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: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 271 x^{8} + 309 x^{7} + 24456 x^{6} - 33410 x^{5} - 822204 x^{4} + 1367872 x^{3} + 7443872 x^{2} - 12856224 x - 7036608 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-9.20891\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.20891 | 1.62792 | 0.813960 | − | 0.580921i | \(-0.197307\pi\) | ||||
0.813960 | + | 0.580921i | \(0.197307\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 52.8039 | 1.65012 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 82.8802 | 0.939880 | ||||||||
\(7\) | −195.275 | −1.50626 | −0.753131 | − | 0.657870i | \(-0.771458\pi\) | ||||
−0.753131 | + | 0.657870i | \(0.771458\pi\) | |||||||
\(8\) | 191.582 | 1.05835 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 475.236 | 0.952699 | ||||||||
\(13\) | −457.051 | −0.750078 | −0.375039 | − | 0.927009i | \(-0.622371\pi\) | ||||
−0.375039 | + | 0.927009i | \(0.622371\pi\) | |||||||
\(14\) | −1798.27 | −2.45208 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 74.5305 | 0.0727837 | ||||||||
\(17\) | 1237.33 | 1.03840 | 0.519200 | − | 0.854653i | \(-0.326230\pi\) | ||||
0.519200 | + | 0.854653i | \(0.326230\pi\) | |||||||
\(18\) | 745.921 | 0.542640 | ||||||||
\(19\) | 2140.85 | 1.36051 | 0.680255 | − | 0.732976i | \(-0.261869\pi\) | ||||
0.680255 | + | 0.732976i | \(0.261869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1757.47 | −0.869641 | ||||||||
\(22\) | 1114.28 | 0.490836 | ||||||||
\(23\) | 2272.80 | 0.895861 | 0.447931 | − | 0.894068i | \(-0.352161\pi\) | ||||
0.447931 | + | 0.894068i | \(0.352161\pi\) | |||||||
\(24\) | 1724.23 | 0.611038 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4208.94 | −1.22107 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −10311.3 | −2.48552 | ||||||||
\(29\) | 6561.91 | 1.44889 | 0.724445 | − | 0.689333i | \(-0.242096\pi\) | ||||
0.724445 | + | 0.689333i | \(0.242096\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6349.26 | 1.18664 | 0.593320 | − | 0.804967i | \(-0.297817\pi\) | ||||
0.593320 | + | 0.804967i | \(0.297817\pi\) | |||||||
\(32\) | −5444.27 | −0.939863 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 11394.5 | 1.69043 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4277.12 | 0.550041 | ||||||||
\(37\) | −3376.37 | −0.405457 | −0.202729 | − | 0.979235i | \(-0.564981\pi\) | ||||
−0.202729 | + | 0.979235i | \(0.564981\pi\) | |||||||
\(38\) | 19714.9 | 2.21480 | ||||||||
\(39\) | −4113.46 | −0.433058 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3970.52 | 0.368882 | 0.184441 | − | 0.982844i | \(-0.440953\pi\) | ||||
0.184441 | + | 0.982844i | \(0.440953\pi\) | |||||||
\(42\) | −16184.4 | −1.41571 | ||||||||
\(43\) | 3901.82 | 0.321807 | 0.160904 | − | 0.986970i | \(-0.448559\pi\) | ||||
0.160904 | + | 0.986970i | \(0.448559\pi\) | |||||||
\(44\) | 6389.28 | 0.497531 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 20930.0 | 1.45839 | ||||||||
\(47\) | −1267.66 | −0.0837065 | −0.0418532 | − | 0.999124i | \(-0.513326\pi\) | ||||
−0.0418532 | + | 0.999124i | \(0.513326\pi\) | |||||||
\(48\) | 670.775 | 0.0420217 | ||||||||
\(49\) | 21325.2 | 1.26883 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11136.0 | 0.599521 | ||||||||
\(52\) | −24134.1 | −1.23772 | ||||||||
\(53\) | 10563.3 | 0.516546 | 0.258273 | − | 0.966072i | \(-0.416847\pi\) | ||||
0.258273 | + | 0.966072i | \(0.416847\pi\) | |||||||
\(54\) | 6713.29 | 0.313293 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −37411.0 | −1.59415 | ||||||||
\(57\) | 19267.6 | 0.785490 | ||||||||
\(58\) | 60428.0 | 2.35868 | ||||||||
\(59\) | 43579.8 | 1.62988 | 0.814938 | − | 0.579548i | \(-0.196771\pi\) | ||||
0.814938 | + | 0.579548i | \(0.196771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 49086.8 | 1.68904 | 0.844521 | − | 0.535522i | \(-0.179885\pi\) | ||||
0.844521 | + | 0.535522i | \(0.179885\pi\) | |||||||
\(62\) | 58469.8 | 1.93176 | ||||||||
\(63\) | −15817.2 | −0.502088 | ||||||||
\(64\) | −52520.7 | −1.60280 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10028.5 | 0.283384 | ||||||||
\(67\) | 14785.3 | 0.402386 | 0.201193 | − | 0.979552i | \(-0.435518\pi\) | ||||
0.201193 | + | 0.979552i | \(0.435518\pi\) | |||||||
\(68\) | 65336.1 | 1.71349 | ||||||||
\(69\) | 20455.2 | 0.517226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8961.61 | 0.210979 | 0.105490 | − | 0.994420i | \(-0.466359\pi\) | ||||
0.105490 | + | 0.994420i | \(0.466359\pi\) | |||||||
\(72\) | 15518.1 | 0.352783 | ||||||||
\(73\) | −83352.2 | −1.83067 | −0.915335 | − | 0.402694i | \(-0.868074\pi\) | ||||
−0.915335 | + | 0.402694i | \(0.868074\pi\) | |||||||
\(74\) | −31092.6 | −0.660052 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 113045. | 2.24501 | ||||||||
\(77\) | −23628.2 | −0.454155 | ||||||||
\(78\) | −37880.5 | −0.704983 | ||||||||
\(79\) | −17858.5 | −0.321942 | −0.160971 | − | 0.986959i | \(-0.551463\pi\) | ||||
−0.160971 | + | 0.986959i | \(0.551463\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 36564.1 | 0.600511 | ||||||||
\(83\) | −66830.4 | −1.06483 | −0.532413 | − | 0.846485i | \(-0.678715\pi\) | ||||
−0.532413 | + | 0.846485i | \(0.678715\pi\) | |||||||
\(84\) | −92801.5 | −1.43502 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 35931.5 | 0.523877 | ||||||||
\(87\) | 59057.2 | 0.836517 | ||||||||
\(88\) | 23181.4 | 0.319104 | ||||||||
\(89\) | −117907. | −1.57784 | −0.788921 | − | 0.614495i | \(-0.789360\pi\) | ||||
−0.788921 | + | 0.614495i | \(0.789360\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 89250.5 | 1.12981 | ||||||||
\(92\) | 120013. | 1.47828 | ||||||||
\(93\) | 57143.4 | 0.685107 | ||||||||
\(94\) | −11673.8 | −0.136267 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −48998.4 | −0.542630 | ||||||||
\(97\) | 156797. | 1.69203 | 0.846017 | − | 0.533155i | \(-0.178994\pi\) | ||||
0.846017 | + | 0.533155i | \(0.178994\pi\) | |||||||
\(98\) | 196382. | 2.06555 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −89018.4 | −0.868313 | −0.434156 | − | 0.900838i | \(-0.642953\pi\) | ||||
−0.434156 | + | 0.900838i | \(0.642953\pi\) | |||||||
\(102\) | 102550. | 0.975972 | ||||||||
\(103\) | 100268. | 0.931253 | 0.465626 | − | 0.884981i | \(-0.345829\pi\) | ||||
0.465626 | + | 0.884981i | \(0.345829\pi\) | |||||||
\(104\) | −87562.6 | −0.793844 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 97276.1 | 0.840895 | ||||||||
\(107\) | −132681. | −1.12033 | −0.560167 | − | 0.828380i | \(-0.689263\pi\) | ||||
−0.560167 | + | 0.828380i | \(0.689263\pi\) | |||||||
\(108\) | 38494.1 | 0.317566 | ||||||||
\(109\) | 88547.8 | 0.713857 | 0.356929 | − | 0.934132i | \(-0.383824\pi\) | ||||
0.356929 | + | 0.934132i | \(0.383824\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −30387.3 | −0.234091 | ||||||||
\(112\) | −14553.9 | −0.109631 | ||||||||
\(113\) | 92355.2 | 0.680401 | 0.340201 | − | 0.940353i | \(-0.389505\pi\) | ||||
