Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 176x^{6} + 272x^{5} + 9055x^{4} - 15851x^{3} - 118840x^{2} + 149572x - 33248 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-8.09383\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.09383 | −1.25402 | −0.627012 | − | 0.779010i | \(-0.715722\pi\) | ||||
−0.627012 | + | 0.779010i | \(0.715722\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 18.3224 | 0.572574 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 63.8444 | 0.724011 | ||||||||
\(7\) | 4.62438 | 0.0356705 | 0.0178352 | − | 0.999841i | \(-0.494323\pi\) | ||||
0.0178352 | + | 0.999841i | \(0.494323\pi\) | |||||||
\(8\) | 97.0268 | 0.536002 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −164.901 | −0.330576 | ||||||||
\(13\) | −38.0995 | −0.0625261 | −0.0312631 | − | 0.999511i | \(-0.509953\pi\) | ||||
−0.0312631 | + | 0.999511i | \(0.509953\pi\) | |||||||
\(14\) | −32.8046 | −0.0447316 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1274.61 | −1.24473 | ||||||||
\(17\) | −610.281 | −0.512163 | −0.256081 | − | 0.966655i | \(-0.582431\pi\) | ||||
−0.256081 | + | 0.966655i | \(0.582431\pi\) | |||||||
\(18\) | −574.600 | −0.418008 | ||||||||
\(19\) | 2102.49 | 1.33614 | 0.668068 | − | 0.744100i | \(-0.267121\pi\) | ||||
0.668068 | + | 0.744100i | \(0.267121\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −41.6194 | −0.0205944 | ||||||||
\(22\) | 858.353 | 0.378102 | ||||||||
\(23\) | 3875.26 | 1.52750 | 0.763750 | − | 0.645513i | \(-0.223356\pi\) | ||||
0.763750 | + | 0.645513i | \(0.223356\pi\) | |||||||
\(24\) | −873.241 | −0.309461 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 270.272 | 0.0784092 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 84.7296 | 0.0204240 | ||||||||
\(29\) | −8371.56 | −1.84847 | −0.924233 | − | 0.381829i | \(-0.875294\pi\) | ||||
−0.924233 | + | 0.381829i | \(0.875294\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1417.68 | −0.264957 | −0.132479 | − | 0.991186i | \(-0.542294\pi\) | ||||
−0.132479 | + | 0.991186i | \(0.542294\pi\) | |||||||
\(32\) | 5936.98 | 1.02492 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 4329.23 | 0.642264 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1484.11 | 0.190858 | ||||||||
\(37\) | −3071.11 | −0.368800 | −0.184400 | − | 0.982851i | \(-0.559034\pi\) | ||||
−0.184400 | + | 0.982851i | \(0.559034\pi\) | |||||||
\(38\) | −14914.7 | −1.67555 | ||||||||
\(39\) | 342.896 | 0.0360995 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −591.131 | −0.0549192 | −0.0274596 | − | 0.999623i | \(-0.508742\pi\) | ||||
−0.0274596 | + | 0.999623i | \(0.508742\pi\) | |||||||
\(42\) | 295.241 | 0.0258258 | ||||||||
\(43\) | −19206.4 | −1.58407 | −0.792037 | − | 0.610474i | \(-0.790979\pi\) | ||||
−0.792037 | + | 0.610474i | \(0.790979\pi\) | |||||||
\(44\) | −2217.01 | −0.172638 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −27490.4 | −1.91552 | ||||||||
\(47\) | 11447.9 | 0.755929 | 0.377965 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377965 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(48\) | 11471.5 | 0.718647 | ||||||||
\(49\) | −16785.6 | −0.998728 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5492.53 | 0.295697 | ||||||||
\(52\) | −698.074 | −0.0358008 | ||||||||
\(53\) | 17463.0 | 0.853944 | 0.426972 | − | 0.904265i | \(-0.359580\pi\) | ||||
0.426972 | + | 0.904265i | \(0.359580\pi\) | |||||||
\(54\) | 5171.40 | 0.241337 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 448.689 | 0.0191194 | ||||||||
\(57\) | −18922.5 | −0.771419 | ||||||||
\(58\) | 59386.4 | 2.31802 | ||||||||
\(59\) | −16917.0 | −0.632692 | −0.316346 | − | 0.948644i | \(-0.602456\pi\) | ||||
−0.316346 | + | 0.948644i | \(0.602456\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2597.86 | −0.0893904 | −0.0446952 | − | 0.999001i | \(-0.514232\pi\) | ||||
−0.0446952 | + | 0.999001i | \(0.514232\pi\) | |||||||
\(62\) | 10056.8 | 0.332262 | ||||||||
\(63\) | 374.575 | 0.0118902 | ||||||||
\(64\) | −1328.50 | −0.0405426 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7725.18 | −0.218297 | ||||||||
\(67\) | 59848.5 | 1.62879 | 0.814397 | − | 0.580308i | \(-0.197068\pi\) | ||||
0.814397 | + | 0.580308i | \(0.197068\pi\) | |||||||
\(68\) | −11181.8 | −0.293251 | ||||||||
\(69\) | −34877.3 | −0.881902 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −62258.0 | −1.46572 | −0.732858 | − | 0.680382i | \(-0.761814\pi\) | ||||
−0.732858 | + | 0.680382i | \(0.761814\pi\) | |||||||
\(72\) | 7859.17 | 0.178667 | ||||||||
\(73\) | 35314.1 | 0.775605 | 0.387803 | − | 0.921742i | \(-0.373234\pi\) | ||||
0.387803 | + | 0.921742i | \(0.373234\pi\) | |||||||
\(74\) | 21785.9 | 0.462484 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 38522.7 | 0.765037 | ||||||||
\(77\) | −559.550 | −0.0107550 | ||||||||
\(78\) | −2432.44 | −0.0452696 | ||||||||
\(79\) | 78372.2 | 1.41284 | 0.706422 | − | 0.707791i | \(-0.250308\pi\) | ||||
0.706422 | + | 0.707791i | \(0.250308\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 4193.38 | 0.0688700 | ||||||||
\(83\) | 39714.4 | 0.632781 | 0.316390 | − | 0.948629i | \(-0.397529\pi\) | ||||
0.316390 | + | 0.948629i | \(0.397529\pi\) | |||||||
\(84\) | −762.567 | −0.0117918 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 136247. | 1.98646 | ||||||||
\(87\) | 75344.0 | 1.06721 | ||||||||
\(88\) | −11740.2 | −0.161611 | ||||||||
\(89\) | 54307.3 | 0.726747 | 0.363374 | − | 0.931643i | \(-0.381625\pi\) | ||||
0.363374 | + | 0.931643i | \(0.381625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −176.187 | −0.00223034 | ||||||||
\(92\) | 71003.9 | 0.874606 | ||||||||
\(93\) | 12759.2 | 0.152973 | ||||||||
\(94\) | −81209.4 | −0.947953 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −53432.8 | −0.591739 | ||||||||
\(97\) | 33574.1 | 0.362305 | 0.181153 | − | 0.983455i | \(-0.442017\pi\) | ||||
0.181153 | + | 0.983455i | \(0.442017\pi\) | |||||||
\(98\) | 119074. | 1.25243 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −203384. | −1.98387 | −0.991935 | − | 0.126750i | \(-0.959545\pi\) | ||||
−0.991935 | + | 0.126750i | \(0.959545\pi\) | |||||||
\(102\) | −38963.1 | −0.370811 | ||||||||
\(103\) | −95955.0 | −0.891199 | −0.445599 | − | 0.895233i | \(-0.647009\pi\) | ||||
−0.445599 | + | 0.895233i | \(0.647009\pi\) | |||||||
\(104\) | −3696.68 | −0.0335141 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −123880. | −1.07087 | ||||||||
\(107\) | 170934. | 1.44334 | 0.721669 | − | 0.692239i | \(-0.243375\pi\) | ||||
0.721669 | + | 0.692239i | \(0.243375\pi\) | |||||||
\(108\) | −13357.0 | −0.110192 | ||||||||
\(109\) | −62167.4 | −0.501183 | −0.250592 | − | 0.968093i | \(-0.580625\pi\) | ||||
−0.250592 | + | 0.968093i | \(0.580625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27640.0 | 0.212927 | ||||||||
\(112\) | −5894.27 | −0.0444002 | ||||||||
\(113\) | 75966.1 | 0.559660 | 0.279830 | − | 0.960050i | \(-0.409722\pi\) | ||||
0.279830 | + | 0.960050i | \(0.409722\pi\) | |||||||
