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: | \(0\) |
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: | \( x^{13} - 306 x^{11} - 206 x^{10} + 34574 x^{9} + 39928 x^{8} - 1788312 x^{7} - 2591628 x^{6} + \cdots + 522579400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 5^{7} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-3.97394\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.97394 | 0.879277 | 0.439639 | − | 0.898175i | \(-0.355107\pi\) | ||||
0.439639 | + | 0.898175i | \(0.355107\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −7.25990 | −0.226872 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 44.7655 | 0.507651 | ||||||||
\(7\) | −155.412 | −1.19878 | −0.599388 | − | 0.800459i | \(-0.704589\pi\) | ||||
−0.599388 | + | 0.800459i | \(0.704589\pi\) | |||||||
\(8\) | −195.276 | −1.07876 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −65.3391 | −0.130985 | ||||||||
\(13\) | −1173.30 | −1.92554 | −0.962770 | − | 0.270323i | \(-0.912869\pi\) | ||||
−0.962770 | + | 0.270323i | \(0.912869\pi\) | |||||||
\(14\) | −773.008 | −1.05406 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −738.977 | −0.721657 | ||||||||
\(17\) | −898.118 | −0.753721 | −0.376861 | − | 0.926270i | \(-0.622996\pi\) | ||||
−0.376861 | + | 0.926270i | \(0.622996\pi\) | |||||||
\(18\) | 402.889 | 0.293092 | ||||||||
\(19\) | −2407.95 | −1.53026 | −0.765128 | − | 0.643879i | \(-0.777324\pi\) | ||||
−0.765128 | + | 0.643879i | \(0.777324\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1398.70 | −0.692114 | ||||||||
\(22\) | 601.847 | 0.265112 | ||||||||
\(23\) | 4121.12 | 1.62441 | 0.812205 | − | 0.583372i | \(-0.198267\pi\) | ||||
0.812205 | + | 0.583372i | \(0.198267\pi\) | |||||||
\(24\) | −1757.49 | −0.622823 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5835.95 | −1.69308 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 1128.27 | 0.271969 | ||||||||
\(29\) | 75.4479 | 0.0166591 | 0.00832957 | − | 0.999965i | \(-0.497349\pi\) | ||||
0.00832957 | + | 0.999965i | \(0.497349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3595.47 | 0.671972 | 0.335986 | − | 0.941867i | \(-0.390931\pi\) | ||||
0.335986 | + | 0.941867i | \(0.390931\pi\) | |||||||
\(32\) | 2573.22 | 0.444224 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | −4467.18 | −0.662730 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −588.052 | −0.0756240 | ||||||||
\(37\) | 16063.1 | 1.92897 | 0.964483 | − | 0.264145i | \(-0.0850898\pi\) | ||||
0.964483 | + | 0.264145i | \(0.0850898\pi\) | |||||||
\(38\) | −11977.0 | −1.34552 | ||||||||
\(39\) | −10559.7 | −1.11171 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15062.8 | 1.39941 | 0.699705 | − | 0.714432i | \(-0.253315\pi\) | ||||
0.699705 | + | 0.714432i | \(0.253315\pi\) | |||||||
\(42\) | −6957.07 | −0.608560 | ||||||||
\(43\) | 12867.8 | 1.06129 | 0.530643 | − | 0.847595i | \(-0.321950\pi\) | ||||
0.530643 | + | 0.847595i | \(0.321950\pi\) | |||||||
\(44\) | −878.448 | −0.0684045 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 20498.2 | 1.42831 | ||||||||
\(47\) | 6698.84 | 0.442339 | 0.221169 | − | 0.975235i | \(-0.429013\pi\) | ||||
0.221169 | + | 0.975235i | \(0.429013\pi\) | |||||||
\(48\) | −6650.79 | −0.416649 | ||||||||
\(49\) | 7345.75 | 0.437065 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8083.06 | −0.435161 | ||||||||
\(52\) | 8518.07 | 0.436851 | ||||||||
\(53\) | −22850.8 | −1.11741 | −0.558705 | − | 0.829367i | \(-0.688702\pi\) | ||||
−0.558705 | + | 0.829367i | \(0.688702\pi\) | |||||||
\(54\) | 3626.00 | 0.169217 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 30348.2 | 1.29319 | ||||||||
\(57\) | −21671.6 | −0.883493 | ||||||||
\(58\) | 375.274 | 0.0146480 | ||||||||
\(59\) | −13021.3 | −0.486995 | −0.243498 | − | 0.969901i | \(-0.578295\pi\) | ||||
−0.243498 | + | 0.969901i | \(0.578295\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 882.310 | 0.0303596 | 0.0151798 | − | 0.999885i | \(-0.495168\pi\) | ||||
0.0151798 | + | 0.999885i | \(0.495168\pi\) | |||||||
\(62\) | 17883.6 | 0.590849 | ||||||||
\(63\) | −12588.3 | −0.399592 | ||||||||
\(64\) | 36446.3 | 1.11225 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5416.62 | 0.153062 | ||||||||
\(67\) | 14191.7 | 0.386231 | 0.193115 | − | 0.981176i | \(-0.438141\pi\) | ||||
0.193115 | + | 0.981176i | \(0.438141\pi\) | |||||||
\(68\) | 6520.24 | 0.170998 | ||||||||
\(69\) | 37090.1 | 0.937854 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −78746.0 | −1.85388 | −0.926942 | − | 0.375205i | \(-0.877572\pi\) | ||||
−0.926942 | + | 0.375205i | \(0.877572\pi\) | |||||||
\(72\) | −15817.4 | −0.359587 | ||||||||
\(73\) | −34227.3 | −0.751736 | −0.375868 | − | 0.926673i | \(-0.622655\pi\) | ||||
−0.375868 | + | 0.926673i | \(0.622655\pi\) | |||||||
\(74\) | 79896.8 | 1.69610 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17481.5 | 0.347172 | ||||||||
\(77\) | −18804.8 | −0.361445 | ||||||||
\(78\) | −52523.5 | −0.977502 | ||||||||
\(79\) | −48694.6 | −0.877835 | −0.438917 | − | 0.898527i | \(-0.644638\pi\) | ||||
−0.438917 | + | 0.898527i | \(0.644638\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 74921.3 | 1.23047 | ||||||||
\(83\) | 95905.3 | 1.52809 | 0.764043 | − | 0.645166i | \(-0.223212\pi\) | ||||
0.764043 | + | 0.645166i | \(0.223212\pi\) | |||||||
\(84\) | 10154.5 | 0.157021 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 64003.6 | 0.933165 | ||||||||
\(87\) | 679.031 | 0.00961815 | ||||||||
\(88\) | −23628.5 | −0.325258 | ||||||||
\(89\) | 1342.55 | 0.0179662 | 0.00898308 | − | 0.999960i | \(-0.497141\pi\) | ||||
0.00898308 | + | 0.999960i | \(0.497141\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 182345. | 2.30829 | ||||||||
\(92\) | −29918.9 | −0.368533 | ||||||||
\(93\) | 32359.2 | 0.387963 | ||||||||
\(94\) | 33319.6 | 0.388938 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 23159.0 | 0.256473 | ||||||||
\(97\) | −80938.9 | −0.873430 | −0.436715 | − | 0.899600i | \(-0.643858\pi\) | ||||
−0.436715 | + | 0.899600i | \(0.643858\pi\) | |||||||
\(98\) | 36537.3 | 0.384301 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19225.2 | 0.187529 | 0.0937644 | − | 0.995594i | \(-0.470110\pi\) | ||||
0.0937644 | + | 0.995594i | \(0.470110\pi\) | |||||||
\(102\) | −40204.7 | −0.382627 | ||||||||
\(103\) | 126651. | 1.17630 | 0.588148 | − | 0.808753i | \(-0.299857\pi\) | ||||
0.588148 | + | 0.808753i | \(0.299857\pi\) | |||||||
\(104\) | 229119. | 2.07720 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −113659. | −0.982513 | ||||||||
\(107\) | −77773.3 | −0.656706 | −0.328353 | − | 0.944555i | \(-0.606494\pi\) | ||||
−0.328353 | + | 0.944555i | \(0.606494\pi\) | |||||||
\(108\) | −5292.47 | −0.0436615 | ||||||||
\(109\) | 68872.6 | 0.555240 | 0.277620 | − | 0.960691i | \(-0.410454\pi\) | ||||
0.277620 | + | 0.960691i | \(0.410454\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 144568. | 1.11369 | ||||||||
\(112\) | 114846. | 0.865106 | ||||||||