0.340201 | + | 0.940353i | \(0.389505\pi\) | |||||||
\(114\) | 177434. | 1.27872 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 346495. | 2.39085 | ||||||||
\(117\) | −37021.1 | −0.250026 | ||||||||
\(118\) | 401322. | 2.65331 | ||||||||
\(119\) | −241620. | −1.56410 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 452036. | 2.74963 | ||||||||
\(123\) | 35734.7 | 0.212974 | ||||||||
\(124\) | 335266. | 1.95810 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −145660. | −0.817358 | ||||||||
\(127\) | −70624.6 | −0.388550 | −0.194275 | − | 0.980947i | \(-0.562235\pi\) | ||||
−0.194275 | + | 0.980947i | \(0.562235\pi\) | |||||||
\(128\) | −309442. | −1.66938 | ||||||||
\(129\) | 35116.4 | 0.185796 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 155328. | 0.790809 | 0.395404 | − | 0.918507i | \(-0.370604\pi\) | ||||
0.395404 | + | 0.918507i | \(0.370604\pi\) | |||||||
\(132\) | 57503.5 | 0.287250 | ||||||||
\(133\) | −418053. | −2.04928 | ||||||||
\(134\) | 136156. | 0.655053 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 237051. | 1.09899 | ||||||||
\(137\) | 70583.9 | 0.321295 | 0.160647 | − | 0.987012i | \(-0.448642\pi\) | ||||
0.160647 | + | 0.987012i | \(0.448642\pi\) | |||||||
\(138\) | 188370. | 0.842002 | ||||||||
\(139\) | −400133. | −1.75658 | −0.878290 | − | 0.478129i | \(-0.841315\pi\) | ||||
−0.878290 | + | 0.478129i | \(0.841315\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11409.0 | −0.0483279 | ||||||||
\(142\) | 82526.6 | 0.343458 | ||||||||
\(143\) | −55303.2 | −0.226157 | ||||||||
\(144\) | 6036.97 | 0.0242612 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −767583. | −2.98018 | ||||||||
\(147\) | 191927. | 0.732558 | ||||||||
\(148\) | −178285. | −0.669055 | ||||||||
\(149\) | 27434.0 | 0.101233 | 0.0506166 | − | 0.998718i | \(-0.483881\pi\) | ||||
0.0506166 | + | 0.998718i | \(0.483881\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 111764. | 0.398894 | 0.199447 | − | 0.979909i | \(-0.436085\pi\) | ||||
0.199447 | + | 0.979909i | \(0.436085\pi\) | |||||||
\(152\) | 410147. | 1.43989 | ||||||||
\(153\) | 100224. | 0.346133 | ||||||||
\(154\) | −217590. | −0.739329 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −217207. | −0.714598 | ||||||||
\(157\) | 231260. | 0.748775 | 0.374388 | − | 0.927272i | \(-0.377853\pi\) | ||||
0.374388 | + | 0.927272i | \(0.377853\pi\) | |||||||
\(158\) | −164458. | −0.524096 | ||||||||
\(159\) | 95069.4 | 0.298228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −443819. | −1.34940 | ||||||||
\(162\) | 60419.6 | 0.180880 | ||||||||
\(163\) | −219113. | −0.645949 | −0.322974 | − | 0.946408i | \(-0.604683\pi\) | ||||
−0.322974 | + | 0.946408i | \(0.604683\pi\) | |||||||
\(164\) | 209659. | 0.608701 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −615435. | −1.73345 | ||||||||
\(167\) | 138345. | 0.383859 | 0.191929 | − | 0.981409i | \(-0.438526\pi\) | ||||
0.191929 | + | 0.981409i | \(0.438526\pi\) | |||||||
\(168\) | −336699. | −0.920384 | ||||||||
\(169\) | −162397. | −0.437383 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 173409. | 0.453503 | ||||||||
\(172\) | 206031. | 0.531022 | ||||||||
\(173\) | −314475. | −0.798860 | −0.399430 | − | 0.916764i | \(-0.630792\pi\) | ||||
−0.399430 | + | 0.916764i | \(0.630792\pi\) | |||||||
\(174\) | 543852. | 1.36178 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9018.19 | 0.0219451 | ||||||||
\(177\) | 392218. | 0.941010 | ||||||||
\(178\) | −1.08579e6 | −2.56860 | ||||||||
\(179\) | −725112. | −1.69150 | −0.845751 | − | 0.533578i | \(-0.820847\pi\) | ||||
−0.845751 | + | 0.533578i | \(0.820847\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 843502. | 1.91377 | 0.956885 | − | 0.290466i | \(-0.0938102\pi\) | ||||
0.956885 | + | 0.290466i | \(0.0938102\pi\) | |||||||
\(182\) | 821899. | 1.83925 | ||||||||
\(183\) | 441782. | 0.975169 | ||||||||
\(184\) | 435426. | 0.948134 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 526228. | 1.11530 | ||||||||
\(187\) | 149717. | 0.313089 | ||||||||
\(188\) | −66937.6 | −0.138126 | ||||||||
\(189\) | −142355. | −0.289880 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −659387. | −1.30785 | −0.653923 | − | 0.756561i | \(-0.726878\pi\) | ||||
−0.653923 | + | 0.756561i | \(0.726878\pi\) | |||||||
\(192\) | −472686. | −0.925380 | ||||||||
\(193\) | −350322. | −0.676978 | −0.338489 | − | 0.940970i | \(-0.609916\pi\) | ||||
−0.338489 | + | 0.940970i | \(0.609916\pi\) | |||||||
\(194\) | 1.44393e6 | 2.75450 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.12605e6 | 2.09372 | ||||||||
\(197\) | 504269. | 0.925757 | 0.462878 | − | 0.886422i | \(-0.346817\pi\) | ||||
0.462878 | + | 0.886422i | \(0.346817\pi\) | |||||||
\(198\) | 90256.5 | 0.163612 | ||||||||
\(199\) | −939943. | −1.68255 | −0.841276 | − | 0.540605i | \(-0.818195\pi\) | ||||
−0.841276 | + | 0.540605i | \(0.818195\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 133068. | 0.232318 | ||||||||
\(202\) | −819762. | −1.41354 | ||||||||
\(203\) | −1.28137e6 | −2.18241 | ||||||||
\(204\) | 588025. | 0.989283 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 923355. | 1.51601 | ||||||||
\(207\) | 184096. | 0.298620 | ||||||||
\(208\) | −34064.2 | −0.0545934 | ||||||||
\(209\) | 259042. | 0.410209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 666610. | 1.03078 | 0.515390 | − | 0.856956i | \(-0.327647\pi\) | ||||
0.515390 | + | 0.856956i | \(0.327647\pi\) | |||||||
\(212\) | 557782. | 0.852364 | ||||||||
\(213\) | 80654.5 | 0.121809 | ||||||||
\(214\) | −1.22184e6 | −1.82381 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 139663. | 0.203679 | ||||||||
\(217\) | −1.23985e6 | −1.78739 | ||||||||
\(218\) | 815428. | 1.16210 | ||||||||
\(219\) | −750170. | −1.05694 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −565525. | −0.778881 | ||||||||
\(222\) | −279834. | −0.381081 | ||||||||
\(223\) | −459829. | −0.619205 | −0.309602 | − | 0.950866i | \(-0.600196\pi\) | ||||
−0.309602 | + | 0.950866i | \(0.600196\pi\) | |||||||
\(224\) | 1.06313e6 | 1.41568 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 850490. | 1.10764 | ||||||||
\(227\) | 1.11522e6 | 1.43647 | 0.718236 | − | 0.695799i | \(-0.244950\pi\) | ||||
0.718236 | + | 0.695799i | \(0.244950\pi\) | |||||||
\(228\) | 1.01741e6 | 1.29616 | ||||||||
\(229\) | 1.19306e6 | 1.50340 | 0.751700 | − | 0.659505i | \(-0.229234\pi\) | ||||
0.751700 | + | 0.659505i | \(0.229234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −212654. | −0.262207 | ||||||||
\(232\) | 1.25714e6 | 1.53343 | ||||||||
\(233\) | 675874. | 0.815598 | 0.407799 | − | 0.913072i | \(-0.366296\pi\) | ||||
0.407799 | + | 0.913072i | \(0.366296\pi\) | |||||||
\(234\) | −340924. | −0.407022 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.30118e6 | 2.68950 | ||||||||
\(237\) | −160727. | −0.185873 | ||||||||
\(238\) | −2.22506e6 | −2.54624 | ||||||||
\(239\) | 436348. | 0.494127 | 0.247063 | − | 0.968999i | \(-0.420534\pi\) | ||||
