Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,6,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("230.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(36.8882785570\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 774x^{3} - 197x^{2} + 66287x + 154128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-25.4526\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −25.4526 | −1.63278 | −0.816392 | − | 0.577498i | \(-0.804029\pi\) | ||||
−0.816392 | + | 0.577498i | \(0.804029\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 101.810 | 1.15455 | ||||||||
\(7\) | 169.151 | 1.30476 | 0.652379 | − | 0.757893i | \(-0.273771\pi\) | ||||
0.652379 | + | 0.757893i | \(0.273771\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 404.834 | 1.66598 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 240.544 | 0.599395 | 0.299698 | − | 0.954034i | \(-0.403114\pi\) | ||||
0.299698 | + | 0.954034i | \(0.403114\pi\) | |||||||
\(12\) | −407.241 | −0.816392 | ||||||||
\(13\) | 999.685 | 1.64061 | 0.820304 | − | 0.571928i | \(-0.193804\pi\) | ||||
0.820304 | + | 0.571928i | \(0.193804\pi\) | |||||||
\(14\) | −676.605 | −0.922603 | ||||||||
\(15\) | −636.315 | −0.730203 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 215.789 | 0.181095 | 0.0905475 | − | 0.995892i | \(-0.471138\pi\) | ||||
0.0905475 | + | 0.995892i | \(0.471138\pi\) | |||||||
\(18\) | −1619.34 | −1.17803 | ||||||||
\(19\) | 299.903 | 0.190589 | 0.0952943 | − | 0.995449i | \(-0.469621\pi\) | ||||
0.0952943 | + | 0.995449i | \(0.469621\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | −4305.33 | −2.13039 | ||||||||
\(22\) | −962.177 | −0.423836 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | 1628.97 | 0.577276 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −3998.74 | −1.16008 | ||||||||
\(27\) | −4119.09 | −1.08741 | ||||||||
\(28\) | 2706.42 | 0.652379 | ||||||||
\(29\) | −7682.61 | −1.69634 | −0.848172 | − | 0.529721i | \(-0.822297\pi\) | ||||
−0.848172 | + | 0.529721i | \(0.822297\pi\) | |||||||
\(30\) | 2545.26 | 0.516332 | ||||||||
\(31\) | −588.167 | −0.109925 | −0.0549625 | − | 0.998488i | \(-0.517504\pi\) | ||||
−0.0549625 | + | 0.998488i | \(0.517504\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −6122.47 | −0.978683 | ||||||||
\(34\) | −863.155 | −0.128053 | ||||||||
\(35\) | 4228.78 | 0.583505 | ||||||||
\(36\) | 6477.34 | 0.832991 | ||||||||
\(37\) | 5651.69 | 0.678694 | 0.339347 | − | 0.940661i | \(-0.389794\pi\) | ||||
0.339347 | + | 0.940661i | \(0.389794\pi\) | |||||||
\(38\) | −1199.61 | −0.134766 | ||||||||
\(39\) | −25444.6 | −2.67876 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | 6430.35 | 0.597414 | 0.298707 | − | 0.954345i | \(-0.403445\pi\) | ||||
0.298707 | + | 0.954345i | \(0.403445\pi\) | |||||||
\(42\) | 17221.3 | 1.50641 | ||||||||
\(43\) | 5905.18 | 0.487037 | 0.243519 | − | 0.969896i | \(-0.421698\pi\) | ||||
0.243519 | + | 0.969896i | \(0.421698\pi\) | |||||||
\(44\) | 3848.71 | 0.299698 | ||||||||
\(45\) | 10120.8 | 0.745050 | ||||||||
\(46\) | 2116.00 | 0.147442 | ||||||||
\(47\) | 460.615 | 0.0304154 | 0.0152077 | − | 0.999884i | \(-0.495159\pi\) | ||||
0.0152077 | + | 0.999884i | \(0.495159\pi\) | |||||||
\(48\) | −6515.86 | −0.408196 | ||||||||
\(49\) | 11805.1 | 0.702393 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −5492.38 | −0.295689 | ||||||||
\(52\) | 15995.0 | 0.820304 | ||||||||
\(53\) | 36032.9 | 1.76202 | 0.881008 | − | 0.473101i | \(-0.156865\pi\) | ||||
0.881008 | + | 0.473101i | \(0.156865\pi\) | |||||||
\(54\) | 16476.4 | 0.768912 | ||||||||
\(55\) | 6013.61 | 0.268058 | ||||||||
\(56\) | −10825.7 | −0.461302 | ||||||||
\(57\) | −7633.31 | −0.311190 | ||||||||
\(58\) | 30730.4 | 1.19950 | ||||||||
\(59\) | −34687.4 | −1.29731 | −0.648653 | − | 0.761084i | \(-0.724667\pi\) | ||||
−0.648653 | + | 0.761084i | \(0.724667\pi\) | |||||||
\(60\) | −10181.0 | −0.365102 | ||||||||
\(61\) | 21860.1 | 0.752189 | 0.376094 | − | 0.926581i | \(-0.377267\pi\) | ||||
0.376094 | + | 0.926581i | \(0.377267\pi\) | |||||||
\(62\) | 2352.67 | 0.0777287 | ||||||||
\(63\) | 68478.1 | 2.17370 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 24992.1 | 0.733702 | ||||||||
\(66\) | 24489.9 | 0.692033 | ||||||||
\(67\) | −14495.5 | −0.394499 | −0.197249 | − | 0.980353i | \(-0.563201\pi\) | ||||
−0.197249 | + | 0.980353i | \(0.563201\pi\) | |||||||
\(68\) | 3452.62 | 0.0905475 | ||||||||
\(69\) | 13464.4 | 0.340459 | ||||||||
\(70\) | −16915.1 | −0.412601 | ||||||||
\(71\) | 58307.9 | 1.37272 | 0.686359 | − | 0.727263i | \(-0.259208\pi\) | ||||
0.686359 | + | 0.727263i | \(0.259208\pi\) | |||||||
\(72\) | −25909.4 | −0.589014 | ||||||||
\(73\) | 42901.9 | 0.942257 | 0.471129 | − | 0.882065i | \(-0.343847\pi\) | ||||
0.471129 | + | 0.882065i | \(0.343847\pi\) | |||||||
\(74\) | −22606.8 | −0.479909 | ||||||||
\(75\) | −15907.9 | −0.326557 | ||||||||
\(76\) | 4798.45 | 0.0952943 | ||||||||
\(77\) | 40688.3 | 0.782066 | ||||||||
\(78\) | 101778. | 1.89417 | ||||||||
\(79\) | −60159.1 | −1.08451 | −0.542255 | − | 0.840214i | \(-0.682429\pi\) | ||||
−0.542255 | + | 0.840214i | \(0.682429\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 6466.82 | 0.109516 | ||||||||
\(82\) | −25721.4 | −0.422435 | ||||||||
\(83\) | −76998.4 | −1.22684 | −0.613418 | − | 0.789758i | \(-0.710206\pi\) | ||||
−0.613418 | + | 0.789758i | \(0.710206\pi\) | |||||||
\(84\) | −68885.3 | −1.06519 | ||||||||
\(85\) | 5394.72 | 0.0809881 | ||||||||
\(86\) | −23620.7 | −0.344387 | ||||||||
\(87\) | 195542. | 2.76976 | ||||||||
\(88\) | −15394.8 | −0.211918 | ||||||||
\(89\) | −79117.2 | −1.05876 | −0.529378 | − | 0.848386i | \(-0.677575\pi\) | ||||
−0.529378 | + | 0.848386i | \(0.677575\pi\) | |||||||
\(90\) | −40483.4 | −0.526830 | ||||||||
\(91\) | 169098. | 2.14060 | ||||||||
\(92\) | −8464.00 | −0.104257 | ||||||||
\(93\) | 14970.4 | 0.179484 | ||||||||
\(94\) | −1842.46 | −0.0215069 | ||||||||
\(95\) | 7497.58 | 0.0852338 | ||||||||
\(96\) | 26063.4 | 0.288638 | ||||||||
\(97\) | 39420.5 | 0.425395 | 0.212698 | − | 0.977118i | \(-0.431775\pi\) | ||||
0.212698 | + | 0.977118i | \(0.431775\pi\) | |||||||
\(98\) | −47220.5 | −0.496667 | ||||||||
\(99\) | 97380.5 | 0.998582 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 8515.21 | 0.0830600 | 0.0415300 | − | 0.999137i | \(-0.486777\pi\) | ||||
0.0415300 | + | 0.999137i | \(0.486777\pi\) | |||||||
\(102\) | 21969.5 | 0.209084 | ||||||||
\(103\) | −33578.8 | −0.311869 | −0.155935 | − | 0.987767i | \(-0.549839\pi\) | ||||
−0.155935 | + | 0.987767i | \(0.549839\pi\) | |||||||
\(104\) | −63979.8 | −0.580042 | ||||||||
\(105\) | −107633. | −0.952738 | ||||||||
\(106\) | −144132. | −1.24593 | ||||||||
\(107\) | −79790.6 | −0.673740 | −0.336870 | − | 0.941551i | \(-0.609368\pi\) | ||||
−0.336870 | + | 0.941551i | \(0.609368\pi\) | |||||||
\(108\) | −65905.4 | −0.543703 | ||||||||
\(109\) | 40944.8 | 0.330090 | 0.165045 | − | 0.986286i | \(-0.447223\pi\) | ||||
0.165045 | + | 0.986286i | \(0.447223\pi\) | |||||||
\(110\) | −24054.4 | −0.189545 | ||||||||
\(111\) | −143850. | −1.10816 | ||||||||
\(112\) | 43302.7 | 0.326189 | ||||||||
\(113\) | 79669.5 | 0.586943 | 0.293471 | − | 0.955968i | \(-0.405189\pi\) | ||||
0.293471 | + | 0.955968i | \(0.405189\pi\) | |||||||