\(114\) | 134233. | 0.967377 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −153387. | −1.05838 | ||||||||
\(117\) | −3086.06 | −0.0208420 | ||||||||
\(118\) | 120006. | 0.793410 | ||||||||
\(119\) | −2822.17 | −0.0182691 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 18428.8 | 0.112098 | ||||||||
\(123\) | 5320.18 | 0.0317076 | ||||||||
\(124\) | −25975.3 | −0.151707 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2657.17 | −0.0149105 | ||||||||
\(127\) | −100022. | −0.550285 | −0.275143 | − | 0.961403i | \(-0.588725\pi\) | ||||
−0.275143 | + | 0.961403i | \(0.588725\pi\) | |||||||
\(128\) | −180559. | −0.974080 | ||||||||
\(129\) | 172858. | 0.914565 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 322642. | 1.64264 | 0.821319 | − | 0.570469i | \(-0.193238\pi\) | ||||
0.821319 | + | 0.570469i | \(0.193238\pi\) | |||||||
\(132\) | 19953.1 | 0.0996723 | ||||||||
\(133\) | 9722.74 | 0.0476606 | ||||||||
\(134\) | −424555. | −2.04255 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −59213.6 | −0.274520 | ||||||||
\(137\) | 325855. | 1.48328 | 0.741639 | − | 0.670799i | \(-0.234049\pi\) | ||||
0.741639 | + | 0.670799i | \(0.234049\pi\) | |||||||
\(138\) | 247414. | 1.10593 | ||||||||
\(139\) | 415444. | 1.82379 | 0.911895 | − | 0.410422i | \(-0.134619\pi\) | ||||
0.911895 | + | 0.410422i | \(0.134619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −103031. | −0.436436 | ||||||||
\(142\) | 441648. | 1.83804 | ||||||||
\(143\) | 4610.04 | 0.0188523 | ||||||||
\(144\) | −103243. | −0.414911 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −250512. | −0.972627 | ||||||||
\(147\) | 151071. | 0.576616 | ||||||||
\(148\) | −56270.0 | −0.211165 | ||||||||
\(149\) | 306627. | 1.13147 | 0.565737 | − | 0.824585i | \(-0.308592\pi\) | ||||
0.565737 | + | 0.824585i | \(0.308592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −90347.8 | −0.322460 | −0.161230 | − | 0.986917i | \(-0.551546\pi\) | ||||
−0.161230 | + | 0.986917i | \(0.551546\pi\) | |||||||
\(152\) | 203998. | 0.716172 | ||||||||
\(153\) | −49432.8 | −0.170721 | ||||||||
\(154\) | 3969.35 | 0.0134871 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6282.66 | 0.0206696 | ||||||||
\(157\) | 81270.2 | 0.263137 | 0.131569 | − | 0.991307i | \(-0.457999\pi\) | ||||
0.131569 | + | 0.991307i | \(0.457999\pi\) | |||||||
\(158\) | −555959. | −1.77174 | ||||||||
\(159\) | −157167. | −0.493025 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17920.7 | 0.0544866 | ||||||||
\(162\) | −46542.6 | −0.139336 | ||||||||
\(163\) | −178404. | −0.525940 | −0.262970 | − | 0.964804i | \(-0.584702\pi\) | ||||
−0.262970 | + | 0.964804i | \(0.584702\pi\) | |||||||
\(164\) | −10830.9 | −0.0314453 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −281727. | −0.793522 | ||||||||
\(167\) | 626513. | 1.73836 | 0.869178 | − | 0.494500i | \(-0.164649\pi\) | ||||
0.869178 | + | 0.494500i | \(0.164649\pi\) | |||||||
\(168\) | −4038.20 | −0.0110386 | ||||||||
\(169\) | −369841. | −0.996090 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 170302. | 0.445379 | ||||||||
\(172\) | −351907. | −0.906999 | ||||||||
\(173\) | −325238. | −0.826202 | −0.413101 | − | 0.910685i | \(-0.635554\pi\) | ||||
−0.413101 | + | 0.910685i | \(0.635554\pi\) | |||||||
\(174\) | −534478. | −1.33831 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 154227. | 0.375301 | ||||||||
\(177\) | 152253. | 0.365285 | ||||||||
\(178\) | −385247. | −0.911358 | ||||||||
\(179\) | 183002. | 0.426897 | 0.213449 | − | 0.976954i | \(-0.431530\pi\) | ||||
0.213449 | + | 0.976954i | \(0.431530\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −623259. | −1.41407 | −0.707037 | − | 0.707177i | \(-0.749968\pi\) | ||||
−0.707037 | + | 0.707177i | \(0.749968\pi\) | |||||||
\(182\) | 1249.84 | 0.00279689 | ||||||||
\(183\) | 23380.7 | 0.0516096 | ||||||||
\(184\) | 376004. | 0.818743 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −90511.3 | −0.191832 | ||||||||
\(187\) | 73844.0 | 0.154423 | ||||||||
\(188\) | 209753. | 0.432826 | ||||||||
\(189\) | −3371.18 | −0.00686478 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 179426. | 0.355879 | 0.177939 | − | 0.984041i | \(-0.443057\pi\) | ||||
0.177939 | + | 0.984041i | \(0.443057\pi\) | |||||||
\(192\) | 11956.5 | 0.0234073 | ||||||||
\(193\) | −904409. | −1.74772 | −0.873859 | − | 0.486179i | \(-0.838390\pi\) | ||||
−0.873859 | + | 0.486179i | \(0.838390\pi\) | |||||||
\(194\) | −238169. | −0.454339 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −307552. | −0.571845 | ||||||||
\(197\) | −494917. | −0.908588 | −0.454294 | − | 0.890852i | \(-0.650108\pi\) | ||||
−0.454294 | + | 0.890852i | \(0.650108\pi\) | |||||||
\(198\) | 69526.6 | 0.126034 | ||||||||
\(199\) | −824334. | −1.47561 | −0.737804 | − | 0.675015i | \(-0.764137\pi\) | ||||
−0.737804 | + | 0.675015i | \(0.764137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −538636. | −0.940385 | ||||||||
\(202\) | 1.44277e6 | 2.48782 | ||||||||
\(203\) | −38713.3 | −0.0659356 | ||||||||
\(204\) | 100636. | 0.169308 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 680688. | 1.11758 | ||||||||
\(207\) | 313896. | 0.509166 | ||||||||
\(208\) | 48561.9 | 0.0778283 | ||||||||
\(209\) | −254402. | −0.402860 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4819.05 | 0.00745170 | 0.00372585 | − | 0.999993i | \(-0.498814\pi\) | ||||
0.00372585 | + | 0.999993i | \(0.498814\pi\) | |||||||
\(212\) | 319964. | 0.488946 | ||||||||
\(213\) | 560322. | 0.846231 | ||||||||
\(214\) | −1.21257e6 | −1.80998 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −70732.5 | −0.103154 | ||||||||
\(217\) | −6555.92 | −0.00945114 | ||||||||
\(218\) | 441005. | 0.628495 | ||||||||
\(219\) | −317827. | −0.447796 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23251.4 | 0.0320235 | ||||||||
\(222\) | −196073. | −0.267015 | ||||||||
\(223\) | −225057. | −0.303062 | −0.151531 | − | 0.988453i | \(-0.548420\pi\) | ||||
−0.151531 | + | 0.988453i | \(0.548420\pi\) | |||||||
\(224\) | 27454.9 | 0.0365594 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −538891. | −0.701826 | ||||||||
\(227\) | 847198. | 1.09124 | 0.545620 | − | 0.838033i | \(-0.316294\pi\) | ||||
0.545620 | + | 0.838033i | \(0.316294\pi\) | |||||||
\(228\) | −346704. | −0.441694 | ||||||||
\(229\) | 901257. | 1.13569 | 0.567845 | − | 0.823135i | \(-0.307777\pi\) | ||||
0.567845 | + | 0.823135i | \(0.307777\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5035.95 | 0.00620943 | ||||||||
\(232\) | −812265. | −0.990782 | ||||||||
\(233\) | −439120. | −0.529900 | −0.264950 | − | 0.964262i | \(-0.585355\pi\) | ||||
−0.264950 | + | 0.964262i | \(0.585355\pi\) | |||||||
\(234\) | 21892.0 | 0.0261364 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −309959. | −0.362263 | ||||||||
\(237\) | −705350. | −0.815706 | ||||||||
\(238\) | 20020.0 | 0.0229098 | ||||||||
\(239\) | −922328. | −1.04446 | −0.522229 | − | 0.852805i | \(-0.674899\pi\) | ||||