0.247063 | + | 0.968999i | \(0.420534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 597010. | 0.662123 | 0.331062 | − | 0.943609i | \(-0.392593\pi\) | ||||
0.331062 | + | 0.943609i | \(0.392593\pi\) | |||||||
\(242\) | 134828. | 0.147993 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 2.59198e6 | 2.78713 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 329077. | 0.346705 | ||||||||
\(247\) | −978476. | −1.02049 | ||||||||
\(248\) | 1.21640e6 | 1.25588 | ||||||||
\(249\) | −601474. | −0.614778 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −75812.0 | −0.0759545 | −0.0379773 | − | 0.999279i | \(-0.512091\pi\) | ||||
−0.0379773 | + | 0.999279i | \(0.512091\pi\) | |||||||
\(252\) | −835213. | −0.828507 | ||||||||
\(253\) | 275008. | 0.270112 | ||||||||
\(254\) | −650376. | −0.632528 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.16896e6 | −1.11480 | ||||||||
\(257\) | −1.20303e6 | −1.13617 | −0.568087 | − | 0.822969i | \(-0.692316\pi\) | ||||
−0.568087 | + | 0.822969i | \(0.692316\pi\) | |||||||
\(258\) | 323383. | 0.302460 | ||||||||
\(259\) | 659319. | 0.610725 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 531515. | 0.482963 | ||||||||
\(262\) | 1.43040e6 | 1.28737 | ||||||||
\(263\) | 332575. | 0.296483 | 0.148242 | − | 0.988951i | \(-0.452639\pi\) | ||||
0.148242 | + | 0.988951i | \(0.452639\pi\) | |||||||
\(264\) | 208632. | 0.184235 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.84981e6 | −3.33607 | ||||||||
\(267\) | −1.06116e6 | −0.910968 | ||||||||
\(268\) | 780722. | 0.663987 | ||||||||
\(269\) | 1.60565e6 | 1.35291 | 0.676455 | − | 0.736484i | \(-0.263515\pi\) | ||||
0.676455 | + | 0.736484i | \(0.263515\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −973760. | −0.805432 | −0.402716 | − | 0.915325i | \(-0.631934\pi\) | ||||
−0.402716 | + | 0.915325i | \(0.631934\pi\) | |||||||
\(272\) | 92219.2 | 0.0755786 | ||||||||
\(273\) | 803254. | 0.652299 | ||||||||
\(274\) | 650000. | 0.523043 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.08011e6 | 0.853486 | ||||||||
\(277\) | −430301. | −0.336956 | −0.168478 | − | 0.985705i | \(-0.553885\pi\) | ||||
−0.168478 | + | 0.985705i | \(0.553885\pi\) | |||||||
\(278\) | −3.68479e6 | −2.85957 | ||||||||
\(279\) | 514290. | 0.395547 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −566489. | −0.427982 | −0.213991 | − | 0.976836i | \(-0.568646\pi\) | ||||
−0.213991 | + | 0.976836i | \(0.568646\pi\) | |||||||
\(282\) | −105064. | −0.0786740 | ||||||||
\(283\) | −962280. | −0.714225 | −0.357113 | − | 0.934061i | \(-0.616239\pi\) | ||||
−0.357113 | + | 0.934061i | \(0.616239\pi\) | |||||||
\(284\) | 473208. | 0.348142 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −509282. | −0.368165 | ||||||||
\(287\) | −775342. | −0.555633 | ||||||||
\(288\) | −440986. | −0.313288 | ||||||||
\(289\) | 111140. | 0.0782753 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.41118e6 | 0.976897 | ||||||||
\(292\) | −4.40133e6 | −3.02083 | ||||||||
\(293\) | −762793. | −0.519084 | −0.259542 | − | 0.965732i | \(-0.583572\pi\) | ||||
−0.259542 | + | 0.965732i | \(0.583572\pi\) | |||||||
\(294\) | 1.76744e6 | 1.19255 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −646850. | −0.429115 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | 252637. | 0.164800 | ||||||||
\(299\) | −1.03878e6 | −0.671966 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −761926. | −0.484726 | ||||||||
\(302\) | 1.02922e6 | 0.649368 | ||||||||
\(303\) | −801165. | −0.501321 | ||||||||
\(304\) | 159558. | 0.0990229 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 922954. | 0.563478 | ||||||||
\(307\) | 3.02419e6 | 1.83132 | 0.915658 | − | 0.401958i | \(-0.131670\pi\) | ||||
0.915658 | + | 0.401958i | \(0.131670\pi\) | |||||||
\(308\) | −1.24766e6 | −0.749412 | ||||||||
\(309\) | 902408. | 0.537659 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.33903e6 | 1.37131 | 0.685654 | − | 0.727928i | \(-0.259516\pi\) | ||||
0.685654 | + | 0.727928i | \(0.259516\pi\) | |||||||
\(312\) | −788063. | −0.458326 | ||||||||
\(313\) | 1.42601e6 | 0.822740 | 0.411370 | − | 0.911469i | \(-0.365050\pi\) | ||||
0.411370 | + | 0.911469i | \(0.365050\pi\) | |||||||
\(314\) | 2.12965e6 | 1.21895 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −943001. | −0.531244 | ||||||||
\(317\) | −1.60632e6 | −0.897809 | −0.448904 | − | 0.893580i | \(-0.648186\pi\) | ||||
−0.448904 | + | 0.893580i | \(0.648186\pi\) | |||||||
\(318\) | 875485. | 0.485491 | ||||||||
\(319\) | 793991. | 0.436857 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.19412e6 | −0.646825 | ||||||||
\(322\) | −4.08709e6 | −2.19672 | ||||||||
\(323\) | 2.64894e6 | 1.41275 | ||||||||
\(324\) | 346447. | 0.183347 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.01779e6 | −1.05155 | ||||||||
\(327\) | 796930. | 0.412146 | ||||||||
\(328\) | 760678. | 0.390406 | ||||||||
\(329\) | 247542. | 0.126084 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.11538e6 | 1.56294 | 0.781469 | − | 0.623945i | \(-0.214471\pi\) | ||||
0.781469 | + | 0.623945i | \(0.214471\pi\) | |||||||
\(332\) | −3.52891e6 | −1.75710 | ||||||||
\(333\) | −273486. | −0.135152 | ||||||||
\(334\) | 1.27400e6 | 0.624892 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −130985. | −0.0632957 | ||||||||
\(337\) | −1.61111e6 | −0.772768 | −0.386384 | − | 0.922338i | \(-0.626276\pi\) | ||||
−0.386384 | + | 0.922338i | \(0.626276\pi\) | |||||||
\(338\) | −1.49550e6 | −0.712025 | ||||||||
\(339\) | 831197. | 0.392830 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 768261. | 0.357786 | ||||||||
\(342\) | 1.59690e6 | 0.738267 | ||||||||
\(343\) | −882288. | −0.404925 | ||||||||
\(344\) | 747517. | 0.340584 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.89597e6 | −1.30048 | ||||||||
\(347\) | 847409. | 0.377806 | 0.188903 | − | 0.981996i | \(-0.439507\pi\) | ||||
0.188903 | + | 0.981996i | \(0.439507\pi\) | |||||||
\(348\) | 3.11845e6 | 1.38036 | ||||||||
\(349\) | 2.75989e6 | 1.21291 | 0.606455 | − | 0.795118i | \(-0.292591\pi\) | ||||
0.606455 | + | 0.795118i | \(0.292591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −333190. | −0.144353 | ||||||||
\(352\) | −658756. | −0.283379 | ||||||||
\(353\) | −4.12207e6 | −1.76067 | −0.880336 | − | 0.474351i | \(-0.842683\pi\) | ||||
−0.880336 | + | 0.474351i | \(0.842683\pi\) | |||||||
\(354\) | 3.61190e6 | 1.53189 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.22594e6 | −2.60363 | ||||||||
\(357\) | −2.17458e6 | −0.903036 | ||||||||
\(358\) | −6.67749e6 | −2.75363 | ||||||||
\(359\) | 585248. | 0.239664 | 0.119832 | − | 0.992794i | \(-0.461764\pi\) | ||||
0.119832 | + | 0.992794i | \(0.461764\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.10712e6 | 0.850985 | ||||||||
\(362\) | 7.76773e6 | 3.11547 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 4.71278e6 | 1.86433 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.06832e6 | 1.58750 | ||||||||