\(113\) | 43794.9 | 0.322647 | 0.161323 | − | 0.986902i | \(-0.448424\pi\) | ||||
0.161323 | + | 0.986902i | \(0.448424\pi\) | |||||||
\(114\) | −107793. | −0.776835 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −547.745 | −0.00377949 | ||||||||
\(117\) | −95037.7 | −0.641846 | ||||||||
\(118\) | −64767.3 | −0.428204 | ||||||||
\(119\) | 139578. | 0.903543 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 4388.56 | 0.0266945 | ||||||||
\(123\) | 135565. | 0.807949 | ||||||||
\(124\) | −26102.7 | −0.152452 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −62613.6 | −0.351352 | ||||||||
\(127\) | 209089. | 1.15033 | 0.575165 | − | 0.818037i | \(-0.304938\pi\) | ||||
0.575165 | + | 0.818037i | \(0.304938\pi\) | |||||||
\(128\) | 98938.8 | 0.533755 | ||||||||
\(129\) | 115810. | 0.612734 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −85677.3 | −0.436202 | −0.218101 | − | 0.975926i | \(-0.569986\pi\) | ||||
−0.218101 | + | 0.975926i | \(0.569986\pi\) | |||||||
\(132\) | −7906.03 | −0.0394933 | ||||||||
\(133\) | 374224. | 1.83443 | ||||||||
\(134\) | 70588.6 | 0.339604 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 175381. | 0.813085 | ||||||||
\(137\) | −115510. | −0.525795 | −0.262898 | − | 0.964824i | \(-0.584678\pi\) | ||||
−0.262898 | + | 0.964824i | \(0.584678\pi\) | |||||||
\(138\) | 184484. | 0.824633 | ||||||||
\(139\) | −120621. | −0.529523 | −0.264761 | − | 0.964314i | \(-0.585293\pi\) | ||||
−0.264761 | + | 0.964314i | \(0.585293\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 60289.5 | 0.255384 | ||||||||
\(142\) | −391678. | −1.63008 | ||||||||
\(143\) | −141970. | −0.580572 | ||||||||
\(144\) | −59857.1 | −0.240552 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −170245. | −0.660984 | ||||||||
\(147\) | 66111.7 | 0.252339 | ||||||||
\(148\) | −116616. | −0.437628 | ||||||||
\(149\) | 49190.8 | 0.181517 | 0.0907587 | − | 0.995873i | \(-0.471071\pi\) | ||||
0.0907587 | + | 0.995873i | \(0.471071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −490808. | −1.75174 | −0.875870 | − | 0.482547i | \(-0.839712\pi\) | ||||
−0.875870 | + | 0.482547i | \(0.839712\pi\) | |||||||
\(152\) | 470216. | 1.65078 | ||||||||
\(153\) | −72747.5 | −0.251240 | ||||||||
\(154\) | −93534.0 | −0.317810 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 76662.7 | 0.252216 | ||||||||
\(157\) | 273703. | 0.886199 | 0.443099 | − | 0.896473i | \(-0.353879\pi\) | ||||
0.443099 | + | 0.896473i | \(0.353879\pi\) | |||||||
\(158\) | −242204. | −0.771860 | ||||||||
\(159\) | −205657. | −0.645137 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −640470. | −1.94730 | ||||||||
\(162\) | 32634.0 | 0.0976974 | ||||||||
\(163\) | −64881.0 | −0.191271 | −0.0956354 | − | 0.995416i | \(-0.530488\pi\) | ||||
−0.0956354 | + | 0.995416i | \(0.530488\pi\) | |||||||
\(164\) | −109354. | −0.317487 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 477028. | 1.34361 | ||||||||
\(167\) | −379513. | −1.05302 | −0.526508 | − | 0.850170i | \(-0.676499\pi\) | ||||
−0.526508 | + | 0.850170i | \(0.676499\pi\) | |||||||
\(168\) | 273134. | 0.746625 | ||||||||
\(169\) | 1.00535e6 | 2.70770 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −195044. | −0.510085 | ||||||||
\(172\) | −93418.8 | −0.240776 | ||||||||
\(173\) | 509354. | 1.29391 | 0.646955 | − | 0.762528i | \(-0.276042\pi\) | ||||
0.646955 | + | 0.762528i | \(0.276042\pi\) | |||||||
\(174\) | 3377.46 | 0.00845702 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −89416.2 | −0.217588 | ||||||||
\(177\) | −117192. | −0.281167 | ||||||||
\(178\) | 6677.76 | 0.0157972 | ||||||||
\(179\) | 706267. | 1.64754 | 0.823771 | − | 0.566923i | \(-0.191866\pi\) | ||||
0.823771 | + | 0.566923i | \(0.191866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 250646. | 0.568674 | 0.284337 | − | 0.958724i | \(-0.408227\pi\) | ||||
0.284337 | + | 0.958724i | \(0.408227\pi\) | |||||||
\(182\) | 906974. | 2.02963 | ||||||||
\(183\) | 7940.79 | 0.0175281 | ||||||||
\(184\) | −804758. | −1.75235 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 160953. | 0.341127 | ||||||||
\(187\) | −108672. | −0.227256 | ||||||||
\(188\) | −48632.9 | −0.100354 | ||||||||
\(189\) | −113295. | −0.230705 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −592850. | −1.17588 | −0.587938 | − | 0.808906i | \(-0.700060\pi\) | ||||
−0.587938 | + | 0.808906i | \(0.700060\pi\) | |||||||
\(192\) | 328017. | 0.642160 | ||||||||
\(193\) | 965415. | 1.86561 | 0.932804 | − | 0.360383i | \(-0.117354\pi\) | ||||
0.932804 | + | 0.360383i | \(0.117354\pi\) | |||||||
\(194\) | −402585. | −0.767986 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −53329.4 | −0.0991577 | ||||||||
\(197\) | 175247. | 0.321725 | 0.160862 | − | 0.986977i | \(-0.448573\pi\) | ||||
0.160862 | + | 0.986977i | \(0.448573\pi\) | |||||||
\(198\) | 48749.6 | 0.0883707 | ||||||||
\(199\) | −48708.5 | −0.0871911 | −0.0435955 | − | 0.999049i | \(-0.513881\pi\) | ||||
−0.0435955 | + | 0.999049i | \(0.513881\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 127725. | 0.222990 | ||||||||
\(202\) | 95625.1 | 0.164890 | ||||||||
\(203\) | −11725.5 | −0.0199706 | ||||||||
\(204\) | 58682.2 | 0.0987259 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 629956. | 1.03429 | ||||||||
\(207\) | 333811. | 0.541470 | ||||||||
\(208\) | 867045. | 1.38958 | ||||||||
\(209\) | −291362. | −0.461389 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 662206. | 1.02397 | 0.511985 | − | 0.858995i | \(-0.328910\pi\) | ||||
0.511985 | + | 0.858995i | \(0.328910\pi\) | |||||||
\(212\) | 165895. | 0.253509 | ||||||||
\(213\) | −708714. | −1.07034 | ||||||||
\(214\) | −386840. | −0.577427 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −142357. | −0.207608 | ||||||||
\(217\) | −558777. | −0.805544 | ||||||||
\(218\) | 342568. | 0.488209 | ||||||||
\(219\) | −308046. | −0.434015 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.05377e6 | 1.45132 | ||||||||
\(222\) | 719071. | 0.979241 | ||||||||
\(223\) | 44174.7 | 0.0594855 | 0.0297428 | − | 0.999558i | \(-0.490531\pi\) | ||||
0.0297428 | + | 0.999558i | \(0.490531\pi\) | |||||||
\(224\) | −399908. | −0.532525 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 217833. | 0.283696 | ||||||||
\(227\) | −585184. | −0.753750 | −0.376875 | − | 0.926264i | \(-0.623001\pi\) | ||||
−0.376875 | + | 0.926264i | \(0.623001\pi\) | |||||||
\(228\) | 157333. | 0.200440 | ||||||||
\(229\) | 914300. | 1.15213 | 0.576063 | − | 0.817405i | \(-0.304588\pi\) | ||||
0.576063 | + | 0.817405i | \(0.304588\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −169243. | −0.208680 | ||||||||
\(232\) | −14733.2 | −0.0179712 | ||||||||
\(233\) | −702641. | −0.847898 | −0.423949 | − | 0.905686i | \(-0.639356\pi\) | ||||
−0.423949 | + | 0.905686i | \(0.639356\pi\) | |||||||
\(234\) | −472712. | −0.564361 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 94533.5 | 0.110486 | ||||||||
\(237\) | −438251. | −0.506818 | ||||||||
\(238\) | 694252. | 0.794465 | ||||||||