−0.522229 | + | 0.852805i | \(0.674899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −891658. | −0.988907 | −0.494454 | − | 0.869204i | \(-0.664632\pi\) | ||||
−0.494454 | + | 0.869204i | \(0.664632\pi\) | |||||||
\(242\) | −103861. | −0.114002 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −47598.9 | −0.0511826 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −37740.4 | −0.0397621 | ||||||||
\(247\) | −80104.1 | −0.0835434 | ||||||||
\(248\) | −137553. | −0.142018 | ||||||||
\(249\) | −357430. | −0.365336 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −125904. | −0.126141 | −0.0630704 | − | 0.998009i | \(-0.520089\pi\) | ||||
−0.0630704 | + | 0.998009i | \(0.520089\pi\) | |||||||
\(252\) | 6863.10 | 0.00680799 | ||||||||
\(253\) | −468906. | −0.460558 | ||||||||
\(254\) | 709541. | 0.690070 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.32337e6 | 1.26206 | ||||||||
\(257\) | −864526. | −0.816479 | −0.408240 | − | 0.912875i | \(-0.633857\pi\) | ||||
−0.408240 | + | 0.912875i | \(0.633857\pi\) | |||||||
\(258\) | −1.22622e6 | −1.14689 | ||||||||
\(259\) | −14202.0 | −0.0131553 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −678096. | −0.616155 | ||||||||
\(262\) | −2.28876e6 | −2.05991 | ||||||||
\(263\) | −860845. | −0.767424 | −0.383712 | − | 0.923453i | \(-0.625355\pi\) | ||||
−0.383712 | + | 0.923453i | \(0.625355\pi\) | |||||||
\(264\) | 105662. | 0.0933060 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −68971.4 | −0.0597675 | ||||||||
\(267\) | −488766. | −0.419588 | ||||||||
\(268\) | 1.09657e6 | 0.932605 | ||||||||
\(269\) | −169703. | −0.142991 | −0.0714956 | − | 0.997441i | \(-0.522777\pi\) | ||||
−0.0714956 | + | 0.997441i | \(0.522777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −368847. | −0.305087 | −0.152543 | − | 0.988297i | \(-0.548746\pi\) | ||||
−0.152543 | + | 0.988297i | \(0.548746\pi\) | |||||||
\(272\) | 777869. | 0.637506 | ||||||||
\(273\) | 1585.68 | 0.00128768 | ||||||||
\(274\) | −2.31156e6 | −1.86006 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −639035. | −0.504954 | ||||||||
\(277\) | −423587. | −0.331698 | −0.165849 | − | 0.986151i | \(-0.553036\pi\) | ||||
−0.165849 | + | 0.986151i | \(0.553036\pi\) | |||||||
\(278\) | −2.94708e6 | −2.28708 | ||||||||
\(279\) | −114832. | −0.0883190 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.39124e6 | 1.80658 | 0.903290 | − | 0.429031i | \(-0.141145\pi\) | ||||
0.903290 | + | 0.429031i | \(0.141145\pi\) | |||||||
\(282\) | 730885. | 0.547301 | ||||||||
\(283\) | 238848. | 0.177279 | 0.0886393 | − | 0.996064i | \(-0.471748\pi\) | ||||
0.0886393 | + | 0.996064i | \(0.471748\pi\) | |||||||
\(284\) | −1.14071e6 | −0.839230 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −32702.9 | −0.0236413 | ||||||||
\(287\) | −2733.62 | −0.00195899 | ||||||||
\(288\) | 480895. | 0.341641 | ||||||||
\(289\) | −1.04741e6 | −0.737690 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −302167. | −0.209177 | ||||||||
\(292\) | 647037. | 0.444091 | ||||||||
\(293\) | 289624. | 0.197091 | 0.0985454 | − | 0.995133i | \(-0.468581\pi\) | ||||
0.0985454 | + | 0.995133i | \(0.468581\pi\) | |||||||
\(294\) | −1.07167e6 | −0.723089 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −297980. | −0.197678 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | −2.17516e6 | −1.41890 | ||||||||
\(299\) | −147646. | −0.0955086 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −88817.8 | −0.0565046 | ||||||||
\(302\) | 640912. | 0.404372 | ||||||||
\(303\) | 1.83045e6 | 1.14539 | ||||||||
\(304\) | −2.67985e6 | −1.66313 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 350668. | 0.214088 | ||||||||
\(307\) | −2.74983e6 | −1.66517 | −0.832586 | − | 0.553895i | \(-0.813141\pi\) | ||||
−0.832586 | + | 0.553895i | \(0.813141\pi\) | |||||||
\(308\) | −10252.3 | −0.00615806 | ||||||||
\(309\) | 863595. | 0.514534 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −669544. | −0.392534 | −0.196267 | − | 0.980550i | \(-0.562882\pi\) | ||||
−0.196267 | + | 0.980550i | \(0.562882\pi\) | |||||||
\(312\) | 33270.1 | 0.0193494 | ||||||||
\(313\) | −458501. | −0.264533 | −0.132266 | − | 0.991214i | \(-0.542225\pi\) | ||||
−0.132266 | + | 0.991214i | \(0.542225\pi\) | |||||||
\(314\) | −576516. | −0.329980 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.43596e6 | 0.808958 | ||||||||
\(317\) | 1.69327e6 | 0.946406 | 0.473203 | − | 0.880953i | \(-0.343098\pi\) | ||||
0.473203 | + | 0.880953i | \(0.343098\pi\) | |||||||
\(318\) | 1.11492e6 | 0.618264 | ||||||||
\(319\) | 1.01296e6 | 0.557333 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.53840e6 | −0.833311 | ||||||||
\(322\) | −127126. | −0.0683275 | ||||||||
\(323\) | −1.28311e6 | −0.684319 | ||||||||
\(324\) | 120213. | 0.0636193 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.26557e6 | 0.659540 | ||||||||
\(327\) | 559507. | 0.289358 | ||||||||
\(328\) | −57355.6 | −0.0294368 | ||||||||
\(329\) | 52939.5 | 0.0269644 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.96369e6 | −1.48684 | −0.743418 | − | 0.668827i | \(-0.766797\pi\) | ||||
−0.743418 | + | 0.668827i | \(0.766797\pi\) | |||||||
\(332\) | 727663. | 0.362314 | ||||||||
\(333\) | −248760. | −0.122933 | ||||||||
\(334\) | −4.44437e6 | −2.17994 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 53048.4 | 0.0256345 | ||||||||
\(337\) | −2.28507e6 | −1.09604 | −0.548018 | − | 0.836466i | \(-0.684618\pi\) | ||||
−0.548018 | + | 0.836466i | \(0.684618\pi\) | |||||||
\(338\) | 2.62359e6 | 1.24912 | ||||||||
\(339\) | −683695. | −0.323120 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 171540. | 0.0798875 | ||||||||
\(342\) | −1.20809e6 | −0.558515 | ||||||||
\(343\) | −155345. | −0.0712955 | ||||||||
\(344\) | −1.86354e6 | −0.849067 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.30718e6 | 1.03608 | ||||||||
\(347\) | −427019. | −0.190381 | −0.0951905 | − | 0.995459i | \(-0.530346\pi\) | ||||
−0.0951905 | + | 0.995459i | \(0.530346\pi\) | |||||||
\(348\) | 1.38048e6 | 0.611058 | ||||||||
\(349\) | −2.34367e6 | −1.02999 | −0.514995 | − | 0.857193i | \(-0.672206\pi\) | ||||
−0.514995 | + | 0.857193i | \(0.672206\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27774.6 | 0.0120332 | ||||||||
\(352\) | −718375. | −0.309026 | ||||||||
\(353\) | −1.63784e6 | −0.699574 | −0.349787 | − | 0.936829i | \(-0.613746\pi\) | ||||
−0.349787 | + | 0.936829i | \(0.613746\pi\) | |||||||
\(354\) | −1.08005e6 | −0.458076 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 995039. | 0.416117 | ||||||||
\(357\) | 25399.6 | 0.0105477 | ||||||||
\(358\) | −1.29819e6 | −0.535339 | ||||||||
\(359\) | 2.80870e6 | 1.15019 | 0.575095 | − | 0.818087i | \(-0.304965\pi\) | ||||
0.575095 | + | 0.818087i | \(0.304965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.94439e6 | 0.785261 | ||||||||
\(362\) | 4.42129e6 | 1.77328 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −3228.16 | −0.00127703 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −165859. | −0.0647196 | ||||||||