\(367\) | 3.47515e6 | 1.34681 | 0.673407 | − | 0.739272i | \(-0.264830\pi\) | ||||
0.673407 | + | 0.739272i | \(0.264830\pi\) | |||||||
\(368\) | 169393. | 0.0652041 | ||||||||
\(369\) | 321612. | 0.122961 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.06274e6 | −0.778053 | ||||||||
\(372\) | 3.01740e6 | 1.13051 | ||||||||
\(373\) | 2.08904e6 | 0.777453 | 0.388726 | − | 0.921353i | \(-0.372915\pi\) | ||||
0.388726 | + | 0.921353i | \(0.372915\pi\) | |||||||
\(374\) | 1.37873e6 | 0.509685 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −242861. | −0.0885906 | ||||||||
\(377\) | −2.99913e6 | −1.08678 | ||||||||
\(378\) | −1.31094e6 | −0.471902 | ||||||||
\(379\) | −1.41198e6 | −0.504931 | −0.252466 | − | 0.967606i | \(-0.581241\pi\) | ||||
−0.252466 | + | 0.967606i | \(0.581241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −635622. | −0.224329 | ||||||||
\(382\) | −6.07223e6 | −2.12907 | ||||||||
\(383\) | −2.02171e6 | −0.704241 | −0.352121 | − | 0.935955i | \(-0.614539\pi\) | ||||
−0.352121 | + | 0.935955i | \(0.614539\pi\) | |||||||
\(384\) | −2.78498e6 | −0.963814 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.22608e6 | −1.10207 | ||||||||
\(387\) | 316047. | 0.107269 | ||||||||
\(388\) | 8.27952e6 | 2.79207 | ||||||||
\(389\) | −2.12481e6 | −0.711943 | −0.355971 | − | 0.934497i | \(-0.615850\pi\) | ||||
−0.355971 | + | 0.934497i | \(0.615850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.81221e6 | 0.930263 | ||||||||
\(392\) | 4.08551e6 | 1.34286 | ||||||||
\(393\) | 1.39795e6 | 0.456574 | ||||||||
\(394\) | 4.64377e6 | 1.50706 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 517531. | 0.165844 | ||||||||
\(397\) | 2.11404e6 | 0.673188 | 0.336594 | − | 0.941650i | \(-0.390725\pi\) | ||||
0.336594 | + | 0.941650i | \(0.390725\pi\) | |||||||
\(398\) | −8.65584e6 | −2.73906 | ||||||||
\(399\) | −3.76248e6 | −1.18315 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00967e6 | 0.313558 | 0.156779 | − | 0.987634i | \(-0.449889\pi\) | ||||
0.156779 | + | 0.987634i | \(0.449889\pi\) | |||||||
\(402\) | 1.22541e6 | 0.378195 | ||||||||
\(403\) | −2.90194e6 | −0.890073 | ||||||||
\(404\) | −4.70052e6 | −1.43282 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.18001e7 | −3.55279 | ||||||||
\(407\) | −408540. | −0.122250 | ||||||||
\(408\) | 2.13345e6 | 0.634502 | ||||||||
\(409\) | −190771. | −0.0563904 | −0.0281952 | − | 0.999602i | \(-0.508976\pi\) | ||||
−0.0281952 | + | 0.999602i | \(0.508976\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 635255. | 0.185500 | ||||||||
\(412\) | 5.29453e6 | 1.53668 | ||||||||
\(413\) | −8.51002e6 | −2.45502 | ||||||||
\(414\) | 1.69533e6 | 0.486130 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.48831e6 | 0.704970 | ||||||||
\(417\) | −3.60120e6 | −1.01416 | ||||||||
\(418\) | 2.38550e6 | 0.667787 | ||||||||
\(419\) | −4.82015e6 | −1.34130 | −0.670650 | − | 0.741774i | \(-0.733985\pi\) | ||||
−0.670650 | + | 0.741774i | \(0.733985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.47210e6 | −0.404791 | −0.202395 | − | 0.979304i | \(-0.564873\pi\) | ||||
−0.202395 | + | 0.979304i | \(0.564873\pi\) | |||||||
\(422\) | 6.13875e6 | 1.67803 | ||||||||
\(423\) | −102681. | −0.0279022 | ||||||||
\(424\) | 2.02373e6 | 0.546685 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 742739. | 0.198295 | ||||||||
\(427\) | −9.58542e6 | −2.54414 | ||||||||
\(428\) | −7.00605e6 | −1.84869 | ||||||||
\(429\) | −497729. | −0.130572 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.75922e6 | −0.974774 | −0.487387 | − | 0.873186i | \(-0.662050\pi\) | ||||
−0.487387 | + | 0.873186i | \(0.662050\pi\) | |||||||
\(432\) | 54332.8 | 0.0140072 | ||||||||
\(433\) | −3.03901e6 | −0.778955 | −0.389478 | − | 0.921036i | \(-0.627344\pi\) | ||||
−0.389478 | + | 0.921036i | \(0.627344\pi\) | |||||||
\(434\) | −1.14177e7 | −2.90973 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.67567e6 | 1.17795 | ||||||||
\(437\) | 4.86571e6 | 1.21883 | ||||||||
\(438\) | −6.90824e6 | −1.72061 | ||||||||
\(439\) | −395912. | −0.0980477 | −0.0490239 | − | 0.998798i | \(-0.515611\pi\) | ||||
−0.0490239 | + | 0.998798i | \(0.515611\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.72734e6 | 0.422943 | ||||||||
\(442\) | −5.20787e6 | −1.26796 | ||||||||
\(443\) | 6.25166e6 | 1.51351 | 0.756757 | − | 0.653697i | \(-0.226783\pi\) | ||||
0.756757 | + | 0.653697i | \(0.226783\pi\) | |||||||
\(444\) | −1.60457e6 | −0.386279 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.23452e6 | −1.00802 | ||||||||
\(447\) | 246906. | 0.0584470 | ||||||||
\(448\) | 1.02560e7 | 2.41425 | ||||||||
\(449\) | −3.94443e6 | −0.923355 | −0.461678 | − | 0.887048i | \(-0.652752\pi\) | ||||
−0.461678 | + | 0.887048i | \(0.652752\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 480433. | 0.111222 | ||||||||
\(452\) | 4.87672e6 | 1.12275 | ||||||||
\(453\) | 1.00587e6 | 0.230302 | ||||||||
\(454\) | 1.02700e7 | 2.33846 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.69132e6 | 0.831323 | ||||||||
\(457\) | 6.70635e6 | 1.50209 | 0.751045 | − | 0.660251i | \(-0.229550\pi\) | ||||
0.751045 | + | 0.660251i | \(0.229550\pi\) | |||||||
\(458\) | 1.09868e7 | 2.44741 | ||||||||
\(459\) | 902017. | 0.199840 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.66837e6 | −1.02309 | −0.511544 | − | 0.859257i | \(-0.670926\pi\) | ||||
−0.511544 | + | 0.859257i | \(0.670926\pi\) | |||||||
\(462\) | −1.95831e6 | −0.426852 | ||||||||
\(463\) | 5.02305e6 | 1.08897 | 0.544484 | − | 0.838771i | \(-0.316725\pi\) | ||||
0.544484 | + | 0.838771i | \(0.316725\pi\) | |||||||
\(464\) | 489063. | 0.105456 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.22406e6 | 1.32773 | ||||||||
\(467\) | 1.73795e6 | 0.368762 | 0.184381 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184381 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(468\) | −1.95486e6 | −0.412574 | ||||||||
\(469\) | −2.88719e6 | −0.606099 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.08134e6 | 0.432306 | ||||||||
\(472\) | 8.34908e6 | 1.72498 | ||||||||
\(473\) | 472120. | 0.0970285 | ||||||||
\(474\) | −1.48012e6 | −0.302587 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.27585e7 | −2.58096 | ||||||||
\(477\) | 855625. | 0.172182 | ||||||||
\(478\) | 4.01829e6 | 0.804398 | ||||||||
\(479\) | −761980. | −0.151742 | −0.0758708 | − | 0.997118i | \(-0.524174\pi\) | ||||
−0.0758708 | + | 0.997118i | \(0.524174\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.54317e6 | 0.304125 | ||||||||
\(482\) | 5.49781e6 | 1.07788 | ||||||||
\(483\) | −3.99438e6 | −0.779078 | ||||||||
\(484\) | 773103. | 0.150011 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 543777. | 0.104431 | ||||||||
\(487\) | 840046. | 0.160502 | 0.0802510 | − | 0.996775i | \(-0.474428\pi\) | ||||
0.0802510 | + | 0.996775i | \(0.474428\pi\) | |||||||
\(488\) | 9.40413e6 | 1.78760 | ||||||||