\(239\) | 572014. | 0.647757 | 0.323879 | − | 0.946099i | \(-0.395013\pi\) | ||||
0.323879 | + | 0.946099i | \(0.395013\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −485324. | −0.538256 | −0.269128 | − | 0.963104i | \(-0.586736\pi\) | ||||
−0.269128 | + | 0.963104i | \(0.586736\pi\) | |||||||
\(242\) | 72823.5 | 0.0799343 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −6405.48 | −0.00688775 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 674291. | 0.710411 | ||||||||
\(247\) | 2.82526e6 | 2.94657 | ||||||||
\(248\) | −702110. | −0.724897 | ||||||||
\(249\) | 863148. | 0.882240 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25755.4 | 0.0258039 | 0.0129019 | − | 0.999917i | \(-0.495893\pi\) | ||||
0.0129019 | + | 0.999917i | \(0.495893\pi\) | |||||||
\(252\) | 91390.1 | 0.0906562 | ||||||||
\(253\) | 498656. | 0.489778 | ||||||||
\(254\) | 1.04000e6 | 1.01146 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −674166. | −0.642935 | ||||||||
\(257\) | −243229. | −0.229711 | −0.114856 | − | 0.993382i | \(-0.536641\pi\) | ||||
−0.114856 | + | 0.993382i | \(0.536641\pi\) | |||||||
\(258\) | 576032. | 0.538763 | ||||||||
\(259\) | −2.49639e6 | −2.31240 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6111.28 | 0.00555304 | ||||||||
\(262\) | −426154. | −0.383542 | ||||||||
\(263\) | −46278.0 | −0.0412558 | −0.0206279 | − | 0.999787i | \(-0.506567\pi\) | ||||
−0.0206279 | + | 0.999787i | \(0.506567\pi\) | |||||||
\(264\) | −212656. | −0.187788 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.86137e6 | 1.61298 | ||||||||
\(267\) | 12082.9 | 0.0103728 | ||||||||
\(268\) | −103030. | −0.0876249 | ||||||||
\(269\) | 174634. | 0.147146 | 0.0735729 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735729 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.78096e6 | −1.47309 | −0.736546 | − | 0.676387i | \(-0.763545\pi\) | ||||
−0.736546 | + | 0.676387i | \(0.763545\pi\) | |||||||
\(272\) | 663688. | 0.543929 | ||||||||
\(273\) | 1.64111e6 | 1.33269 | ||||||||
\(274\) | −574538. | −0.462320 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −269270. | −0.212773 | ||||||||
\(277\) | −545088. | −0.426842 | −0.213421 | − | 0.976960i | \(-0.568461\pi\) | ||||
−0.213421 | + | 0.976960i | \(0.568461\pi\) | |||||||
\(278\) | −599960. | −0.465597 | ||||||||
\(279\) | 291233. | 0.223991 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 85469.5 | 0.0645722 | 0.0322861 | − | 0.999479i | \(-0.489721\pi\) | ||||
0.0322861 | + | 0.999479i | \(0.489721\pi\) | |||||||
\(282\) | 299877. | 0.224554 | ||||||||
\(283\) | 1.51069e6 | 1.12127 | 0.560634 | − | 0.828064i | \(-0.310558\pi\) | ||||
0.560634 | + | 0.828064i | \(0.310558\pi\) | |||||||
\(284\) | 571688. | 0.420594 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −706150. | −0.510484 | ||||||||
\(287\) | −2.34093e6 | −1.67758 | ||||||||
\(288\) | 208431. | 0.148075 | ||||||||
\(289\) | −613242. | −0.431904 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −728450. | −0.504275 | ||||||||
\(292\) | 248487. | 0.170548 | ||||||||
\(293\) | 1.05179e6 | 0.715746 | 0.357873 | − | 0.933770i | \(-0.383502\pi\) | ||||
0.357873 | + | 0.933770i | \(0.383502\pi\) | |||||||
\(294\) | 328836. | 0.221876 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.13674e6 | −2.08089 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | 244672. | 0.159604 | ||||||||
\(299\) | −4.83533e6 | −3.12787 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.99980e6 | −1.27224 | ||||||||
\(302\) | −2.44125e6 | −1.54026 | ||||||||
\(303\) | 173027. | 0.108270 | ||||||||
\(304\) | 1.77942e6 | 1.10432 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −361842. | −0.220910 | ||||||||
\(307\) | 1.68373e6 | 1.01959 | 0.509796 | − | 0.860295i | \(-0.329721\pi\) | ||||
0.509796 | + | 0.860295i | \(0.329721\pi\) | |||||||
\(308\) | 136521. | 0.0820016 | ||||||||
\(309\) | 1.13986e6 | 0.679135 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.72412e6 | −1.59707 | −0.798536 | − | 0.601947i | \(-0.794392\pi\) | ||||
−0.798536 | + | 0.601947i | \(0.794392\pi\) | |||||||
\(312\) | 2.06207e6 | 1.19927 | ||||||||
\(313\) | −1.69158e6 | −0.975959 | −0.487979 | − | 0.872855i | \(-0.662266\pi\) | ||||
−0.487979 | + | 0.872855i | \(0.662266\pi\) | |||||||
\(314\) | 1.36138e6 | 0.779214 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 353518. | 0.199156 | ||||||||
\(317\) | 371370. | 0.207567 | 0.103784 | − | 0.994600i | \(-0.466905\pi\) | ||||
0.103784 | + | 0.994600i | \(0.466905\pi\) | |||||||
\(318\) | −1.02293e6 | −0.567254 | ||||||||
\(319\) | 9129.20 | 0.00502292 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −699960. | −0.379149 | ||||||||
\(322\) | −3.18566e6 | −1.71222 | ||||||||
\(323\) | 2.16262e6 | 1.15339 | ||||||||
\(324\) | −47632.2 | −0.0252080 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −322714. | −0.168180 | ||||||||
\(327\) | 619854. | 0.320568 | ||||||||
\(328\) | −2.94140e6 | −1.50963 | ||||||||
\(329\) | −1.04108e6 | −0.530265 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.54525e6 | 0.775229 | 0.387614 | − | 0.921822i | \(-0.373299\pi\) | ||||
0.387614 | + | 0.921822i | \(0.373299\pi\) | |||||||
\(332\) | −696263. | −0.346680 | ||||||||
\(333\) | 1.30111e6 | 0.642989 | ||||||||
\(334\) | −1.88767e6 | −0.925893 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.03361e6 | 0.499469 | ||||||||
\(337\) | 1.56563e6 | 0.750956 | 0.375478 | − | 0.926831i | \(-0.377479\pi\) | ||||
0.375478 | + | 0.926831i | \(0.377479\pi\) | |||||||
\(338\) | 5.00055e6 | 2.38082 | ||||||||
\(339\) | 394154. | 0.186280 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 435052. | 0.202607 | ||||||||
\(342\) | −970138. | −0.448506 | ||||||||
\(343\) | 1.47039e6 | 0.674833 | ||||||||
\(344\) | −2.51277e6 | −1.14487 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.53350e6 | 1.13771 | ||||||||
\(347\) | −2.21769e6 | −0.988727 | −0.494364 | − | 0.869255i | \(-0.664599\pi\) | ||||
−0.494364 | + | 0.869255i | \(0.664599\pi\) | |||||||
\(348\) | −4929.70 | −0.00218209 | ||||||||
\(349\) | −3.10101e6 | −1.36283 | −0.681413 | − | 0.731899i | \(-0.738634\pi\) | ||||
−0.681413 | + | 0.731899i | \(0.738634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −855339. | −0.370570 | ||||||||
\(352\) | 311359. | 0.133938 | ||||||||
\(353\) | 2.34837e6 | 1.00307 | 0.501534 | − | 0.865138i | \(-0.332769\pi\) | ||||
0.501534 | + | 0.865138i | \(0.332769\pi\) | |||||||
\(354\) | −582905. | −0.247224 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9746.77 | −0.00407602 | ||||||||
\(357\) | 1.25620e6 | 0.521661 | ||||||||
\(358\) | 3.51293e6 | 1.44865 | ||||||||
\(359\) | 1.76347e6 | 0.722158 | 0.361079 | − | 0.932535i | \(-0.382408\pi\) | ||||
0.361079 | + | 0.932535i | \(0.382408\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.32213e6 | 1.34168 | ||||||||
\(362\) | 1.24670e6 | 0.500022 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | −1.32381e6 | −0.523686 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 39497.0 | 0.0154121 | ||||||||