\(367\) | 40056.0 | 0.0155239 | 0.00776197 | − | 0.999970i | \(-0.497529\pi\) | ||||
0.00776197 | + | 0.999970i | \(0.497529\pi\) | |||||||
\(368\) | −4.93943e6 | −1.90133 | ||||||||
\(369\) | −47881.6 | −0.0183064 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 80755.6 | 0.0304606 | ||||||||
\(372\) | 233778. | 0.0875884 | ||||||||
\(373\) | 1.60363e6 | 0.596806 | 0.298403 | − | 0.954440i | \(-0.403546\pi\) | ||||
0.298403 | + | 0.954440i | \(0.403546\pi\) | |||||||
\(374\) | −523837. | −0.193650 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.11075e6 | 0.405180 | ||||||||
\(377\) | 318953. | 0.115577 | ||||||||
\(378\) | 23914.5 | 0.00860860 | ||||||||
\(379\) | 2.12659e6 | 0.760476 | 0.380238 | − | 0.924889i | \(-0.375842\pi\) | ||||
0.380238 | + | 0.924889i | \(0.375842\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 900201. | 0.317707 | ||||||||
\(382\) | −1.27282e6 | −0.446280 | ||||||||
\(383\) | −3.69333e6 | −1.28653 | −0.643267 | − | 0.765642i | \(-0.722421\pi\) | ||||
−0.643267 | + | 0.765642i | \(0.722421\pi\) | |||||||
\(384\) | 1.62503e6 | 0.562386 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.41572e6 | 2.19168 | ||||||||
\(387\) | −1.55572e6 | −0.528024 | ||||||||
\(388\) | 615157. | 0.207447 | ||||||||
\(389\) | −215626. | −0.0722482 | −0.0361241 | − | 0.999347i | \(-0.511501\pi\) | ||||
−0.0361241 | + | 0.999347i | \(0.511501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.36500e6 | −0.782328 | ||||||||
\(392\) | −1.62865e6 | −0.535320 | ||||||||
\(393\) | −2.90377e6 | −0.948378 | ||||||||
\(394\) | 3.51086e6 | 1.13939 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −179578. | −0.0575458 | ||||||||
\(397\) | 4.45417e6 | 1.41837 | 0.709186 | − | 0.705021i | \(-0.249062\pi\) | ||||
0.709186 | + | 0.705021i | \(0.249062\pi\) | |||||||
\(398\) | 5.84769e6 | 1.85045 | ||||||||
\(399\) | −87504.7 | −0.0275169 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.31987e6 | 1.65211 | 0.826057 | − | 0.563586i | \(-0.190579\pi\) | ||||
0.826057 | + | 0.563586i | \(0.190579\pi\) | |||||||
\(402\) | 3.82099e6 | 1.17926 | ||||||||
\(403\) | 54013.1 | 0.0165667 | ||||||||
\(404\) | −3.72647e6 | −1.13591 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 274625. | 0.0826848 | ||||||||
\(407\) | 371604. | 0.111197 | ||||||||
\(408\) | 532923. | 0.158494 | ||||||||
\(409\) | −3.81493e6 | −1.12766 | −0.563830 | − | 0.825891i | \(-0.690673\pi\) | ||||
−0.563830 | + | 0.825891i | \(0.690673\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.93269e6 | −0.856371 | ||||||||
\(412\) | −1.75812e6 | −0.510277 | ||||||||
\(413\) | −78230.5 | −0.0225684 | ||||||||
\(414\) | −2.22672e6 | −0.638506 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −226196. | −0.0640844 | ||||||||
\(417\) | −3.73899e6 | −1.05297 | ||||||||
\(418\) | 1.80468e6 | 0.505196 | ||||||||
\(419\) | −3.59908e6 | −1.00151 | −0.500756 | − | 0.865588i | \(-0.666945\pi\) | ||||
−0.500756 | + | 0.865588i | \(0.666945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.15462e6 | −0.592467 | −0.296234 | − | 0.955115i | \(-0.595731\pi\) | ||||
−0.296234 | + | 0.955115i | \(0.595731\pi\) | |||||||
\(422\) | −34185.5 | −0.00934460 | ||||||||
\(423\) | 927280. | 0.251976 | ||||||||
\(424\) | 1.69438e6 | 0.457716 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.97483e6 | −1.06119 | ||||||||
\(427\) | −12013.5 | −0.00318860 | ||||||||
\(428\) | 3.13191e6 | 0.826417 | ||||||||
\(429\) | −41490.4 | −0.0108844 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.10237e6 | −0.545149 | −0.272575 | − | 0.962135i | \(-0.587875\pi\) | ||||
−0.272575 | + | 0.962135i | \(0.587875\pi\) | |||||||
\(432\) | 929188. | 0.239549 | ||||||||
\(433\) | 41848.5 | 0.0107265 | 0.00536327 | − | 0.999986i | \(-0.498293\pi\) | ||||
0.00536327 | + | 0.999986i | \(0.498293\pi\) | |||||||
\(434\) | 46506.5 | 0.0118519 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.13905e6 | −0.286964 | ||||||||
\(437\) | 8.14771e6 | 2.04095 | ||||||||
\(438\) | 2.25461e6 | 0.561546 | ||||||||
\(439\) | −5.35761e6 | −1.32681 | −0.663407 | − | 0.748259i | \(-0.730890\pi\) | ||||
−0.663407 | + | 0.748259i | \(0.730890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.35963e6 | −0.332909 | ||||||||
\(442\) | −164942. | −0.0401582 | ||||||||
\(443\) | −4.69738e6 | −1.13722 | −0.568612 | − | 0.822606i | \(-0.692520\pi\) | ||||
−0.568612 | + | 0.822606i | \(0.692520\pi\) | |||||||
\(444\) | 506430. | 0.121916 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.59652e6 | 0.380046 | ||||||||
\(447\) | −2.75964e6 | −0.653257 | ||||||||
\(448\) | −6143.50 | −0.00144617 | ||||||||
\(449\) | 7.10537e6 | 1.66330 | 0.831650 | − | 0.555300i | \(-0.187397\pi\) | ||||
0.831650 | + | 0.555300i | \(0.187397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 71526.9 | 0.0165588 | ||||||||
\(452\) | 1.39188e6 | 0.320447 | ||||||||
\(453\) | 813131. | 0.186172 | ||||||||
\(454\) | −6.00987e6 | −1.36844 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.83598e6 | −0.413482 | ||||||||
\(457\) | −4.82566e6 | −1.08085 | −0.540426 | − | 0.841392i | \(-0.681737\pi\) | ||||
−0.540426 | + | 0.841392i | \(0.681737\pi\) | |||||||
\(458\) | −6.39336e6 | −1.42418 | ||||||||
\(459\) | 444895. | 0.0985657 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.03634e6 | −0.227117 | −0.113558 | − | 0.993531i | \(-0.536225\pi\) | ||||
−0.113558 | + | 0.993531i | \(0.536225\pi\) | |||||||
\(462\) | −35724.2 | −0.00778677 | ||||||||
\(463\) | −457904. | −0.0992709 | −0.0496355 | − | 0.998767i | \(-0.515806\pi\) | ||||
−0.0496355 | + | 0.998767i | \(0.515806\pi\) | |||||||
\(464\) | 1.06704e7 | 2.30085 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.11504e6 | 0.664507 | ||||||||
\(467\) | −2.02783e6 | −0.430268 | −0.215134 | − | 0.976584i | \(-0.569019\pi\) | ||||
−0.215134 | + | 0.976584i | \(0.569019\pi\) | |||||||
\(468\) | −56544.0 | −0.0119336 | ||||||||
\(469\) | 276762. | 0.0580998 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −731431. | −0.151922 | ||||||||
\(472\) | −1.64140e6 | −0.339124 | ||||||||
\(473\) | 2.32398e6 | 0.477616 | ||||||||
\(474\) | 5.00363e6 | 1.02291 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −51708.9 | −0.0104604 | ||||||||
\(477\) | 1.41450e6 | 0.284648 | ||||||||
\(478\) | 6.54284e6 | 1.30977 | ||||||||
\(479\) | 3.41441e6 | 0.679949 | 0.339975 | − | 0.940435i | \(-0.389582\pi\) | ||||
0.339975 | + | 0.940435i | \(0.389582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 117008. | 0.0230596 | ||||||||
\(482\) | 6.32526e6 | 1.24011 | ||||||||
\(483\) | −161286. | −0.0314579 | ||||||||
\(484\) | 268258. | 0.0520522 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 418883. | 0.0804456 | ||||||||
\(487\) | 1.21543e6 | 0.232224 | 0.116112 | − | 0.993236i | \(-0.462957\pi\) | ||||
0.116112 | + | 0.993236i | \(0.462957\pi\) | |||||||
\(488\) | −252062. | −0.0479134 | ||||||||