\(114\) | 30533.2 | 0.220045 | ||||||||
\(115\) | −13225.0 | −0.0932505 | ||||||||
\(116\) | −122922. | −0.848172 | ||||||||
\(117\) | 404706. | 2.73322 | ||||||||
\(118\) | 138750. | 0.917334 | ||||||||
\(119\) | 36500.9 | 0.236285 | ||||||||
\(120\) | 40724.1 | 0.258166 | ||||||||
\(121\) | −103189. | −0.640725 | ||||||||
\(122\) | −87440.3 | −0.531878 | ||||||||
\(123\) | −163669. | −0.975447 | ||||||||
\(124\) | −9410.68 | −0.0549625 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −273912. | −1.53704 | ||||||||
\(127\) | 34102.4 | 0.187619 | 0.0938093 | − | 0.995590i | \(-0.470096\pi\) | ||||
0.0938093 | + | 0.995590i | \(0.470096\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −150302. | −0.795226 | ||||||||
\(130\) | −99968.5 | −0.518806 | ||||||||
\(131\) | 279481. | 1.42290 | 0.711450 | − | 0.702737i | \(-0.248039\pi\) | ||||
0.711450 | + | 0.702737i | \(0.248039\pi\) | |||||||
\(132\) | −97959.6 | −0.489341 | ||||||||
\(133\) | 50728.9 | 0.248672 | ||||||||
\(134\) | 57981.9 | 0.278953 | ||||||||
\(135\) | −102977. | −0.486303 | ||||||||
\(136\) | −13810.5 | −0.0640267 | ||||||||
\(137\) | 271428. | 1.23553 | 0.617766 | − | 0.786362i | \(-0.288038\pi\) | ||||
0.617766 | + | 0.786362i | \(0.288038\pi\) | |||||||
\(138\) | −53857.7 | −0.240741 | ||||||||
\(139\) | 212751. | 0.933973 | 0.466986 | − | 0.884264i | \(-0.345340\pi\) | ||||
0.466986 | + | 0.884264i | \(0.345340\pi\) | |||||||
\(140\) | 67660.5 | 0.291753 | ||||||||
\(141\) | −11723.8 | −0.0496617 | ||||||||
\(142\) | −233232. | −0.970659 | ||||||||
\(143\) | 240468. | 0.983372 | ||||||||
\(144\) | 103637. | 0.416496 | ||||||||
\(145\) | −192065. | −0.758628 | ||||||||
\(146\) | −171608. | −0.666276 | ||||||||
\(147\) | −300471. | −1.14686 | ||||||||
\(148\) | 90427.0 | 0.339347 | ||||||||
\(149\) | −188369. | −0.695093 | −0.347547 | − | 0.937663i | \(-0.612985\pi\) | ||||
−0.347547 | + | 0.937663i | \(0.612985\pi\) | |||||||
\(150\) | 63631.5 | 0.230910 | ||||||||
\(151\) | −296787. | −1.05926 | −0.529631 | − | 0.848228i | \(-0.677669\pi\) | ||||
−0.529631 | + | 0.848228i | \(0.677669\pi\) | |||||||
\(152\) | −19193.8 | −0.0673832 | ||||||||
\(153\) | 87358.6 | 0.301701 | ||||||||
\(154\) | −162753. | −0.553004 | ||||||||
\(155\) | −14704.2 | −0.0491600 | ||||||||
\(156\) | −407113. | −1.33938 | ||||||||
\(157\) | 310583. | 1.00561 | 0.502804 | − | 0.864401i | \(-0.332302\pi\) | ||||
0.502804 | + | 0.864401i | \(0.332302\pi\) | |||||||
\(158\) | 240636. | 0.766865 | ||||||||
\(159\) | −917131. | −2.87699 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −89481.0 | −0.272061 | ||||||||
\(162\) | −25867.3 | −0.0774396 | ||||||||
\(163\) | 562164. | 1.65727 | 0.828637 | − | 0.559787i | \(-0.189117\pi\) | ||||
0.828637 | + | 0.559787i | \(0.189117\pi\) | |||||||
\(164\) | 102886. | 0.298707 | ||||||||
\(165\) | −153062. | −0.437680 | ||||||||
\(166\) | 307994. | 0.867504 | ||||||||
\(167\) | −371802. | −1.03162 | −0.515811 | − | 0.856703i | \(-0.672509\pi\) | ||||
−0.515811 | + | 0.856703i | \(0.672509\pi\) | |||||||
\(168\) | 275541. | 0.753206 | ||||||||
\(169\) | 628077. | 1.69159 | ||||||||
\(170\) | −21578.9 | −0.0572673 | ||||||||
\(171\) | 121411. | 0.317517 | ||||||||
\(172\) | 94482.9 | 0.243519 | ||||||||
\(173\) | 694698. | 1.76474 | 0.882371 | − | 0.470555i | \(-0.155946\pi\) | ||||
0.882371 | + | 0.470555i | \(0.155946\pi\) | |||||||
\(174\) | −782169. | −1.95852 | ||||||||
\(175\) | 105719. | 0.260952 | ||||||||
\(176\) | 61579.3 | 0.149849 | ||||||||
\(177\) | 882885. | 2.11822 | ||||||||
\(178\) | 316469. | 0.748654 | ||||||||
\(179\) | −564212. | −1.31616 | −0.658082 | − | 0.752946i | \(-0.728632\pi\) | ||||
−0.658082 | + | 0.752946i | \(0.728632\pi\) | |||||||
\(180\) | 161934. | 0.372525 | ||||||||
\(181\) | −215759. | −0.489523 | −0.244762 | − | 0.969583i | \(-0.578710\pi\) | ||||
−0.244762 | + | 0.969583i | \(0.578710\pi\) | |||||||
\(182\) | −676392. | −1.51363 | ||||||||
\(183\) | −556395. | −1.22816 | ||||||||
\(184\) | 33856.0 | 0.0737210 | ||||||||
\(185\) | 141292. | 0.303521 | ||||||||
\(186\) | −59881.5 | −0.126914 | ||||||||
\(187\) | 51906.7 | 0.108547 | ||||||||
\(188\) | 7369.83 | 0.0152077 | ||||||||
\(189\) | −696749. | −1.41880 | ||||||||
\(190\) | −29990.3 | −0.0602694 | ||||||||
\(191\) | 87833.2 | 0.174211 | 0.0871054 | − | 0.996199i | \(-0.472238\pi\) | ||||
0.0871054 | + | 0.996199i | \(0.472238\pi\) | |||||||
\(192\) | −104254. | −0.204098 | ||||||||
\(193\) | −597918. | −1.15544 | −0.577721 | − | 0.816234i | \(-0.696058\pi\) | ||||
−0.577721 | + | 0.816234i | \(0.696058\pi\) | |||||||
\(194\) | −157682. | −0.300800 | ||||||||
\(195\) | −636114. | −1.19798 | ||||||||
\(196\) | 188882. | 0.351196 | ||||||||
\(197\) | 374115. | 0.686814 | 0.343407 | − | 0.939187i | \(-0.388419\pi\) | ||||
0.343407 | + | 0.939187i | \(0.388419\pi\) | |||||||
\(198\) | −389522. | −0.706104 | ||||||||
\(199\) | 477078. | 0.853998 | 0.426999 | − | 0.904252i | \(-0.359571\pi\) | ||||
0.426999 | + | 0.904252i | \(0.359571\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 368947. | 0.644131 | ||||||||
\(202\) | −34060.8 | −0.0587323 | ||||||||
\(203\) | −1.29952e6 | −2.21332 | ||||||||
\(204\) | −87878.1 | −0.147844 | ||||||||
\(205\) | 160759. | 0.267171 | ||||||||
\(206\) | 134315. | 0.220525 | ||||||||
\(207\) | −214157. | −0.347381 | ||||||||
\(208\) | 255919. | 0.410152 | ||||||||
\(209\) | 72140.0 | 0.114238 | ||||||||
\(210\) | 430533. | 0.673688 | ||||||||
\(211\) | −846061. | −1.30826 | −0.654132 | − | 0.756380i | \(-0.726966\pi\) | ||||
−0.654132 | + | 0.756380i | \(0.726966\pi\) | |||||||
\(212\) | 576527. | 0.881008 | ||||||||
\(213\) | −1.48409e6 | −2.24135 | ||||||||
\(214\) | 319163. | 0.476406 | ||||||||
\(215\) | 147630. | 0.217810 | ||||||||
\(216\) | 263622. | 0.384456 | ||||||||
\(217\) | −99489.2 | −0.143426 | ||||||||
\(218\) | −163779. | −0.233409 | ||||||||
\(219\) | −1.09196e6 | −1.53850 | ||||||||
\(220\) | 96217.7 | 0.134029 | ||||||||
\(221\) | 215721. | 0.297106 | ||||||||
\(222\) | 575400. | 0.783588 | ||||||||
\(223\) | −303728. | −0.408999 | −0.204499 | − | 0.978867i | \(-0.565557\pi\) | ||||
−0.204499 | + | 0.978867i | \(0.565557\pi\) | |||||||
\(224\) | −173211. | −0.230651 | ||||||||
\(225\) | 253021. | 0.333197 | ||||||||
\(226\) | −318678. | −0.415031 | ||||||||
\(227\) | −1.38861e6 | −1.78861 | −0.894304 | − | 0.447461i | \(-0.852328\pi\) | ||||
−0.894304 | + | 0.447461i | \(0.852328\pi\) | |||||||
\(228\) | −122133. | −0.155595 | ||||||||
\(229\) | 665265. | 0.838313 | 0.419156 | − | 0.907914i | \(-0.362326\pi\) | ||||
0.419156 | + | 0.907914i | \(0.362326\pi\) | |||||||
\(230\) | 52900.0 | 0.0659380 | ||||||||
\(231\) | −1.03562e6 | −1.27694 | ||||||||
\(232\) | 491687. | 0.599748 | ||||||||
\(233\) | −1.37961e6 | −1.66481 | −0.832407 | − | 0.554165i | \(-0.813038\pi\) | ||||
−0.832407 | + | 0.554165i | \(0.813038\pi\) | |||||||
\(234\) | −1.61883e6 | −1.93268 | ||||||||
\(235\) | 11515.4 | 0.0136022 | ||||||||
\(236\) | −554999. | −0.648653 | ||||||||
\(237\) | 1.53120e6 | 1.77077 | ||||||||
\(238\) | −146004. | −0.167079 | ||||||||
\(239\) | 1.22532e6 | 1.38757 | 0.693783 | − | 0.720184i | \(-0.255943\pi\) | ||||
0.693783 | + | 0.720184i | \(0.255943\pi\) | |||||||