\(489\) | −1.97201e6 | −0.372939 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.05708e7 | 1.97882 | 0.989409 | − | 0.145156i | \(-0.0463684\pi\) | ||||
0.989409 | + | 0.145156i | \(0.0463684\pi\) | |||||||
\(492\) | 1.88693e6 | 0.351434 | ||||||||
\(493\) | 8.11928e6 | 1.50453 | ||||||||
\(494\) | −9.01069e6 | −1.66127 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 473214. | 0.0863681 | ||||||||
\(497\) | −1.74997e6 | −0.317790 | ||||||||
\(498\) | −5.53891e6 | −1.00081 | ||||||||
\(499\) | 2.87438e6 | 0.516765 | 0.258382 | − | 0.966043i | \(-0.416811\pi\) | ||||
0.258382 | + | 0.966043i | \(0.416811\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.24510e6 | 0.221621 | ||||||||
\(502\) | −698145. | −0.123648 | ||||||||
\(503\) | 1.40949e6 | 0.248395 | 0.124197 | − | 0.992258i | \(-0.460364\pi\) | ||||
0.124197 | + | 0.992258i | \(0.460364\pi\) | |||||||
\(504\) | −3.03029e6 | −0.531384 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.53253e6 | 0.439721 | ||||||||
\(507\) | −1.46158e6 | −0.252523 | ||||||||
\(508\) | −3.72926e6 | −0.641156 | ||||||||
\(509\) | −7.60203e6 | −1.30057 | −0.650287 | − | 0.759688i | \(-0.725352\pi\) | ||||
−0.650287 | + | 0.759688i | \(0.725352\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.62766e7 | 2.75747 | ||||||||
\(512\) | −862682. | −0.145437 | ||||||||
\(513\) | 1.56068e6 | 0.261830 | ||||||||
\(514\) | −1.10786e7 | −1.84960 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.85428e6 | 0.306586 | ||||||||
\(517\) | −153387. | −0.0252384 | ||||||||
\(518\) | 6.07160e6 | 0.994212 | ||||||||
\(519\) | −2.83027e6 | −0.461222 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.35016e6 | −0.379318 | −0.189659 | − | 0.981850i | \(-0.560738\pi\) | ||||
−0.189659 | + | 0.981850i | \(0.560738\pi\) | |||||||
\(522\) | 4.89467e6 | 0.786225 | ||||||||
\(523\) | −8.59353e6 | −1.37378 | −0.686891 | − | 0.726761i | \(-0.741025\pi\) | ||||
−0.686891 | + | 0.726761i | \(0.741025\pi\) | |||||||
\(524\) | 8.20193e6 | 1.30493 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.06265e6 | 0.482651 | ||||||||
\(527\) | 7.85616e6 | 1.23221 | ||||||||
\(528\) | 81163.7 | 0.0126700 | ||||||||
\(529\) | −1.27074e6 | −0.197432 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.52996e6 | 0.543292 | ||||||||
\(532\) | −2.20748e7 | −3.38157 | ||||||||
\(533\) | −1.81473e6 | −0.276690 | ||||||||
\(534\) | −9.77213e6 | −1.48298 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.83259e6 | 0.425865 | ||||||||
\(537\) | −6.52601e6 | −0.976589 | ||||||||
\(538\) | 1.47862e7 | 2.20243 | ||||||||
\(539\) | 2.58035e6 | 0.382566 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.76377e6 | −0.552878 | −0.276439 | − | 0.961031i | \(-0.589154\pi\) | ||||
−0.276439 | + | 0.961031i | \(0.589154\pi\) | |||||||
\(542\) | −8.96726e6 | −1.31118 | ||||||||
\(543\) | 7.59152e6 | 1.10492 | ||||||||
\(544\) | −6.73638e6 | −0.975954 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.39709e6 | 1.06189 | ||||||||
\(547\) | −8.53624e6 | −1.21983 | −0.609914 | − | 0.792468i | \(-0.708796\pi\) | ||||
−0.609914 | + | 0.792468i | \(0.708796\pi\) | |||||||
\(548\) | 3.72711e6 | 0.530176 | ||||||||
\(549\) | 3.97603e6 | 0.563014 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.40480e7 | 1.97123 | ||||||||
\(552\) | 3.91883e6 | 0.547405 | ||||||||
\(553\) | 3.48732e6 | 0.484930 | ||||||||
\(554\) | −3.96260e6 | −0.548537 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.11286e7 | −2.89857 | ||||||||
\(557\) | 5.80583e6 | 0.792915 | 0.396457 | − | 0.918053i | \(-0.370239\pi\) | ||||
0.396457 | + | 0.918053i | \(0.370239\pi\) | |||||||
\(558\) | 4.73605e6 | 0.643919 | ||||||||
\(559\) | −1.78333e6 | −0.241380 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.34746e6 | 0.180762 | ||||||||
\(562\) | −5.21674e6 | −0.696720 | ||||||||
\(563\) | −7.65501e6 | −1.01783 | −0.508914 | − | 0.860817i | \(-0.669953\pi\) | ||||
−0.508914 | + | 0.860817i | \(0.669953\pi\) | |||||||
\(564\) | −602438. | −0.0797471 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.86154e6 | −1.16270 | ||||||||
\(567\) | −1.28120e6 | −0.167363 | ||||||||
\(568\) | 1.71688e6 | 0.223290 | ||||||||
\(569\) | 1.92933e6 | 0.249819 | 0.124909 | − | 0.992168i | \(-0.460136\pi\) | ||||
0.124909 | + | 0.992168i | \(0.460136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.05928e7 | −1.35962 | −0.679812 | − | 0.733386i | \(-0.737939\pi\) | ||||
−0.679812 | + | 0.733386i | \(0.737939\pi\) | |||||||
\(572\) | −2.92023e6 | −0.373187 | ||||||||
\(573\) | −5.93448e6 | −0.755086 | ||||||||
\(574\) | −7.14005e6 | −0.904527 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.25418e6 | −0.534268 | ||||||||
\(577\) | −3.01519e6 | −0.377030 | −0.188515 | − | 0.982070i | \(-0.560367\pi\) | ||||
−0.188515 | + | 0.982070i | \(0.560367\pi\) | |||||||
\(578\) | 1.02348e6 | 0.127426 | ||||||||
\(579\) | −3.15290e6 | −0.390853 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.30503e7 | 1.60391 | ||||||||
\(582\) | 1.29954e7 | 1.59031 | ||||||||
\(583\) | 1.27816e6 | 0.155744 | ||||||||
\(584\) | −1.59687e7 | −1.93749 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.02449e6 | −0.845027 | ||||||||
\(587\) | 2.91411e6 | 0.349069 | 0.174534 | − | 0.984651i | \(-0.444158\pi\) | ||||
0.174534 | + | 0.984651i | \(0.444158\pi\) | |||||||
\(588\) | 1.01345e7 | 1.20881 | ||||||||
\(589\) | 1.35928e7 | 1.61444 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.53842e6 | 0.534486 | ||||||||
\(592\) | −251642. | −0.0295107 | ||||||||
\(593\) | −1.55954e7 | −1.82121 | −0.910607 | − | 0.413274i | \(-0.864385\pi\) | ||||
−0.910607 | + | 0.413274i | \(0.864385\pi\) | |||||||
\(594\) | 812308. | 0.0944615 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.44862e6 | 0.167047 | ||||||||
\(597\) | −8.45948e6 | −0.971422 | ||||||||
\(598\) | −9.56606e6 | −1.09391 | ||||||||
\(599\) | −3.70805e6 | −0.422259 | −0.211130 | − | 0.977458i | \(-0.567714\pi\) | ||||
−0.211130 | + | 0.977458i | \(0.567714\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.22245e6 | 0.815640 | 0.407820 | − | 0.913062i | \(-0.366289\pi\) | ||||
0.407820 | + | 0.913062i | \(0.366289\pi\) | |||||||
\(602\) | −7.01651e6 | −0.789096 | ||||||||
\(603\) | 1.19761e6 | 0.134129 | ||||||||
\(604\) | 5.90156e6 | 0.658225 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.37785e6 | −0.816110 | ||||||||
\(607\) | −1.06431e7 | −1.17246 | −0.586228 | − | 0.810146i | \(-0.699388\pi\) | ||||
−0.586228 | + | 0.810146i | \(0.699388\pi\) | |||||||
\(608\) | −1.16553e7 | −1.27869 | ||||||||
\(609\) | −1.15324e7 | −1.26001 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 579386. | 0.0627863 | ||||||||
\(612\) | 5.29223e6 | 0.571163 | ||||||||
\(613\) | −7.11493e6 | −0.764750 | −0.382375 | − | 0.924007i | \(-0.624894\pi\) | ||||
−0.382375 | + | 0.924007i | \(0.624894\pi\) | |||||||
\(614\) | 2.78495e7 | 2.98124 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.52673e6 | −0.480655 | ||||||||