\(489\) | 1.60564e6 | 0.303651 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.85480e6 | −0.908798 | −0.454399 | − | 0.890798i | \(-0.650146\pi\) | ||||
−0.454399 | + | 0.890798i | \(0.650146\pi\) | |||||||
\(492\) | 97478.3 | 0.0181550 | ||||||||
\(493\) | 5.10901e6 | 0.946715 | ||||||||
\(494\) | 568244. | 0.104765 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.80699e6 | 0.329801 | ||||||||
\(497\) | −287905. | −0.0522827 | ||||||||
\(498\) | 2.53555e6 | 0.458140 | ||||||||
\(499\) | 7.01256e6 | 1.26074 | 0.630370 | − | 0.776295i | \(-0.282903\pi\) | ||||
0.630370 | + | 0.776295i | \(0.282903\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.63861e6 | −1.00364 | ||||||||
\(502\) | 893142. | 0.158184 | ||||||||
\(503\) | −7.65551e6 | −1.34913 | −0.674565 | − | 0.738215i | \(-0.735669\pi\) | ||||
−0.674565 | + | 0.738215i | \(0.735669\pi\) | |||||||
\(504\) | 36343.8 | 0.00637315 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.32634e6 | 0.577551 | ||||||||
\(507\) | 3.32857e6 | 0.575093 | ||||||||
\(508\) | −1.83265e6 | −0.315079 | ||||||||
\(509\) | 7.70001e6 | 1.31734 | 0.658669 | − | 0.752433i | \(-0.271120\pi\) | ||||
0.658669 | + | 0.752433i | \(0.271120\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 163306. | 0.0276662 | ||||||||
\(512\) | −3.60985e6 | −0.608574 | ||||||||
\(513\) | −1.53272e6 | −0.257140 | ||||||||
\(514\) | 6.13279e6 | 1.02388 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.16716e6 | 0.523656 | ||||||||
\(517\) | −1.38520e6 | −0.227921 | ||||||||
\(518\) | 100746. | 0.0164970 | ||||||||
\(519\) | 2.92714e6 | 0.477008 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.03644e6 | −0.490083 | −0.245042 | − | 0.969513i | \(-0.578802\pi\) | ||||
−0.245042 | + | 0.969513i | \(0.578802\pi\) | |||||||
\(522\) | 4.81030e6 | 0.772673 | ||||||||
\(523\) | 7.75936e6 | 1.24043 | 0.620214 | − | 0.784432i | \(-0.287046\pi\) | ||||
0.620214 | + | 0.784432i | \(0.287046\pi\) | |||||||
\(524\) | 5.91156e6 | 0.940532 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.10669e6 | 0.962368 | ||||||||
\(527\) | 865187. | 0.135701 | ||||||||
\(528\) | −1.38805e6 | −0.216680 | ||||||||
\(529\) | 8.58128e6 | 1.33325 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.37027e6 | −0.210897 | ||||||||
\(532\) | 178144. | 0.0272892 | ||||||||
\(533\) | 22521.8 | 0.00343389 | ||||||||
\(534\) | 3.46722e6 | 0.526173 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.80691e6 | 0.873037 | ||||||||
\(537\) | −1.64702e6 | −0.246469 | ||||||||
\(538\) | 1.20385e6 | 0.179314 | ||||||||
\(539\) | 2.03106e6 | 0.301128 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.80224e6 | −1.29300 | −0.646502 | − | 0.762912i | \(-0.723769\pi\) | ||||
−0.646502 | + | 0.762912i | \(0.723769\pi\) | |||||||
\(542\) | 2.61654e6 | 0.382586 | ||||||||
\(543\) | 5.60933e6 | 0.816416 | ||||||||
\(544\) | −3.62323e6 | −0.524927 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11248.6 | −0.00161479 | ||||||||
\(547\) | −3.58640e6 | −0.512496 | −0.256248 | − | 0.966611i | \(-0.582486\pi\) | ||||
−0.256248 | + | 0.966611i | \(0.582486\pi\) | |||||||
\(548\) | 5.97043e6 | 0.849286 | ||||||||
\(549\) | −210426. | −0.0297968 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.76012e7 | −2.46980 | ||||||||
\(552\) | −3.38403e6 | −0.472701 | ||||||||
\(553\) | 362423. | 0.0503968 | ||||||||
\(554\) | 3.00485e6 | 0.415957 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.61191e6 | 1.04426 | ||||||||
\(557\) | 4.61032e6 | 0.629641 | 0.314821 | − | 0.949151i | \(-0.398056\pi\) | ||||
0.314821 | + | 0.949151i | \(0.398056\pi\) | |||||||
\(558\) | 814602. | 0.110754 | ||||||||
\(559\) | 731756. | 0.0990459 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −664596. | −0.0891561 | ||||||||
\(562\) | −1.69630e7 | −2.26549 | ||||||||
\(563\) | 2.16200e6 | 0.287464 | 0.143732 | − | 0.989617i | \(-0.454090\pi\) | ||||
0.143732 | + | 0.989617i | \(0.454090\pi\) | |||||||
\(564\) | −1.88777e6 | −0.249892 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.69435e6 | −0.222311 | ||||||||
\(567\) | 30340.6 | 0.00396338 | ||||||||
\(568\) | −6.04070e6 | −0.785627 | ||||||||
\(569\) | 1.71372e6 | 0.221901 | 0.110951 | − | 0.993826i | \(-0.464610\pi\) | ||||
0.110951 | + | 0.993826i | \(0.464610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.80446e6 | −0.488318 | −0.244159 | − | 0.969735i | \(-0.578512\pi\) | ||||
−0.244159 | + | 0.969735i | \(0.578512\pi\) | |||||||
\(572\) | 84466.9 | 0.0107944 | ||||||||
\(573\) | −1.61484e6 | −0.205467 | ||||||||
\(574\) | 19391.8 | 0.00245662 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −107609. | −0.0135142 | ||||||||
\(577\) | −9.84742e6 | −1.23135 | −0.615677 | − | 0.787998i | \(-0.711117\pi\) | ||||
−0.615677 | + | 0.787998i | \(0.711117\pi\) | |||||||
\(578\) | 7.43017e6 | 0.925080 | ||||||||
\(579\) | 8.13968e6 | 1.00905 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 183655. | 0.0225716 | ||||||||
\(582\) | 2.14352e6 | 0.262313 | ||||||||
\(583\) | −2.11302e6 | −0.257474 | ||||||||
\(584\) | 3.42641e6 | 0.415726 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.05455e6 | −0.247156 | ||||||||
\(587\) | 4.48517e6 | 0.537258 | 0.268629 | − | 0.963244i | \(-0.413429\pi\) | ||||
0.268629 | + | 0.963244i | \(0.413429\pi\) | |||||||
\(588\) | 2.76797e6 | 0.330155 | ||||||||
\(589\) | −2.98067e6 | −0.354019 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.45426e6 | 0.524574 | ||||||||
\(592\) | 3.91446e6 | 0.459058 | ||||||||
\(593\) | 1.57719e7 | 1.84182 | 0.920909 | − | 0.389777i | \(-0.127448\pi\) | ||||
0.920909 | + | 0.389777i | \(0.127448\pi\) | |||||||
\(594\) | −625739. | −0.0727658 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.61813e6 | 0.647853 | ||||||||
\(597\) | 7.41901e6 | 0.851942 | ||||||||
\(598\) | 1.04737e6 | 0.119770 | ||||||||
\(599\) | −8.13287e6 | −0.926140 | −0.463070 | − | 0.886322i | \(-0.653252\pi\) | ||||
−0.463070 | + | 0.886322i | \(0.653252\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.56975e6 | 0.741930 | 0.370965 | − | 0.928647i | \(-0.379027\pi\) | ||||
0.370965 | + | 0.928647i | \(0.379027\pi\) | |||||||
\(602\) | 630058. | 0.0708581 | ||||||||
\(603\) | 4.84773e6 | 0.542931 | ||||||||
\(604\) | −1.65539e6 | −0.184632 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.29849e7 | −1.43634 | ||||||||
\(607\) | −5.13693e6 | −0.565890 | −0.282945 | − | 0.959136i | \(-0.591311\pi\) | ||||
−0.282945 | + | 0.959136i | \(0.591311\pi\) | |||||||
\(608\) | 1.24825e7 | 1.36944 | ||||||||
\(609\) | 348420. | 0.0380680 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −436160. | −0.0472653 | ||||||||
\(612\) | −905726. | −0.0977503 | ||||||||
\(613\) | −4.41922e6 | −0.475001 | −0.237501 | − | 0.971387i | \(-0.576328\pi\) | ||||
−0.237501 | + | 0.971387i | \(0.576328\pi\) | |||||||
\(614\) | 1.95068e7 | 2.08817 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −54291.4 | −0.00576473 | ||||||||
\(617\) | −5.70350e6 | −0.603154 | −0.301577 | − | 0.953442i | \(-0.597513\pi\) | ||||