\(240\) | −162897. | −0.182551 | ||||||||
\(241\) | 1.47454e6 | 1.63536 | 0.817681 | − | 0.575671i | \(-0.195259\pi\) | ||||
0.817681 | + | 0.575671i | \(0.195259\pi\) | |||||||
\(242\) | 412758. | 0.453061 | ||||||||
\(243\) | 836341. | 0.908590 | ||||||||
\(244\) | 349761. | 0.376094 | ||||||||
\(245\) | 295128. | 0.314120 | ||||||||
\(246\) | 654676. | 0.689745 | ||||||||
\(247\) | 299809. | 0.312681 | ||||||||
\(248\) | 37642.7 | 0.0388644 | ||||||||
\(249\) | 1.95981e6 | 2.00316 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | 1.36196e6 | 1.36452 | 0.682259 | − | 0.731111i | \(-0.260998\pi\) | ||||
0.682259 | + | 0.731111i | \(0.260998\pi\) | |||||||
\(252\) | 1.09565e6 | 1.08685 | ||||||||
\(253\) | −127248. | −0.124983 | ||||||||
\(254\) | −136410. | −0.132666 | ||||||||
\(255\) | −137309. | −0.132236 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.46440e6 | 1.38302 | 0.691508 | − | 0.722369i | \(-0.256947\pi\) | ||||
0.691508 | + | 0.722369i | \(0.256947\pi\) | |||||||
\(258\) | 601208. | 0.562310 | ||||||||
\(259\) | 955990. | 0.885531 | ||||||||
\(260\) | 399874. | 0.366851 | ||||||||
\(261\) | −3.11018e6 | −2.82608 | ||||||||
\(262\) | −1.11792e6 | −1.00614 | ||||||||
\(263\) | −190615. | −0.169930 | −0.0849648 | − | 0.996384i | \(-0.527078\pi\) | ||||
−0.0849648 | + | 0.996384i | \(0.527078\pi\) | |||||||
\(264\) | 391838. | 0.346017 | ||||||||
\(265\) | 900824. | 0.787998 | ||||||||
\(266\) | −202916. | −0.175838 | ||||||||
\(267\) | 2.01374e6 | 1.72872 | ||||||||
\(268\) | −231928. | −0.197249 | ||||||||
\(269\) | 2.19576e6 | 1.85014 | 0.925070 | − | 0.379798i | \(-0.124006\pi\) | ||||
0.925070 | + | 0.379798i | \(0.124006\pi\) | |||||||
\(270\) | 411909. | 0.343868 | ||||||||
\(271\) | 907122. | 0.750313 | 0.375156 | − | 0.926962i | \(-0.377589\pi\) | ||||
0.375156 | + | 0.926962i | \(0.377589\pi\) | |||||||
\(272\) | 55241.9 | 0.0452737 | ||||||||
\(273\) | −4.30398e6 | −3.49513 | ||||||||
\(274\) | −1.08571e6 | −0.873653 | ||||||||
\(275\) | 150340. | 0.119879 | ||||||||
\(276\) | 215431. | 0.170229 | ||||||||
\(277\) | 1.78919e6 | 1.40106 | 0.700529 | − | 0.713624i | \(-0.252948\pi\) | ||||
0.700529 | + | 0.713624i | \(0.252948\pi\) | |||||||
\(278\) | −851003. | −0.660419 | ||||||||
\(279\) | −238110. | −0.183133 | ||||||||
\(280\) | −270642. | −0.206300 | ||||||||
\(281\) | 2.52548e6 | 1.90800 | 0.953999 | − | 0.299810i | \(-0.0969231\pi\) | ||||
0.953999 | + | 0.299810i | \(0.0969231\pi\) | |||||||
\(282\) | 46895.3 | 0.0351161 | ||||||||
\(283\) | 1.64560e6 | 1.22140 | 0.610700 | − | 0.791862i | \(-0.290888\pi\) | ||||
0.610700 | + | 0.791862i | \(0.290888\pi\) | |||||||
\(284\) | 932926. | 0.686359 | ||||||||
\(285\) | −190833. | −0.139168 | ||||||||
\(286\) | −961874. | −0.695349 | ||||||||
\(287\) | 1.08770e6 | 0.779480 | ||||||||
\(288\) | −414550. | −0.294507 | ||||||||
\(289\) | −1.37329e6 | −0.967205 | ||||||||
\(290\) | 768261. | 0.536431 | ||||||||
\(291\) | −1.00335e6 | −0.694578 | ||||||||
\(292\) | 686430. | 0.471129 | ||||||||
\(293\) | −1.55555e6 | −1.05856 | −0.529279 | − | 0.848448i | \(-0.677538\pi\) | ||||
−0.529279 | + | 0.848448i | \(0.677538\pi\) | |||||||
\(294\) | 1.20188e6 | 0.810950 | ||||||||
\(295\) | −867186. | −0.580173 | ||||||||
\(296\) | −361708. | −0.239955 | ||||||||
\(297\) | −990823. | −0.651786 | ||||||||
\(298\) | 753475. | 0.491505 | ||||||||
\(299\) | −528833. | −0.342090 | ||||||||
\(300\) | −254526. | −0.163278 | ||||||||
\(301\) | 998868. | 0.635466 | ||||||||
\(302\) | 1.18715e6 | 0.749011 | ||||||||
\(303\) | −216734. | −0.135619 | ||||||||
\(304\) | 76775.2 | 0.0476471 | ||||||||
\(305\) | 546502. | 0.336389 | ||||||||
\(306\) | −349434. | −0.213335 | ||||||||
\(307\) | 952533. | 0.576812 | 0.288406 | − | 0.957508i | \(-0.406875\pi\) | ||||
0.288406 | + | 0.957508i | \(0.406875\pi\) | |||||||
\(308\) | 651013. | 0.391033 | ||||||||
\(309\) | 854667. | 0.509215 | ||||||||
\(310\) | 58816.7 | 0.0347614 | ||||||||
\(311\) | −2.61902e6 | −1.53546 | −0.767728 | − | 0.640775i | \(-0.778613\pi\) | ||||
−0.767728 | + | 0.640775i | \(0.778613\pi\) | |||||||
\(312\) | 1.62845e6 | 0.947084 | ||||||||
\(313\) | −1.07061e6 | −0.617691 | −0.308846 | − | 0.951112i | \(-0.599943\pi\) | ||||
−0.308846 | + | 0.951112i | \(0.599943\pi\) | |||||||
\(314\) | −1.24233e6 | −0.711072 | ||||||||
\(315\) | 1.71195e6 | 0.972110 | ||||||||
\(316\) | −962546. | −0.542255 | ||||||||
\(317\) | 1.11608e6 | 0.623802 | 0.311901 | − | 0.950115i | \(-0.399034\pi\) | ||||
0.311901 | + | 0.950115i | \(0.399034\pi\) | |||||||
\(318\) | 3.66853e6 | 2.03434 | ||||||||
\(319\) | −1.84801e6 | −1.01678 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 2.03088e6 | 1.10007 | ||||||||
\(322\) | 357924. | 0.192376 | ||||||||
\(323\) | 64715.7 | 0.0345146 | ||||||||
\(324\) | 103469. | 0.0547581 | ||||||||
\(325\) | 624803. | 0.328122 | ||||||||
\(326\) | −2.24866e6 | −1.17187 | ||||||||
\(327\) | −1.04215e6 | −0.538965 | ||||||||
\(328\) | −411542. | −0.211218 | ||||||||
\(329\) | 77913.5 | 0.0396847 | ||||||||
\(330\) | 612247. | 0.309487 | ||||||||
\(331\) | 1.65065e6 | 0.828102 | 0.414051 | − | 0.910254i | \(-0.364114\pi\) | ||||
0.414051 | + | 0.910254i | \(0.364114\pi\) | |||||||
\(332\) | −1.23197e6 | −0.613418 | ||||||||
\(333\) | 2.28800e6 | 1.13069 | ||||||||
\(334\) | 1.48721e6 | 0.729467 | ||||||||
\(335\) | −362387. | −0.176425 | ||||||||
\(336\) | −1.10217e6 | −0.532597 | ||||||||
\(337\) | 3.91464e6 | 1.87766 | 0.938830 | − | 0.344380i | \(-0.111911\pi\) | ||||
0.938830 | + | 0.344380i | \(0.111911\pi\) | |||||||
\(338\) | −2.51231e6 | −1.19614 | ||||||||
\(339\) | −2.02779e6 | −0.958351 | ||||||||
\(340\) | 86315.5 | 0.0404941 | ||||||||
\(341\) | −141480. | −0.0658885 | ||||||||
\(342\) | −485644. | −0.224519 | ||||||||
\(343\) | −846074. | −0.388305 | ||||||||
\(344\) | −377932. | −0.172194 | ||||||||
\(345\) | 336610. | 0.152258 | ||||||||
\(346\) | −2.77879e6 | −1.24786 | ||||||||
\(347\) | −3.61919e6 | −1.61357 | −0.806785 | − | 0.590845i | \(-0.798794\pi\) | ||||
−0.806785 | + | 0.590845i | \(0.798794\pi\) | |||||||
\(348\) | 3.12868e6 | 1.38488 | ||||||||
\(349\) | −2.65790e6 | −1.16809 | −0.584043 | − | 0.811723i | \(-0.698530\pi\) | ||||
−0.584043 | + | 0.811723i | \(0.698530\pi\) | |||||||
\(350\) | −422878. | −0.184521 | ||||||||
\(351\) | −4.11779e6 | −1.78401 | ||||||||
\(352\) | −246317. | −0.105959 | ||||||||
\(353\) | −2.77508e6 | −1.18533 | −0.592664 | − | 0.805450i | \(-0.701924\pi\) | ||||
−0.592664 | + | 0.805450i | \(0.701924\pi\) | |||||||
\(354\) | −3.53154e6 | −1.49781 | ||||||||
\(355\) | 1.45770e6 | 0.613898 | ||||||||
\(356\) | −1.26588e6 | −0.529378 | ||||||||
\(357\) | −929042. | −0.385802 | ||||||||
\(358\) | 2.25685e6 | 0.930668 | ||||||||
\(359\) | −3.79810e6 | −1.55536 | −0.777678 | − | 0.628662i | \(-0.783603\pi\) | ||||
−0.777678 | + | 0.628662i | \(0.783603\pi\) | |||||||
\(360\) | −647734. | −0.263415 | ||||||||
\(361\) | −2.38616e6 | −0.963676 | ||||||||
\(362\) | 863038. | 0.346145 | ||||||||
\(363\) | 2.62644e6 | 1.04617 | ||||||||
\(364\) | 2.70557e6 | 1.07030 | ||||||||
\(365\) | 1.07255e6 | 0.421390 | ||||||||
\(366\) | 2.22558e6 | 0.868441 | ||||||||
\(367\) | −182257. | −0.0706350 | −0.0353175 | − | 0.999376i | \(-0.511244\pi\) | ||||