\(617\) | −1.83690e6 | −0.194255 | −0.0971277 | − | 0.995272i | \(-0.530966\pi\) | ||||
−0.0971277 | + | 0.995272i | \(0.530966\pi\) | |||||||
\(618\) | 8.31019e6 | 0.875266 | ||||||||
\(619\) | 1.10798e7 | 1.16226 | 0.581132 | − | 0.813810i | \(-0.302610\pi\) | ||||
0.581132 | + | 0.813810i | \(0.302610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.65687e6 | 0.172409 | ||||||||
\(622\) | 2.15399e7 | 2.23238 | ||||||||
\(623\) | 2.30242e7 | 2.37665 | ||||||||
\(624\) | −306578. | −0.0315195 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.31320e7 | 1.33935 | ||||||||
\(627\) | 2.33138e6 | 0.236834 | ||||||||
\(628\) | 1.22114e7 | 1.23557 | ||||||||
\(629\) | −4.17769e6 | −0.421027 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.34216e7 | 1.34193 | 0.670966 | − | 0.741488i | \(-0.265880\pi\) | ||||
0.670966 | + | 0.741488i | \(0.265880\pi\) | |||||||
\(632\) | −3.42137e6 | −0.340727 | ||||||||
\(633\) | 5.99949e6 | 0.595121 | ||||||||
\(634\) | −1.47924e7 | −1.46156 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.02004e6 | 0.492112 | ||||||||
\(637\) | −9.74670e6 | −0.951720 | ||||||||
\(638\) | 7.31179e6 | 0.711168 | ||||||||
\(639\) | 725890. | 0.0703265 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.26487e6 | 0.794495 | 0.397247 | − | 0.917712i | \(-0.369965\pi\) | ||||
0.397247 | + | 0.917712i | \(0.369965\pi\) | |||||||
\(642\) | −1.09966e7 | −1.05298 | ||||||||
\(643\) | −9.43394e6 | −0.899841 | −0.449920 | − | 0.893069i | \(-0.648548\pi\) | ||||
−0.449920 | + | 0.893069i | \(0.648548\pi\) | |||||||
\(644\) | −2.34354e7 | −2.22668 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.43939e7 | 2.29985 | ||||||||
\(647\) | −9.83647e6 | −0.923802 | −0.461901 | − | 0.886932i | \(-0.652832\pi\) | ||||
−0.461901 | + | 0.886932i | \(0.652832\pi\) | |||||||
\(648\) | 1.25697e6 | 0.117594 | ||||||||
\(649\) | 5.27315e6 | 0.491426 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.11587e7 | −1.03195 | ||||||||
\(652\) | −1.15700e7 | −1.06590 | ||||||||
\(653\) | −2.07669e7 | −1.90585 | −0.952924 | − | 0.303208i | \(-0.901942\pi\) | ||||
−0.952924 | + | 0.303208i | \(0.901942\pi\) | |||||||
\(654\) | 7.33885e6 | 0.670940 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 295925. | 0.0268486 | ||||||||
\(657\) | −6.75153e6 | −0.610223 | ||||||||
\(658\) | 2.27959e6 | 0.205255 | ||||||||
\(659\) | −1.74284e7 | −1.56331 | −0.781654 | − | 0.623713i | \(-0.785624\pi\) | ||||
−0.781654 | + | 0.623713i | \(0.785624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.91510e7 | −1.70486 | −0.852428 | − | 0.522844i | \(-0.824871\pi\) | ||||
−0.852428 | + | 0.522844i | \(0.824871\pi\) | |||||||
\(662\) | 2.86893e7 | 2.54434 | ||||||||
\(663\) | −5.08972e6 | −0.449687 | ||||||||
\(664\) | −1.28035e7 | −1.12696 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.51850e6 | −0.220017 | ||||||||
\(667\) | 1.49139e7 | 1.29800 | ||||||||
\(668\) | 7.30515e6 | 0.633415 | ||||||||
\(669\) | −4.13846e6 | −0.357498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.93951e6 | 0.509265 | ||||||||
\(672\) | 9.56815e6 | 0.817343 | ||||||||
\(673\) | −342635. | −0.0291605 | −0.0145802 | − | 0.999894i | \(-0.504641\pi\) | ||||
−0.0145802 | + | 0.999894i | \(0.504641\pi\) | |||||||
\(674\) | −1.48365e7 | −1.25801 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.57522e6 | −0.721737 | ||||||||
\(677\) | −4.92746e6 | −0.413191 | −0.206596 | − | 0.978426i | \(-0.566238\pi\) | ||||
−0.206596 | + | 0.978426i | \(0.566238\pi\) | |||||||
\(678\) | 7.65441e6 | 0.639496 | ||||||||
\(679\) | −3.06185e7 | −2.54865 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.00370e7 | 0.829348 | ||||||||
\(682\) | 7.07484e6 | 0.582446 | ||||||||
\(683\) | −1.73541e7 | −1.42348 | −0.711740 | − | 0.702443i | \(-0.752093\pi\) | ||||
−0.711740 | + | 0.702443i | \(0.752093\pi\) | |||||||
\(684\) | 9.15666e6 | 0.748336 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.12491e6 | −0.659186 | ||||||||
\(687\) | 1.07376e7 | 0.867988 | ||||||||
\(688\) | 290805. | 0.0234223 | ||||||||
\(689\) | −4.82795e6 | −0.387449 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.50935e7 | 1.20253 | 0.601264 | − | 0.799051i | \(-0.294664\pi\) | ||||
0.601264 | + | 0.799051i | \(0.294664\pi\) | |||||||
\(692\) | −1.66055e7 | −1.31822 | ||||||||
\(693\) | −1.91389e6 | −0.151385 | ||||||||
\(694\) | 7.80371e6 | 0.615039 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.13143e7 | 0.885326 | ||||||||
\(697\) | 4.91286e6 | 0.383047 | ||||||||
\(698\) | 2.54156e7 | 1.97452 | ||||||||
\(699\) | 6.08287e6 | 0.470886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.70526e7 | 1.31068 | 0.655338 | − | 0.755336i | \(-0.272526\pi\) | ||||
0.655338 | + | 0.755336i | \(0.272526\pi\) | |||||||
\(702\) | −3.06832e6 | −0.234994 | ||||||||
\(703\) | −7.22828e6 | −0.551628 | ||||||||
\(704\) | −6.35501e6 | −0.483264 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.79597e7 | −2.86623 | ||||||||
\(707\) | 1.73830e7 | 1.30791 | ||||||||
\(708\) | 2.07106e7 | 1.55278 | ||||||||
\(709\) | 4.47464e6 | 0.334305 | 0.167152 | − | 0.985931i | \(-0.446543\pi\) | ||||
0.167152 | + | 0.985931i | \(0.446543\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.44654e6 | −0.107314 | ||||||||
\(712\) | −2.25888e7 | −1.66991 | ||||||||
\(713\) | 1.44306e7 | 1.06307 | ||||||||
\(714\) | −2.00255e7 | −1.47007 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.82888e7 | −2.79119 | ||||||||
\(717\) | 3.92713e6 | 0.285284 | ||||||||
\(718\) | 5.38949e6 | 0.390155 | ||||||||
\(719\) | 2.05300e7 | 1.48104 | 0.740519 | − | 0.672036i | \(-0.234580\pi\) | ||||
0.740519 | + | 0.672036i | \(0.234580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.95797e7 | −1.40271 | ||||||||
\(722\) | 1.94043e7 | 1.38534 | ||||||||
\(723\) | 5.37309e6 | 0.382277 | ||||||||
\(724\) | 4.45403e7 | 3.15796 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.21345e6 | 0.0854436 | ||||||||
\(727\) | −1.49603e7 | −1.04979 | −0.524897 | − | 0.851166i | \(-0.675896\pi\) | ||||
−0.524897 | + | 0.851166i | \(0.675896\pi\) | |||||||
\(728\) | 1.70987e7 | 1.19574 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.82785e6 | 0.334165 | ||||||||
\(732\) | 2.33278e7 | 1.60915 | ||||||||
\(733\) | −2.26287e7 | −1.55561 | −0.777804 | − | 0.628507i | \(-0.783666\pi\) | ||||
−0.777804 | + | 0.628507i | \(0.783666\pi\) | |||||||
\(734\) | 3.20023e7 | 2.19251 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.23737e7 | −0.841987 | ||||||||
\(737\) | 1.78902e6 | 0.121324 | ||||||||
\(738\) | 2.96169e6 | 0.200170 | ||||||||
\(739\) | −1.39790e7 | −0.941597 | −0.470798 | − | 0.882241i | \(-0.656034\pi\) | ||||
−0.470798 | + | 0.882241i | \(0.656034\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.80628e6 | −0.589179 | ||||||||
\(742\) | −1.89956e7 | −1.26661 | ||||||||
\(743\) | 5.66041e6 | 0.376163 | 0.188081 | − | 0.982153i | \(-0.439773\pi\) | ||||
0.188081 | + | 0.982153i | \(0.439773\pi\) | |||||||