\(367\) | 2.99827e6 | 1.16200 | 0.580999 | − | 0.813904i | \(-0.302662\pi\) | ||||
0.580999 | + | 0.813904i | \(0.302662\pi\) | |||||||
\(368\) | −3.04541e6 | −1.17227 | ||||||||
\(369\) | 1.22008e6 | 0.466470 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.55128e6 | 1.33952 | ||||||||
\(372\) | −234925. | −0.0880179 | ||||||||
\(373\) | 2.01705e6 | 0.750663 | 0.375331 | − | 0.926891i | \(-0.377529\pi\) | ||||
0.375331 | + | 0.926891i | \(0.377529\pi\) | |||||||
\(374\) | −540529. | −0.199821 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.30813e6 | −0.477177 | ||||||||
\(377\) | −88523.4 | −0.0320778 | ||||||||
\(378\) | −563523. | −0.202853 | ||||||||
\(379\) | 3.78909e6 | 1.35499 | 0.677497 | − | 0.735526i | \(-0.263065\pi\) | ||||
0.677497 | + | 0.735526i | \(0.263065\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.88180e6 | 0.664144 | ||||||||
\(382\) | −2.94880e6 | −1.03392 | ||||||||
\(383\) | 2.72827e6 | 0.950366 | 0.475183 | − | 0.879887i | \(-0.342382\pi\) | ||||
0.475183 | + | 0.879887i | \(0.342382\pi\) | |||||||
\(384\) | 890449. | 0.308163 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.80192e6 | 1.64039 | ||||||||
\(387\) | 1.04229e6 | 0.353762 | ||||||||
\(388\) | 587608. | 0.198157 | ||||||||
\(389\) | 432266. | 0.144836 | 0.0724181 | − | 0.997374i | \(-0.476928\pi\) | ||||
0.0724181 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.70125e6 | −1.22435 | ||||||||
\(392\) | −1.43445e6 | −0.471488 | ||||||||
\(393\) | −771095. | −0.251841 | ||||||||
\(394\) | 871667. | 0.282885 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −71154.3 | −0.0228015 | ||||||||
\(397\) | 3.90462e6 | 1.24338 | 0.621688 | − | 0.783265i | \(-0.286447\pi\) | ||||
0.621688 | + | 0.783265i | \(0.286447\pi\) | |||||||
\(398\) | −242273. | −0.0766651 | ||||||||
\(399\) | 3.36801e6 | 1.05911 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.60863e6 | 1.43124 | 0.715618 | − | 0.698492i | \(-0.246145\pi\) | ||||
0.715618 | + | 0.698492i | \(0.246145\pi\) | |||||||
\(402\) | 635297. | 0.196070 | ||||||||
\(403\) | −4.21858e6 | −1.29391 | ||||||||
\(404\) | −139573. | −0.0425450 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −58321.9 | −0.0175597 | ||||||||
\(407\) | 1.94363e6 | 0.581605 | ||||||||
\(408\) | 1.57843e6 | 0.469435 | ||||||||
\(409\) | −3.86604e6 | −1.14277 | −0.571384 | − | 0.820683i | \(-0.693593\pi\) | ||||
−0.571384 | + | 0.820683i | \(0.693593\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.03959e6 | −0.303568 | ||||||||
\(412\) | −919476. | −0.266868 | ||||||||
\(413\) | 2.02366e6 | 0.583799 | ||||||||
\(414\) | 1.66036e6 | 0.476102 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.01917e6 | −0.855370 | ||||||||
\(417\) | −1.08559e6 | −0.305720 | ||||||||
\(418\) | −1.44922e6 | −0.405689 | ||||||||
\(419\) | 3.60488e6 | 1.00313 | 0.501563 | − | 0.865121i | \(-0.332759\pi\) | ||||
0.501563 | + | 0.865121i | \(0.332759\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.69664e6 | 0.741510 | 0.370755 | − | 0.928731i | \(-0.379099\pi\) | ||||
0.370755 | + | 0.928731i | \(0.379099\pi\) | |||||||
\(422\) | 3.29377e6 | 0.900353 | ||||||||
\(423\) | 542606. | 0.147446 | ||||||||
\(424\) | 4.46223e6 | 1.20542 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.52510e6 | −0.941126 | ||||||||
\(427\) | −137121. | −0.0363944 | ||||||||
\(428\) | 564626. | 0.148988 | ||||||||
\(429\) | −1.27773e6 | −0.335193 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −337978. | −0.0876385 | −0.0438193 | − | 0.999039i | \(-0.513953\pi\) | ||||
−0.0438193 | + | 0.999039i | \(0.513953\pi\) | |||||||
\(432\) | −538714. | −0.138883 | ||||||||
\(433\) | −5.43565e6 | −1.39326 | −0.696629 | − | 0.717431i | \(-0.745318\pi\) | ||||
−0.696629 | + | 0.717431i | \(0.745318\pi\) | |||||||
\(434\) | −2.77932e6 | −0.708296 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −500008. | −0.125968 | ||||||||
\(437\) | −9.92346e6 | −2.48576 | ||||||||
\(438\) | −1.53220e6 | −0.381620 | ||||||||
\(439\) | −170878. | −0.0423180 | −0.0211590 | − | 0.999776i | \(-0.506736\pi\) | ||||
−0.0211590 | + | 0.999776i | \(0.506736\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 595006. | 0.145688 | ||||||||
\(442\) | 5.24137e6 | 1.27611 | ||||||||
\(443\) | −6.94673e6 | −1.68179 | −0.840893 | − | 0.541201i | \(-0.817970\pi\) | ||||
−0.840893 | + | 0.541201i | \(0.817970\pi\) | |||||||
\(444\) | −1.04955e6 | −0.252665 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 219722. | 0.0523043 | ||||||||
\(447\) | 442717. | 0.104799 | ||||||||
\(448\) | −5.66418e6 | −1.33334 | ||||||||
\(449\) | −1.91825e6 | −0.449045 | −0.224522 | − | 0.974469i | \(-0.572082\pi\) | ||||
−0.224522 | + | 0.974469i | \(0.572082\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.82259e6 | 0.421938 | ||||||||
\(452\) | −317946. | −0.0731995 | ||||||||
\(453\) | −4.41728e6 | −1.01137 | ||||||||
\(454\) | −2.91067e6 | −0.662755 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.23195e6 | 0.953077 | ||||||||
\(457\) | 1.14248e6 | 0.255892 | 0.127946 | − | 0.991781i | \(-0.459162\pi\) | ||||
0.127946 | + | 0.991781i | \(0.459162\pi\) | |||||||
\(458\) | 4.54768e6 | 1.01304 | ||||||||
\(459\) | −654728. | −0.145054 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.63295e6 | 0.796172 | 0.398086 | − | 0.917348i | \(-0.369675\pi\) | ||||
0.398086 | + | 0.917348i | \(0.369675\pi\) | |||||||
\(462\) | −841806. | −0.183488 | ||||||||
\(463\) | 6.29651e6 | 1.36505 | 0.682523 | − | 0.730864i | \(-0.260883\pi\) | ||||
0.682523 | + | 0.730864i | \(0.260883\pi\) | |||||||
\(464\) | −55754.3 | −0.0120222 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.49490e6 | −0.745537 | ||||||||
\(467\) | −46216.3 | −0.00980624 | −0.00490312 | − | 0.999988i | \(-0.501561\pi\) | ||||
−0.00490312 | + | 0.999988i | \(0.501561\pi\) | |||||||
\(468\) | 689964. | 0.145617 | ||||||||
\(469\) | −2.20555e6 | −0.463004 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.46333e6 | 0.511647 | ||||||||
\(472\) | 2.54276e6 | 0.525351 | ||||||||
\(473\) | 1.55700e6 | 0.319990 | ||||||||
\(474\) | −2.17983e6 | −0.445633 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.01332e6 | −0.204989 | ||||||||
\(477\) | −1.85092e6 | −0.372470 | ||||||||
\(478\) | 2.84517e6 | 0.569558 | ||||||||
\(479\) | 1.87454e6 | 0.373299 | 0.186649 | − | 0.982427i | \(-0.440237\pi\) | ||||
0.186649 | + | 0.982427i | \(0.440237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.88469e7 | −3.71430 | ||||||||
\(482\) | −2.41397e6 | −0.473276 | ||||||||
\(483\) | −5.76423e6 | −1.12428 | ||||||||
\(484\) | −106292. | −0.0206247 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 293706. | 0.0564056 | ||||||||
\(487\) | 2.93849e6 | 0.561439 | 0.280719 | − | 0.959790i | \(-0.409427\pi\) | ||||
0.280719 | + | 0.959790i | \(0.409427\pi\) | |||||||
\(488\) | −172294. | −0.0327508 | ||||||||
\(489\) | −583929. | −0.110430 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.56455e6 | 1.41605 | 0.708026 | − | 0.706186i | \(-0.249586\pi\) | ||||