−0.301577 | + | 0.953442i | \(0.597513\pi\) | |||||||
\(618\) | −6.12619e6 | −0.645237 | ||||||||
\(619\) | 381437. | 0.0400125 | 0.0200063 | − | 0.999800i | \(-0.493631\pi\) | ||||
0.0200063 | + | 0.999800i | \(0.493631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.82506e6 | −0.293967 | ||||||||
\(622\) | 4.74963e6 | 0.492247 | ||||||||
\(623\) | 251138. | 0.0259234 | ||||||||
\(624\) | −437057. | −0.0449342 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.25253e6 | 0.331730 | ||||||||
\(627\) | 2.28962e6 | 0.232592 | ||||||||
\(628\) | 1.48906e6 | 0.150665 | ||||||||
\(629\) | 1.87424e6 | 0.188886 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.26994e6 | −0.526905 | −0.263453 | − | 0.964672i | \(-0.584861\pi\) | ||||
−0.263453 | + | 0.964672i | \(0.584861\pi\) | |||||||
\(632\) | 7.60420e6 | 0.757288 | ||||||||
\(633\) | −43371.5 | −0.00430224 | ||||||||
\(634\) | −1.20117e7 | −1.18682 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.87967e6 | −0.282293 | ||||||||
\(637\) | 639524. | 0.0624466 | ||||||||
\(638\) | −7.18575e6 | −0.698909 | ||||||||
\(639\) | −5.04290e6 | −0.488572 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −735036. | −0.0706584 | −0.0353292 | − | 0.999376i | \(-0.511248\pi\) | ||||
−0.0353292 | + | 0.999376i | \(0.511248\pi\) | |||||||
\(642\) | 1.09132e7 | 1.04499 | ||||||||
\(643\) | −1.45125e7 | −1.38425 | −0.692125 | − | 0.721778i | \(-0.743325\pi\) | ||||
−0.692125 | + | 0.721778i | \(0.743325\pi\) | |||||||
\(644\) | 328349. | 0.0311976 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.10218e6 | 0.858152 | ||||||||
\(647\) | 1.87650e6 | 0.176233 | 0.0881167 | − | 0.996110i | \(-0.471915\pi\) | ||||
0.0881167 | + | 0.996110i | \(0.471915\pi\) | |||||||
\(648\) | 636593. | 0.0595558 | ||||||||
\(649\) | 2.04695e6 | 0.190764 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 59003.3 | 0.00545662 | ||||||||
\(652\) | −3.26879e6 | −0.301139 | ||||||||
\(653\) | −1.72496e7 | −1.58306 | −0.791529 | − | 0.611131i | \(-0.790715\pi\) | ||||
−0.791529 | + | 0.611131i | \(0.790715\pi\) | |||||||
\(654\) | −3.96904e6 | −0.362862 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 753460. | 0.0683598 | ||||||||
\(657\) | 2.86044e6 | 0.258535 | ||||||||
\(658\) | −375544. | −0.0338139 | ||||||||
\(659\) | 7.60070e6 | 0.681773 | 0.340887 | − | 0.940104i | \(-0.389273\pi\) | ||||
0.340887 | + | 0.940104i | \(0.389273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −74179.4 | −0.00660358 | −0.00330179 | − | 0.999995i | \(-0.501051\pi\) | ||||
−0.00330179 | + | 0.999995i | \(0.501051\pi\) | |||||||
\(662\) | 2.10239e7 | 1.86453 | ||||||||
\(663\) | −209263. | −0.0184888 | ||||||||
\(664\) | 3.85336e6 | 0.339172 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.76466e6 | 0.154161 | ||||||||
\(667\) | −3.24420e7 | −2.82353 | ||||||||
\(668\) | 1.14792e7 | 0.995337 | ||||||||
\(669\) | 2.02552e6 | 0.174973 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 314341. | 0.0269522 | ||||||||
\(672\) | −247094. | −0.0211076 | ||||||||
\(673\) | −5.80762e6 | −0.494265 | −0.247133 | − | 0.968982i | \(-0.579488\pi\) | ||||
−0.247133 | + | 0.968982i | \(0.579488\pi\) | |||||||
\(674\) | 1.62099e7 | 1.37446 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.77637e6 | −0.570335 | ||||||||
\(677\) | −1.91692e7 | −1.60743 | −0.803716 | − | 0.595013i | \(-0.797147\pi\) | ||||
−0.803716 | + | 0.595013i | \(0.797147\pi\) | |||||||
\(678\) | 4.85002e6 | 0.405199 | ||||||||
\(679\) | 155259. | 0.0129236 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.62478e6 | −0.630028 | ||||||||
\(682\) | −1.21687e6 | −0.100181 | ||||||||
\(683\) | 2.11907e7 | 1.73817 | 0.869087 | − | 0.494660i | \(-0.164707\pi\) | ||||
0.869087 | + | 0.494660i | \(0.164707\pi\) | |||||||
\(684\) | 3.12034e6 | 0.255012 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.10199e6 | 0.0894062 | ||||||||
\(687\) | −8.11132e6 | −0.655691 | ||||||||
\(688\) | 2.44806e7 | 1.97175 | ||||||||
\(689\) | −665332. | −0.0533938 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.24582e7 | 0.992565 | 0.496282 | − | 0.868161i | \(-0.334698\pi\) | ||||
0.496282 | + | 0.868161i | \(0.334698\pi\) | |||||||
\(692\) | −5.95913e6 | −0.473062 | ||||||||
\(693\) | −45323.6 | −0.00358502 | ||||||||
\(694\) | 3.02920e6 | 0.238742 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.31039e6 | 0.572028 | ||||||||
\(697\) | 360756. | 0.0281276 | ||||||||
\(698\) | 1.66256e7 | 1.29163 | ||||||||
\(699\) | 3.95208e6 | 0.305938 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 582671. | 0.0447845 | 0.0223923 | − | 0.999749i | \(-0.492872\pi\) | ||||
0.0223923 | + | 0.999749i | \(0.492872\pi\) | |||||||
\(702\) | −197028. | −0.0150899 | ||||||||
\(703\) | −6.45699e6 | −0.492767 | ||||||||
\(704\) | 160749. | 0.0122241 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.16185e7 | 0.877282 | ||||||||
\(707\) | −940525. | −0.0707655 | ||||||||
\(708\) | 2.78963e6 | 0.209153 | ||||||||
\(709\) | −3.31741e6 | −0.247847 | −0.123923 | − | 0.992292i | \(-0.539548\pi\) | ||||
−0.123923 | + | 0.992292i | \(0.539548\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.34815e6 | 0.470948 | ||||||||
\(712\) | 5.26926e6 | 0.389538 | ||||||||
\(713\) | −5.49389e6 | −0.404722 | ||||||||
\(714\) | −180180. | −0.0132270 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.35303e6 | 0.244430 | ||||||||
\(717\) | 8.30096e6 | 0.603018 | ||||||||
\(718\) | −1.99244e7 | −1.44236 | ||||||||
\(719\) | −8.22478e6 | −0.593338 | −0.296669 | − | 0.954980i | \(-0.595876\pi\) | ||||
−0.296669 | + | 0.954980i | \(0.595876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −443733. | −0.0317895 | ||||||||
\(722\) | −1.37931e7 | −0.984736 | ||||||||
\(723\) | 8.02492e6 | 0.570946 | ||||||||
\(724\) | −1.14196e7 | −0.809661 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 934746. | 0.0658191 | ||||||||
\(727\) | 5.99896e6 | 0.420959 | 0.210479 | − | 0.977598i | \(-0.432497\pi\) | ||||
0.210479 | + | 0.977598i | \(0.432497\pi\) | |||||||
\(728\) | −17094.8 | −0.00119546 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.17213e7 | 0.811303 | ||||||||
\(732\) | 428390. | 0.0295503 | ||||||||
\(733\) | 1.02874e7 | 0.707204 | 0.353602 | − | 0.935396i | \(-0.384957\pi\) | ||||
0.353602 | + | 0.935396i | \(0.384957\pi\) | |||||||
\(734\) | −284150. | −0.0194674 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.30073e7 | 1.56557 | ||||||||
\(737\) | −7.24167e6 | −0.491100 | ||||||||
\(738\) | 339664. | 0.0229567 | ||||||||
\(739\) | 4.35478e6 | 0.293329 | 0.146665 | − | 0.989186i | \(-0.453146\pi\) | ||||
0.146665 | + | 0.989186i | \(0.453146\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 720937. | 0.0482338 | ||||||||
\(742\) | −572866. | −0.0381983 | ||||||||
\(743\) | −6.54892e6 | −0.435209 | −0.217604 | − | 0.976037i | \(-0.569824\pi\) | ||||
−0.217604 | + | 0.976037i | \(0.569824\pi\) | |||||||