−0.0353175 | + | 0.999376i | \(0.511244\pi\) | |||||||
\(368\) | −135424. | −0.0521286 | ||||||||
\(369\) | 2.60322e6 | 0.995281 | ||||||||
\(370\) | −565169. | −0.214622 | ||||||||
\(371\) | 6.09501e6 | 2.29901 | ||||||||
\(372\) | 239526. | 0.0897419 | ||||||||
\(373\) | 3.35300e6 | 1.24785 | 0.623924 | − | 0.781485i | \(-0.285537\pi\) | ||||
0.623924 | + | 0.781485i | \(0.285537\pi\) | |||||||
\(374\) | −207627. | −0.0767546 | ||||||||
\(375\) | −397697. | −0.146041 | ||||||||
\(376\) | −29479.3 | −0.0107535 | ||||||||
\(377\) | −7.68019e6 | −2.78303 | ||||||||
\(378\) | 2.78699e6 | 1.00324 | ||||||||
\(379\) | 3.74552e6 | 1.33941 | 0.669706 | − | 0.742626i | \(-0.266420\pi\) | ||||
0.669706 | + | 0.742626i | \(0.266420\pi\) | |||||||
\(380\) | 119961. | 0.0426169 | ||||||||
\(381\) | −867994. | −0.306341 | ||||||||
\(382\) | −351333. | −0.123186 | ||||||||
\(383\) | −5.35082e6 | −1.86390 | −0.931951 | − | 0.362584i | \(-0.881894\pi\) | ||||
−0.931951 | + | 0.362584i | \(0.881894\pi\) | |||||||
\(384\) | 417015. | 0.144319 | ||||||||
\(385\) | 1.01721e6 | 0.349750 | ||||||||
\(386\) | 2.39167e6 | 0.817021 | ||||||||
\(387\) | 2.39062e6 | 0.811396 | ||||||||
\(388\) | 630728. | 0.212698 | ||||||||
\(389\) | −412875. | −0.138339 | −0.0691695 | − | 0.997605i | \(-0.522035\pi\) | ||||
−0.0691695 | + | 0.997605i | \(0.522035\pi\) | |||||||
\(390\) | 2.54446e6 | 0.847098 | ||||||||
\(391\) | −114152. | −0.0377609 | ||||||||
\(392\) | −755528. | −0.248333 | ||||||||
\(393\) | −7.11352e6 | −2.32329 | ||||||||
\(394\) | −1.49646e6 | −0.485651 | ||||||||
\(395\) | −1.50398e6 | −0.485008 | ||||||||
\(396\) | 1.55809e6 | 0.499291 | ||||||||
\(397\) | 368652. | 0.117393 | 0.0586963 | − | 0.998276i | \(-0.481306\pi\) | ||||
0.0586963 | + | 0.998276i | \(0.481306\pi\) | |||||||
\(398\) | −1.90831e6 | −0.603868 | ||||||||
\(399\) | −1.29118e6 | −0.406027 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −3.55558e6 | −1.10420 | −0.552102 | − | 0.833776i | \(-0.686174\pi\) | ||||
−0.552102 | + | 0.833776i | \(0.686174\pi\) | |||||||
\(402\) | −1.47579e6 | −0.455469 | ||||||||
\(403\) | −587982. | −0.180344 | ||||||||
\(404\) | 136243. | 0.0415300 | ||||||||
\(405\) | 161670. | 0.0489771 | ||||||||
\(406\) | 5.19809e6 | 1.56505 | ||||||||
\(407\) | 1.35948e6 | 0.406806 | ||||||||
\(408\) | 351512. | 0.104542 | ||||||||
\(409\) | 2.15855e6 | 0.638049 | 0.319025 | − | 0.947746i | \(-0.396645\pi\) | ||||
0.319025 | + | 0.947746i | \(0.396645\pi\) | |||||||
\(410\) | −643035. | −0.188919 | ||||||||
\(411\) | −6.90855e6 | −2.01736 | ||||||||
\(412\) | −537261. | −0.155935 | ||||||||
\(413\) | −5.86742e6 | −1.69267 | ||||||||
\(414\) | 856628. | 0.245636 | ||||||||
\(415\) | −1.92496e6 | −0.548658 | ||||||||
\(416\) | −1.02368e6 | −0.290021 | ||||||||
\(417\) | −5.41506e6 | −1.52498 | ||||||||
\(418\) | −288560. | −0.0807784 | ||||||||
\(419\) | 4.89868e6 | 1.36315 | 0.681576 | − | 0.731748i | \(-0.261295\pi\) | ||||
0.681576 | + | 0.731748i | \(0.261295\pi\) | |||||||
\(420\) | −1.72213e6 | −0.476369 | ||||||||
\(421\) | 3.43890e6 | 0.945615 | 0.472808 | − | 0.881166i | \(-0.343241\pi\) | ||||
0.472808 | + | 0.881166i | \(0.343241\pi\) | |||||||
\(422\) | 3.38424e6 | 0.925082 | ||||||||
\(423\) | 186472. | 0.0506715 | ||||||||
\(424\) | −2.30611e6 | −0.622967 | ||||||||
\(425\) | 134868. | 0.0362190 | ||||||||
\(426\) | 5.93635e6 | 1.58488 | ||||||||
\(427\) | 3.69766e6 | 0.981424 | ||||||||
\(428\) | −1.27665e6 | −0.336870 | ||||||||
\(429\) | −6.12054e6 | −1.60563 | ||||||||
\(430\) | −590518. | −0.154015 | ||||||||
\(431\) | 1.71556e6 | 0.444850 | 0.222425 | − | 0.974950i | \(-0.428603\pi\) | ||||
0.222425 | + | 0.974950i | \(0.428603\pi\) | |||||||
\(432\) | −1.05449e6 | −0.271852 | ||||||||
\(433\) | −313478. | −0.0803502 | −0.0401751 | − | 0.999193i | \(-0.512792\pi\) | ||||
−0.0401751 | + | 0.999193i | \(0.512792\pi\) | |||||||
\(434\) | 397957. | 0.101417 | ||||||||
\(435\) | 4.88856e6 | 1.23868 | ||||||||
\(436\) | 655116. | 0.165045 | ||||||||
\(437\) | −158649. | −0.0397405 | ||||||||
\(438\) | 4.36786e6 | 1.08789 | ||||||||
\(439\) | −6.71649e6 | −1.66334 | −0.831670 | − | 0.555271i | \(-0.812615\pi\) | ||||
−0.831670 | + | 0.555271i | \(0.812615\pi\) | |||||||
\(440\) | −384871. | −0.0947727 | ||||||||
\(441\) | 4.77911e6 | 1.17017 | ||||||||
\(442\) | −862883. | −0.210086 | ||||||||
\(443\) | 1.83925e6 | 0.445278 | 0.222639 | − | 0.974901i | \(-0.428533\pi\) | ||||
0.222639 | + | 0.974901i | \(0.428533\pi\) | |||||||
\(444\) | −2.30160e6 | −0.554080 | ||||||||
\(445\) | −1.97793e6 | −0.473490 | ||||||||
\(446\) | 1.21491e6 | 0.289206 | ||||||||
\(447\) | 4.79447e6 | 1.13494 | ||||||||
\(448\) | 692843. | 0.163095 | ||||||||
\(449\) | −2.63530e6 | −0.616899 | −0.308450 | − | 0.951241i | \(-0.599810\pi\) | ||||
−0.308450 | + | 0.951241i | \(0.599810\pi\) | |||||||
\(450\) | −1.01208e6 | −0.235606 | ||||||||
\(451\) | 1.54678e6 | 0.358087 | ||||||||
\(452\) | 1.27471e6 | 0.293471 | ||||||||
\(453\) | 7.55400e6 | 1.72954 | ||||||||
\(454\) | 5.55443e6 | 1.26474 | ||||||||
\(455\) | 4.22745e6 | 0.957304 | ||||||||
\(456\) | 488532. | 0.110022 | ||||||||
\(457\) | −401844. | −0.0900051 | −0.0450025 | − | 0.998987i | \(-0.514330\pi\) | ||||
−0.0450025 | + | 0.998987i | \(0.514330\pi\) | |||||||
\(458\) | −2.66106e6 | −0.592777 | ||||||||
\(459\) | −888853. | −0.196924 | ||||||||
\(460\) | −211600. | −0.0466252 | ||||||||
\(461\) | −4.16723e6 | −0.913261 | −0.456631 | − | 0.889656i | \(-0.650944\pi\) | ||||
−0.456631 | + | 0.889656i | \(0.650944\pi\) | |||||||
\(462\) | 4.14249e6 | 0.902936 | ||||||||
\(463\) | 7.48839e6 | 1.62344 | 0.811719 | − | 0.584048i | \(-0.198532\pi\) | ||||
0.811719 | + | 0.584048i | \(0.198532\pi\) | |||||||
\(464\) | −1.96675e6 | −0.424086 | ||||||||
\(465\) | 374259. | 0.0802676 | ||||||||
\(466\) | 5.51843e6 | 1.17720 | ||||||||
\(467\) | −3.22859e6 | −0.685047 | −0.342523 | − | 0.939509i | \(-0.611282\pi\) | ||||
−0.342523 | + | 0.939509i | \(0.611282\pi\) | |||||||
\(468\) | 6.47530e6 | 1.36661 | ||||||||
\(469\) | −2.45193e6 | −0.514725 | ||||||||
\(470\) | −46061.5 | −0.00961818 | ||||||||
\(471\) | −7.90514e6 | −1.64194 | ||||||||
\(472\) | 2.22000e6 | 0.458667 | ||||||||
\(473\) | 1.42046e6 | 0.291928 | ||||||||
\(474\) | −6.12482e6 | −1.25212 | ||||||||
\(475\) | 187439. | 0.0381177 | ||||||||
\(476\) | 584014. | 0.118143 | ||||||||
\(477\) | 1.45874e7 | 2.93549 | ||||||||
\(478\) | −4.90127e6 | −0.981157 | ||||||||
\(479\) | 154527. | 0.0307728 | 0.0153864 | − | 0.999882i | \(-0.495102\pi\) | ||||
0.0153864 | + | 0.999882i | \(0.495102\pi\) | |||||||
\(480\) | 651586. | 0.129083 | ||||||||
\(481\) | 5.64991e6 | 1.11347 | ||||||||
\(482\) | −5.89816e6 | −1.15638 | ||||||||
\(483\) | 2.27752e6 | 0.444216 | ||||||||
\(484\) | −1.65103e6 | −0.320363 | ||||||||
\(485\) | 985512. | 0.190243 | ||||||||
\(486\) | −3.34537e6 | −0.642470 | ||||||||
\(487\) | −4.84229e6 | −0.925185 | −0.462592 | − | 0.886571i | \(-0.653081\pi\) | ||||
−0.462592 | + | 0.886571i | \(0.653081\pi\) | |||||||
\(488\) | −1.39904e6 | −0.265939 | ||||||||
\(489\) | −1.43085e7 | −2.70597 | ||||||||
\(490\) | −1.18051e6 | −0.222116 | ||||||||
\(491\) | 4.55109e6 | 0.851945 | 0.425972 | − | 0.904736i | \(-0.359932\pi\) | ||||