\(744\) | 1.09476e7 | 0.725082 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.92377e7 | 1.26563 | ||||||||
\(747\) | −5.41326e6 | −0.354942 | ||||||||
\(748\) | 7.90567e6 | 0.516636 | ||||||||
\(749\) | 2.59091e7 | 1.68752 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.77912e7 | −1.15108 | −0.575540 | − | 0.817774i | \(-0.695208\pi\) | ||||
−0.575540 | + | 0.817774i | \(0.695208\pi\) | |||||||
\(752\) | −94479.5 | −0.00609247 | ||||||||
\(753\) | −682308. | −0.0438524 | ||||||||
\(754\) | −2.76187e7 | −1.76919 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.51692e6 | −0.478338 | ||||||||
\(757\) | −2.55861e7 | −1.62280 | −0.811398 | − | 0.584494i | \(-0.801293\pi\) | ||||
−0.811398 | + | 0.584494i | \(0.801293\pi\) | |||||||
\(758\) | −1.30028e7 | −0.821987 | ||||||||
\(759\) | 2.47507e6 | 0.155949 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.89006e6 | −0.556472 | −0.278236 | − | 0.960513i | \(-0.589750\pi\) | ||||
−0.278236 | + | 0.960513i | \(0.589750\pi\) | |||||||
\(762\) | −5.85338e6 | −0.365190 | ||||||||
\(763\) | −1.72911e7 | −1.07526 | ||||||||
\(764\) | −3.48182e7 | −2.15811 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.86177e7 | −1.14645 | ||||||||
\(767\) | −1.99182e7 | −1.22253 | ||||||||
\(768\) | −1.05206e7 | −0.643633 | ||||||||
\(769\) | −2.70789e7 | −1.65126 | −0.825629 | − | 0.564213i | \(-0.809180\pi\) | ||||
−0.825629 | + | 0.564213i | \(0.809180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.08273e7 | −0.655970 | ||||||||
\(772\) | −1.84984e7 | −1.11710 | ||||||||
\(773\) | 3.17581e7 | 1.91164 | 0.955820 | − | 0.293953i | \(-0.0949708\pi\) | ||||
0.955820 | + | 0.293953i | \(0.0949708\pi\) | |||||||
\(774\) | 2.91045e6 | 0.174626 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.00395e7 | 1.79076 | ||||||||
\(777\) | 5.93387e6 | 0.352602 | ||||||||
\(778\) | −1.95671e7 | −1.15899 | ||||||||
\(779\) | 8.50027e6 | 0.501868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.08435e6 | 0.0636127 | ||||||||
\(782\) | 2.58974e7 | 1.51439 | ||||||||
\(783\) | 4.78363e6 | 0.278839 | ||||||||
\(784\) | 1.58938e6 | 0.0923500 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.28736e7 | 0.743265 | ||||||||
\(787\) | −4.19625e6 | −0.241504 | −0.120752 | − | 0.992683i | \(-0.538531\pi\) | ||||
−0.120752 | + | 0.992683i | \(0.538531\pi\) | |||||||
\(788\) | 2.66274e7 | 1.52761 | ||||||||
\(789\) | 2.99318e6 | 0.171175 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.80346e7 | −1.02486 | ||||||||
\(792\) | 1.87769e6 | 0.106368 | ||||||||
\(793\) | −2.24352e7 | −1.26691 | ||||||||
\(794\) | 1.94680e7 | 1.09590 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.96327e7 | −2.77642 | ||||||||
\(797\) | 320849. | 0.0178918 | 0.00894591 | − | 0.999960i | \(-0.497152\pi\) | ||||
0.00894591 | + | 0.999960i | \(0.497152\pi\) | |||||||
\(798\) | −3.46483e7 | −1.92608 | ||||||||
\(799\) | −1.56852e6 | −0.0869208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.55044e6 | −0.525947 | ||||||||
\(802\) | 9.29794e6 | 0.510447 | ||||||||
\(803\) | −1.00856e7 | −0.551968 | ||||||||
\(804\) | 7.02650e6 | 0.383353 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.67237e7 | −1.44897 | ||||||||
\(807\) | 1.44508e7 | 0.781103 | ||||||||
\(808\) | −1.70543e7 | −0.918978 | ||||||||
\(809\) | 2.32915e7 | 1.25120 | 0.625600 | − | 0.780144i | \(-0.284854\pi\) | ||||
0.625600 | + | 0.780144i | \(0.284854\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.65090e7 | 0.881389 | 0.440695 | − | 0.897657i | \(-0.354732\pi\) | ||||
0.440695 | + | 0.897657i | \(0.354732\pi\) | |||||||
\(812\) | −6.76616e7 | −3.60124 | ||||||||
\(813\) | −8.76384e6 | −0.465016 | ||||||||
\(814\) | −3.76221e6 | −0.199013 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 829973. | 0.0436353 | ||||||||
\(817\) | 8.35319e6 | 0.437822 | ||||||||
\(818\) | −1.75680e6 | −0.0917990 | ||||||||
\(819\) | 7.22929e6 | 0.376605 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.37457e7 | −1.74727 | −0.873637 | − | 0.486578i | \(-0.838245\pi\) | ||||
−0.873637 | + | 0.486578i | \(0.838245\pi\) | |||||||
\(822\) | 5.85000e6 | 0.301979 | ||||||||
\(823\) | 1.19897e7 | 0.617036 | 0.308518 | − | 0.951219i | \(-0.400167\pi\) | ||||
0.308518 | + | 0.951219i | \(0.400167\pi\) | |||||||
\(824\) | 1.92094e7 | 0.985590 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.83680e7 | −3.99658 | ||||||||
\(827\) | −2.29575e7 | −1.16724 | −0.583620 | − | 0.812027i | \(-0.698364\pi\) | ||||
−0.583620 | + | 0.812027i | \(0.698364\pi\) | |||||||
\(828\) | 9.72102e6 | 0.492761 | ||||||||
\(829\) | 2.33662e7 | 1.18087 | 0.590435 | − | 0.807085i | \(-0.298956\pi\) | ||||
0.590435 | + | 0.807085i | \(0.298956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.87271e6 | −0.194542 | ||||||||
\(832\) | 2.40046e7 | 1.20223 | ||||||||
\(833\) | 2.63864e7 | 1.31755 | ||||||||
\(834\) | −3.31631e7 | −1.65097 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.36785e7 | 0.676895 | ||||||||
\(837\) | 4.62861e6 | 0.228369 | ||||||||
\(838\) | −4.43883e7 | −2.18353 | ||||||||
\(839\) | 1.72966e7 | 0.848315 | 0.424157 | − | 0.905588i | \(-0.360570\pi\) | ||||
0.424157 | + | 0.905588i | \(0.360570\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.25475e7 | 1.09928 | ||||||||
\(842\) | −1.35564e7 | −0.658967 | ||||||||
\(843\) | −5.09840e6 | −0.247096 | ||||||||
\(844\) | 3.51997e7 | 1.70091 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −945576. | −0.0454225 | ||||||||
\(847\) | −2.85902e6 | −0.136933 | ||||||||
\(848\) | 787286. | 0.0375961 | ||||||||
\(849\) | −8.66052e6 | −0.412358 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.67379e6 | −0.363234 | ||||||||
\(852\) | 4.25887e6 | 0.201000 | ||||||||
\(853\) | 9.73772e6 | 0.458231 | 0.229116 | − | 0.973399i | \(-0.426417\pi\) | ||||
0.229116 | + | 0.973399i | \(0.426417\pi\) | |||||||
\(854\) | −8.82712e7 | −4.14166 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.54191e7 | −1.18570 | ||||||||
\(857\) | −1.49824e7 | −0.696832 | −0.348416 | − | 0.937340i | \(-0.613280\pi\) | ||||
−0.348416 | + | 0.937340i | \(0.613280\pi\) | |||||||
\(858\) | −4.58353e6 | −0.212560 | ||||||||
\(859\) | −2.41887e7 | −1.11848 | −0.559242 | − | 0.829004i | \(-0.688908\pi\) | ||||
−0.559242 | + | 0.829004i | \(0.688908\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.97808e6 | −0.320795 | ||||||||
\(862\) | −3.46183e7 | −1.58685 | ||||||||
\(863\) | 1.77029e7 | 0.809126 | 0.404563 | − | 0.914510i | \(-0.367424\pi\) | ||||
0.404563 | + | 0.914510i | \(0.367424\pi\) | |||||||
\(864\) | −3.96887e6 | −0.180877 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.79860e7 | −1.26808 | ||||||||
\(867\) | 1.00026e6 | 0.0451923 | ||||||||
\(868\) | −6.54690e7 | −2.94942 | ||||||||
\(869\) | −2.16088e6 | −0.0970692 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.75764e6 | −0.301821 | ||||||||
\(872\) | 1.69641e7 | 0.755510 | ||||||||
\(873\) | 1.27006e7 | 0.564012 | ||||||||