\(744\) | 1.23798e6 | 0.0819939 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.13759e7 | −0.748409 | ||||||||
\(747\) | 3.21687e6 | 0.210927 | ||||||||
\(748\) | 1.35300e6 | 0.0884185 | ||||||||
\(749\) | 790462. | 0.0514845 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.42508e6 | 0.0922019 | 0.0461009 | − | 0.998937i | \(-0.485320\pi\) | ||||
0.0461009 | + | 0.998937i | \(0.485320\pi\) | |||||||
\(752\) | −1.45916e7 | −0.940930 | ||||||||
\(753\) | 1.13314e6 | 0.0728275 | ||||||||
\(754\) | −2.26259e6 | −0.144937 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −61767.9 | −0.00393060 | ||||||||
\(757\) | 1.59943e7 | 1.01443 | 0.507217 | − | 0.861818i | \(-0.330674\pi\) | ||||
0.507217 | + | 0.861818i | \(0.330674\pi\) | |||||||
\(758\) | −1.50856e7 | −0.953654 | ||||||||
\(759\) | 4.22016e6 | 0.265904 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.04747e7 | −1.90756 | −0.953778 | − | 0.300512i | \(-0.902843\pi\) | ||||
−0.953778 | + | 0.300512i | \(0.902843\pi\) | |||||||
\(762\) | −6.38587e6 | −0.398412 | ||||||||
\(763\) | −287486. | −0.0178774 | ||||||||
\(764\) | 3.28751e6 | 0.203767 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.61998e7 | 1.61334 | ||||||||
\(767\) | 644529. | 0.0395598 | ||||||||
\(768\) | −1.19103e7 | −0.728652 | ||||||||
\(769\) | 8.77682e6 | 0.535206 | 0.267603 | − | 0.963529i | \(-0.413768\pi\) | ||||
0.267603 | + | 0.963529i | \(0.413768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.78073e6 | 0.471394 | ||||||||
\(772\) | −1.65709e7 | −1.00070 | ||||||||
\(773\) | −867299. | −0.0522060 | −0.0261030 | − | 0.999659i | \(-0.508310\pi\) | ||||
−0.0261030 | + | 0.999659i | \(0.508310\pi\) | |||||||
\(774\) | 1.10360e7 | 0.662155 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.25758e6 | 0.194196 | ||||||||
\(777\) | 127818. | 0.00759520 | ||||||||
\(778\) | 1.52961e6 | 0.0906009 | ||||||||
\(779\) | −1.24285e6 | −0.0733796 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.53322e6 | 0.441930 | ||||||||
\(782\) | 1.67769e7 | 0.981057 | ||||||||
\(783\) | 6.10287e6 | 0.355737 | ||||||||
\(784\) | 2.13951e7 | 1.24315 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.05989e7 | 1.18929 | ||||||||
\(787\) | −2.23177e7 | −1.28444 | −0.642218 | − | 0.766522i | \(-0.721985\pi\) | ||||
−0.642218 | + | 0.766522i | \(0.721985\pi\) | |||||||
\(788\) | −9.06806e6 | −0.520234 | ||||||||
\(789\) | 7.74761e6 | 0.443073 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 351297. | 0.0199633 | ||||||||
\(792\) | −950959. | −0.0538702 | ||||||||
\(793\) | 98977.2 | 0.00558923 | ||||||||
\(794\) | −3.15971e7 | −1.77867 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.51038e7 | −0.844894 | ||||||||
\(797\) | −1.21353e7 | −0.676716 | −0.338358 | − | 0.941018i | \(-0.609871\pi\) | ||||
−0.338358 | + | 0.941018i | \(0.609871\pi\) | |||||||
\(798\) | 620743. | 0.0345068 | ||||||||
\(799\) | −6.98644e6 | −0.387159 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.39889e6 | 0.242249 | ||||||||
\(802\) | −3.77382e7 | −2.07179 | ||||||||
\(803\) | −4.27300e6 | −0.233854 | ||||||||
\(804\) | −9.86909e6 | −0.538440 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −383160. | −0.0207751 | ||||||||
\(807\) | 1.52733e6 | 0.0825561 | ||||||||
\(808\) | −1.97337e7 | −1.06336 | ||||||||
\(809\) | −1.25683e7 | −0.675160 | −0.337580 | − | 0.941297i | \(-0.609608\pi\) | ||||
−0.337580 | + | 0.941297i | \(0.609608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.29850e6 | 0.336268 | 0.168134 | − | 0.985764i | \(-0.446226\pi\) | ||||
0.168134 | + | 0.985764i | \(0.446226\pi\) | |||||||
\(812\) | −709319. | −0.0377530 | ||||||||
\(813\) | 3.31963e6 | 0.176142 | ||||||||
\(814\) | −2.63610e6 | −0.139444 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.00082e6 | −0.368064 | ||||||||
\(817\) | −4.03814e7 | −2.11654 | ||||||||
\(818\) | 2.70624e7 | 1.41411 | ||||||||
\(819\) | −14271.1 | −0.000743445 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.89136e7 | 0.979303 | 0.489651 | − | 0.871918i | \(-0.337124\pi\) | ||||
0.489651 | + | 0.871918i | \(0.337124\pi\) | |||||||
\(822\) | 2.08040e7 | 1.07391 | ||||||||
\(823\) | −2.67549e7 | −1.37691 | −0.688453 | − | 0.725281i | \(-0.741710\pi\) | ||||
−0.688453 | + | 0.725281i | \(0.741710\pi\) | |||||||
\(824\) | −9.31020e6 | −0.477684 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 554954. | 0.0283013 | ||||||||
\(827\) | 1.76676e7 | 0.898283 | 0.449142 | − | 0.893461i | \(-0.351730\pi\) | ||||
0.449142 | + | 0.893461i | \(0.351730\pi\) | |||||||
\(828\) | 5.75132e6 | 0.291535 | ||||||||
\(829\) | −2.37092e7 | −1.19820 | −0.599102 | − | 0.800673i | \(-0.704476\pi\) | ||||
−0.599102 | + | 0.800673i | \(0.704476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.81228e6 | 0.191506 | ||||||||
\(832\) | 50615.3 | 0.00253497 | ||||||||
\(833\) | 1.02439e7 | 0.511511 | ||||||||
\(834\) | 2.65238e7 | 1.32044 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.66124e6 | −0.230667 | ||||||||
\(837\) | 1.03349e6 | 0.0509910 | ||||||||
\(838\) | 2.55312e7 | 1.25592 | ||||||||
\(839\) | −1.98735e7 | −0.974696 | −0.487348 | − | 0.873208i | \(-0.662036\pi\) | ||||
−0.487348 | + | 0.873208i | \(0.662036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.95719e7 | 2.41683 | ||||||||
\(842\) | 1.52845e7 | 0.742968 | ||||||||
\(843\) | −2.15211e7 | −1.04303 | ||||||||
\(844\) | 88296.4 | 0.00426665 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.57796e6 | −0.315984 | ||||||||
\(847\) | 67705.6 | 0.00324277 | ||||||||
\(848\) | −2.22585e7 | −1.06293 | ||||||||
\(849\) | −2.14964e6 | −0.102352 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.19013e7 | −0.563342 | ||||||||
\(852\) | 1.02664e7 | 0.484530 | ||||||||
\(853\) | 5.52250e6 | 0.259874 | 0.129937 | − | 0.991522i | \(-0.458522\pi\) | ||||
0.129937 | + | 0.991522i | \(0.458522\pi\) | |||||||
\(854\) | 85221.6 | 0.00399857 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.65851e7 | 0.773632 | ||||||||
\(857\) | −2.02109e7 | −0.940014 | −0.470007 | − | 0.882663i | \(-0.655749\pi\) | ||||
−0.470007 | + | 0.882663i | \(0.655749\pi\) | |||||||
\(858\) | 294326. | 0.0136493 | ||||||||
\(859\) | 2.05904e7 | 0.952097 | 0.476048 | − | 0.879419i | \(-0.342069\pi\) | ||||
0.476048 | + | 0.879419i | \(0.342069\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24602.6 | 0.00113103 | ||||||||
\(862\) | 1.49138e7 | 0.683630 | ||||||||
\(863\) | 1.59735e7 | 0.730086 | 0.365043 | − | 0.930991i | \(-0.381054\pi\) | ||||
0.365043 | + | 0.930991i | \(0.381054\pi\) | |||||||
\(864\) | −4.32806e6 | −0.197246 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −296866. | −0.0134513 | ||||||||
\(867\) | 9.42672e6 | 0.425905 | ||||||||
\(868\) | −120120. | −0.00541148 | ||||||||
\(869\) | −9.48304e6 | −0.425989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.28020e6 | −0.101842 | ||||||||
\(872\) | −6.03190e6 | −0.268635 | ||||||||
\(873\) | 2.71950e6 | 0.120768 | ||||||||
\(874\) | −5.77984e7 | −2.55940 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.82334e6 | −0.256396 | ||||||||