0.425972 | + | 0.904736i | \(0.359932\pi\) | |||||||
\(492\) | −2.61870e6 | −0.487724 | ||||||||
\(493\) | −1.65782e6 | −0.307199 | ||||||||
\(494\) | −1.19923e6 | −0.221099 | ||||||||
\(495\) | 2.43451e6 | 0.446580 | ||||||||
\(496\) | −150571. | −0.0274813 | ||||||||
\(497\) | 9.86285e6 | 1.79107 | ||||||||
\(498\) | −7.83923e6 | −1.41645 | ||||||||
\(499\) | −2.22752e6 | −0.400470 | −0.200235 | − | 0.979748i | \(-0.564171\pi\) | ||||
−0.200235 | + | 0.979748i | \(0.564171\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 9.46332e6 | 1.68441 | ||||||||
\(502\) | −5.44783e6 | −0.964860 | ||||||||
\(503\) | −1.03865e7 | −1.83041 | −0.915206 | − | 0.402985i | \(-0.867973\pi\) | ||||
−0.915206 | + | 0.402985i | \(0.867973\pi\) | |||||||
\(504\) | −4.38260e6 | −0.768520 | ||||||||
\(505\) | 212880. | 0.0371456 | ||||||||
\(506\) | 508992. | 0.0883760 | ||||||||
\(507\) | −1.59862e7 | −2.76201 | ||||||||
\(508\) | 545639. | 0.0938093 | ||||||||
\(509\) | −9.14281e6 | −1.56417 | −0.782087 | − | 0.623169i | \(-0.785845\pi\) | ||||
−0.782087 | + | 0.623169i | \(0.785845\pi\) | |||||||
\(510\) | 549238. | 0.0935050 | ||||||||
\(511\) | 7.25691e6 | 1.22942 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −1.23533e6 | −0.207247 | ||||||||
\(514\) | −5.85760e6 | −0.977939 | ||||||||
\(515\) | −839470. | −0.139472 | ||||||||
\(516\) | −2.40483e6 | −0.397613 | ||||||||
\(517\) | 110798. | 0.0182308 | ||||||||
\(518\) | −3.82396e6 | −0.626165 | ||||||||
\(519\) | −1.76819e7 | −2.88144 | ||||||||
\(520\) | −1.59950e6 | −0.259403 | ||||||||
\(521\) | −2.83343e6 | −0.457319 | −0.228659 | − | 0.973507i | \(-0.573434\pi\) | ||||
−0.228659 | + | 0.973507i | \(0.573434\pi\) | |||||||
\(522\) | 1.24407e7 | 1.99834 | ||||||||
\(523\) | −1.24391e6 | −0.198854 | −0.0994268 | − | 0.995045i | \(-0.531701\pi\) | ||||
−0.0994268 | + | 0.995045i | \(0.531701\pi\) | |||||||
\(524\) | 4.47170e6 | 0.711450 | ||||||||
\(525\) | −2.69083e6 | −0.426077 | ||||||||
\(526\) | 762462. | 0.120158 | ||||||||
\(527\) | −126920. | −0.0199069 | ||||||||
\(528\) | −1.56735e6 | −0.244671 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −3.60329e6 | −0.557199 | ||||||||
\(531\) | −1.40427e7 | −2.16129 | ||||||||
\(532\) | 811663. | 0.124336 | ||||||||
\(533\) | 6.42833e6 | 0.980121 | ||||||||
\(534\) | −8.05495e6 | −1.22239 | ||||||||
\(535\) | −1.99477e6 | −0.301306 | ||||||||
\(536\) | 927710. | 0.139476 | ||||||||
\(537\) | 1.43607e7 | 2.14901 | ||||||||
\(538\) | −8.78304e6 | −1.30825 | ||||||||
\(539\) | 2.83965e6 | 0.421011 | ||||||||
\(540\) | −1.64764e6 | −0.243151 | ||||||||
\(541\) | −5.14966e6 | −0.756460 | −0.378230 | − | 0.925712i | \(-0.623467\pi\) | ||||
−0.378230 | + | 0.925712i | \(0.623467\pi\) | |||||||
\(542\) | −3.62849e6 | −0.530551 | ||||||||
\(543\) | 5.49164e6 | 0.799286 | ||||||||
\(544\) | −220968. | −0.0320134 | ||||||||
\(545\) | 1.02362e6 | 0.147621 | ||||||||
\(546\) | 1.72159e7 | 2.47143 | ||||||||
\(547\) | 3.02112e6 | 0.431718 | 0.215859 | − | 0.976425i | \(-0.430745\pi\) | ||||
0.215859 | + | 0.976425i | \(0.430745\pi\) | |||||||
\(548\) | 4.34285e6 | 0.617766 | ||||||||
\(549\) | 8.84969e6 | 1.25313 | ||||||||
\(550\) | −601361. | −0.0847673 | ||||||||
\(551\) | −2.30404e6 | −0.323304 | ||||||||
\(552\) | −861723. | −0.120370 | ||||||||
\(553\) | −1.01760e7 | −1.41502 | ||||||||
\(554\) | −7.15674e6 | −0.990697 | ||||||||
\(555\) | −3.59625e6 | −0.495584 | ||||||||
\(556\) | 3.40401e6 | 0.466986 | ||||||||
\(557\) | 2.17046e6 | 0.296425 | 0.148212 | − | 0.988956i | \(-0.452648\pi\) | ||||
0.148212 | + | 0.988956i | \(0.452648\pi\) | |||||||
\(558\) | 952440. | 0.129495 | ||||||||
\(559\) | 5.90332e6 | 0.799037 | ||||||||
\(560\) | 1.08257e6 | 0.145876 | ||||||||
\(561\) | −1.32116e6 | −0.177235 | ||||||||
\(562\) | −1.01019e7 | −1.34916 | ||||||||
\(563\) | 8.97877e6 | 1.19384 | 0.596920 | − | 0.802301i | \(-0.296391\pi\) | ||||
0.596920 | + | 0.802301i | \(0.296391\pi\) | |||||||
\(564\) | −187581. | −0.0248309 | ||||||||
\(565\) | 1.99174e6 | 0.262489 | ||||||||
\(566\) | −6.58239e6 | −0.863660 | ||||||||
\(567\) | 1.09387e6 | 0.142892 | ||||||||
\(568\) | −3.73171e6 | −0.485329 | ||||||||
\(569\) | 1.25296e7 | 1.62240 | 0.811199 | − | 0.584771i | \(-0.198816\pi\) | ||||
0.811199 | + | 0.584771i | \(0.198816\pi\) | |||||||
\(570\) | 763331. | 0.0984069 | ||||||||
\(571\) | 4.60900e6 | 0.591583 | 0.295792 | − | 0.955252i | \(-0.404417\pi\) | ||||
0.295792 | + | 0.955252i | \(0.404417\pi\) | |||||||
\(572\) | 3.84750e6 | 0.491686 | ||||||||
\(573\) | −2.23558e6 | −0.284449 | ||||||||
\(574\) | −4.35081e6 | −0.551176 | ||||||||
\(575\) | −330625. | −0.0417029 | ||||||||
\(576\) | 1.65820e6 | 0.208248 | ||||||||
\(577\) | −201007. | −0.0251346 | −0.0125673 | − | 0.999921i | \(-0.504000\pi\) | ||||
−0.0125673 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(578\) | 5.49317e6 | 0.683917 | ||||||||
\(579\) | 1.52186e7 | 1.88659 | ||||||||
\(580\) | −3.07304e6 | −0.379314 | ||||||||
\(581\) | −1.30244e7 | −1.60072 | ||||||||
\(582\) | 4.01341e6 | 0.491141 | ||||||||
\(583\) | 8.66752e6 | 1.05614 | ||||||||
\(584\) | −2.74572e6 | −0.333138 | ||||||||
\(585\) | 1.01177e7 | 1.22234 | ||||||||
\(586\) | 6.22220e6 | 0.748514 | ||||||||
\(587\) | 1.47103e6 | 0.176208 | 0.0881040 | − | 0.996111i | \(-0.471919\pi\) | ||||
0.0881040 | + | 0.996111i | \(0.471919\pi\) | |||||||
\(588\) | −4.80753e6 | −0.573428 | ||||||||
\(589\) | −176393. | −0.0209505 | ||||||||
\(590\) | 3.46874e6 | 0.410244 | ||||||||
\(591\) | −9.52219e6 | −1.12142 | ||||||||
\(592\) | 1.44683e6 | 0.169673 | ||||||||
\(593\) | 6.68412e6 | 0.780562 | 0.390281 | − | 0.920696i | \(-0.372378\pi\) | ||||
0.390281 | + | 0.920696i | \(0.372378\pi\) | |||||||
\(594\) | 3.96329e6 | 0.460882 | ||||||||
\(595\) | 912523. | 0.105670 | ||||||||
\(596\) | −3.01390e6 | −0.347547 | ||||||||
\(597\) | −1.21429e7 | −1.39439 | ||||||||
\(598\) | 2.11533e6 | 0.241894 | ||||||||
\(599\) | −3.51121e6 | −0.399843 | −0.199922 | − | 0.979812i | \(-0.564069\pi\) | ||||
−0.199922 | + | 0.979812i | \(0.564069\pi\) | |||||||
\(600\) | 1.01810e6 | 0.115455 | ||||||||
\(601\) | 2.60155e6 | 0.293797 | 0.146898 | − | 0.989152i | \(-0.453071\pi\) | ||||
0.146898 | + | 0.989152i | \(0.453071\pi\) | |||||||
\(602\) | −3.99547e6 | −0.449342 | ||||||||
\(603\) | −5.86826e6 | −0.657228 | ||||||||
\(604\) | −4.74860e6 | −0.529631 | ||||||||
\(605\) | −2.57974e6 | −0.286541 | ||||||||
\(606\) | 866936. | 0.0958971 | ||||||||
\(607\) | −9.10876e6 | −1.00343 | −0.501715 | − | 0.865033i | \(-0.667298\pi\) | ||||
−0.501715 | + | 0.865033i | \(0.667298\pi\) | |||||||
\(608\) | −307101. | −0.0336916 | ||||||||
\(609\) | 3.30762e7 | 3.61387 | ||||||||
\(610\) | −2.18601e6 | −0.237863 | ||||||||
\(611\) | 460469. | 0.0498997 | ||||||||
\(612\) | 1.39774e6 | 0.150851 | ||||||||
\(613\) | 1.26518e7 | 1.35988 | 0.679941 | − | 0.733267i | \(-0.262005\pi\) | ||||
0.679941 | + | 0.733267i | \(0.262005\pi\) | |||||||
\(614\) | −3.81013e6 | −0.407867 | ||||||||
\(615\) | −4.09173e6 | −0.436233 | ||||||||
\(616\) | −2.60405e6 | −0.276502 | ||||||||
\(617\) | −3.93498e6 | −0.416130 | −0.208065 | − | 0.978115i | \(-0.566717\pi\) | ||||
−0.208065 | + | 0.978115i | \(0.566717\pi\) | |||||||