0.708026 | + | 0.706186i | \(0.249586\pi\) | |||||||
\(492\) | −984187. | −0.183301 | ||||||||
\(493\) | −67761.1 | −0.0125563 | ||||||||
\(494\) | 1.40527e7 | 2.59085 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.65697e6 | −0.484933 | ||||||||
\(497\) | 1.22380e7 | 2.22239 | ||||||||
\(498\) | 4.29325e6 | 0.775734 | ||||||||
\(499\) | −3.96894e6 | −0.713548 | −0.356774 | − | 0.934191i | \(-0.616123\pi\) | ||||
−0.356774 | + | 0.934191i | \(0.616123\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.41561e6 | −0.607959 | ||||||||
\(502\) | 128106. | 0.0226887 | ||||||||
\(503\) | −7.67415e6 | −1.35242 | −0.676208 | − | 0.736711i | \(-0.736378\pi\) | ||||
−0.676208 | + | 0.736711i | \(0.736378\pi\) | |||||||
\(504\) | 2.45821e6 | 0.431064 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.48028e6 | 0.430651 | ||||||||
\(507\) | 9.04815e6 | 1.56329 | ||||||||
\(508\) | −1.51797e6 | −0.260978 | ||||||||
\(509\) | −2.34465e6 | −0.401129 | −0.200564 | − | 0.979681i | \(-0.564278\pi\) | ||||
−0.200564 | + | 0.979681i | \(0.564278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.31932e6 | 0.901164 | ||||||||
\(512\) | −6.51930e6 | −1.09907 | ||||||||
\(513\) | −1.75540e6 | −0.294498 | ||||||||
\(514\) | −1.20981e6 | −0.201980 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −840769. | −0.139012 | ||||||||
\(517\) | 810559. | 0.133370 | ||||||||
\(518\) | −1.24169e7 | −2.03324 | ||||||||
\(519\) | 4.58418e6 | 0.747040 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.60694e6 | −0.743563 | −0.371782 | − | 0.928320i | \(-0.621253\pi\) | ||||
−0.371782 | + | 0.928320i | \(0.621253\pi\) | |||||||
\(522\) | 30397.2 | 0.00488266 | ||||||||
\(523\) | 3.79276e6 | 0.606319 | 0.303159 | − | 0.952940i | \(-0.401959\pi\) | ||||
0.303159 | + | 0.952940i | \(0.401959\pi\) | |||||||
\(524\) | 622008. | 0.0989619 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −230184. | −0.0362753 | ||||||||
\(527\) | −3.22915e6 | −0.506480 | ||||||||
\(528\) | −804746. | −0.125624 | ||||||||
\(529\) | 1.05473e7 | 1.63871 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.05473e6 | −0.162332 | ||||||||
\(532\) | −2.71683e6 | −0.416181 | ||||||||
\(533\) | −1.76732e7 | −2.69462 | ||||||||
\(534\) | 60099.9 | 0.00912053 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.77130e6 | −0.416650 | ||||||||
\(537\) | 6.35640e6 | 0.951208 | ||||||||
\(538\) | 868619. | 0.129382 | ||||||||
\(539\) | 888835. | 0.131780 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.95976e6 | −1.31614 | −0.658072 | − | 0.752955i | \(-0.728628\pi\) | ||||
−0.658072 | + | 0.752955i | \(0.728628\pi\) | |||||||
\(542\) | −8.85837e6 | −1.29526 | ||||||||
\(543\) | 2.25581e6 | 0.328324 | ||||||||
\(544\) | −2.31105e6 | −0.334821 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.16276e6 | 1.17181 | ||||||||
\(547\) | −2.79065e6 | −0.398783 | −0.199391 | − | 0.979920i | \(-0.563896\pi\) | ||||
−0.199391 | + | 0.979920i | \(0.563896\pi\) | |||||||
\(548\) | 838588. | 0.119288 | ||||||||
\(549\) | 71467.1 | 0.0101199 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −181675. | −0.0254927 | ||||||||
\(552\) | −7.24282e6 | −1.01172 | ||||||||
\(553\) | 7.56770e6 | 1.05233 | ||||||||
\(554\) | −2.71124e6 | −0.375313 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 875694. | 0.120134 | ||||||||
\(557\) | −1.22903e7 | −1.67851 | −0.839256 | − | 0.543736i | \(-0.817009\pi\) | ||||
−0.839256 | + | 0.543736i | \(0.817009\pi\) | |||||||
\(558\) | 1.44858e6 | 0.196950 | ||||||||
\(559\) | −1.50978e7 | −2.04355 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −978050. | −0.131206 | ||||||||
\(562\) | 425120. | 0.0567768 | ||||||||
\(563\) | −1.13900e7 | −1.51444 | −0.757220 | − | 0.653160i | \(-0.773443\pi\) | ||||
−0.757220 | + | 0.653160i | \(0.773443\pi\) | |||||||
\(564\) | −437696. | −0.0579395 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.51408e6 | 0.985905 | ||||||||
\(567\) | −1.01966e6 | −0.133197 | ||||||||
\(568\) | 1.53772e7 | 1.99990 | ||||||||
\(569\) | 4.71367e6 | 0.610350 | 0.305175 | − | 0.952296i | \(-0.401285\pi\) | ||||
0.305175 | + | 0.952296i | \(0.401285\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.49421e6 | 0.961913 | 0.480957 | − | 0.876744i | \(-0.340289\pi\) | ||||
0.480957 | + | 0.876744i | \(0.340289\pi\) | |||||||
\(572\) | 1.03069e6 | 0.131715 | ||||||||
\(573\) | −5.33565e6 | −0.678893 | ||||||||
\(574\) | −1.16436e7 | −1.47506 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.95215e6 | 0.370751 | ||||||||
\(577\) | 5.77654e6 | 0.722318 | 0.361159 | − | 0.932504i | \(-0.382381\pi\) | ||||
0.361159 | + | 0.932504i | \(0.382381\pi\) | |||||||
\(578\) | −3.05023e6 | −0.379763 | ||||||||
\(579\) | 8.68873e6 | 1.07711 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.49048e7 | −1.83183 | ||||||||
\(582\) | −3.62327e6 | −0.443397 | ||||||||
\(583\) | −2.76495e6 | −0.336912 | ||||||||
\(584\) | 6.68379e6 | 0.810943 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.23153e6 | 0.629339 | ||||||||
\(587\) | 1.19273e6 | 0.142872 | 0.0714358 | − | 0.997445i | \(-0.477242\pi\) | ||||
0.0714358 | + | 0.997445i | \(0.477242\pi\) | |||||||
\(588\) | −479965. | −0.0572487 | ||||||||
\(589\) | −8.65771e6 | −1.02829 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.57722e6 | 0.185748 | ||||||||
\(592\) | −1.18702e7 | −1.39205 | ||||||||
\(593\) | 1.14801e7 | 1.34064 | 0.670318 | − | 0.742074i | \(-0.266158\pi\) | ||||
0.670318 | + | 0.742074i | \(0.266158\pi\) | |||||||
\(594\) | 438746. | 0.0510208 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −357120. | −0.0411812 | ||||||||
\(597\) | −438376. | −0.0503398 | ||||||||
\(598\) | −2.40506e7 | −2.75026 | ||||||||
\(599\) | 1.07989e7 | 1.22974 | 0.614869 | − | 0.788630i | \(-0.289209\pi\) | ||||
0.614869 | + | 0.788630i | \(0.289209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.43742e6 | 0.726986 | 0.363493 | − | 0.931597i | \(-0.381584\pi\) | ||||
0.363493 | + | 0.931597i | \(0.381584\pi\) | |||||||
\(602\) | −9.94690e6 | −1.11866 | ||||||||
\(603\) | 1.14953e6 | 0.128744 | ||||||||
\(604\) | 3.56322e6 | 0.397421 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 860626. | 0.0951991 | ||||||||
\(607\) | −2.78009e6 | −0.306258 | −0.153129 | − | 0.988206i | \(-0.548935\pi\) | ||||
−0.153129 | + | 0.988206i | \(0.548935\pi\) | |||||||
\(608\) | −6.19619e6 | −0.679776 | ||||||||
\(609\) | −105529. | −0.0115300 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.85978e6 | −0.851740 | ||||||||
\(612\) | 528140. | 0.0569994 | ||||||||
\(613\) | 1.25907e7 | 1.35331 | 0.676657 | − | 0.736299i | \(-0.263428\pi\) | ||||
0.676657 | + | 0.736299i | \(0.263428\pi\) | |||||||
\(614\) | 8.37477e6 | 0.896504 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.67213e6 | 0.389912 | ||||||||
\(617\) | −1.20724e6 | −0.127668 | −0.0638339 | − | 0.997961i | \(-0.520333\pi\) | ||||
−0.0638339 | + | 0.997961i | \(0.520333\pi\) | |||||||
