||
\(782\) | 1.76222e7 | 1.03049 | ||||||||
\(783\) | 471327. | 0.0274737 | ||||||||
\(784\) | 1.49505e7 | 0.868691 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.60036e7 | 0.923977 | ||||||||
\(787\) | −1.92570e7 | −1.10829 | −0.554143 | − | 0.832421i | \(-0.686954\pi\) | ||||
−0.554143 | + | 0.832421i | \(0.686954\pi\) | |||||||
\(788\) | 1.06632e6 | 0.0611750 | ||||||||
\(789\) | −1.51040e7 | −0.863774 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.97203e6 | 0.168893 | ||||||||
\(792\) | −1.83716e6 | −0.104072 | ||||||||
\(793\) | 1.54528e7 | 0.872617 | ||||||||
\(794\) | −9.60544e6 | −0.540712 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −744849. | −0.0416664 | ||||||||
\(797\) | 1.99816e7 | 1.11425 | 0.557127 | − | 0.830427i | \(-0.311903\pi\) | ||||
0.557127 | + | 0.830427i | \(0.311903\pi\) | |||||||
\(798\) | 1.99040e6 | 0.110645 | ||||||||
\(799\) | −6.41176e6 | −0.355312 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.48493e6 | −0.191917 | ||||||||
\(802\) | −1.49608e7 | −0.821331 | ||||||||
\(803\) | 6.57688e6 | 0.359941 | ||||||||
\(804\) | −97449.9 | −0.00531669 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.97601e6 | −0.107140 | ||||||||
\(807\) | 1.87993e7 | 1.01615 | ||||||||
\(808\) | 1.42900e7 | 0.770023 | ||||||||
\(809\) | 6.88532e6 | 0.369873 | 0.184936 | − | 0.982750i | \(-0.440792\pi\) | ||||
0.184936 | + | 0.982750i | \(0.440792\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.40242e7 | 0.748729 | 0.374365 | − | 0.927282i | \(-0.377861\pi\) | ||||
0.374365 | + | 0.927282i | \(0.377861\pi\) | |||||||
\(812\) | −47551.5 | −0.00253089 | ||||||||
\(813\) | 532485. | 0.0282541 | ||||||||
\(814\) | 5.11219e6 | 0.270424 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.74646e6 | 0.302117 | ||||||||
\(817\) | −1.20037e6 | −0.0629159 | ||||||||
\(818\) | 1.28805e7 | 0.673054 | ||||||||
\(819\) | 1.02052e6 | 0.0531635 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.51193e7 | −0.782843 | −0.391421 | − | 0.920212i | \(-0.628016\pi\) | ||||
−0.391421 | + | 0.920212i | \(0.628016\pi\) | |||||||
\(822\) | −2.00914e7 | −1.03712 | ||||||||
\(823\) | −1.05051e7 | −0.540633 | −0.270316 | − | 0.962772i | \(-0.587128\pi\) | ||||
−0.270316 | + | 0.962772i | \(0.587128\pi\) | |||||||
\(824\) | −2.03637e6 | −0.104481 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.84597e6 | −0.349128 | ||||||||
\(827\) | 2.78766e7 | 1.41735 | 0.708673 | − | 0.705537i | \(-0.249294\pi\) | ||||
0.708673 | + | 0.705537i | \(0.249294\pi\) | |||||||
\(828\) | −975130. | −0.0494296 | ||||||||
\(829\) | −1.72518e7 | −0.871865 | −0.435933 | − | 0.899979i | \(-0.643581\pi\) | ||||
−0.435933 | + | 0.899979i | \(0.643581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.23986e7 | −0.622831 | ||||||||
\(832\) | −1.51272e7 | −0.757620 | ||||||||
\(833\) | −1.08793e7 | −0.543234 | ||||||||
\(834\) | −1.87940e7 | −0.935632 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −428309. | −0.0211954 | ||||||||