\(618\) | −3.41867e6 | −0.360069 | ||||||||
\(619\) | −1.78491e7 | −1.87236 | −0.936181 | − | 0.351519i | \(-0.885665\pi\) | ||||
−0.936181 | + | 0.351519i | \(0.885665\pi\) | |||||||
\(620\) | −235267. | −0.0245800 | ||||||||
\(621\) | 2.17900e6 | 0.226740 | ||||||||
\(622\) | 1.04761e7 | 1.08573 | ||||||||
\(623\) | −1.33828e7 | −1.38142 | ||||||||
\(624\) | −6.51381e6 | −0.669689 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 4.28245e6 | 0.436774 | ||||||||
\(627\) | −1.83615e6 | −0.186526 | ||||||||
\(628\) | 4.96933e6 | 0.502804 | ||||||||
\(629\) | 1.21957e6 | 0.122908 | ||||||||
\(630\) | −6.84781e6 | −0.687386 | ||||||||
\(631\) | −9.46157e6 | −0.945997 | −0.472998 | − | 0.881063i | \(-0.656828\pi\) | ||||
−0.472998 | + | 0.881063i | \(0.656828\pi\) | |||||||
\(632\) | 3.85018e6 | 0.383432 | ||||||||
\(633\) | 2.15344e7 | 2.13611 | ||||||||
\(634\) | −4.46432e6 | −0.441095 | ||||||||
\(635\) | 852560. | 0.0839056 | ||||||||
\(636\) | −1.46741e7 | −1.43850 | ||||||||
\(637\) | 1.18014e7 | 1.15235 | ||||||||
\(638\) | 7.39203e6 | 0.718972 | ||||||||
\(639\) | 2.36050e7 | 2.28693 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | 4.84828e6 | 0.466061 | 0.233031 | − | 0.972469i | \(-0.425136\pi\) | ||||
0.233031 | + | 0.972469i | \(0.425136\pi\) | |||||||
\(642\) | −8.12351e6 | −0.777868 | ||||||||
\(643\) | 1.22864e7 | 1.17192 | 0.585959 | − | 0.810341i | \(-0.300718\pi\) | ||||
0.585959 | + | 0.810341i | \(0.300718\pi\) | |||||||
\(644\) | −1.43170e6 | −0.136030 | ||||||||
\(645\) | −3.75755e6 | −0.355636 | ||||||||
\(646\) | −258863. | −0.0244055 | ||||||||
\(647\) | 7.30521e6 | 0.686075 | 0.343038 | − | 0.939322i | \(-0.388544\pi\) | ||||
0.343038 | + | 0.939322i | \(0.388544\pi\) | |||||||
\(648\) | −413876. | −0.0387198 | ||||||||
\(649\) | −8.34387e6 | −0.777599 | ||||||||
\(650\) | −2.49921e6 | −0.232017 | ||||||||
\(651\) | 2.53226e6 | 0.234183 | ||||||||
\(652\) | 8.99463e6 | 0.828637 | ||||||||
\(653\) | −7.94070e6 | −0.728746 | −0.364373 | − | 0.931253i | \(-0.618717\pi\) | ||||
−0.364373 | + | 0.931253i | \(0.618717\pi\) | |||||||
\(654\) | 4.16860e6 | 0.381106 | ||||||||
\(655\) | 6.98703e6 | 0.636340 | ||||||||
\(656\) | 1.64617e6 | 0.149353 | ||||||||
\(657\) | 1.73681e7 | 1.56978 | ||||||||
\(658\) | −311654. | −0.0280613 | ||||||||
\(659\) | 1.72628e7 | 1.54845 | 0.774227 | − | 0.632908i | \(-0.218139\pi\) | ||||
0.774227 | + | 0.632908i | \(0.218139\pi\) | |||||||
\(660\) | −2.44899e6 | −0.218840 | ||||||||
\(661\) | −1.09394e7 | −0.973848 | −0.486924 | − | 0.873444i | \(-0.661881\pi\) | ||||
−0.486924 | + | 0.873444i | \(0.661881\pi\) | |||||||
\(662\) | −6.60258e6 | −0.585556 | ||||||||
\(663\) | −5.49065e6 | −0.485110 | ||||||||
\(664\) | 4.92790e6 | 0.433752 | ||||||||
\(665\) | 1.26822e6 | 0.111209 | ||||||||
\(666\) | −9.15198e6 | −0.799520 | ||||||||
\(667\) | 4.06410e6 | 0.353712 | ||||||||
\(668\) | −5.94883e6 | −0.515811 | ||||||||
\(669\) | 7.73065e6 | 0.667807 | ||||||||
\(670\) | 1.44955e6 | 0.124751 | ||||||||
\(671\) | 5.25831e6 | 0.450858 | ||||||||
\(672\) | 4.40866e6 | 0.376603 | ||||||||
\(673\) | −1.64061e7 | −1.39626 | −0.698132 | − | 0.715969i | \(-0.745985\pi\) | ||||
−0.698132 | + | 0.715969i | \(0.745985\pi\) | |||||||
\(674\) | −1.56586e7 | −1.32771 | ||||||||
\(675\) | −2.57443e6 | −0.217481 | ||||||||
\(676\) | 1.00492e7 | 0.845797 | ||||||||
\(677\) | −6.33131e6 | −0.530911 | −0.265456 | − | 0.964123i | \(-0.585522\pi\) | ||||
−0.265456 | + | 0.964123i | \(0.585522\pi\) | |||||||
\(678\) | 8.11117e6 | 0.677656 | ||||||||
\(679\) | 6.66802e6 | 0.555038 | ||||||||
\(680\) | −345262. | −0.0286336 | ||||||||
\(681\) | 3.53437e7 | 2.92041 | ||||||||
\(682\) | 565921. | 0.0465902 | ||||||||
\(683\) | 9.38546e6 | 0.769846 | 0.384923 | − | 0.922949i | \(-0.374228\pi\) | ||||
0.384923 | + | 0.922949i | \(0.374228\pi\) | |||||||
\(684\) | 1.94257e6 | 0.158759 | ||||||||
\(685\) | 6.78571e6 | 0.552547 | ||||||||
\(686\) | 3.38430e6 | 0.274573 | ||||||||
\(687\) | −1.69327e7 | −1.36878 | ||||||||
\(688\) | 1.51173e6 | 0.121759 | ||||||||
\(689\) | 3.60216e7 | 2.89078 | ||||||||
\(690\) | −1.34644e6 | −0.107663 | ||||||||
\(691\) | 1.09619e7 | 0.873351 | 0.436676 | − | 0.899619i | \(-0.356156\pi\) | ||||
0.436676 | + | 0.899619i | \(0.356156\pi\) | |||||||
\(692\) | 1.11152e7 | 0.882371 | ||||||||
\(693\) | 1.64720e7 | 1.30291 | ||||||||
\(694\) | 1.44768e7 | 1.14097 | ||||||||
\(695\) | 5.31877e6 | 0.417685 | ||||||||
\(696\) | −1.25147e7 | −0.979259 | ||||||||
\(697\) | 1.38760e6 | 0.108189 | ||||||||
\(698\) | 1.06316e7 | 0.825962 | ||||||||
\(699\) | 3.51146e7 | 2.71828 | ||||||||
\(700\) | 1.69151e6 | 0.130476 | ||||||||
\(701\) | −689912. | −0.0530272 | −0.0265136 | − | 0.999648i | \(-0.508441\pi\) | ||||
−0.0265136 | + | 0.999648i | \(0.508441\pi\) | |||||||
\(702\) | 1.64712e7 | 1.26148 | ||||||||
\(703\) | 1.69496e6 | 0.129351 | ||||||||
\(704\) | 985269. | 0.0749244 | ||||||||
\(705\) | −293096. | −0.0222094 | ||||||||
\(706\) | 1.11003e7 | 0.838153 | ||||||||
\(707\) | 1.44036e6 | 0.108373 | ||||||||
\(708\) | 1.41262e7 | 1.05911 | ||||||||
\(709\) | 1.63410e7 | 1.22085 | 0.610427 | − | 0.792072i | \(-0.290998\pi\) | ||||
0.610427 | + | 0.792072i | \(0.290998\pi\) | |||||||
\(710\) | −5.83079e6 | −0.434092 | ||||||||
\(711\) | −2.43544e7 | −1.80678 | ||||||||
\(712\) | 5.06350e6 | 0.374327 | ||||||||
\(713\) | 311141. | 0.0229210 | ||||||||
\(714\) | 3.71617e6 | 0.272803 | ||||||||
\(715\) | 6.01171e6 | 0.439778 | ||||||||
\(716\) | −9.02740e6 | −0.658082 | ||||||||
\(717\) | −3.11875e7 | −2.26560 | ||||||||
\(718\) | 1.51924e7 | 1.09980 | ||||||||
\(719\) | −1.10616e7 | −0.797988 | −0.398994 | − | 0.916954i | \(-0.630641\pi\) | ||||
−0.398994 | + | 0.916954i | \(0.630641\pi\) | |||||||
\(720\) | 2.59094e6 | 0.186263 | ||||||||
\(721\) | −5.67990e6 | −0.406914 | ||||||||
\(722\) | 9.54463e6 | 0.681422 | ||||||||
\(723\) | −3.75309e7 | −2.67019 | ||||||||
\(724\) | −3.45215e6 | −0.244762 | ||||||||
\(725\) | −4.80163e6 | −0.339269 | ||||||||
\(726\) | −1.05058e7 | −0.739751 | ||||||||
\(727\) | 8.18627e6 | 0.574447 | 0.287224 | − | 0.957864i | \(-0.407268\pi\) | ||||
0.287224 | + | 0.957864i | \(0.407268\pi\) | |||||||
\(728\) | −1.08223e7 | −0.756815 | ||||||||
\(729\) | −2.28585e7 | −1.59305 | ||||||||
\(730\) | −4.29019e6 | −0.297968 | ||||||||
\(731\) | 1.27427e6 | 0.0882000 | ||||||||
\(732\) | −8.90232e6 | −0.614081 | ||||||||
\(733\) | 4.88960e6 | 0.336135 | 0.168067 | − | 0.985776i | \(-0.446247\pi\) | ||||
0.168067 | + | 0.985776i | \(0.446247\pi\) | |||||||
\(734\) | 729029. | 0.0499465 | ||||||||
\(735\) | −7.51177e6 | −0.512890 | ||||||||
\(736\) | 541696. | 0.0368605 | ||||||||
\(737\) | −3.48680e6 | −0.236461 | ||||||||
\(738\) | −1.04129e7 | −0.703770 | ||||||||
\(739\) | 8.19880e6 | 0.552254 | 0.276127 | − | 0.961121i | \(-0.410949\pi\) | ||||
0.276127 | + | 0.961121i | \(0.410949\pi\) | |||||||
\(740\) | 2.26068e6 | 0.151761 | ||||||||
\(741\) | −7.63090e6 | −0.510541 | ||||||||
\(742\) | −2.43801e7 | −1.62564 | ||||||||
\(743\) | −1.06637e7 | −0.708657 | −0.354329 | − | 0.935121i | \(-0.615291\pi\) | ||||
−0.354329 | + | 0.935121i | \(0.615291\pi\) | |||||||
\(744\) | −958104. | −0.0634571 | ||||||||
\(745\) | −4.70922e6 | −0.310855 | ||||||||