\(618\) | 5.66960e6 | 0.597147 | ||||||||
\(619\) | 1.03935e7 | 1.09028 | 0.545138 | − | 0.838346i | \(-0.316477\pi\) | ||||
0.545138 | + | 0.838346i | \(0.316477\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00430e6 | 0.312618 | ||||||||
\(622\) | −1.35496e7 | −1.40427 | ||||||||
\(623\) | −208648. | −0.0215374 | ||||||||
\(624\) | 7.80341e6 | 0.802274 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.41381e6 | −0.858138 | ||||||||
\(627\) | −2.62226e6 | −0.266383 | ||||||||
\(628\) | −1.98706e6 | −0.201054 | ||||||||
\(629\) | −1.44265e7 | −1.45390 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 389320. | 0.0389254 | 0.0194627 | − | 0.999811i | \(-0.493804\pi\) | ||||
0.0194627 | + | 0.999811i | \(0.493804\pi\) | |||||||
\(632\) | 9.50890e6 | 0.946973 | ||||||||
\(633\) | 5.95985e6 | 0.591189 | ||||||||
\(634\) | 1.84717e6 | 0.182509 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.49305e6 | 0.146363 | ||||||||
\(637\) | −8.61880e6 | −0.841585 | ||||||||
\(638\) | 45408.1 | 0.00441654 | ||||||||
\(639\) | −6.37843e6 | −0.617961 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.85176e6 | 0.947041 | 0.473520 | − | 0.880783i | \(-0.342983\pi\) | ||||
0.473520 | + | 0.880783i | \(0.342983\pi\) | |||||||
\(642\) | −3.48156e6 | −0.333377 | ||||||||
\(643\) | −9.41361e6 | −0.897901 | −0.448951 | − | 0.893557i | \(-0.648202\pi\) | ||||
−0.448951 | + | 0.893557i | \(0.648202\pi\) | |||||||
\(644\) | 4.64975e6 | 0.441789 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.07568e7 | 1.01415 | ||||||||
\(647\) | 8.37846e6 | 0.786871 | 0.393435 | − | 0.919352i | \(-0.371287\pi\) | ||||
0.393435 | + | 0.919352i | \(0.371287\pi\) | |||||||
\(648\) | −1.28121e6 | −0.119862 | ||||||||
\(649\) | −1.57558e6 | −0.146835 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.02899e6 | −0.465081 | ||||||||
\(652\) | 471030. | 0.0433940 | ||||||||
\(653\) | 1.87196e7 | 1.71796 | 0.858979 | − | 0.512011i | \(-0.171099\pi\) | ||||
0.858979 | + | 0.512011i | \(0.171099\pi\) | |||||||
\(654\) | 3.08312e6 | 0.281868 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.11310e7 | −1.00989 | ||||||||
\(657\) | −2.77241e6 | −0.250579 | ||||||||
\(658\) | −5.17826e6 | −0.466250 | ||||||||
\(659\) | −7.53086e6 | −0.675509 | −0.337755 | − | 0.941234i | \(-0.609667\pi\) | ||||
−0.337755 | + | 0.941234i | \(0.609667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.12673e7 | −1.00304 | −0.501518 | − | 0.865147i | \(-0.667225\pi\) | ||||
−0.501518 | + | 0.865147i | \(0.667225\pi\) | |||||||
\(662\) | 7.68600e6 | 0.681641 | ||||||||
\(663\) | 9.48389e6 | 0.837920 | ||||||||
\(664\) | −1.87281e7 | −1.64844 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.47164e6 | 0.565365 | ||||||||
\(667\) | 310930. | 0.0270613 | ||||||||
\(668\) | 2.75522e6 | 0.238900 | ||||||||
\(669\) | 397572. | 0.0343440 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 106759. | 0.00915377 | ||||||||
\(672\) | −3.59917e6 | −0.307453 | ||||||||
\(673\) | −747965. | −0.0636566 | −0.0318283 | − | 0.999493i | \(-0.510133\pi\) | ||||
−0.0318283 | + | 0.999493i | \(0.510133\pi\) | |||||||
\(674\) | 7.78735e6 | 0.660298 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.29874e6 | −0.614301 | ||||||||
\(677\) | 1.52419e7 | 1.27811 | 0.639056 | − | 0.769160i | \(-0.279325\pi\) | ||||
0.639056 | + | 0.769160i | \(0.279325\pi\) | |||||||
\(678\) | 1.96050e6 | 0.163792 | ||||||||
\(679\) | 1.25788e7 | 1.04705 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.26665e6 | −0.435178 | ||||||||
\(682\) | 2.16392e6 | 0.178148 | ||||||||
\(683\) | −891262. | −0.0731061 | −0.0365531 | − | 0.999332i | \(-0.511638\pi\) | ||||
−0.0365531 | + | 0.999332i | \(0.511638\pi\) | |||||||
\(684\) | 1.41600e6 | 0.115724 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.31362e6 | 0.593366 | ||||||||
\(687\) | 8.22870e6 | 0.665180 | ||||||||
\(688\) | −9.50899e6 | −0.765885 | ||||||||
\(689\) | 2.68110e7 | 2.15162 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.23692e6 | −0.178220 | −0.0891100 | − | 0.996022i | \(-0.528402\pi\) | ||||
−0.0891100 | + | 0.996022i | \(0.528402\pi\) | |||||||
\(692\) | −3.69786e6 | −0.293552 | ||||||||
\(693\) | −1.52319e6 | −0.120482 | ||||||||
\(694\) | −1.10306e7 | −0.869365 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −132599. | −0.0103757 | ||||||||
\(697\) | −1.35281e7 | −1.05476 | ||||||||
\(698\) | −1.54243e7 | −1.19830 | ||||||||
\(699\) | −6.32377e6 | −0.489534 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.23251e6 | −0.709618 | −0.354809 | − | 0.934939i | \(-0.615454\pi\) | ||||
−0.354809 | + | 0.934939i | \(0.615454\pi\) | |||||||
\(702\) | −4.25441e6 | −0.325834 | ||||||||
\(703\) | −3.86791e7 | −2.95181 | ||||||||
\(704\) | 4.41000e6 | 0.335357 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.16807e7 | 0.881975 | ||||||||
\(707\) | −2.98782e6 | −0.224805 | ||||||||
\(708\) | 850801. | 0.0637889 | ||||||||
\(709\) | −1.91122e7 | −1.42789 | −0.713945 | − | 0.700201i | \(-0.753094\pi\) | ||||
−0.713945 | + | 0.700201i | \(0.753094\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.94426e6 | −0.292612 | ||||||||
\(712\) | −262168. | −0.0193812 | ||||||||
\(713\) | 1.48174e7 | 1.09156 | ||||||||
\(714\) | 6.24827e6 | 0.458685 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.12743e6 | −0.373781 | ||||||||
\(717\) | 5.14813e6 | 0.373983 | ||||||||
\(718\) | 8.77140e6 | 0.634977 | ||||||||
\(719\) | 3.98132e6 | 0.287213 | 0.143607 | − | 0.989635i | \(-0.454130\pi\) | ||||
0.143607 | + | 0.989635i | \(0.454130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.96831e7 | −1.41012 | ||||||||
\(722\) | 1.65241e7 | 1.17971 | ||||||||
\(723\) | −4.36792e6 | −0.310762 | ||||||||
\(724\) | −1.81966e6 | −0.129016 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 655411. | 0.0461501 | ||||||||
\(727\) | 2.31098e6 | 0.162166 | 0.0810832 | − | 0.996707i | \(-0.474162\pi\) | ||||
0.0810832 | + | 0.996707i | \(0.474162\pi\) | |||||||
\(728\) | −3.56077e7 | −2.49009 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.15568e7 | −0.799914 | ||||||||
\(732\) | −57649.3 | −0.00397664 | ||||||||
\(733\) | −1.76034e7 | −1.21015 | −0.605073 | − | 0.796170i | \(-0.706856\pi\) | ||||
−0.605073 | + | 0.796170i | \(0.706856\pi\) | |||||||
\(734\) | 1.49132e7 | 1.02172 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.06045e7 | 0.721601 | ||||||||
\(737\) | 1.71719e6 | 0.116453 | ||||||||
\(738\) | 6.06862e6 | 0.410156 | ||||||||
\(739\) | −8.91956e6 | −0.600803 | −0.300402 | − | 0.953813i | \(-0.597121\pi\) | ||||
−0.300402 | + | 0.953813i | \(0.597121\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.54273e7 | 1.70120 | ||||||||
\(742\) | 1.76639e7 | 1.17781 | ||||||||
\(743\) | −3.22802e6 | −0.214519 | −0.107259 | − | 0.994231i | \(-0.534207\pi\) | ||||
−0.107259 | + | 0.994231i | \(0.534207\pi\) | |||||||
\(744\) | −6.31899e6 | −0.418519 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.00327e7 | 0.660040 | ||||||||
\(747\) | 7.76833e6 | 0.509362 | ||||||||