\(837\) | −612729. | −0.0302311 | ||||||||
\(838\) | −8.42791e6 | −0.414581 | ||||||||
\(839\) | 7.21252e6 | 0.353738 | 0.176869 | − | 0.984234i | \(-0.443403\pi\) | ||||
0.176869 | + | 0.984234i | \(0.443403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00931e7 | −0.979620 | ||||||||
\(842\) | −9.32744e6 | −0.453401 | ||||||||
\(843\) | −3.13394e6 | −0.151887 | ||||||||
\(844\) | −2.00262e6 | −0.0967704 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.13634e6 | −0.198697 | ||||||||
\(847\) | −425957. | −0.0204013 | ||||||||
\(848\) | 3.64270e7 | 1.73954 | ||||||||
\(849\) | −1.24690e7 | −0.593693 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.70612e7 | 1.75427 | ||||||||
\(852\) | 17995.2 | 0.000849295 0 | ||||||||
\(853\) | −807294. | −0.0379891 | −0.0189946 | − | 0.999820i | \(-0.506047\pi\) | ||||
−0.0189946 | + | 0.999820i | \(0.506047\pi\) | |||||||
\(854\) | 5.63592e6 | 0.264436 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.28630e7 | 0.600011 | ||||||||
\(857\) | −1.65206e7 | −0.768376 | −0.384188 | − | 0.923255i | \(-0.625519\pi\) | ||||
−0.384188 | + | 0.923255i | \(0.625519\pi\) | |||||||
\(858\) | 2.56021e6 | 0.118729 | ||||||||
\(859\) | −1.50645e7 | −0.696580 | −0.348290 | − | 0.937387i | \(-0.613237\pi\) | ||||
−0.348290 | + | 0.937387i | \(0.613237\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.13460e6 | −0.190075 | ||||||||
\(862\) | −1.59540e7 | −0.731310 | ||||||||
\(863\) | 3.63009e6 | 0.165917 | 0.0829584 | − | 0.996553i | \(-0.473563\pi\) | ||||
0.0829584 | + | 0.996553i | \(0.473563\pi\) | |||||||
\(864\) | −665596. | −0.0303338 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.60686e7 | 1.63431 | ||||||||
\(867\) | 8.59709e6 | 0.388422 | ||||||||
\(868\) | 61817.3 | 0.00278491 | ||||||||
\(869\) | 2.98363e6 | 0.134028 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.85484e6 | 0.0828442 | ||||||||
\(872\) | 1.98288e7 | 0.883090 | ||||||||
\(873\) | −6.26121e6 | −0.278050 | ||||||||
\(874\) | 3.61998e7 | 1.60298 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.23666e6 | 0.0544491 | ||||||||
\(877\) | 3.86808e7 | 1.69823 | 0.849116 | − | 0.528207i | \(-0.177136\pi\) | ||||
0.849116 | + | 0.528207i | \(0.177136\pi\) | |||||||
\(878\) | 1.03671e7 | 0.453858 | ||||||||
\(879\) | −1.26956e7 | −0.554220 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.53508e6 | 0.370483 | 0.185241 | − | 0.982693i | \(-0.440693\pi\) | ||||
0.185241 | + | 0.982693i | \(0.440693\pi\) | |||||||
\(882\) | −7.01840e6 | −0.303785 | ||||||||
\(883\) | −2.01181e7 | −0.868331 | −0.434165 | − | 0.900833i | \(-0.642957\pi\) | ||||
−0.434165 | + | 0.900833i | \(0.642957\pi\) | |||||||
\(884\) | 746221. | 0.0321171 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.54937e7 | −1.09106 | ||||||||
\(887\) | −1.42523e7 | −0.608243 | −0.304122 | − | 0.952633i | \(-0.598363\pi\) | ||||
−0.304122 | + | 0.952633i | \(0.598363\pi\) | |||||||
\(888\) | 1.31291e7 | 0.558731 | ||||||||