\(746\) | −1.34120e7 | −0.882362 | ||||||||
\(747\) | −3.11716e7 | −2.04389 | ||||||||
\(748\) | 830508. | 0.0542737 | ||||||||
\(749\) | −1.34967e7 | −0.879068 | ||||||||
\(750\) | 1.59079e6 | 0.103266 | ||||||||
\(751\) | 1.59879e7 | 1.03441 | 0.517203 | − | 0.855863i | \(-0.326973\pi\) | ||||
0.517203 | + | 0.855863i | \(0.326973\pi\) | |||||||
\(752\) | 117917. | 0.00760384 | ||||||||
\(753\) | −3.46653e7 | −2.22796 | ||||||||
\(754\) | 3.07208e7 | 1.96790 | ||||||||
\(755\) | −7.41968e6 | −0.473716 | ||||||||
\(756\) | −1.11480e7 | −0.709401 | ||||||||
\(757\) | 1.70840e7 | 1.08355 | 0.541776 | − | 0.840523i | \(-0.317752\pi\) | ||||
0.541776 | + | 0.840523i | \(0.317752\pi\) | |||||||
\(758\) | −1.49821e7 | −0.947107 | ||||||||
\(759\) | 3.23879e6 | 0.204069 | ||||||||
\(760\) | −479845. | −0.0301347 | ||||||||
\(761\) | −7.03448e6 | −0.440322 | −0.220161 | − | 0.975464i | \(-0.570658\pi\) | ||||
−0.220161 | + | 0.975464i | \(0.570658\pi\) | |||||||
\(762\) | 3.47198e6 | 0.216615 | ||||||||
\(763\) | 6.92586e6 | 0.430687 | ||||||||
\(764\) | 1.40533e6 | 0.0871054 | ||||||||
\(765\) | 2.18396e6 | 0.134925 | ||||||||
\(766\) | 2.14033e7 | 1.31798 | ||||||||
\(767\) | −3.46765e7 | −2.12837 | ||||||||
\(768\) | −1.66806e6 | −0.102049 | ||||||||
\(769\) | 4.81600e6 | 0.293677 | 0.146839 | − | 0.989160i | \(-0.453090\pi\) | ||||
0.146839 | + | 0.989160i | \(0.453090\pi\) | |||||||
\(770\) | −4.06883e6 | −0.247311 | ||||||||
\(771\) | −3.72728e7 | −2.25816 | ||||||||
\(772\) | −9.56669e6 | −0.577721 | ||||||||
\(773\) | −2.25375e7 | −1.35661 | −0.678307 | − | 0.734778i | \(-0.737286\pi\) | ||||
−0.678307 | + | 0.734778i | \(0.737286\pi\) | |||||||
\(774\) | −9.56247e6 | −0.573743 | ||||||||
\(775\) | −367605. | −0.0219850 | ||||||||
\(776\) | −2.52291e6 | −0.150400 | ||||||||
\(777\) | −2.43324e7 | −1.44588 | ||||||||
\(778\) | 1.65150e6 | 0.0978204 | ||||||||
\(779\) | 1.92848e6 | 0.113860 | ||||||||
\(780\) | −1.01778e7 | −0.598988 | ||||||||
\(781\) | 1.40256e7 | 0.822801 | ||||||||
\(782\) | 456609. | 0.0267010 | ||||||||
\(783\) | 3.16454e7 | 1.84461 | ||||||||
\(784\) | 3.02211e6 | 0.175598 | ||||||||
\(785\) | 7.76457e6 | 0.449721 | ||||||||
\(786\) | 2.84541e7 | 1.64281 | ||||||||
\(787\) | −5.11852e6 | −0.294583 | −0.147291 | − | 0.989093i | \(-0.547056\pi\) | ||||
−0.147291 | + | 0.989093i | \(0.547056\pi\) | |||||||
\(788\) | 5.98584e6 | 0.343407 | ||||||||
\(789\) | 4.85166e6 | 0.277458 | ||||||||
\(790\) | 6.01591e6 | 0.342952 | ||||||||
\(791\) | 1.34762e7 | 0.765818 | ||||||||
\(792\) | −6.23235e6 | −0.353052 | ||||||||
\(793\) | 2.18532e7 | 1.23405 | ||||||||
\(794\) | −1.47461e6 | −0.0830091 | ||||||||
\(795\) | −2.29283e7 | −1.28663 | ||||||||
\(796\) | 7.63325e6 | 0.426999 | ||||||||
\(797\) | 9.29099e6 | 0.518103 | 0.259052 | − | 0.965863i | \(-0.416590\pi\) | ||||
0.259052 | + | 0.965863i | \(0.416590\pi\) | |||||||
\(798\) | 5.16473e6 | 0.287105 | ||||||||
\(799\) | 99395.4 | 0.00550807 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | −3.20293e7 | −1.76387 | ||||||||
\(802\) | 1.42223e7 | 0.780791 | ||||||||
\(803\) | 1.03198e7 | 0.564784 | ||||||||
\(804\) | 5.90315e6 | 0.322065 | ||||||||
\(805\) | −2.23702e6 | −0.121669 | ||||||||
\(806\) | 2.35193e6 | 0.127522 | ||||||||
\(807\) | −5.58878e7 | −3.02088 | ||||||||
\(808\) | −544973. | −0.0293661 | ||||||||
\(809\) | −2.28564e7 | −1.22783 | −0.613914 | − | 0.789373i | \(-0.710406\pi\) | ||||
−0.613914 | + | 0.789373i | \(0.710406\pi\) | |||||||
\(810\) | −646682. | −0.0346320 | ||||||||
\(811\) | −2.17000e7 | −1.15853 | −0.579266 | − | 0.815138i | \(-0.696661\pi\) | ||||
−0.579266 | + | 0.815138i | \(0.696661\pi\) | |||||||
\(812\) | −2.07924e7 | −1.10666 | ||||||||
\(813\) | −2.30886e7 | −1.22510 | ||||||||
\(814\) | −5.43793e6 | −0.287655 | ||||||||
\(815\) | 1.40541e7 | 0.741155 | ||||||||
\(816\) | −1.40605e6 | −0.0739222 | ||||||||
\(817\) | 1.77098e6 | 0.0928237 | ||||||||
\(818\) | −8.63421e6 | −0.451169 | ||||||||
\(819\) | 6.84565e7 | 3.56620 | ||||||||
\(820\) | 2.57214e6 | 0.133586 | ||||||||
\(821\) | 3.83945e6 | 0.198798 | 0.0993989 | − | 0.995048i | \(-0.468308\pi\) | ||||
0.0993989 | + | 0.995048i | \(0.468308\pi\) | |||||||
\(822\) | 2.76342e7 | 1.42649 | ||||||||
\(823\) | −2.86377e7 | −1.47380 | −0.736899 | − | 0.676002i | \(-0.763711\pi\) | ||||
−0.736899 | + | 0.676002i | \(0.763711\pi\) | |||||||
\(824\) | 2.14904e6 | 0.110262 | ||||||||
\(825\) | −3.82654e6 | −0.195737 | ||||||||
\(826\) | 2.34697e7 | 1.19690 | ||||||||
\(827\) | 2.90771e7 | 1.47838 | 0.739192 | − | 0.673495i | \(-0.235208\pi\) | ||||
0.739192 | + | 0.673495i | \(0.235208\pi\) | |||||||
\(828\) | −3.42651e6 | −0.173691 | ||||||||
\(829\) | −3.54717e7 | −1.79265 | −0.896326 | − | 0.443395i | \(-0.853774\pi\) | ||||
−0.896326 | + | 0.443395i | \(0.853774\pi\) | |||||||
\(830\) | 7.69984e6 | 0.387960 | ||||||||
\(831\) | −4.55394e7 | −2.28762 | ||||||||
\(832\) | 4.09471e6 | 0.205076 | ||||||||
\(833\) | 2.54741e6 | 0.127200 | ||||||||
\(834\) | 2.16602e7 | 1.07832 | ||||||||
\(835\) | −9.29505e6 | −0.461355 | ||||||||
\(836\) | 1.15424e6 | 0.0571189 | ||||||||
\(837\) | 2.42271e6 | 0.119533 | ||||||||
\(838\) | −1.95947e7 | −0.963894 | ||||||||
\(839\) | 1.77405e7 | 0.870081 | 0.435041 | − | 0.900411i | \(-0.356734\pi\) | ||||
0.435041 | + | 0.900411i | \(0.356734\pi\) | |||||||
\(840\) | 6.88853e6 | 0.336844 | ||||||||
\(841\) | 3.85114e7 | 1.87758 | ||||||||
\(842\) | −1.37556e7 | −0.668651 | ||||||||
\(843\) | −6.42800e7 | −3.11535 | ||||||||
\(844\) | −1.35370e7 | −0.654132 | ||||||||
\(845\) | 1.57019e7 | 0.756504 | ||||||||
\(846\) | −745889. | −0.0358301 | ||||||||
\(847\) | −1.74546e7 | −0.835991 | ||||||||
\(848\) | 9.22443e6 | 0.440504 | ||||||||
\(849\) | −4.18847e7 | −1.99428 | ||||||||
\(850\) | −539472. | −0.0256107 | ||||||||
\(851\) | −2.98974e6 | −0.141517 | ||||||||
\(852\) | −2.37454e7 | −1.12068 | ||||||||
\(853\) | 2.78617e7 | 1.31110 | 0.655549 | − | 0.755153i | \(-0.272437\pi\) | ||||
0.655549 | + | 0.755153i | \(0.272437\pi\) | |||||||
\(854\) | −1.47906e7 | −0.693972 | ||||||||
\(855\) | 3.03527e6 | 0.141998 | ||||||||
\(856\) | 5.10660e6 | 0.238203 | ||||||||
\(857\) | 6.75848e6 | 0.314338 | 0.157169 | − | 0.987572i | \(-0.449763\pi\) | ||||
0.157169 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(858\) | 2.44822e7 | 1.13536 | ||||||||
\(859\) | 4.15982e6 | 0.192350 | 0.0961749 | − | 0.995364i | \(-0.469339\pi\) | ||||
0.0961749 | + | 0.995364i | \(0.469339\pi\) | |||||||
\(860\) | 2.36207e6 | 0.108905 | ||||||||
\(861\) | −2.76848e7 | −1.27272 | ||||||||
\(862\) | −6.86226e6 | −0.314557 | ||||||||
\(863\) | −1.08955e7 | −0.497991 | −0.248995 | − | 0.968505i | \(-0.580100\pi\) | ||||
−0.248995 | + | 0.968505i | \(0.580100\pi\) | |||||||
\(864\) | 4.21795e6 | 0.192228 | ||||||||
\(865\) | 1.73675e7 | 0.789216 | ||||||||
\(866\) | 1.25391e6 | 0.0568161 | ||||||||
\(867\) | 3.49538e7 | 1.57924 | ||||||||
\(868\) | −1.59183e6 | −0.0717128 | ||||||||
\(869\) | −1.44709e7 | −0.650050 | ||||||||
\(870\) | −1.95542e7 | −0.875876 | ||||||||
\(871\) | −1.44909e7 | −0.647217 | ||||||||
\(872\) | −2.62047e6 | −0.116704 | ||||||||
\(873\) | 1.59587e7 | 0.708701 | ||||||||
\(874\) | 634595. | 0.0281008 | ||||||||