\(748\) | 788950. | 0.0515579 | ||||||||
\(749\) | 1.20869e7 | 0.787244 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.04930e6 | −0.132588 | −0.0662942 | − | 0.997800i | \(-0.521118\pi\) | ||||
−0.0662942 | + | 0.997800i | \(0.521118\pi\) | |||||||
\(752\) | −4.95029e6 | −0.319217 | ||||||||
\(753\) | 231799. | 0.0148979 | ||||||||
\(754\) | −440310. | −0.0282053 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 822511. | 0.0523404 | ||||||||
\(757\) | −2.62464e6 | −0.166468 | −0.0832340 | − | 0.996530i | \(-0.526525\pi\) | ||||
−0.0832340 | + | 0.996530i | \(0.526525\pi\) | |||||||
\(758\) | 1.88467e7 | 1.19141 | ||||||||
\(759\) | 4.48790e6 | 0.282773 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.90240e7 | 1.19080 | 0.595401 | − | 0.803428i | \(-0.296993\pi\) | ||||
0.595401 | + | 0.803428i | \(0.296993\pi\) | |||||||
\(762\) | 9.35999e6 | 0.583966 | ||||||||
\(763\) | −1.07036e7 | −0.665608 | ||||||||
\(764\) | 4.30404e6 | 0.266773 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.35703e7 | 0.835635 | ||||||||
\(767\) | 1.52780e7 | 0.937729 | ||||||||
\(768\) | −6.06749e6 | −0.371198 | ||||||||
\(769\) | −1.84565e7 | −1.12547 | −0.562735 | − | 0.826637i | \(-0.690251\pi\) | ||||
−0.562735 | + | 0.826637i | \(0.690251\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.18906e6 | −0.132624 | ||||||||
\(772\) | −7.00881e6 | −0.423254 | ||||||||
\(773\) | 6.98835e6 | 0.420655 | 0.210327 | − | 0.977631i | \(-0.432547\pi\) | ||||
0.210327 | + | 0.977631i | \(0.432547\pi\) | |||||||
\(774\) | 5.18429e6 | 0.311055 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.58055e7 | 0.942221 | ||||||||
\(777\) | −2.24675e7 | −1.33506 | ||||||||
\(778\) | 2.15007e6 | 0.127351 | ||||||||
\(779\) | −3.62704e7 | −2.14145 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.52826e6 | −0.558967 | ||||||||
\(782\) | −1.84098e7 | −1.07655 | ||||||||
\(783\) | 55001.5 | 0.00320605 | ||||||||
\(784\) | −5.42834e6 | −0.315411 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.83538e6 | −0.221438 | ||||||||
\(787\) | 1.02434e7 | 0.589533 | 0.294766 | − | 0.955569i | \(-0.404758\pi\) | ||||
0.294766 | + | 0.955569i | \(0.404758\pi\) | |||||||
\(788\) | −1.27227e6 | −0.0729903 | ||||||||
\(789\) | −416502. | −0.0238190 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.80623e6 | −0.386781 | ||||||||
\(792\) | −1.91390e6 | −0.108419 | ||||||||
\(793\) | −1.03522e6 | −0.0584587 | ||||||||
\(794\) | 1.94213e7 | 1.09327 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 353619. | 0.0197812 | ||||||||
\(797\) | −1.36372e7 | −0.760466 | −0.380233 | − | 0.924891i | \(-0.624156\pi\) | ||||
−0.380233 | + | 0.924891i | \(0.624156\pi\) | |||||||
\(798\) | 1.67523e7 | 0.931252 | ||||||||
\(799\) | −6.01634e6 | −0.333400 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 108746. | 0.00598872 | ||||||||
\(802\) | 2.29231e7 | 1.25845 | ||||||||
\(803\) | −4.14150e6 | −0.226657 | ||||||||
\(804\) | −927271. | −0.0505902 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.09830e7 | −1.13770 | ||||||||
\(807\) | 1.57171e6 | 0.0849547 | ||||||||
\(808\) | −3.75423e6 | −0.202299 | ||||||||
\(809\) | −2.94019e7 | −1.57944 | −0.789722 | − | 0.613465i | \(-0.789775\pi\) | ||||
−0.789722 | + | 0.613465i | \(0.789775\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.42304e7 | −0.759737 | −0.379869 | − | 0.925040i | \(-0.624031\pi\) | ||||
−0.379869 | + | 0.925040i | \(0.624031\pi\) | |||||||
\(812\) | 85125.8 | 0.00453076 | ||||||||
\(813\) | −1.60286e7 | −0.850490 | ||||||||
\(814\) | 9.66752e6 | 0.511392 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.97319e6 | 0.314037 | ||||||||
\(817\) | −3.09850e7 | −1.62404 | ||||||||
\(818\) | −1.92294e7 | −1.00481 | ||||||||
\(819\) | 1.47699e7 | 0.769430 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.28257e7 | 1.18186 | 0.590931 | − | 0.806722i | \(-0.298761\pi\) | ||||
0.590931 | + | 0.806722i | \(0.298761\pi\) | |||||||
\(822\) | −5.17084e6 | −0.266920 | ||||||||
\(823\) | 1.12391e6 | 0.0578405 | 0.0289202 | − | 0.999582i | \(-0.490793\pi\) | ||||
0.0289202 | + | 0.999582i | \(0.490793\pi\) | |||||||
\(824\) | −2.47320e7 | −1.26894 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.00656e7 | 0.513321 | ||||||||
\(827\) | 2.69107e7 | 1.36824 | 0.684119 | − | 0.729370i | \(-0.260187\pi\) | ||||
0.684119 | + | 0.729370i | \(0.260187\pi\) | |||||||
\(828\) | −2.42343e6 | −0.122844 | ||||||||
\(829\) | −6.83042e6 | −0.345192 | −0.172596 | − | 0.984993i | \(-0.555216\pi\) | ||||
−0.172596 | + | 0.984993i | \(0.555216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.90580e6 | −0.246438 | ||||||||
\(832\) | −4.27626e7 | −2.14169 | ||||||||
\(833\) | −6.59734e6 | −0.329425 | ||||||||
\(834\) | −5.39964e6 | −0.268813 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.11526e6 | 0.104676 | ||||||||
\(837\) | 2.62110e6 | 0.129321 | ||||||||
\(838\) | 1.79305e7 | 0.882026 | ||||||||
\(839\) | −1.37641e7 | −0.675061 | −0.337531 | − | 0.941315i | \(-0.609592\pi\) | ||||
−0.337531 | + | 0.941315i | \(0.609592\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.05055e7 | −0.999722 | ||||||||
\(842\) | 1.34129e7 | 0.651993 | ||||||||
\(843\) | 769225. | 0.0372808 | ||||||||
\(844\) | −4.80755e6 | −0.232310 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.69889e6 | 0.129646 | ||||||||
\(847\) | −2.27538e6 | −0.108980 | ||||||||
\(848\) | 1.68862e7 | 0.806387 | ||||||||
\(849\) | 1.35962e7 | 0.647364 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.61979e7 | 3.13343 | ||||||||
\(852\) | 5.14519e6 | 0.242830 | ||||||||
\(853\) | 2.38141e7 | 1.12063 | 0.560313 | − | 0.828281i | \(-0.310681\pi\) | ||||
0.560313 | + | 0.828281i | \(0.310681\pi\) | |||||||
\(854\) | −682032. | −0.0320008 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.51873e7 | 0.708428 | ||||||||
\(857\) | 1.96463e7 | 0.913751 | 0.456875 | − | 0.889531i | \(-0.348969\pi\) | ||||
0.456875 | + | 0.889531i | \(0.348969\pi\) | |||||||
\(858\) | −6.35535e6 | −0.294728 | ||||||||
\(859\) | −4.10315e7 | −1.89729 | −0.948646 | − | 0.316339i | \(-0.897546\pi\) | ||||
−0.948646 | + | 0.316339i | \(0.897546\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.10683e7 | −0.968550 | ||||||||
\(862\) | −1.68108e6 | −0.0770585 | ||||||||
\(863\) | 1.10401e7 | 0.504599 | 0.252300 | − | 0.967649i | \(-0.418813\pi\) | ||||
0.252300 | + | 0.967649i | \(0.418813\pi\) | |||||||
\(864\) | 1.87588e6 | 0.0854909 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.70366e7 | −1.22506 | ||||||||
\(867\) | −5.51918e6 | −0.249360 | ||||||||
\(868\) | 4.05667e6 | 0.182755 | ||||||||
\(869\) | −5.89204e6 | −0.264677 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.66512e7 | −0.743702 | ||||||||
\(872\) | −1.34492e7 | −0.598970 | ||||||||
\(873\) | −6.55605e6 | −0.291143 | ||||||||
\(874\) | −4.93587e7 | −2.18567 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.23638e6 | 0.0984658 | ||||||||
\(877\) | 2.06101e7 | 0.904861 | 0.452430 | − | 0.891800i | \(-0.350557\pi\) | ||||
0.452430 | + | 0.891800i | \(0.350557\pi\) | |||||||
\(878\) | −849937. | −0.0372092 | ||||||||
\(879\) | 9.46608e6 | 0.413236 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.17874e6 | −0.311608 | −0.155804 | − | 0.987788i | \(-0.549797\pi\) | ||||
−0.155804 | + | 0.987788i | \(0.549797\pi\) | |||||||
\(882\) | 2.95952e6 | 0.128100 | ||||||||
\(883\) | −1.55190e6 | −0.0669824 | −0.0334912 | − | 0.999439i | \(-0.510663\pi\) | ||||
−0.0334912 | + | 0.999439i | \(0.510663\pi\) | |||||||
\(884\) | −7.65023e6 | −0.329264 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.45526e7 | −1.47876 | ||||||||
\(887\) | 3.39646e7 | 1.44950 | 0.724748 | − | 0.689014i | \(-0.241956\pi\) | ||||
0.724748 | + | 0.689014i | \(0.241956\pi\) | |||||||
\(888\) | −2.82307e7 | −1.20140 | ||||||||
\(889\) | −3.24949e7 | −1.37899 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −320704. | −0.0134956 | ||||||||
\(893\) | −1.61305e7 | −0.676891 | ||||||||
\(894\) | 2.20205e6 | 0.0921474 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.53762e7 | −0.639853 | ||||||||
\(897\) | −4.35180e7 | −1.80587 | ||||||||
\(898\) | −9.54127e6 | −0.394835 | ||||||||
\(899\) | 271271. | 0.0111945 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.05227e7 | 0.842216 | ||||||||
\(902\) | 9.06547e6 | 0.371000 | ||||||||
\(903\) | −1.79982e7 | −0.734531 | ||||||||
\(904\) | −8.55211e6 | −0.348058 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.19713e7 | −0.889272 | ||||||||
\(907\) | 2.58319e7 | 1.04265 | 0.521324 | − | 0.853359i | \(-0.325438\pi\) | ||||
0.521324 | + | 0.853359i | \(0.325438\pi\) | |||||||
\(908\) | 4.24837e6 | 0.171005 | ||||||||
\(909\) | 1.55724e6 | 0.0625096 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 549431. | 0.0219340 | 0.0109670 | − | 0.999940i | \(-0.496509\pi\) | ||||
0.0109670 | + | 0.999940i | \(0.496509\pi\) | |||||||
\(912\) | 1.60148e7 | 0.637579 | ||||||||
\(913\) | 1.16045e7 | 0.460735 | ||||||||
\(914\) | 5.68262e6 | 0.225000 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.63773e6 | −0.261385 | ||||||||
\(917\) | 1.33152e7 | 0.522908 | ||||||||
\(918\) | −3.25658e6 | −0.127542 | ||||||||
\(919\) | 3.84177e7 | 1.50052 | 0.750261 | − | 0.661142i | \(-0.229928\pi\) | ||||
0.750261 | + | 0.661142i | \(0.229928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.51536e7 | 0.588662 | ||||||||
\(922\) | 1.80701e7 | 0.700055 | ||||||||
\(923\) | 9.23930e7 | 3.56973 | ||||||||
\(924\) | 1.22869e6 | 0.0473437 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.13185e7 | 1.20025 | ||||||||
\(927\) | 1.02588e7 | 0.392099 | ||||||||
\(928\) | 194144. | 0.00740038 | ||||||||
\(929\) | 1.50560e7 | 0.572360 | 0.286180 | − | 0.958176i | \(-0.407614\pi\) | ||||
0.286180 | + | 0.958176i | \(0.407614\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.76882e7 | −0.668821 | ||||||||
\(932\) | 5.10110e6 | 0.192364 | ||||||||
\(933\) | −2.45170e7 | −0.922070 | ||||||||
\(934\) | −229877. | −0.00862240 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.85586e7 | 0.692398 | ||||||||
\(937\) | −1.83320e7 | −0.682119 | −0.341059 | − | 0.940042i | \(-0.610786\pi\) | ||||
−0.341059 | + | 0.940042i | \(0.610786\pi\) | |||||||
\(938\) | −1.09703e7 | −0.407109 | ||||||||
\(939\) | −1.52242e7 | −0.563470 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.82211e7 | −1.40711 | −0.703557 | − | 0.710639i | \(-0.748406\pi\) | ||||
−0.703557 | + | 0.710639i | \(0.748406\pi\) | |||||||
\(942\) | 1.22525e7 | 0.449879 | ||||||||
\(943\) | 6.20754e7 | 2.27321 | ||||||||
\(944\) | 9.62245e6 | 0.351444 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.74444e6 | 0.281360 | ||||||||
\(947\) | −3.35057e7 | −1.21407 | −0.607035 | − | 0.794675i | \(-0.707641\pi\) | ||||
−0.607035 | + | 0.794675i | \(0.707641\pi\) | |||||||
\(948\) | 3.18166e6 | 0.114983 | ||||||||
\(949\) | 4.01590e7 | 1.44750 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.34233e6 | 0.119839 | ||||||||
\(952\) | −2.72563e7 | −0.974707 | ||||||||
\(953\) | 3.29329e7 | 1.17462 | 0.587310 | − | 0.809362i | \(-0.300187\pi\) | ||||
0.587310 | + | 0.809362i | \(0.300187\pi\) | |||||||
\(954\) | −9.20636e6 | −0.327504 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.15277e6 | −0.146958 | ||||||||
\(957\) | 82162.8 | 0.00289998 | ||||||||
\(958\) | 9.32386e6 | 0.328233 | ||||||||
\(959\) | 1.79515e7 | 0.630311 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.57018e7 | −0.548454 | ||||||||
\(962\) | −9.37433e7 | −3.26590 | ||||||||
\(963\) | −6.29964e6 | −0.218902 | ||||||||
\(964\) | 3.52340e6 | 0.122115 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.86709e7 | −0.988551 | ||||||||
\(967\) | −2.24586e7 | −0.772353 | −0.386177 | − | 0.922425i | \(-0.626204\pi\) | ||||
−0.386177 | + | 0.922425i | \(0.626204\pi\) | |||||||
\(968\) | −2.85904e6 | −0.0980691 | ||||||||
\(969\) | 1.94636e7 | 0.665908 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.76102e7 | 1.28014 | 0.640069 | − | 0.768317i | \(-0.278906\pi\) | ||||
0.640069 | + | 0.768317i | \(0.278906\pi\) | |||||||
\(972\) | −428690. | −0.0145538 | ||||||||
\(973\) | 1.87458e7 | 0.634780 | ||||||||
\(974\) | 1.46159e7 | 0.493660 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −652007. | −0.0219092 | ||||||||
\(977\) | 1.90408e7 | 0.638187 | 0.319094 | − | 0.947723i | \(-0.396622\pi\) | ||||
0.319094 | + | 0.947723i | \(0.396622\pi\) | |||||||
\(978\) | −2.90443e6 | −0.0970987 | ||||||||
\(979\) | 162448. | 0.00541700 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.57868e6 | 0.185080 | ||||||||
\(982\) | 3.76256e7 | 1.24510 | ||||||||
\(983\) | 3.59407e7 | 1.18632 | 0.593162 | − | 0.805083i | \(-0.297880\pi\) | ||||
0.593162 | + | 0.805083i | \(0.297880\pi\) | |||||||
\(984\) | −2.64726e7 | −0.871584 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −337040. | −0.0110405 | ||||||||
\(987\) | −9.36969e6 | −0.306149 | ||||||||
\(988\) | −2.05111e7 | −0.668493 | ||||||||
\(989\) | 5.30297e7 | 1.72396 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.52119e7 | 0.815495 | 0.407748 | − | 0.913095i | \(-0.366314\pi\) | ||||
0.407748 | + | 0.913095i | \(0.366314\pi\) | |||||||
\(992\) | 9.25192e6 | 0.298506 | ||||||||
\(993\) | 1.39073e7 | 0.447578 | ||||||||
\(994\) | 6.08713e7 | 1.95410 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.26637e6 | −0.200156 | ||||||||
\(997\) | −4.86935e6 | −0.155143 | −0.0775716 | − | 0.996987i | \(-0.524717\pi\) | ||||
−0.0775716 | + | 0.996987i | \(0.524717\pi\) | |||||||
\(998\) | −1.97413e7 | −0.627406 | ||||||||
\(999\) | 1.17100e7 | 0.371230 |
(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.y.1.8 | 13 | ||
5.2 | odd | 4 | 165.6.c.b.34.18 | yes | 26 | ||
5.3 | odd | 4 | 165.6.c.b.34.9 | ✓ | 26 | ||
5.4 | even | 2 | 825.6.a.v.1.6 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.9 | ✓ | 26 | 5.3 | odd | 4 | ||
165.6.c.b.34.18 | yes | 26 | 5.2 | odd | 4 | ||
825.6.a.v.1.6 | 13 | 5.4 | even | 2 | |||
825.6.a.y.1.8 | 13 | 1.1 | even | 1 | trivial |