\(889\) | 8.81372e6 | 0.374029 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −329895. | −0.0138824 | ||||||||
\(893\) | −1.31712e7 | −0.552708 | ||||||||
\(894\) | 3.00671e6 | 0.125819 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.66717e6 | −0.194215 | ||||||||
\(897\) | 1.85605e7 | 0.770207 | ||||||||
\(898\) | 2.48009e7 | 1.02631 | ||||||||
\(899\) | −543420. | −0.0224252 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.65074e7 | −1.08782 | ||||||||
\(902\) | −1.03726e7 | −0.424492 | ||||||||
\(903\) | −224469. | −0.00916086 | ||||||||
\(904\) | 1.91484e7 | 0.779313 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.64956e7 | 0.667649 | ||||||||
\(907\) | −2.45446e7 | −0.990689 | −0.495345 | − | 0.868697i | \(-0.664958\pi\) | ||||
−0.495345 | + | 0.868697i | \(0.664958\pi\) | |||||||
\(908\) | 1.55610e6 | 0.0626358 | ||||||||
\(909\) | −6.17506e6 | −0.247874 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.04542e7 | 1.61498 | 0.807491 | − | 0.589880i | \(-0.200825\pi\) | ||||
0.807491 | + | 0.589880i | \(0.200825\pi\) | |||||||
\(912\) | 1.18045e7 | 0.469959 | ||||||||
\(913\) | 8.20202e6 | 0.325645 | ||||||||
\(914\) | 1.70525e7 | 0.675183 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.76529e6 | 0.0695149 | ||||||||
\(917\) | 9.52940e6 | 0.374233 | ||||||||
\(918\) | −2.69764e6 | −0.105652 | ||||||||
\(919\) | −3.79964e7 | −1.48407 | −0.742033 | − | 0.670363i | \(-0.766138\pi\) | ||||
−0.742033 | + | 0.670363i | \(0.766138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.79582e7 | −0.697612 | ||||||||
\(922\) | 6.87468e6 | 0.266333 | ||||||||
\(923\) | −342518. | −0.0132336 | ||||||||
\(924\) | −80093.5 | −0.00308615 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.00128e7 | −0.383733 | ||||||||
\(927\) | 879964. | 0.0336330 | ||||||||
\(928\) | −590307. | −0.0225013 | ||||||||
\(929\) | −4.20556e6 | −0.159876 | −0.0799382 | − | 0.996800i | \(-0.525472\pi\) | ||||
−0.0799382 | + | 0.996800i | \(0.525472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.23484e7 | −0.845030 | ||||||||
\(932\) | 1.59399e6 | 0.0601099 | ||||||||
\(933\) | 1.78842e7 | 0.672613 | ||||||||
\(934\) | −1.68811e7 | −0.633190 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.57512e6 | 0.245309 | ||||||||
\(937\) | 3.39406e6 | 0.126291 | 0.0631453 | − | 0.998004i | \(-0.479887\pi\) | ||||
0.0631453 | + | 0.998004i | \(0.479887\pi\) | |||||||
\(938\) | 676496. | 0.0251049 | ||||||||
\(939\) | −6.63566e6 | −0.245595 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.89822e6 | 0.217144 | 0.108572 | − | 0.994089i | \(-0.465372\pi\) | ||||
0.108572 | + | 0.994089i | \(0.465372\pi\) | |||||||
\(942\) | 2.22432e7 | 0.816714 | ||||||||
\(943\) | −7.51968e7 | −2.75372 | ||||||||
\(944\) | −4.06014e7 | −1.48290 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −563129. | −0.0204588 | ||||||||
\(947\) | 2.92768e7 | 1.06084 | 0.530419 | − | 0.847735i | \(-0.322034\pi\) | ||||
0.530419 | + | 0.847735i | \(0.322034\pi\) | |||||||
\(948\) | 561018. | 0.0202748 | ||||||||
\(949\) | −2.35384e7 | −0.848421 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.32489e7 | −0.833587 | ||||||||
\(952\) | 3.71726e6 | 0.132932 | ||||||||
\(953\) | 7.23007e6 | 0.257876 | 0.128938 | − | 0.991653i | \(-0.458843\pi\) | ||||
0.128938 | + | 0.991653i | \(0.458843\pi\) | |||||||
\(954\) | −1.71004e7 | −0.608325 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.22611e6 | 0.0787775 | ||||||||
\(957\) | 704081. | 0.0248509 | ||||||||
\(958\) | −1.12979e7 | −0.397726 | ||||||||
\(959\) | −1.19635e7 | −0.420060 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.79227e7 | −0.975324 | ||||||||
\(962\) | −1.82963e7 | −0.637421 | ||||||||
\(963\) | −5.55844e6 | −0.193147 | ||||||||
\(964\) | 245930. | 0.00852353 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.76934e6 | 0.233402 | ||||||||
\(967\) | −5.69785e7 | −1.95950 | −0.979748 | − | 0.200233i | \(-0.935830\pi\) | ||||
−0.979748 | + | 0.200233i | \(0.935830\pi\) | |||||||
\(968\) | −2.74440e6 | −0.0941366 | ||||||||
\(969\) | −8.58996e6 | −0.293888 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.34775e6 | 0.216059 | 0.108029 | − | 0.994148i | \(-0.465546\pi\) | ||||
0.108029 | + | 0.994148i | \(0.465546\pi\) | |||||||
\(972\) | 149275. | 0.00506782 | ||||||||
\(973\) | −1.11910e7 | −0.378954 | ||||||||
\(974\) | −2.23487e7 | −0.754841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.34250e7 | 1.12317 | ||||||||
\(977\) | 2.53017e7 | 0.848034 | 0.424017 | − | 0.905654i | \(-0.360620\pi\) | ||||
0.424017 | + | 0.905654i | \(0.360620\pi\) | |||||||
\(978\) | −1.77859e6 | −0.0594606 | ||||||||
\(979\) | −5.20588e6 | −0.173595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.56850e6 | −0.284271 | ||||||||
\(982\) | −4.78832e7 | −1.58454 | ||||||||
\(983\) | −5.27528e7 | −1.74125 | −0.870627 | − | 0.491944i | \(-0.836287\pi\) | ||||
−0.870627 | + | 0.491944i | \(0.836287\pi\) | |||||||
\(984\) | −2.66388e7 | −0.877054 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.39249e6 | −0.0783715 | ||||||||
\(987\) | −2.46300e6 | −0.0804769 | ||||||||
\(988\) | 1.53290e6 | 0.0499599 | ||||||||
\(989\) | −4.08245e6 | −0.132718 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.05136e6 | −0.0663526 | −0.0331763 | − | 0.999450i | \(-0.510562\pi\) | ||||
−0.0331763 | + | 0.999450i | \(0.510562\pi\) | |||||||
\(992\) | 767404. | 0.0247597 | ||||||||
\(993\) | 2.37075e6 | 0.0762979 | ||||||||
\(994\) | −124923. | −0.00401029 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.54224e6 | 0.0492611 | ||||||||
\(997\) | −4.46568e7 | −1.42282 | −0.711409 | − | 0.702778i | \(-0.751943\pi\) | ||||
−0.711409 | + | 0.702778i | \(0.751943\pi\) | |||||||
\(998\) | 3.63609e7 | 1.15560 | ||||||||
\(999\) | −5.67341e6 | −0.179858 |
(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.o.1.5 | yes | 7 | |
5.4 | even | 2 | 825.6.a.m.1.3 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.m.1.3 | ✓ | 7 | 5.4 | even | 2 | ||
825.6.a.o.1.5 | yes | 7 | 1.1 | even | 1 | trivial |