\(874\) | 4.48078e7 | 1.98415 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.96119e7 | −1.74408 | ||||||||
\(877\) | −3.95853e7 | −1.73794 | −0.868970 | − | 0.494864i | \(-0.835218\pi\) | ||||
−0.868970 | + | 0.494864i | \(0.835218\pi\) | |||||||
\(878\) | −3.64592e6 | −0.159614 | ||||||||
\(879\) | −6.86514e6 | −0.299693 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.06184e7 | −0.460914 | −0.230457 | − | 0.973082i | \(-0.574022\pi\) | ||||
−0.230457 | + | 0.973082i | \(0.574022\pi\) | |||||||
\(882\) | 1.59069e7 | 0.688517 | ||||||||
\(883\) | 798967. | 0.0344848 | 0.0172424 | − | 0.999851i | \(-0.494511\pi\) | ||||
0.0172424 | + | 0.999851i | \(0.494511\pi\) | |||||||
\(884\) | −2.98619e7 | −1.28525 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.75710e7 | 2.46388 | ||||||||
\(887\) | −2.53565e7 | −1.08213 | −0.541065 | − | 0.840981i | \(-0.681979\pi\) | ||||
−0.541065 | + | 0.840981i | \(0.681979\pi\) | |||||||
\(888\) | −5.82165e6 | −0.247750 | ||||||||
\(889\) | 1.37912e7 | 0.585259 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −2.42808e7 | −1.02176 | ||||||||
\(893\) | −2.71387e6 | −0.113883 | ||||||||
\(894\) | 2.27373e6 | 0.0951470 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.04261e7 | 2.51452 | ||||||||
\(897\) | −9.34905e6 | −0.387960 | ||||||||
\(898\) | −3.63239e7 | −1.50315 | ||||||||
\(899\) | 4.16633e7 | 1.71931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.30703e7 | 0.536381 | ||||||||
\(902\) | 4.42426e6 | 0.181061 | ||||||||
\(903\) | −6.85734e6 | −0.279857 | ||||||||
\(904\) | 1.76936e7 | 0.720102 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.26298e6 | 0.374913 | ||||||||
\(907\) | 2.39197e6 | 0.0965468 | 0.0482734 | − | 0.998834i | \(-0.484628\pi\) | ||||
0.0482734 | + | 0.998834i | \(0.484628\pi\) | |||||||
\(908\) | 5.88882e7 | 2.37036 | ||||||||
\(909\) | −7.21049e6 | −0.289438 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.84437e7 | 1.13551 | 0.567754 | − | 0.823198i | \(-0.307813\pi\) | ||||
0.567754 | + | 0.823198i | \(0.307813\pi\) | |||||||
\(912\) | 1.43603e6 | 0.0571709 | ||||||||
\(913\) | −8.08648e6 | −0.321057 | ||||||||
\(914\) | 6.17582e7 | 2.44528 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.29984e7 | 2.48079 | ||||||||
\(917\) | −3.03316e7 | −1.19117 | ||||||||
\(918\) | 8.30659e6 | 0.325324 | ||||||||
\(919\) | −1.05298e7 | −0.411273 | −0.205636 | − | 0.978628i | \(-0.565926\pi\) | ||||
−0.205636 | + | 0.978628i | \(0.565926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.72177e7 | 1.05731 | ||||||||
\(922\) | −4.29906e7 | −1.66550 | ||||||||
\(923\) | −4.09591e6 | −0.158251 | ||||||||
\(924\) | −1.12290e7 | −0.432673 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.62568e7 | 1.77275 | ||||||||
\(927\) | 8.12168e6 | 0.310418 | ||||||||
\(928\) | −3.57248e7 | −1.36176 | ||||||||
\(929\) | 1.19595e7 | 0.454647 | 0.227323 | − | 0.973819i | \(-0.427003\pi\) | ||||
0.227323 | + | 0.973819i | \(0.427003\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.56540e7 | 1.72625 | ||||||||
\(932\) | 3.56888e7 | 1.34584 | ||||||||
\(933\) | 2.10513e7 | 0.791725 | ||||||||
\(934\) | 1.60047e7 | 0.600315 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.09257e6 | −0.264615 | ||||||||
\(937\) | −2.02229e7 | −0.752480 | −0.376240 | − | 0.926522i | \(-0.622783\pi\) | ||||
−0.376240 | + | 0.926522i | \(0.622783\pi\) | |||||||
\(938\) | −2.65879e7 | −0.986681 | ||||||||
\(939\) | 1.28341e7 | 0.475009 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.13506e7 | 0.786026 | 0.393013 | − | 0.919533i | \(-0.371433\pi\) | ||||
0.393013 | + | 0.919533i | \(0.371433\pi\) | |||||||
\(942\) | 1.91669e7 | 0.703759 | ||||||||
\(943\) | 9.02418e6 | 0.330467 | ||||||||
\(944\) | 3.24802e6 | 0.118628 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.34771e6 | 0.157955 | ||||||||
\(947\) | 3.13109e6 | 0.113454 | 0.0567271 | − | 0.998390i | \(-0.481934\pi\) | ||||
0.0567271 | + | 0.998390i | \(0.481934\pi\) | |||||||
\(948\) | −8.48701e6 | −0.306714 | ||||||||
\(949\) | 3.80962e7 | 1.37314 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.44569e7 | −0.518350 | ||||||||
\(952\) | −4.62900e7 | −1.65537 | ||||||||
\(953\) | 4.65632e7 | 1.66077 | 0.830387 | − | 0.557188i | \(-0.188120\pi\) | ||||
0.830387 | + | 0.557188i | \(0.188120\pi\) | |||||||
\(954\) | 7.87937e6 | 0.280298 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.30409e7 | 0.815370 | ||||||||
\(957\) | 7.14592e6 | 0.252219 | ||||||||
\(958\) | −7.01700e6 | −0.247023 | ||||||||
\(959\) | −1.37832e7 | −0.483955 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.16840e7 | 0.408116 | ||||||||
\(962\) | 1.42109e7 | 0.495090 | ||||||||
\(963\) | −1.07471e7 | −0.373445 | ||||||||
\(964\) | 3.15245e7 | 1.09258 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.67838e7 | −1.26828 | ||||||||
\(967\) | 3.64320e7 | 1.25290 | 0.626450 | − | 0.779462i | \(-0.284507\pi\) | ||||
0.626450 | + | 0.779462i | \(0.284507\pi\) | |||||||
\(968\) | 2.80495e6 | 0.0962135 | ||||||||
\(969\) | 2.38405e7 | 0.815653 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.45693e7 | 0.836267 | 0.418134 | − | 0.908386i | \(-0.362684\pi\) | ||||
0.418134 | + | 0.908386i | \(0.362684\pi\) | |||||||
\(972\) | 3.11802e6 | 0.105855 | ||||||||
\(973\) | 7.81359e7 | 2.64587 | ||||||||
\(974\) | 7.73591e6 | 0.261285 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.65847e6 | 0.122935 | ||||||||
\(977\) | −4.28557e7 | −1.43639 | −0.718194 | − | 0.695842i | \(-0.755031\pi\) | ||||
−0.718194 | + | 0.695842i | \(0.755031\pi\) | |||||||
\(978\) | −1.81601e7 | −0.607115 | ||||||||
\(979\) | −1.42667e7 | −0.475737 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.17237e6 | 0.237952 | ||||||||
\(982\) | 9.73459e7 | 3.22136 | ||||||||
\(983\) | −3.25942e7 | −1.07586 | −0.537931 | − | 0.842989i | \(-0.680794\pi\) | ||||
−0.537931 | + | 0.842989i | \(0.680794\pi\) | |||||||
\(984\) | 6.84611e6 | 0.225401 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.47697e7 | 2.44925 | ||||||||
\(987\) | 2.22788e6 | 0.0727946 | ||||||||
\(988\) | −5.16674e7 | −1.68393 | ||||||||
\(989\) | 8.86804e6 | 0.288295 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.81427e7 | −0.586836 | −0.293418 | − | 0.955984i | \(-0.594793\pi\) | ||||
−0.293418 | + | 0.955984i | \(0.594793\pi\) | |||||||
\(992\) | −3.45671e7 | −1.11528 | ||||||||
\(993\) | 2.80384e7 | 0.902362 | ||||||||
\(994\) | −1.61154e7 | −0.517337 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.17602e7 | −1.01446 | ||||||||
\(997\) | −9.28807e6 | −0.295929 | −0.147965 | − | 0.988993i | \(-0.547272\pi\) | ||||
−0.147965 | + | 0.988993i | \(0.547272\pi\) | |||||||
\(998\) | 2.64699e7 | 0.841252 | ||||||||
\(999\) | −2.46137e6 | −0.0780303 |
(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.t.1.9 | ✓ | 10 | |
5.4 | even | 2 | 825.6.a.u.1.2 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.t.1.9 | ✓ | 10 | 1.1 | even | 1 | trivial | |
825.6.a.u.1.2 | yes | 10 | 5.4 | even | 2 |