\(877\) | −1.40128e7 | −0.615215 | −0.307607 | − | 0.951513i | \(-0.599528\pi\) | ||||
−0.307607 | + | 0.951513i | \(0.599528\pi\) | |||||||
\(878\) | 3.80060e7 | 1.66386 | ||||||||
\(879\) | −2.60662e6 | −0.113790 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.71339e7 | −1.17780 | −0.588901 | − | 0.808205i | \(-0.700439\pi\) | ||||
−0.588901 | + | 0.808205i | \(0.700439\pi\) | |||||||
\(882\) | 9.64501e6 | 0.417476 | ||||||||
\(883\) | −1.60023e7 | −0.690687 | −0.345344 | − | 0.938476i | \(-0.612238\pi\) | ||||
−0.345344 | + | 0.938476i | \(0.612238\pi\) | |||||||
\(884\) | 426021. | 0.0183358 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.33224e7 | 1.42611 | ||||||||
\(887\) | −2.23865e7 | −0.955381 | −0.477690 | − | 0.878528i | \(-0.658526\pi\) | ||||
−0.477690 | + | 0.878528i | \(0.658526\pi\) | |||||||
\(888\) | 2.68182e6 | 0.114129 | ||||||||
\(889\) | −462542. | −0.0196289 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | −4.12358e6 | −0.173525 | ||||||||
\(893\) | 2.40692e7 | 1.01003 | ||||||||
\(894\) | 1.95764e7 | 0.819200 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −834975. | −0.0347459 | ||||||||
\(897\) | 1.32881e6 | 0.0551419 | ||||||||
\(898\) | −5.04042e7 | −2.08582 | ||||||||
\(899\) | 1.18682e7 | 0.489764 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.06573e7 | −0.437358 | ||||||||
\(902\) | −507399. | −0.0207651 | ||||||||
\(903\) | 799361. | 0.0326230 | ||||||||
\(904\) | 7.37075e6 | 0.299979 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.76821e6 | −0.233464 | ||||||||
\(907\) | 6.33552e6 | 0.255719 | 0.127860 | − | 0.991792i | \(-0.459189\pi\) | ||||
0.127860 | + | 0.991792i | \(0.459189\pi\) | |||||||
\(908\) | 1.55227e7 | 0.624816 | ||||||||
\(909\) | −1.64741e7 | −0.661290 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.57264e6 | 0.262388 | 0.131194 | − | 0.991357i | \(-0.458119\pi\) | ||||
0.131194 | + | 0.991357i | \(0.458119\pi\) | |||||||
\(912\) | 2.41187e7 | 0.960211 | ||||||||
\(913\) | −4.80545e6 | −0.190791 | ||||||||
\(914\) | 3.42324e7 | 1.35541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.65132e7 | 0.650267 | ||||||||
\(917\) | 1.49202e6 | 0.0585937 | ||||||||
\(918\) | −3.15601e6 | −0.123604 | ||||||||
\(919\) | −4.55407e7 | −1.77873 | −0.889366 | − | 0.457196i | \(-0.848854\pi\) | ||||
−0.889366 | + | 0.457196i | \(0.848854\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.47484e7 | 0.961388 | ||||||||
\(922\) | 7.35160e6 | 0.284809 | ||||||||
\(923\) | 2.37200e6 | 0.0916455 | ||||||||
\(924\) | 92270.6 | 0.00355536 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.24829e6 | 0.124488 | ||||||||
\(927\) | −7.77235e6 | −0.297066 | ||||||||
\(928\) | −4.97018e7 | −1.89453 | ||||||||
\(929\) | −3.24053e7 | −1.23190 | −0.615952 | − | 0.787784i | \(-0.711229\pi\) | ||||
−0.615952 | + | 0.787784i | \(0.711229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.52917e7 | −1.33444 | ||||||||
\(932\) | −8.04572e6 | −0.303407 | ||||||||
\(933\) | 6.02589e6 | 0.226630 | ||||||||
\(934\) | 1.43851e7 | 0.539567 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −299431. | −0.0111714 | ||||||||
\(937\) | −1.53794e7 | −0.572257 | −0.286129 | − | 0.958191i | \(-0.592368\pi\) | ||||
−0.286129 | + | 0.958191i | \(0.592368\pi\) | |||||||
\(938\) | −1.96330e6 | −0.0728585 | ||||||||
\(939\) | 4.12651e6 | 0.152728 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.92624e7 | −1.07730 | −0.538648 | − | 0.842531i | \(-0.681065\pi\) | ||||
−0.538648 | + | 0.842531i | \(0.681065\pi\) | |||||||
\(942\) | 5.18865e6 | 0.190514 | ||||||||
\(943\) | −2.29079e6 | −0.0838891 | ||||||||
\(944\) | 2.15625e7 | 0.787533 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.64859e7 | −0.598942 | ||||||||
\(947\) | −2.32692e7 | −0.843154 | −0.421577 | − | 0.906793i | \(-0.638523\pi\) | ||||
−0.421577 | + | 0.906793i | \(0.638523\pi\) | |||||||
\(948\) | −1.29237e7 | −0.467052 | ||||||||
\(949\) | −1.34545e6 | −0.0484956 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.52394e7 | −0.546408 | ||||||||
\(952\) | −273826. | −0.00979226 | ||||||||
\(953\) | −1.42689e7 | −0.508932 | −0.254466 | − | 0.967082i | \(-0.581900\pi\) | ||||
−0.254466 | + | 0.967082i | \(0.581900\pi\) | |||||||
\(954\) | −1.00342e7 | −0.356955 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.68992e7 | −0.598029 | ||||||||
\(957\) | −9.11663e6 | −0.321777 | ||||||||
\(958\) | −2.42212e7 | −0.852672 | ||||||||
\(959\) | 1.50688e6 | 0.0529092 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.66193e7 | −0.929798 | ||||||||
\(962\) | −830034. | −0.0289173 | ||||||||
\(963\) | 1.38456e7 | 0.481112 | ||||||||
\(964\) | −1.63373e7 | −0.566223 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.14414e6 | 0.0394489 | ||||||||
\(967\) | −4.25962e7 | −1.46489 | −0.732444 | − | 0.680827i | \(-0.761620\pi\) | ||||
−0.732444 | + | 0.680827i | \(0.761620\pi\) | |||||||
\(968\) | 1.42057e6 | 0.0487275 | ||||||||
\(969\) | 1.15480e7 | 0.395092 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.93095e7 | −1.33798 | −0.668990 | − | 0.743271i | \(-0.733273\pi\) | ||||
−0.668990 | + | 0.743271i | \(0.733273\pi\) | |||||||
\(972\) | −1.08192e6 | −0.0367306 | ||||||||
\(973\) | 1.92117e6 | 0.0650555 | ||||||||
\(974\) | −8.62205e6 | −0.291215 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.31125e6 | 0.111267 | ||||||||
\(977\) | 5.54613e7 | 1.85889 | 0.929444 | − | 0.368962i | \(-0.120287\pi\) | ||||
0.929444 | + | 0.368962i | \(0.120287\pi\) | |||||||
\(978\) | −1.13901e7 | −0.380786 | ||||||||
\(979\) | −6.57119e6 | −0.219123 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.03556e6 | −0.167061 | ||||||||
\(982\) | 3.44391e7 | 1.13965 | ||||||||
\(983\) | 5.37070e7 | 1.77275 | 0.886375 | − | 0.462968i | \(-0.153216\pi\) | ||||
0.886375 | + | 0.462968i | \(0.153216\pi\) | |||||||
\(984\) | 516200. | 0.0169954 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.62424e7 | −1.18720 | ||||||||
\(987\) | −476455. | −0.0155679 | ||||||||
\(988\) | −1.46770e6 | −0.0478348 | ||||||||
\(989\) | −7.44298e7 | −2.41967 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −803096. | −0.0259767 | −0.0129883 | − | 0.999916i | \(-0.504134\pi\) | ||||
−0.0129883 | + | 0.999916i | \(0.504134\pi\) | |||||||
\(992\) | −8.41677e6 | −0.271560 | ||||||||
\(993\) | 2.66732e7 | 0.858425 | ||||||||
\(994\) | 2.04235e6 | 0.0655638 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.54896e6 | −0.209182 | ||||||||
\(997\) | −6.90977e6 | −0.220154 | −0.110077 | − | 0.993923i | \(-0.535110\pi\) | ||||
−0.110077 | + | 0.993923i | \(0.535110\pi\) | |||||||
\(998\) | −4.97459e7 | −1.58100 | ||||||||
\(999\) | 2.23884e6 | 0.0709756 |
(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.q.1.2 | yes | 8 | |
5.4 | even | 2 | 825.6.a.p.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.p.1.7 | ✓ | 8 | 5.4 | even | 2 | ||
825.6.a.q.1.2 | yes | 8 | 1.1 | even | 1 | trivial |