\(875\) | 2.64299e6 | 0.116701 | ||||||||
\(876\) | −1.74714e7 | −0.769251 | ||||||||
\(877\) | −1.39469e7 | −0.612322 | −0.306161 | − | 0.951980i | \(-0.599045\pi\) | ||||
−0.306161 | + | 0.951980i | \(0.599045\pi\) | |||||||
\(878\) | 2.68659e7 | 1.17616 | ||||||||
\(879\) | 3.95928e7 | 1.72840 | ||||||||
\(880\) | 1.53948e6 | 0.0670144 | ||||||||
\(881\) | 2.48016e7 | 1.07656 | 0.538282 | − | 0.842765i | \(-0.319074\pi\) | ||||
0.538282 | + | 0.842765i | \(0.319074\pi\) | |||||||
\(882\) | −1.91164e7 | −0.827438 | ||||||||
\(883\) | −2.41114e7 | −1.04069 | −0.520344 | − | 0.853957i | \(-0.674196\pi\) | ||||
−0.520344 | + | 0.853957i | \(0.674196\pi\) | |||||||
\(884\) | 3.45153e6 | 0.148553 | ||||||||
\(885\) | 2.20721e7 | 0.947297 | ||||||||
\(886\) | −7.35700e6 | −0.314859 | ||||||||
\(887\) | −5.49493e6 | −0.234506 | −0.117253 | − | 0.993102i | \(-0.537409\pi\) | ||||
−0.117253 | + | 0.993102i | \(0.537409\pi\) | |||||||
\(888\) | 9.20640e6 | 0.391794 | ||||||||
\(889\) | 5.76846e6 | 0.244797 | ||||||||
\(890\) | 7.91172e6 | 0.334808 | ||||||||
\(891\) | 1.55556e6 | 0.0656434 | ||||||||
\(892\) | −4.85964e6 | −0.204499 | ||||||||
\(893\) | 138140. | 0.00579682 | ||||||||
\(894\) | −1.91779e7 | −0.802522 | ||||||||
\(895\) | −1.41053e7 | −0.588606 | ||||||||
\(896\) | −2.77137e6 | −0.115325 | ||||||||
\(897\) | 1.34602e7 | 0.558560 | ||||||||
\(898\) | 1.05412e7 | 0.436214 | ||||||||
\(899\) | 4.51866e6 | 0.186471 | ||||||||
\(900\) | 4.04834e6 | 0.166598 | ||||||||
\(901\) | 7.77550e6 | 0.319092 | ||||||||
\(902\) | −6.18714e6 | −0.253206 | ||||||||
\(903\) | −2.54238e7 | −1.03758 | ||||||||
\(904\) | −5.09885e6 | −0.207516 | ||||||||
\(905\) | −5.39399e6 | −0.218922 | ||||||||
\(906\) | −3.02160e7 | −1.22297 | ||||||||
\(907\) | −3.06421e7 | −1.23680 | −0.618400 | − | 0.785863i | \(-0.712219\pi\) | ||||
−0.618400 | + | 0.785863i | \(0.712219\pi\) | |||||||
\(908\) | −2.22177e7 | −0.894304 | ||||||||
\(909\) | 3.44725e6 | 0.138377 | ||||||||
\(910\) | −1.69098e7 | −0.676916 | ||||||||
\(911\) | 3.88470e7 | 1.55082 | 0.775411 | − | 0.631457i | \(-0.217543\pi\) | ||||
0.775411 | + | 0.631457i | \(0.217543\pi\) | |||||||
\(912\) | −1.95413e6 | −0.0777975 | ||||||||
\(913\) | −1.85215e7 | −0.735360 | ||||||||
\(914\) | 1.60738e6 | 0.0636432 | ||||||||
\(915\) | −1.39099e7 | −0.549251 | ||||||||
\(916\) | 1.06442e7 | 0.419156 | ||||||||
\(917\) | 4.72746e7 | 1.85654 | ||||||||
\(918\) | 3.55541e6 | 0.139246 | ||||||||
\(919\) | 3.44865e7 | 1.34698 | 0.673489 | − | 0.739197i | \(-0.264795\pi\) | ||||
0.673489 | + | 0.739197i | \(0.264795\pi\) | |||||||
\(920\) | 846400. | 0.0329690 | ||||||||
\(921\) | −2.42444e7 | −0.941809 | ||||||||
\(922\) | 1.66689e7 | 0.645773 | ||||||||
\(923\) | 5.82895e7 | 2.25209 | ||||||||
\(924\) | −1.65700e7 | −0.638472 | ||||||||
\(925\) | 3.53231e6 | 0.135739 | ||||||||
\(926\) | −2.99535e7 | −1.14794 | ||||||||
\(927\) | −1.35938e7 | −0.519569 | ||||||||
\(928\) | 7.86699e6 | 0.299874 | ||||||||
\(929\) | −7.65498e6 | −0.291008 | −0.145504 | − | 0.989358i | \(-0.546480\pi\) | ||||
−0.145504 | + | 0.989358i | \(0.546480\pi\) | |||||||
\(930\) | −1.49704e6 | −0.0567578 | ||||||||
\(931\) | 3.54039e6 | 0.133868 | ||||||||
\(932\) | −2.20737e7 | −0.832407 | ||||||||
\(933\) | 6.66608e7 | 2.50707 | ||||||||
\(934\) | 1.29143e7 | 0.484401 | ||||||||
\(935\) | 1.29767e6 | 0.0485439 | ||||||||
\(936\) | −2.59012e7 | −0.966341 | ||||||||
\(937\) | 2.29765e6 | 0.0854938 | 0.0427469 | − | 0.999086i | \(-0.486389\pi\) | ||||
0.0427469 | + | 0.999086i | \(0.486389\pi\) | |||||||
\(938\) | 9.80770e6 | 0.363966 | ||||||||
\(939\) | 2.72498e7 | 1.00856 | ||||||||
\(940\) | 184246. | 0.00680108 | ||||||||
\(941\) | −3.43796e7 | −1.26569 | −0.632844 | − | 0.774280i | \(-0.718112\pi\) | ||||
−0.632844 | + | 0.774280i | \(0.718112\pi\) | |||||||
\(942\) | 3.16205e7 | 1.16103 | ||||||||
\(943\) | −3.40166e6 | −0.124569 | ||||||||
\(944\) | −8.87999e6 | −0.324326 | ||||||||
\(945\) | −1.74187e7 | −0.634507 | ||||||||
\(946\) | −5.68183e6 | −0.206424 | ||||||||
\(947\) | −2.34166e7 | −0.848495 | −0.424247 | − | 0.905546i | \(-0.639461\pi\) | ||||
−0.424247 | + | 0.905546i | \(0.639461\pi\) | |||||||
\(948\) | 2.44993e7 | 0.885385 | ||||||||
\(949\) | 4.28884e7 | 1.54587 | ||||||||
\(950\) | −749758. | −0.0269533 | ||||||||
\(951\) | −2.84071e7 | −1.01853 | ||||||||
\(952\) | −2.33606e6 | −0.0835394 | ||||||||
\(953\) | −2.72455e7 | −0.971769 | −0.485885 | − | 0.874023i | \(-0.661503\pi\) | ||||
−0.485885 | + | 0.874023i | \(0.661503\pi\) | |||||||
\(954\) | −5.83494e7 | −2.07570 | ||||||||
\(955\) | 2.19583e6 | 0.0779095 | ||||||||
\(956\) | 1.96051e7 | 0.693783 | ||||||||
\(957\) | 4.70366e7 | 1.66018 | ||||||||
\(958\) | −618110. | −0.0217597 | ||||||||
\(959\) | 4.59124e7 | 1.61207 | ||||||||
\(960\) | −2.60634e6 | −0.0912754 | ||||||||
\(961\) | −2.82832e7 | −0.987916 | ||||||||
\(962\) | −2.25996e7 | −0.787343 | ||||||||
\(963\) | −3.23020e7 | −1.12244 | ||||||||
\(964\) | 2.35926e7 | 0.817681 | ||||||||
\(965\) | −1.49480e7 | −0.516730 | ||||||||
\(966\) | −9.11009e6 | −0.314108 | ||||||||
\(967\) | −3.00757e7 | −1.03431 | −0.517154 | − | 0.855893i | \(-0.673008\pi\) | ||||
−0.517154 | + | 0.855893i | \(0.673008\pi\) | |||||||
\(968\) | 6.60413e6 | 0.226531 | ||||||||
\(969\) | −1.64718e6 | −0.0563549 | ||||||||
\(970\) | −3.94205e6 | −0.134522 | ||||||||
\(971\) | 5.24741e6 | 0.178606 | 0.0893032 | − | 0.996004i | \(-0.471536\pi\) | ||||
0.0893032 | + | 0.996004i | \(0.471536\pi\) | |||||||
\(972\) | 1.33815e7 | 0.454295 | ||||||||
\(973\) | 3.59871e7 | 1.21861 | ||||||||
\(974\) | 1.93692e7 | 0.654204 | ||||||||
\(975\) | −1.59029e7 | −0.535752 | ||||||||
\(976\) | 5.59618e6 | 0.188047 | ||||||||
\(977\) | 2.88518e7 | 0.967024 | 0.483512 | − | 0.875338i | \(-0.339361\pi\) | ||||
0.483512 | + | 0.875338i | \(0.339361\pi\) | |||||||
\(978\) | 5.72341e7 | 1.91341 | ||||||||
\(979\) | −1.90312e7 | −0.634613 | ||||||||
\(980\) | 4.72205e6 | 0.157060 | ||||||||
\(981\) | 1.65758e7 | 0.549924 | ||||||||
\(982\) | −1.82044e7 | −0.602416 | ||||||||
\(983\) | −1.84505e7 | −0.609008 | −0.304504 | − | 0.952511i | \(-0.598491\pi\) | ||||
−0.304504 | + | 0.952511i | \(0.598491\pi\) | |||||||
\(984\) | 1.04748e7 | 0.344873 | ||||||||
\(985\) | 9.35287e6 | 0.307153 | ||||||||
\(986\) | 6.63128e6 | 0.217223 | ||||||||
\(987\) | −1.98310e6 | −0.0647965 | ||||||||
\(988\) | 4.79694e6 | 0.156341 | ||||||||
\(989\) | −3.12384e6 | −0.101554 | ||||||||
\(990\) | −9.73805e6 | −0.315779 | ||||||||
\(991\) | 1.11449e7 | 0.360488 | 0.180244 | − | 0.983622i | \(-0.442311\pi\) | ||||
0.180244 | + | 0.983622i | \(0.442311\pi\) | |||||||
\(992\) | 602283. | 0.0194322 | ||||||||
\(993\) | −4.20132e7 | −1.35211 | ||||||||
\(994\) | −3.94514e7 | −1.26647 | ||||||||
\(995\) | 1.19270e7 | 0.381919 | ||||||||
\(996\) | 3.13569e7 | 1.00158 | ||||||||
\(997\) | −1.83396e7 | −0.584321 | −0.292160 | − | 0.956369i | \(-0.594374\pi\) | ||||
−0.292160 | + | 0.956369i | \(0.594374\pi\) | |||||||
\(998\) | 8.91007e6 | 0.283175 | ||||||||
\(999\) | −2.32798e7 | −0.738016 |
(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 | 230.6.a.f.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.6.a.f.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial |