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: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 1168x^{4} - 2857x^{3} + 297325x^{2} + 680040x - 8930700 \) |
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 | 1.5 | ||
Root | \(-19.8456\) 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 | ||||||||
\(3\) | 21.8456 | 1.40139 | 0.700697 | − | 0.713459i | \(-0.252872\pi\) | ||||
0.700697 | + | 0.713459i | \(0.252872\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 87.3823 | 0.990935 | ||||||||
\(7\) | 7.44621 | 0.0574368 | 0.0287184 | − | 0.999588i | \(-0.490857\pi\) | ||||
0.0287184 | + | 0.999588i | \(0.490857\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 234.229 | 0.963906 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | −441.618 | −1.10044 | −0.550219 | − | 0.835020i | \(-0.685456\pi\) | ||||
−0.550219 | + | 0.835020i | \(0.685456\pi\) | |||||||
\(12\) | 349.529 | 0.700697 | ||||||||
\(13\) | 785.235 | 1.28867 | 0.644334 | − | 0.764744i | \(-0.277135\pi\) | ||||
0.644334 | + | 0.764744i | \(0.277135\pi\) | |||||||
\(14\) | 29.7848 | 0.0406139 | ||||||||
\(15\) | 546.139 | 0.626723 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 632.287 | 0.530631 | 0.265315 | − | 0.964162i | \(-0.414524\pi\) | ||||
0.265315 | + | 0.964162i | \(0.414524\pi\) | |||||||
\(18\) | 936.917 | 0.681584 | ||||||||
\(19\) | 2085.12 | 1.32510 | 0.662548 | − | 0.749019i | \(-0.269475\pi\) | ||||
0.662548 | + | 0.749019i | \(0.269475\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 162.667 | 0.0804916 | ||||||||
\(22\) | −1766.47 | −0.778127 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 1398.12 | 0.495468 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 3140.94 | 0.911226 | ||||||||
\(27\) | −191.604 | −0.0505820 | ||||||||
\(28\) | 119.139 | 0.0287184 | ||||||||
\(29\) | 3126.22 | 0.690280 | 0.345140 | − | 0.938551i | \(-0.387831\pi\) | ||||
0.345140 | + | 0.938551i | \(0.387831\pi\) | |||||||
\(30\) | 2184.56 | 0.443160 | ||||||||
\(31\) | −416.399 | −0.0778225 | −0.0389113 | − | 0.999243i | \(-0.512389\pi\) | ||||
−0.0389113 | + | 0.999243i | \(0.512389\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −9647.41 | −1.54215 | ||||||||
\(34\) | 2529.15 | 0.375212 | ||||||||
\(35\) | 186.155 | 0.0256865 | ||||||||
\(36\) | 3747.67 | 0.481953 | ||||||||
\(37\) | 744.963 | 0.0894603 | 0.0447301 | − | 0.998999i | \(-0.485757\pi\) | ||||
0.0447301 | + | 0.998999i | \(0.485757\pi\) | |||||||
\(38\) | 8340.49 | 0.936985 | ||||||||
\(39\) | 17153.9 | 1.80593 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | −10179.3 | −0.945707 | −0.472853 | − | 0.881141i | \(-0.656776\pi\) | ||||
−0.472853 | + | 0.881141i | \(0.656776\pi\) | |||||||
\(42\) | 650.667 | 0.0569161 | ||||||||
\(43\) | 20597.2 | 1.69878 | 0.849390 | − | 0.527766i | \(-0.176970\pi\) | ||||
0.849390 | + | 0.527766i | \(0.176970\pi\) | |||||||
\(44\) | −7065.89 | −0.550219 | ||||||||
\(45\) | 5855.73 | 0.431072 | ||||||||
\(46\) | 2116.00 | 0.147442 | ||||||||
\(47\) | −17461.2 | −1.15300 | −0.576500 | − | 0.817097i | \(-0.695582\pi\) | ||||
−0.576500 | + | 0.817097i | \(0.695582\pi\) | |||||||
\(48\) | 5592.47 | 0.350349 | ||||||||
\(49\) | −16751.6 | −0.996701 | ||||||||
\(50\) | 2500.00 | 0.141421 | ||||||||
\(51\) | 13812.7 | 0.743623 | ||||||||
\(52\) | 12563.8 | 0.644334 | ||||||||
\(53\) | −30308.6 | −1.48210 | −0.741048 | − | 0.671452i | \(-0.765671\pi\) | ||||
−0.741048 | + | 0.671452i | \(0.765671\pi\) | |||||||
\(54\) | −766.417 | −0.0357669 | ||||||||
\(55\) | −11040.5 | −0.492131 | ||||||||
\(56\) | 476.557 | 0.0203070 | ||||||||
\(57\) | 45550.7 | 1.85698 | ||||||||
\(58\) | 12504.9 | 0.488102 | ||||||||
\(59\) | −20612.7 | −0.770913 | −0.385456 | − | 0.922726i | \(-0.625956\pi\) | ||||
−0.385456 | + | 0.922726i | \(0.625956\pi\) | |||||||
\(60\) | 8738.23 | 0.313361 | ||||||||
\(61\) | 6553.21 | 0.225491 | 0.112746 | − | 0.993624i | \(-0.464036\pi\) | ||||
0.112746 | + | 0.993624i | \(0.464036\pi\) | |||||||
\(62\) | −1665.60 | −0.0550288 | ||||||||
\(63\) | 1744.12 | 0.0553636 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 19630.9 | 0.576310 | ||||||||
\(66\) | −38589.6 | −1.09046 | ||||||||
\(67\) | 29514.0 | 0.803233 | 0.401616 | − | 0.915808i | \(-0.368449\pi\) | ||||
0.401616 | + | 0.915808i | \(0.368449\pi\) | |||||||
\(68\) | 10116.6 | 0.265315 | ||||||||
\(69\) | 11556.3 | 0.292211 | ||||||||
\(70\) | 744.621 | 0.0181631 | ||||||||
\(71\) | −54219.6 | −1.27647 | −0.638235 | − | 0.769842i | \(-0.720335\pi\) | ||||
−0.638235 | + | 0.769842i | \(0.720335\pi\) | |||||||
\(72\) | 14990.7 | 0.340792 | ||||||||
\(73\) | −81319.3 | −1.78602 | −0.893010 | − | 0.450037i | \(-0.851411\pi\) | ||||
−0.893010 | + | 0.450037i | \(0.851411\pi\) | |||||||
\(74\) | 2979.85 | 0.0632580 | ||||||||
\(75\) | 13653.5 | 0.280279 | ||||||||
\(76\) | 33362.0 | 0.662548 | ||||||||
\(77\) | −3288.38 | −0.0632056 | ||||||||
\(78\) | 68615.6 | 1.27699 | ||||||||
\(79\) | 99309.8 | 1.79029 | 0.895147 | − | 0.445771i | \(-0.147070\pi\) | ||||
0.895147 | + | 0.445771i | \(0.147070\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | −61103.4 | −1.03479 | ||||||||
\(82\) | −40717.0 | −0.668716 | ||||||||
\(83\) | 9250.19 | 0.147386 | 0.0736929 | − | 0.997281i | \(-0.476522\pi\) | ||||
0.0736929 | + | 0.997281i | \(0.476522\pi\) | |||||||
\(84\) | 2602.67 | 0.0402458 | ||||||||
\(85\) | 15807.2 | 0.237305 | ||||||||
\(86\) | 82388.8 | 1.20122 | ||||||||
\(87\) | 68294.2 | 0.967354 | ||||||||
\(88\) | −28263.6 | −0.389063 | ||||||||
\(89\) | 22988.9 | 0.307640 | 0.153820 | − | 0.988099i | \(-0.450842\pi\) | ||||
0.153820 | + | 0.988099i | \(0.450842\pi\) | |||||||
\(90\) | 23422.9 | 0.304814 | ||||||||
\(91\) | 5847.02 | 0.0740170 | ||||||||
\(92\) | 8464.00 | 0.104257 | ||||||||
\(93\) | −9096.47 | −0.109060 | ||||||||
\(94\) | −69844.8 | −0.815294 | ||||||||
\(95\) | 52128.1 | 0.592601 | ||||||||
\(96\) | 22369.9 | 0.247734 | ||||||||
\(97\) | −54909.5 | −0.592541 | −0.296271 | − | 0.955104i | \(-0.595743\pi\) | ||||
−0.296271 | + | 0.955104i | \(0.595743\pi\) | |||||||
\(98\) | −67006.2 | −0.704774 | ||||||||
\(99\) | −103440. | −1.06072 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 189171. | 1.84523 | 0.922614 | − | 0.385724i | \(-0.126048\pi\) | ||||
0.922614 | + | 0.385724i | \(0.126048\pi\) | |||||||
\(102\) | 55250.7 | 0.525821 | ||||||||
\(103\) | −25299.5 | −0.234974 | −0.117487 | − | 0.993074i | \(-0.537484\pi\) | ||||
−0.117487 | + | 0.993074i | \(0.537484\pi\) | |||||||
\(104\) | 50255.0 | 0.455613 | ||||||||
\(105\) | 4066.67 | 0.0359969 | ||||||||
\(106\) | −121234. | −1.04800 | ||||||||
\(107\) | −136708. | −1.15434 | −0.577169 | − | 0.816624i | \(-0.695843\pi\) | ||||
−0.577169 | + | 0.816624i | \(0.695843\pi\) | |||||||
\(108\) | −3065.67 | −0.0252910 | ||||||||
\(109\) | 85251.3 | 0.687282 | 0.343641 | − | 0.939101i | \(-0.388340\pi\) | ||||
0.343641 | + | 0.939101i | \(0.388340\pi\) | |||||||
\(110\) | −44161.8 | −0.347989 | ||||||||
\(111\) | 16274.1 | 0.125369 | ||||||||
\(112\) | 1906.23 | 0.0143592 | ||||||||
\(113\) | 9728.45 | 0.0716717 | 0.0358358 | − | 0.999358i | \(-0.488591\pi\) | ||||
0.0358358 | + | 0.999358i | \(0.488591\pi\) | |||||||
\(114\) | 182203. | 1.31309 | ||||||||
\(115\) | 13225.0 | 0.0932505 | ||||||||
\(116\) | 50019.6 | 0.345140 | ||||||||
\(117\) | 183925. | 1.24216 | ||||||||
\(118\) | −82450.9 | −0.545118 | ||||||||
\(119\) | 4708.14 | 0.0304777 | ||||||||
\(120\) | 34952.9 | 0.221580 | ||||||||
\(121\) | 33975.8 | 0.210963 | ||||||||
\(122\) | 26212.8 | 0.159446 | ||||||||
\(123\) | −222372. | −1.32531 | ||||||||
\(124\) | −6662.38 | −0.0389113 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 6976.48 | 0.0391480 | ||||||||
\(127\) | −170675. | −0.938990 | −0.469495 | − | 0.882935i | \(-0.655564\pi\) | ||||
−0.469495 | + | 0.882935i | \(0.655564\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 449958. | 2.38066 | ||||||||
\(130\) | 78523.5 | 0.407513 | ||||||||
\(131\) | 131578. | 0.669891 | 0.334945 | − | 0.942238i | \(-0.391282\pi\) | ||||
0.334945 | + | 0.942238i | \(0.391282\pi\) | |||||||
\(132\) | −154359. | −0.771074 | ||||||||
\(133\) | 15526.3 | 0.0761093 | ||||||||
\(134\) | 118056. | 0.567971 | ||||||||
\(135\) | −4790.11 | −0.0226210 | ||||||||
\(136\) | 40466.4 | 0.187606 | ||||||||
\(137\) | −143880. | −0.654936 | −0.327468 | − | 0.944862i | \(-0.606195\pi\) | ||||
−0.327468 | + | 0.944862i | \(0.606195\pi\) | |||||||
\(138\) | 46225.2 | 0.206624 | ||||||||
\(139\) | 43271.1 | 0.189960 | 0.0949798 | − | 0.995479i | \(-0.469721\pi\) | ||||
0.0949798 | + | 0.995479i | \(0.469721\pi\) | |||||||
\(140\) | 2978.48 | 0.0128433 | ||||||||
\(141\) | −381450. | −1.61581 | ||||||||
\(142\) | −216878. | −0.902600 | ||||||||
\(143\) | −346774. | −1.41810 | ||||||||
\(144\) | 59962.7 | 0.240976 | ||||||||
\(145\) | 78155.6 | 0.308703 | ||||||||
\(146\) | −325277. | −1.26291 | ||||||||
\(147\) | −365947. | −1.39677 | ||||||||
\(148\) | 11919.4 | 0.0447301 | ||||||||
\(149\) | −371769. | −1.37185 | −0.685927 | − | 0.727670i | \(-0.740603\pi\) | ||||
−0.685927 | + | 0.727670i | \(0.740603\pi\) | |||||||
\(150\) | 54613.9 | 0.198187 | ||||||||
\(151\) | −224317. | −0.800607 | −0.400303 | − | 0.916383i | \(-0.631095\pi\) | ||||
−0.400303 | + | 0.916383i | \(0.631095\pi\) | |||||||
\(152\) | 133448. | 0.468492 | ||||||||
\(153\) | 148100. | 0.511478 | ||||||||
\(154\) | −13153.5 | −0.0446931 | ||||||||
\(155\) | −10410.0 | −0.0348033 | ||||||||
\(156\) | 274463. | 0.902966 | ||||||||
\(157\) | −316299. | −1.02412 | −0.512058 | − | 0.858951i | \(-0.671117\pi\) | ||||
−0.512058 | + | 0.858951i | \(0.671117\pi\) | |||||||
\(158\) | 397239. | 1.26593 | ||||||||
\(159\) | −662109. | −2.07700 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 3939.04 | 0.0119764 | ||||||||
\(162\) | −244414. | −0.731708 | ||||||||
\(163\) | −486020. | −1.43280 | −0.716399 | − | 0.697691i | \(-0.754211\pi\) | ||||
−0.716399 | + | 0.697691i | \(0.754211\pi\) | |||||||
\(164\) | −162868. | −0.472853 | ||||||||
\(165\) | −241185. | −0.689669 | ||||||||
\(166\) | 37000.8 | 0.104217 | ||||||||
\(167\) | 483955. | 1.34281 | 0.671404 | − | 0.741092i | \(-0.265692\pi\) | ||||
0.671404 | + | 0.741092i | \(0.265692\pi\) | |||||||
\(168\) | 10410.7 | 0.0284581 | ||||||||
\(169\) | 245301. | 0.660666 | ||||||||
\(170\) | 63228.7 | 0.167800 | ||||||||
\(171\) | 488396. | 1.27727 | ||||||||
\(172\) | 329555. | 0.849390 | ||||||||
\(173\) | 162216. | 0.412077 | 0.206039 | − | 0.978544i | \(-0.433943\pi\) | ||||
0.206039 | + | 0.978544i | \(0.433943\pi\) | |||||||
\(174\) | 273177. | 0.684023 | ||||||||
\(175\) | 4653.88 | 0.0114874 | ||||||||
\(176\) | −113054. | −0.275109 | ||||||||
\(177\) | −450297. | −1.08035 | ||||||||
\(178\) | 91955.6 | 0.217535 | ||||||||
\(179\) | −285816. | −0.666736 | −0.333368 | − | 0.942797i | \(-0.608185\pi\) | ||||
−0.333368 | + | 0.942797i | \(0.608185\pi\) | |||||||
\(180\) | 93691.7 | 0.215536 | ||||||||
\(181\) | 46992.1 | 0.106617 | 0.0533087 | − | 0.998578i | \(-0.483023\pi\) | ||||
0.0533087 | + | 0.998578i | \(0.483023\pi\) | |||||||
\(182\) | 23388.1 | 0.0523379 | ||||||||
\(183\) | 143159. | 0.316002 | ||||||||
\(184\) | 33856.0 | 0.0737210 | ||||||||
\(185\) | 18624.1 | 0.0400078 | ||||||||
\(186\) | −36385.9 | −0.0771171 | ||||||||
\(187\) | −279230. | −0.583926 | ||||||||
\(188\) | −279379. | −0.576500 | ||||||||
\(189\) | −1426.73 | −0.00290527 | ||||||||
\(190\) | 208512. | 0.419032 | ||||||||
\(191\) | −511443. | −1.01441 | −0.507206 | − | 0.861825i | \(-0.669321\pi\) | ||||
−0.507206 | + | 0.861825i | \(0.669321\pi\) | |||||||
\(192\) | 89479.5 | 0.175174 | ||||||||
\(193\) | −502843. | −0.971716 | −0.485858 | − | 0.874038i | \(-0.661493\pi\) | ||||
−0.485858 | + | 0.874038i | \(0.661493\pi\) | |||||||
\(194\) | −219638. | −0.418990 | ||||||||
\(195\) | 428848. | 0.807638 | ||||||||
\(196\) | −268025. | −0.498351 | ||||||||
\(197\) | 514622. | 0.944763 | 0.472381 | − | 0.881394i | \(-0.343395\pi\) | ||||
0.472381 | + | 0.881394i | \(0.343395\pi\) | |||||||
\(198\) | −413760. | −0.750041 | ||||||||
\(199\) | 426847. | 0.764082 | 0.382041 | − | 0.924145i | \(-0.375221\pi\) | ||||
0.382041 | + | 0.924145i | \(0.375221\pi\) | |||||||
\(200\) | 40000.0 | 0.0707107 | ||||||||
\(201\) | 644751. | 1.12565 | ||||||||
\(202\) | 756682. | 1.30477 | ||||||||
\(203\) | 23278.5 | 0.0396474 | ||||||||
\(204\) | 221003. | 0.371811 | ||||||||
\(205\) | −254482. | −0.422933 | ||||||||
\(206\) | −101198. | −0.166152 | ||||||||
\(207\) | 123907. | 0.200988 | ||||||||
\(208\) | 201020. | 0.322167 | ||||||||
\(209\) | −920828. | −1.45819 | ||||||||
\(210\) | 16266.7 | 0.0254537 | ||||||||
\(211\) | 647680. | 1.00151 | 0.500754 | − | 0.865589i | \(-0.333056\pi\) | ||||
0.500754 | + | 0.865589i | \(0.333056\pi\) | |||||||
\(212\) | −484938. | −0.741048 | ||||||||
\(213\) | −1.18446e6 | −1.78884 | ||||||||
\(214\) | −546830. | −0.816241 | ||||||||
\(215\) | 514930. | 0.759717 | ||||||||
\(216\) | −12262.7 | −0.0178834 | ||||||||
\(217\) | −3100.59 | −0.00446988 | ||||||||
\(218\) | 341005. | 0.485981 | ||||||||
\(219\) | −1.77647e6 | −2.50292 | ||||||||
\(220\) | −176647. | −0.246065 | ||||||||
\(221\) | 496494. | 0.683807 | ||||||||
\(222\) | 65096.5 | 0.0886493 | ||||||||
\(223\) | −534158. | −0.719296 | −0.359648 | − | 0.933088i | \(-0.617103\pi\) | ||||
−0.359648 | + | 0.933088i | \(0.617103\pi\) | |||||||
\(224\) | 7624.92 | 0.0101535 | ||||||||
\(225\) | 146393. | 0.192781 | ||||||||
\(226\) | 38913.8 | 0.0506795 | ||||||||
\(227\) | −205929. | −0.265248 | −0.132624 | − | 0.991166i | \(-0.542340\pi\) | ||||
−0.132624 | + | 0.991166i | \(0.542340\pi\) | |||||||
\(228\) | 728811. | 0.928491 | ||||||||
\(229\) | −934046. | −1.17701 | −0.588504 | − | 0.808494i | \(-0.700283\pi\) | ||||
−0.588504 | + | 0.808494i | \(0.700283\pi\) | |||||||
\(230\) | 52900.0 | 0.0659380 | ||||||||
\(231\) | −71836.6 | −0.0885760 | ||||||||
\(232\) | 200078. | 0.244051 | ||||||||
\(233\) | −529838. | −0.639372 | −0.319686 | − | 0.947524i | \(-0.603577\pi\) | ||||
−0.319686 | + | 0.947524i | \(0.603577\pi\) | |||||||
\(234\) | 735700. | 0.878336 | ||||||||
\(235\) | −436530. | −0.515637 | ||||||||
\(236\) | −329803. | −0.385456 | ||||||||
\(237\) | 2.16948e6 | 2.50891 | ||||||||
\(238\) | 18832.6 | 0.0215510 | ||||||||
\(239\) | −796507. | −0.901975 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(240\) | 139812. | 0.156681 | ||||||||
\(241\) | 492031. | 0.545694 | 0.272847 | − | 0.962057i | \(-0.412035\pi\) | ||||
0.272847 | + | 0.962057i | \(0.412035\pi\) | |||||||
\(242\) | 135903. | 0.149174 | ||||||||
\(243\) | −1.28828e6 | −1.39957 | ||||||||
\(244\) | 104851. | 0.112746 | ||||||||
\(245\) | −418789. | −0.445738 | ||||||||
\(246\) | −889487. | −0.937134 | ||||||||
\(247\) | 1.63731e6 | 1.70761 | ||||||||
\(248\) | −26649.5 | −0.0275144 | ||||||||
\(249\) | 202076. | 0.206546 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | 1.50649e6 | 1.50932 | 0.754661 | − | 0.656115i | \(-0.227801\pi\) | ||||
0.754661 | + | 0.656115i | \(0.227801\pi\) | |||||||
\(252\) | 27905.9 | 0.0276818 | ||||||||
\(253\) | −233616. | −0.229457 | ||||||||
\(254\) | −682700. | −0.663966 | ||||||||
\(255\) | 345317. | 0.332558 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −512195. | −0.483730 | −0.241865 | − | 0.970310i | \(-0.577759\pi\) | ||||
−0.241865 | + | 0.970310i | \(0.577759\pi\) | |||||||
\(258\) | 1.79983e6 | 1.68338 | ||||||||
\(259\) | 5547.15 | 0.00513831 | ||||||||
\(260\) | 314094. | 0.288155 | ||||||||
\(261\) | 732253. | 0.665365 | ||||||||
\(262\) | 526311. | 0.473684 | ||||||||
\(263\) | −1.40580e6 | −1.25324 | −0.626622 | − | 0.779323i | \(-0.715563\pi\) | ||||
−0.626622 | + | 0.779323i | \(0.715563\pi\) | |||||||
\(264\) | −617434. | −0.545231 | ||||||||
\(265\) | −757715. | −0.662814 | ||||||||
\(266\) | 62105.0 | 0.0538174 | ||||||||
\(267\) | 502206. | 0.431125 | ||||||||
\(268\) | 472224. | 0.401616 | ||||||||
\(269\) | 476712. | 0.401675 | 0.200838 | − | 0.979625i | \(-0.435634\pi\) | ||||
0.200838 | + | 0.979625i | \(0.435634\pi\) | |||||||
\(270\) | −19160.4 | −0.0159954 | ||||||||
\(271\) | 918358. | 0.759607 | 0.379803 | − | 0.925067i | \(-0.375992\pi\) | ||||
0.379803 | + | 0.925067i | \(0.375992\pi\) | |||||||
\(272\) | 161866. | 0.132658 | ||||||||
\(273\) | 127732. | 0.103727 | ||||||||
\(274\) | −575520. | −0.463110 | ||||||||
\(275\) | −276012. | −0.220088 | ||||||||
\(276\) | 184901. | 0.146105 | ||||||||
\(277\) | 579006. | 0.453402 | 0.226701 | − | 0.973964i | \(-0.427206\pi\) | ||||
0.226701 | + | 0.973964i | \(0.427206\pi\) | |||||||
\(278\) | 173085. | 0.134322 | ||||||||
\(279\) | −97532.8 | −0.0750136 | ||||||||
\(280\) | 11913.9 | 0.00908155 | ||||||||
\(281\) | 1.30977e6 | 0.989531 | 0.494766 | − | 0.869026i | \(-0.335254\pi\) | ||||
0.494766 | + | 0.869026i | \(0.335254\pi\) | |||||||
\(282\) | −1.52580e6 | −1.14255 | ||||||||
\(283\) | 388018. | 0.287995 | 0.143998 | − | 0.989578i | \(-0.454004\pi\) | ||||
0.143998 | + | 0.989578i | \(0.454004\pi\) | |||||||
\(284\) | −867513. | −0.638235 | ||||||||
\(285\) | 1.13877e6 | 0.830468 | ||||||||
\(286\) | −1.38710e6 | −1.00275 | ||||||||
\(287\) | −75796.9 | −0.0543184 | ||||||||
\(288\) | 239851. | 0.170396 | ||||||||
\(289\) | −1.02007e6 | −0.718431 | ||||||||
\(290\) | 312622. | 0.218286 | ||||||||
\(291\) | −1.19953e6 | −0.830384 | ||||||||
\(292\) | −1.30111e6 | −0.893010 | ||||||||
\(293\) | 1.44959e6 | 0.986453 | 0.493227 | − | 0.869901i | \(-0.335817\pi\) | ||||
0.493227 | + | 0.869901i | \(0.335817\pi\) | |||||||
\(294\) | −1.46379e6 | −0.987666 | ||||||||
\(295\) | −515318. | −0.344763 | ||||||||
\(296\) | 47677.6 | 0.0316290 | ||||||||
\(297\) | 84616.0 | 0.0556623 | ||||||||
\(298\) | −1.48708e6 | −0.970048 | ||||||||
\(299\) | 415389. | 0.268706 | ||||||||
\(300\) | 218456. | 0.140139 | ||||||||
\(301\) | 153371. | 0.0975724 | ||||||||
\(302\) | −897267. | −0.566114 | ||||||||
\(303\) | 4.13254e6 | 2.58589 | ||||||||
\(304\) | 533791. | 0.331274 | ||||||||
\(305\) | 163830. | 0.100843 | ||||||||
\(306\) | 592401. | 0.361670 | ||||||||
\(307\) | 2.28279e6 | 1.38235 | 0.691177 | − | 0.722686i | \(-0.257093\pi\) | ||||
0.691177 | + | 0.722686i | \(0.257093\pi\) | |||||||
\(308\) | −52614.1 | −0.0316028 | ||||||||
\(309\) | −552683. | −0.329291 | ||||||||
\(310\) | −41639.9 | −0.0246096 | ||||||||
\(311\) | 2.19166e6 | 1.28491 | 0.642455 | − | 0.766323i | \(-0.277916\pi\) | ||||
0.642455 | + | 0.766323i | \(0.277916\pi\) | |||||||
\(312\) | 1.09785e6 | 0.638494 | ||||||||
\(313\) | 2.46402e6 | 1.42162 | 0.710810 | − | 0.703384i | \(-0.248329\pi\) | ||||
0.710810 | + | 0.703384i | \(0.248329\pi\) | |||||||
\(314\) | −1.26520e6 | −0.724159 | ||||||||
\(315\) | 43603.0 | 0.0247594 | ||||||||
\(316\) | 1.58896e6 | 0.895147 | ||||||||
\(317\) | 2.25250e6 | 1.25897 | 0.629487 | − | 0.777011i | \(-0.283265\pi\) | ||||
0.629487 | + | 0.777011i | \(0.283265\pi\) | |||||||
\(318\) | −2.64844e6 | −1.46866 | ||||||||
\(319\) | −1.38060e6 | −0.759610 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | −2.98646e6 | −1.61768 | ||||||||
\(322\) | 15756.2 | 0.00846859 | ||||||||
\(323\) | 1.31840e6 | 0.703137 | ||||||||
\(324\) | −977654. | −0.517396 | ||||||||
\(325\) | 490772. | 0.257734 | ||||||||
\(326\) | −1.94408e6 | −1.01314 | ||||||||
\(327\) | 1.86236e6 | 0.963152 | ||||||||
\(328\) | −651473. | −0.334358 | ||||||||
\(329\) | −130020. | −0.0662246 | ||||||||
\(330\) | −964741. | −0.487670 | ||||||||
\(331\) | 743598. | 0.373051 | 0.186525 | − | 0.982450i | \(-0.440277\pi\) | ||||
0.186525 | + | 0.982450i | \(0.440277\pi\) | |||||||
\(332\) | 148003. | 0.0736929 | ||||||||
\(333\) | 174492. | 0.0862313 | ||||||||
\(334\) | 1.93582e6 | 0.949509 | ||||||||
\(335\) | 737851. | 0.359217 | ||||||||
\(336\) | 41642.7 | 0.0201229 | ||||||||
\(337\) | 3.93157e6 | 1.88578 | 0.942891 | − | 0.333103i | \(-0.108096\pi\) | ||||
0.942891 | + | 0.333103i | \(0.108096\pi\) | |||||||
\(338\) | 981203. | 0.467162 | ||||||||
\(339\) | 212524. | 0.100440 | ||||||||
\(340\) | 252915. | 0.118653 | ||||||||
\(341\) | 183889. | 0.0856389 | ||||||||
\(342\) | 1.95359e6 | 0.903165 | ||||||||
\(343\) | −249884. | −0.114684 | ||||||||
\(344\) | 1.31822e6 | 0.600609 | ||||||||
\(345\) | 288908. | 0.130681 | ||||||||
\(346\) | 648864. | 0.291383 | ||||||||
\(347\) | 202520. | 0.0902909 | 0.0451455 | − | 0.998980i | \(-0.485625\pi\) | ||||
0.0451455 | + | 0.998980i | \(0.485625\pi\) | |||||||
\(348\) | 1.09271e6 | 0.483677 | ||||||||
\(349\) | −3.94184e6 | −1.73235 | −0.866174 | − | 0.499742i | \(-0.833428\pi\) | ||||
−0.866174 | + | 0.499742i | \(0.833428\pi\) | |||||||
\(350\) | 18615.5 | 0.00812279 | ||||||||
\(351\) | −150454. | −0.0651834 | ||||||||
\(352\) | −452217. | −0.194532 | ||||||||
\(353\) | 3.29528e6 | 1.40752 | 0.703762 | − | 0.710436i | \(-0.251502\pi\) | ||||
0.703762 | + | 0.710436i | \(0.251502\pi\) | |||||||
\(354\) | −1.80119e6 | −0.763925 | ||||||||
\(355\) | −1.35549e6 | −0.570854 | ||||||||
\(356\) | 367823. | 0.153820 | ||||||||
\(357\) | 102852. | 0.0427113 | ||||||||
\(358\) | −1.14326e6 | −0.471454 | ||||||||
\(359\) | −52181.7 | −0.0213689 | −0.0106845 | − | 0.999943i | \(-0.503401\pi\) | ||||
−0.0106845 | + | 0.999943i | \(0.503401\pi\) | |||||||
\(360\) | 374767. | 0.152407 | ||||||||
\(361\) | 1.87164e6 | 0.755881 | ||||||||
\(362\) | 187968. | 0.0753899 | ||||||||
\(363\) | 742222. | 0.295643 | ||||||||
\(364\) | 93552.3 | 0.0370085 | ||||||||
\(365\) | −2.03298e6 | −0.798732 | ||||||||
\(366\) | 572634. | 0.223447 | ||||||||
\(367\) | −1.28483e6 | −0.497943 | −0.248972 | − | 0.968511i | \(-0.580093\pi\) | ||||
−0.248972 | + | 0.968511i | \(0.580093\pi\) | |||||||
\(368\) | 135424. | 0.0521286 | ||||||||
\(369\) | −2.38428e6 | −0.911573 | ||||||||
\(370\) | 74496.3 | 0.0282898 | ||||||||
\(371\) | −225684. | −0.0851268 | ||||||||
\(372\) | −145544. | −0.0545300 | ||||||||
\(373\) | −850905. | −0.316672 | −0.158336 | − | 0.987385i | \(-0.550613\pi\) | ||||
−0.158336 | + | 0.987385i | \(0.550613\pi\) | |||||||
\(374\) | −1.11692e6 | −0.412898 | ||||||||
\(375\) | 341337. | 0.125345 | ||||||||
\(376\) | −1.11752e6 | −0.407647 | ||||||||
\(377\) | 2.45482e6 | 0.889542 | ||||||||
\(378\) | −5706.90 | −0.00205433 | ||||||||
\(379\) | 4.94210e6 | 1.76731 | 0.883657 | − | 0.468135i | \(-0.155074\pi\) | ||||
0.883657 | + | 0.468135i | \(0.155074\pi\) | |||||||
\(380\) | 834049. | 0.296301 | ||||||||
\(381\) | −3.72850e6 | −1.31589 | ||||||||
\(382\) | −2.04577e6 | −0.717297 | ||||||||
\(383\) | −1.31741e6 | −0.458906 | −0.229453 | − | 0.973320i | \(-0.573694\pi\) | ||||
−0.229453 | + | 0.973320i | \(0.573694\pi\) | |||||||
\(384\) | 357918. | 0.123867 | ||||||||
\(385\) | −82209.6 | −0.0282664 | ||||||||
\(386\) | −2.01137e6 | −0.687107 | ||||||||
\(387\) | 4.82446e6 | 1.63746 | ||||||||
\(388\) | −878553. | −0.296271 | ||||||||
\(389\) | 471710. | 0.158052 | 0.0790262 | − | 0.996873i | \(-0.474819\pi\) | ||||
0.0790262 | + | 0.996873i | \(0.474819\pi\) | |||||||
\(390\) | 1.71539e6 | 0.571086 | ||||||||
\(391\) | 334480. | 0.110644 | ||||||||
\(392\) | −1.07210e6 | −0.352387 | ||||||||
\(393\) | 2.87439e6 | 0.938781 | ||||||||
\(394\) | 2.05849e6 | 0.668048 | ||||||||
\(395\) | 2.48275e6 | 0.800644 | ||||||||
\(396\) | −1.65504e6 | −0.530359 | ||||||||
\(397\) | −1.32333e6 | −0.421398 | −0.210699 | − | 0.977551i | \(-0.567574\pi\) | ||||
−0.210699 | + | 0.977551i | \(0.567574\pi\) | |||||||
\(398\) | 1.70739e6 | 0.540287 | ||||||||
\(399\) | 339180. | 0.106659 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −6.08132e6 | −1.88859 | −0.944293 | − | 0.329107i | \(-0.893252\pi\) | ||||
−0.944293 | + | 0.329107i | \(0.893252\pi\) | |||||||
\(402\) | 2.57900e6 | 0.795952 | ||||||||
\(403\) | −326971. | −0.100287 | ||||||||
\(404\) | 3.02673e6 | 0.922614 | ||||||||
\(405\) | −1.52758e6 | −0.462773 | ||||||||
\(406\) | 93114.1 | 0.0280350 | ||||||||
\(407\) | −328989. | −0.0984454 | ||||||||
\(408\) | 884012. | 0.262910 | ||||||||
\(409\) | −4.49993e6 | −1.33014 | −0.665070 | − | 0.746781i | \(-0.731598\pi\) | ||||
−0.665070 | + | 0.746781i | \(0.731598\pi\) | |||||||
\(410\) | −1.01793e6 | −0.299059 | ||||||||
\(411\) | −3.14314e6 | −0.917823 | ||||||||
\(412\) | −404793. | −0.117487 | ||||||||
\(413\) | −153487. | −0.0442787 | ||||||||
\(414\) | 495629. | 0.142120 | ||||||||
\(415\) | 231255. | 0.0659129 | ||||||||
\(416\) | 804081. | 0.227807 | ||||||||
\(417\) | 945283. | 0.266208 | ||||||||
\(418\) | −3.68331e6 | −1.03109 | ||||||||
\(419\) | 5.74909e6 | 1.59979 | 0.799896 | − | 0.600138i | \(-0.204888\pi\) | ||||
0.799896 | + | 0.600138i | \(0.204888\pi\) | |||||||
\(420\) | 65066.7 | 0.0179985 | ||||||||
\(421\) | −724622. | −0.199254 | −0.0996268 | − | 0.995025i | \(-0.531765\pi\) | ||||
−0.0996268 | + | 0.995025i | \(0.531765\pi\) | |||||||
\(422\) | 2.59072e6 | 0.708173 | ||||||||
\(423\) | −4.08992e6 | −1.11138 | ||||||||
\(424\) | −1.93975e6 | −0.524000 | ||||||||
\(425\) | 395180. | 0.106126 | ||||||||
\(426\) | −4.73783e6 | −1.26490 | ||||||||
\(427\) | 48796.6 | 0.0129515 | ||||||||
\(428\) | −2.18732e6 | −0.577169 | ||||||||
\(429\) | −7.57548e6 | −1.98732 | ||||||||
\(430\) | 2.05972e6 | 0.537201 | ||||||||
\(431\) | 290206. | 0.0752512 | 0.0376256 | − | 0.999292i | \(-0.488021\pi\) | ||||
0.0376256 | + | 0.999292i | \(0.488021\pi\) | |||||||
\(432\) | −49050.7 | −0.0126455 | ||||||||
\(433\) | −3.11729e6 | −0.799018 | −0.399509 | − | 0.916729i | \(-0.630819\pi\) | ||||
−0.399509 | + | 0.916729i | \(0.630819\pi\) | |||||||
\(434\) | −12402.4 | −0.00316068 | ||||||||
\(435\) | 1.70735e6 | 0.432614 | ||||||||
\(436\) | 1.36402e6 | 0.343641 | ||||||||
\(437\) | 1.10303e6 | 0.276302 | ||||||||
\(438\) | −7.10586e6 | −1.76983 | ||||||||
\(439\) | 1.01002e6 | 0.250131 | 0.125065 | − | 0.992148i | \(-0.460086\pi\) | ||||
0.125065 | + | 0.992148i | \(0.460086\pi\) | |||||||
\(440\) | −706589. | −0.173994 | ||||||||
\(441\) | −3.92370e6 | −0.960726 | ||||||||
\(442\) | 1.98598e6 | 0.483525 | ||||||||
\(443\) | −3.15549e6 | −0.763936 | −0.381968 | − | 0.924175i | \(-0.624754\pi\) | ||||
−0.381968 | + | 0.924175i | \(0.624754\pi\) | |||||||
\(444\) | 260386. | 0.0626845 | ||||||||
\(445\) | 574723. | 0.137581 | ||||||||
\(446\) | −2.13663e6 | −0.508619 | ||||||||
\(447\) | −8.12152e6 | −1.92251 | ||||||||
\(448\) | 30499.7 | 0.00717960 | ||||||||
\(449\) | −3.14786e6 | −0.736884 | −0.368442 | − | 0.929651i | \(-0.620109\pi\) | ||||
−0.368442 | + | 0.929651i | \(0.620109\pi\) | |||||||
\(450\) | 585573. | 0.136317 | ||||||||
\(451\) | 4.49535e6 | 1.04069 | ||||||||
\(452\) | 155655. | 0.0358358 | ||||||||
\(453\) | −4.90033e6 | −1.12197 | ||||||||
\(454\) | −823715. | −0.187559 | ||||||||
\(455\) | 146176. | 0.0331014 | ||||||||
\(456\) | 2.91524e6 | 0.656543 | ||||||||
\(457\) | −1.40125e6 | −0.313852 | −0.156926 | − | 0.987610i | \(-0.550158\pi\) | ||||
−0.156926 | + | 0.987610i | \(0.550158\pi\) | |||||||
\(458\) | −3.73618e6 | −0.832271 | ||||||||
\(459\) | −121149. | −0.0268403 | ||||||||
\(460\) | 211600. | 0.0466252 | ||||||||
\(461\) | −3.99638e6 | −0.875820 | −0.437910 | − | 0.899019i | \(-0.644281\pi\) | ||||
−0.437910 | + | 0.899019i | \(0.644281\pi\) | |||||||
\(462\) | −287346. | −0.0626327 | ||||||||
\(463\) | 4.67627e6 | 1.01379 | 0.506894 | − | 0.862009i | \(-0.330794\pi\) | ||||
0.506894 | + | 0.862009i | \(0.330794\pi\) | |||||||
\(464\) | 800313. | 0.172570 | ||||||||
\(465\) | −227412. | −0.0487731 | ||||||||
\(466\) | −2.11935e6 | −0.452104 | ||||||||
\(467\) | 499509. | 0.105987 | 0.0529934 | − | 0.998595i | \(-0.483124\pi\) | ||||
0.0529934 | + | 0.998595i | \(0.483124\pi\) | |||||||
\(468\) | 2.94280e6 | 0.621078 | ||||||||
\(469\) | 219768. | 0.0461351 | ||||||||
\(470\) | −1.74612e6 | −0.364611 | ||||||||
\(471\) | −6.90974e6 | −1.43519 | ||||||||
\(472\) | −1.31921e6 | −0.272559 | ||||||||
\(473\) | −9.09610e6 | −1.86940 | ||||||||
\(474\) | 8.67792e6 | 1.77407 | ||||||||
\(475\) | 1.30320e6 | 0.265019 | ||||||||
\(476\) | 75330.3 | 0.0152389 | ||||||||
\(477\) | −7.09916e6 | −1.42860 | ||||||||
\(478\) | −3.18603e6 | −0.637793 | ||||||||
\(479\) | −7.27067e6 | −1.44789 | −0.723945 | − | 0.689858i | \(-0.757673\pi\) | ||||
−0.723945 | + | 0.689858i | \(0.757673\pi\) | |||||||
\(480\) | 559247. | 0.110790 | ||||||||
\(481\) | 584971. | 0.115285 | ||||||||
\(482\) | 1.96812e6 | 0.385864 | ||||||||
\(483\) | 86050.7 | 0.0167837 | ||||||||
\(484\) | 543613. | 0.105482 | ||||||||
\(485\) | −1.37274e6 | −0.264992 | ||||||||
\(486\) | −5.15312e6 | −0.989644 | ||||||||
\(487\) | 4.39818e6 | 0.840331 | 0.420165 | − | 0.907448i | \(-0.361972\pi\) | ||||
0.420165 | + | 0.907448i | \(0.361972\pi\) | |||||||
\(488\) | 419405. | 0.0797231 | ||||||||
\(489\) | −1.06174e7 | −2.00792 | ||||||||
\(490\) | −1.67516e6 | −0.315185 | ||||||||
\(491\) | 6.73646e6 | 1.26104 | 0.630518 | − | 0.776174i | \(-0.282842\pi\) | ||||
0.630518 | + | 0.776174i | \(0.282842\pi\) | |||||||
\(492\) | −3.55795e6 | −0.662654 | ||||||||
\(493\) | 1.97667e6 | 0.366284 | ||||||||
\(494\) | 6.54924e6 | 1.20746 | ||||||||
\(495\) | −2.58600e6 | −0.474368 | ||||||||
\(496\) | −106598. | −0.0194556 | ||||||||
\(497\) | −403730. | −0.0733163 | ||||||||
\(498\) | 808303. | 0.146050 | ||||||||
\(499\) | 5.10709e6 | 0.918168 | 0.459084 | − | 0.888393i | \(-0.348178\pi\) | ||||
0.459084 | + | 0.888393i | \(0.348178\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 1.05723e7 | 1.88180 | ||||||||
\(502\) | 6.02596e6 | 1.06725 | ||||||||
\(503\) | −3.16963e6 | −0.558584 | −0.279292 | − | 0.960206i | \(-0.590100\pi\) | ||||
−0.279292 | + | 0.960206i | \(0.590100\pi\) | |||||||
\(504\) | 111624. | 0.0195740 | ||||||||
\(505\) | 4.72926e6 | 0.825211 | ||||||||
\(506\) | −934465. | −0.162251 | ||||||||
\(507\) | 5.35874e6 | 0.925854 | ||||||||
\(508\) | −2.73080e6 | −0.469495 | ||||||||
\(509\) | −7.46538e6 | −1.27720 | −0.638598 | − | 0.769540i | \(-0.720485\pi\) | ||||
−0.638598 | + | 0.769540i | \(0.720485\pi\) | |||||||
\(510\) | 1.38127e6 | 0.235154 | ||||||||
\(511\) | −605520. | −0.102583 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −399518. | −0.0670260 | ||||||||
\(514\) | −2.04878e6 | −0.342049 | ||||||||
\(515\) | −632489. | −0.105084 | ||||||||
\(516\) | 7.19932e6 | 1.19033 | ||||||||
\(517\) | 7.71119e6 | 1.26880 | ||||||||
\(518\) | 22188.6 | 0.00363333 | ||||||||
\(519\) | 3.54370e6 | 0.577483 | ||||||||
\(520\) | 1.25638e6 | 0.203756 | ||||||||
\(521\) | −3.67478e6 | −0.593112 | −0.296556 | − | 0.955015i | \(-0.595838\pi\) | ||||
−0.296556 | + | 0.955015i | \(0.595838\pi\) | |||||||
\(522\) | 2.92901e6 | 0.470484 | ||||||||
\(523\) | 8.09022e6 | 1.29332 | 0.646660 | − | 0.762778i | \(-0.276165\pi\) | ||||
0.646660 | + | 0.762778i | \(0.276165\pi\) | |||||||
\(524\) | 2.10524e6 | 0.334945 | ||||||||
\(525\) | 101667. | 0.0160983 | ||||||||
\(526\) | −5.62322e6 | −0.886177 | ||||||||
\(527\) | −263284. | −0.0412950 | ||||||||
\(528\) | −2.46974e6 | −0.385537 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −3.03086e6 | −0.468680 | ||||||||
\(531\) | −4.82810e6 | −0.743087 | ||||||||
\(532\) | 248420. | 0.0380546 | ||||||||
\(533\) | −7.99311e6 | −1.21870 | ||||||||
\(534\) | 2.00882e6 | 0.304852 | ||||||||
\(535\) | −3.41769e6 | −0.516236 | ||||||||
\(536\) | 1.88890e6 | 0.283986 | ||||||||
\(537\) | −6.24382e6 | −0.934360 | ||||||||
\(538\) | 1.90685e6 | 0.284027 | ||||||||
\(539\) | 7.39780e6 | 1.09681 | ||||||||
\(540\) | −76641.7 | −0.0113105 | ||||||||
\(541\) | −2.85957e6 | −0.420056 | −0.210028 | − | 0.977695i | \(-0.567355\pi\) | ||||
−0.210028 | + | 0.977695i | \(0.567355\pi\) | |||||||
\(542\) | 3.67343e6 | 0.537123 | ||||||||
\(543\) | 1.02657e6 | 0.149413 | ||||||||
\(544\) | 647462. | 0.0938031 | ||||||||
\(545\) | 2.13128e6 | 0.307362 | ||||||||
\(546\) | 510926. | 0.0733460 | ||||||||
\(547\) | 8.65627e6 | 1.23698 | 0.618490 | − | 0.785793i | \(-0.287745\pi\) | ||||
0.618490 | + | 0.785793i | \(0.287745\pi\) | |||||||
\(548\) | −2.30208e6 | −0.327468 | ||||||||
\(549\) | 1.53495e6 | 0.217352 | ||||||||
\(550\) | −1.10405e6 | −0.155625 | ||||||||
\(551\) | 6.51856e6 | 0.914687 | ||||||||
\(552\) | 739604. | 0.103312 | ||||||||
\(553\) | 739482. | 0.102829 | ||||||||
\(554\) | 2.31602e6 | 0.320604 | ||||||||
\(555\) | 406853. | 0.0560668 | ||||||||
\(556\) | 692338. | 0.0949798 | ||||||||
\(557\) | 6.77607e6 | 0.925422 | 0.462711 | − | 0.886509i | \(-0.346877\pi\) | ||||
0.462711 | + | 0.886509i | \(0.346877\pi\) | |||||||
\(558\) | −390131. | −0.0530426 | ||||||||
\(559\) | 1.61736e7 | 2.18916 | ||||||||
\(560\) | 47655.7 | 0.00642163 | ||||||||
\(561\) | −6.09994e6 | −0.818310 | ||||||||
\(562\) | 5.23908e6 | 0.699704 | ||||||||
\(563\) | 1.40916e7 | 1.87365 | 0.936824 | − | 0.349800i | \(-0.113751\pi\) | ||||
0.936824 | + | 0.349800i | \(0.113751\pi\) | |||||||
\(564\) | −6.10320e6 | −0.807904 | ||||||||
\(565\) | 243211. | 0.0320526 | ||||||||
\(566\) | 1.55207e6 | 0.203644 | ||||||||
\(567\) | −454989. | −0.0594351 | ||||||||
\(568\) | −3.47005e6 | −0.451300 | ||||||||
\(569\) | 5.42734e6 | 0.702759 | 0.351380 | − | 0.936233i | \(-0.385713\pi\) | ||||
0.351380 | + | 0.936233i | \(0.385713\pi\) | |||||||
\(570\) | 4.55507e6 | 0.587230 | ||||||||
\(571\) | −2.93711e6 | −0.376990 | −0.188495 | − | 0.982074i | \(-0.560361\pi\) | ||||
−0.188495 | + | 0.982074i | \(0.560361\pi\) | |||||||
\(572\) | −5.54839e6 | −0.709050 | ||||||||
\(573\) | −1.11728e7 | −1.42159 | ||||||||
\(574\) | −303188. | −0.0384089 | ||||||||
\(575\) | 330625. | 0.0417029 | ||||||||
\(576\) | 959403. | 0.120488 | ||||||||
\(577\) | 4.20072e6 | 0.525271 | 0.262636 | − | 0.964895i | \(-0.415408\pi\) | ||||
0.262636 | + | 0.964895i | \(0.415408\pi\) | |||||||
\(578\) | −4.08028e6 | −0.508008 | ||||||||
\(579\) | −1.09849e7 | −1.36176 | ||||||||
\(580\) | 1.25049e6 | 0.154351 | ||||||||
\(581\) | 68878.9 | 0.00846536 | ||||||||
\(582\) | −4.79812e6 | −0.587170 | ||||||||
\(583\) | 1.33848e7 | 1.63095 | ||||||||
\(584\) | −5.20443e6 | −0.631453 | ||||||||
\(585\) | 4.59812e6 | 0.555509 | ||||||||
\(586\) | 5.79837e6 | 0.697528 | ||||||||
\(587\) | 1.44189e7 | 1.72718 | 0.863589 | − | 0.504196i | \(-0.168211\pi\) | ||||
0.863589 | + | 0.504196i | \(0.168211\pi\) | |||||||
\(588\) | −5.85516e6 | −0.698386 | ||||||||
\(589\) | −868243. | −0.103122 | ||||||||
\(590\) | −2.06127e6 | −0.243784 | ||||||||
\(591\) | 1.12422e7 | 1.32398 | ||||||||
\(592\) | 190710. | 0.0223651 | ||||||||
\(593\) | 4.05611e6 | 0.473667 | 0.236834 | − | 0.971550i | \(-0.423890\pi\) | ||||
0.236834 | + | 0.971550i | \(0.423890\pi\) | |||||||
\(594\) | 338464. | 0.0393592 | ||||||||
\(595\) | 117704. | 0.0136300 | ||||||||
\(596\) | −5.94831e6 | −0.685927 | ||||||||
\(597\) | 9.32472e6 | 1.07078 | ||||||||
\(598\) | 1.66156e6 | 0.190004 | ||||||||
\(599\) | −1.56448e7 | −1.78157 | −0.890787 | − | 0.454421i | \(-0.849846\pi\) | ||||
−0.890787 | + | 0.454421i | \(0.849846\pi\) | |||||||
\(600\) | 873823. | 0.0990935 | ||||||||
\(601\) | −5.61467e6 | −0.634071 | −0.317036 | − | 0.948414i | \(-0.602687\pi\) | ||||
−0.317036 | + | 0.948414i | \(0.602687\pi\) | |||||||
\(602\) | 613484. | 0.0689941 | ||||||||
\(603\) | 6.91305e6 | 0.774241 | ||||||||
\(604\) | −3.58907e6 | −0.400303 | ||||||||
\(605\) | 849396. | 0.0943456 | ||||||||
\(606\) | 1.65302e7 | 1.82850 | ||||||||
\(607\) | −7.89001e6 | −0.869173 | −0.434586 | − | 0.900630i | \(-0.643105\pi\) | ||||
−0.434586 | + | 0.900630i | \(0.643105\pi\) | |||||||
\(608\) | 2.13517e6 | 0.234246 | ||||||||
\(609\) | 508533. | 0.0555617 | ||||||||
\(610\) | 655321. | 0.0713065 | ||||||||
\(611\) | −1.37111e7 | −1.48583 | ||||||||
\(612\) | 2.36960e6 | 0.255739 | ||||||||
\(613\) | 1.28240e6 | 0.137839 | 0.0689196 | − | 0.997622i | \(-0.478045\pi\) | ||||
0.0689196 | + | 0.997622i | \(0.478045\pi\) | |||||||
\(614\) | 9.13114e6 | 0.977472 | ||||||||
\(615\) | −5.55929e6 | −0.592696 | ||||||||
\(616\) | −210456. | −0.0223466 | ||||||||
\(617\) | 9.12950e6 | 0.965460 | 0.482730 | − | 0.875769i | \(-0.339645\pi\) | ||||
0.482730 | + | 0.875769i | \(0.339645\pi\) | |||||||
\(618\) | −2.21073e6 | −0.232844 | ||||||||
\(619\) | 1.01828e7 | 1.06817 | 0.534087 | − | 0.845430i | \(-0.320655\pi\) | ||||
0.534087 | + | 0.845430i | \(0.320655\pi\) | |||||||
\(620\) | −166560. | −0.0174016 | ||||||||
\(621\) | −101359. | −0.0105471 | ||||||||
\(622\) | 8.76665e6 | 0.908569 | ||||||||
\(623\) | 171180. | 0.0176699 | ||||||||
\(624\) | 4.39140e6 | 0.451483 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 9.85608e6 | 1.00524 | ||||||||
\(627\) | −2.01160e7 | −2.04349 | ||||||||
\(628\) | −5.06079e6 | −0.512058 | ||||||||
\(629\) | 471030. | 0.0474703 | ||||||||
\(630\) | 174412. | 0.0175075 | ||||||||
\(631\) | 6.18377e6 | 0.618273 | 0.309136 | − | 0.951018i | \(-0.399960\pi\) | ||||
0.309136 | + | 0.951018i | \(0.399960\pi\) | |||||||
\(632\) | 6.35583e6 | 0.632965 | ||||||||
\(633\) | 1.41490e7 | 1.40351 | ||||||||
\(634\) | 9.01001e6 | 0.890229 | ||||||||
\(635\) | −4.26688e6 | −0.419929 | ||||||||
\(636\) | −1.05937e7 | −1.03850 | ||||||||
\(637\) | −1.31539e7 | −1.28442 | ||||||||
\(638\) | −5.52239e6 | −0.537125 | ||||||||
\(639\) | −1.26998e7 | −1.23040 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | −1.57251e7 | −1.51164 | −0.755820 | − | 0.654780i | \(-0.772761\pi\) | ||||
−0.755820 | + | 0.654780i | \(0.772761\pi\) | |||||||
\(642\) | −1.19458e7 | −1.14388 | ||||||||
\(643\) | 3.35266e6 | 0.319788 | 0.159894 | − | 0.987134i | \(-0.448885\pi\) | ||||
0.159894 | + | 0.987134i | \(0.448885\pi\) | |||||||
\(644\) | 63024.7 | 0.00598820 | ||||||||
\(645\) | 1.12489e7 | 1.06466 | ||||||||
\(646\) | 5.27359e6 | 0.497193 | ||||||||
\(647\) | −1.21032e7 | −1.13669 | −0.568343 | − | 0.822792i | \(-0.692415\pi\) | ||||
−0.568343 | + | 0.822792i | \(0.692415\pi\) | |||||||
\(648\) | −3.91062e6 | −0.365854 | ||||||||
\(649\) | 9.10295e6 | 0.848341 | ||||||||
\(650\) | 1.96309e6 | 0.182245 | ||||||||
\(651\) | −67734.2 | −0.00626406 | ||||||||
\(652\) | −7.77632e6 | −0.716399 | ||||||||
\(653\) | −1.29405e7 | −1.18759 | −0.593797 | − | 0.804615i | \(-0.702372\pi\) | ||||
−0.593797 | + | 0.804615i | \(0.702372\pi\) | |||||||
\(654\) | 7.44945e6 | 0.681052 | ||||||||
\(655\) | 3.28944e6 | 0.299584 | ||||||||
\(656\) | −2.60589e6 | −0.236427 | ||||||||
\(657\) | −1.90473e7 | −1.72156 | ||||||||
\(658\) | −520079. | −0.0468279 | ||||||||
\(659\) | 6.49902e6 | 0.582954 | 0.291477 | − | 0.956578i | \(-0.405853\pi\) | ||||
0.291477 | + | 0.956578i | \(0.405853\pi\) | |||||||
\(660\) | −3.85896e6 | −0.344835 | ||||||||
\(661\) | 1.22642e7 | 1.09178 | 0.545891 | − | 0.837856i | \(-0.316191\pi\) | ||||
0.545891 | + | 0.837856i | \(0.316191\pi\) | |||||||
\(662\) | 2.97439e6 | 0.263787 | ||||||||
\(663\) | 1.08462e7 | 0.958283 | ||||||||
\(664\) | 592012. | 0.0521087 | ||||||||
\(665\) | 388156. | 0.0340371 | ||||||||
\(666\) | 697968. | 0.0609747 | ||||||||
\(667\) | 1.65377e6 | 0.143933 | ||||||||
\(668\) | 7.74328e6 | 0.671404 | ||||||||
\(669\) | −1.16690e7 | −1.00802 | ||||||||
\(670\) | 2.95140e6 | 0.254005 | ||||||||
\(671\) | −2.89402e6 | −0.248139 | ||||||||
\(672\) | 166571. | 0.0142290 | ||||||||
\(673\) | −7.93539e6 | −0.675353 | −0.337676 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337676 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(674\) | 1.57263e7 | 1.33345 | ||||||||
\(675\) | −119753. | −0.0101164 | ||||||||
\(676\) | 3.92481e6 | 0.330333 | ||||||||
\(677\) | 8.83259e6 | 0.740656 | 0.370328 | − | 0.928901i | \(-0.379245\pi\) | ||||
0.370328 | + | 0.928901i | \(0.379245\pi\) | |||||||
\(678\) | 850095. | 0.0710220 | ||||||||
\(679\) | −408868. | −0.0340337 | ||||||||
\(680\) | 1.01166e6 | 0.0839001 | ||||||||
\(681\) | −4.49863e6 | −0.371717 | ||||||||
\(682\) | 735558. | 0.0605558 | ||||||||
\(683\) | 9.13451e6 | 0.749261 | 0.374631 | − | 0.927174i | \(-0.377769\pi\) | ||||
0.374631 | + | 0.927174i | \(0.377769\pi\) | |||||||
\(684\) | 7.81434e6 | 0.638634 | ||||||||
\(685\) | −3.59700e6 | −0.292896 | ||||||||
\(686\) | −999536. | −0.0810939 | ||||||||
\(687\) | −2.04048e7 | −1.64945 | ||||||||
\(688\) | 5.27288e6 | 0.424695 | ||||||||
\(689\) | −2.37994e7 | −1.90993 | ||||||||
\(690\) | 1.15563e6 | 0.0924052 | ||||||||
\(691\) | 4.27639e6 | 0.340708 | 0.170354 | − | 0.985383i | \(-0.445509\pi\) | ||||
0.170354 | + | 0.985383i | \(0.445509\pi\) | |||||||
\(692\) | 2.59546e6 | 0.206039 | ||||||||
\(693\) | −770235. | −0.0609242 | ||||||||
\(694\) | 810080. | 0.0638453 | ||||||||
\(695\) | 1.08178e6 | 0.0849525 | ||||||||
\(696\) | 4.37083e6 | 0.342011 | ||||||||
\(697\) | −6.43622e6 | −0.501821 | ||||||||
\(698\) | −1.57674e7 | −1.22496 | ||||||||
\(699\) | −1.15746e7 | −0.896012 | ||||||||
\(700\) | 74462.1 | 0.00574368 | ||||||||
\(701\) | −9.09791e6 | −0.699273 | −0.349637 | − | 0.936885i | \(-0.613695\pi\) | ||||
−0.349637 | + | 0.936885i | \(0.613695\pi\) | |||||||
\(702\) | −601818. | −0.0460916 | ||||||||
\(703\) | 1.55334e6 | 0.118543 | ||||||||
\(704\) | −1.80887e6 | −0.137555 | ||||||||
\(705\) | −9.53625e6 | −0.722611 | ||||||||
\(706\) | 1.31811e7 | 0.995270 | ||||||||
\(707\) | 1.40860e6 | 0.105984 | ||||||||
\(708\) | −7.20475e6 | −0.540176 | ||||||||
\(709\) | 1.40966e7 | 1.05317 | 0.526584 | − | 0.850123i | \(-0.323473\pi\) | ||||
0.526584 | + | 0.850123i | \(0.323473\pi\) | |||||||
\(710\) | −5.42196e6 | −0.403655 | ||||||||
\(711\) | 2.32613e7 | 1.72568 | ||||||||
\(712\) | 1.47129e6 | 0.108767 | ||||||||
\(713\) | −220275. | −0.0162271 | ||||||||
\(714\) | 411408. | 0.0302014 | ||||||||
\(715\) | −8.66935e6 | −0.634193 | ||||||||
\(716\) | −4.57306e6 | −0.333368 | ||||||||
\(717\) | −1.74001e7 | −1.26402 | ||||||||
\(718\) | −208727. | −0.0151101 | ||||||||
\(719\) | −7.26273e6 | −0.523936 | −0.261968 | − | 0.965077i | \(-0.584371\pi\) | ||||
−0.261968 | + | 0.965077i | \(0.584371\pi\) | |||||||
\(720\) | 1.49907e6 | 0.107768 | ||||||||
\(721\) | −188386. | −0.0134961 | ||||||||
\(722\) | 7.48655e6 | 0.534489 | ||||||||
\(723\) | 1.07487e7 | 0.764733 | ||||||||
\(724\) | 751874. | 0.0533087 | ||||||||
\(725\) | 1.95389e6 | 0.138056 | ||||||||
\(726\) | 2.96889e6 | 0.209051 | ||||||||
\(727\) | −1.58378e7 | −1.11137 | −0.555687 | − | 0.831392i | \(-0.687545\pi\) | ||||
−0.555687 | + | 0.831392i | \(0.687545\pi\) | |||||||
\(728\) | 374209. | 0.0261689 | ||||||||
\(729\) | −1.32951e7 | −0.926556 | ||||||||
\(730\) | −8.13193e6 | −0.564789 | ||||||||
\(731\) | 1.30233e7 | 0.901424 | ||||||||
\(732\) | 2.29054e6 | 0.158001 | ||||||||
\(733\) | 1.99229e7 | 1.36959 | 0.684797 | − | 0.728734i | \(-0.259891\pi\) | ||||
0.684797 | + | 0.728734i | \(0.259891\pi\) | |||||||
\(734\) | −5.13931e6 | −0.352099 | ||||||||
\(735\) | −9.14868e6 | −0.624655 | ||||||||
\(736\) | 541696. | 0.0368605 | ||||||||
\(737\) | −1.30339e7 | −0.883908 | ||||||||
\(738\) | −9.53712e6 | −0.644579 | ||||||||
\(739\) | 2.55968e7 | 1.72415 | 0.862073 | − | 0.506784i | \(-0.169166\pi\) | ||||
0.862073 | + | 0.506784i | \(0.169166\pi\) | |||||||
\(740\) | 297985. | 0.0200039 | ||||||||
\(741\) | 3.57680e7 | 2.39304 | ||||||||
\(742\) | −902737. | −0.0601938 | ||||||||
\(743\) | −1.10625e7 | −0.735162 | −0.367581 | − | 0.929992i | \(-0.619814\pi\) | ||||
−0.367581 | + | 0.929992i | \(0.619814\pi\) | |||||||
\(744\) | −582174. | −0.0385586 | ||||||||
\(745\) | −9.29424e6 | −0.613512 | ||||||||
\(746\) | −3.40362e6 | −0.223921 | ||||||||
\(747\) | 2.16667e6 | 0.142066 | ||||||||
\(748\) | −4.46768e6 | −0.291963 | ||||||||
\(749\) | −1.01795e6 | −0.0663015 | ||||||||
\(750\) | 1.36535e6 | 0.0886320 | ||||||||
\(751\) | −1.11013e7 | −0.718248 | −0.359124 | − | 0.933290i | \(-0.616925\pi\) | ||||
−0.359124 | + | 0.933290i | \(0.616925\pi\) | |||||||
\(752\) | −4.47007e6 | −0.288250 | ||||||||
\(753\) | 3.29101e7 | 2.11516 | ||||||||
\(754\) | 9.81928e6 | 0.629001 | ||||||||
\(755\) | −5.60792e6 | −0.358042 | ||||||||
\(756\) | −22827.6 | −0.00145263 | ||||||||
\(757\) | 6.41568e6 | 0.406914 | 0.203457 | − | 0.979084i | \(-0.434782\pi\) | ||||
0.203457 | + | 0.979084i | \(0.434782\pi\) | |||||||
\(758\) | 1.97684e7 | 1.24968 | ||||||||
\(759\) | −5.10348e6 | −0.321560 | ||||||||
\(760\) | 3.33620e6 | 0.209516 | ||||||||
\(761\) | 1.71384e7 | 1.07278 | 0.536389 | − | 0.843971i | \(-0.319788\pi\) | ||||
0.536389 | + | 0.843971i | \(0.319788\pi\) | |||||||
\(762\) | −1.49140e7 | −0.930478 | ||||||||
\(763\) | 634799. | 0.0394752 | ||||||||
\(764\) | −8.18309e6 | −0.507206 | ||||||||
\(765\) | 3.70250e6 | 0.228740 | ||||||||
\(766\) | −5.26964e6 | −0.324496 | ||||||||
\(767\) | −1.61858e7 | −0.993451 | ||||||||
\(768\) | 1.43167e6 | 0.0875871 | ||||||||
\(769\) | −6.53211e6 | −0.398325 | −0.199163 | − | 0.979966i | \(-0.563822\pi\) | ||||
−0.199163 | + | 0.979966i | \(0.563822\pi\) | |||||||
\(770\) | −328838. | −0.0199874 | ||||||||
\(771\) | −1.11892e7 | −0.677896 | ||||||||
\(772\) | −8.04550e6 | −0.485858 | ||||||||
\(773\) | −2.94949e6 | −0.177541 | −0.0887705 | − | 0.996052i | \(-0.528294\pi\) | ||||
−0.0887705 | + | 0.996052i | \(0.528294\pi\) | |||||||
\(774\) | 1.92979e7 | 1.15786 | ||||||||
\(775\) | −260249. | −0.0155645 | ||||||||
\(776\) | −3.51421e6 | −0.209495 | ||||||||
\(777\) | 121181. | 0.00720080 | ||||||||
\(778\) | 1.88684e6 | 0.111760 | ||||||||
\(779\) | −2.12250e7 | −1.25315 | ||||||||
\(780\) | 6.86156e6 | 0.403819 | ||||||||
\(781\) | 2.39444e7 | 1.40467 | ||||||||
\(782\) | 1.33792e6 | 0.0782372 | ||||||||
\(783\) | −598998. | −0.0349157 | ||||||||
\(784\) | −4.28840e6 | −0.249175 | ||||||||
\(785\) | −7.90748e6 | −0.457998 | ||||||||
\(786\) | 1.14976e7 | 0.663818 | ||||||||
\(787\) | 4.59906e6 | 0.264687 | 0.132343 | − | 0.991204i | \(-0.457750\pi\) | ||||
0.132343 | + | 0.991204i | \(0.457750\pi\) | |||||||
\(788\) | 8.23395e6 | 0.472381 | ||||||||
\(789\) | −3.07106e7 | −1.75629 | ||||||||
\(790\) | 9.93098e6 | 0.566141 | ||||||||
\(791\) | 72440.1 | 0.00411659 | ||||||||
\(792\) | −6.62015e6 | −0.375021 | ||||||||
\(793\) | 5.14581e6 | 0.290583 | ||||||||
\(794\) | −5.29333e6 | −0.297973 | ||||||||
\(795\) | −1.65527e7 | −0.928863 | ||||||||
\(796\) | 6.82956e6 | 0.382041 | ||||||||
\(797\) | 6.06291e6 | 0.338092 | 0.169046 | − | 0.985608i | \(-0.445931\pi\) | ||||
0.169046 | + | 0.985608i | \(0.445931\pi\) | |||||||
\(798\) | 1.35672e6 | 0.0754194 | ||||||||
\(799\) | −1.10405e7 | −0.611817 | ||||||||
\(800\) | 640000. | 0.0353553 | ||||||||
\(801\) | 5.38467e6 | 0.296536 | ||||||||
\(802\) | −2.43253e7 | −1.33543 | ||||||||
\(803\) | 3.59121e7 | 1.96540 | ||||||||
\(804\) | 1.03160e7 | 0.562823 | ||||||||
\(805\) | 98476.1 | 0.00535601 | ||||||||
\(806\) | −1.30788e6 | −0.0709139 | ||||||||
\(807\) | 1.04140e7 | 0.562905 | ||||||||
\(808\) | 1.21069e7 | 0.652387 | ||||||||
\(809\) | 2.38764e7 | 1.28262 | 0.641310 | − | 0.767282i | \(-0.278391\pi\) | ||||
0.641310 | + | 0.767282i | \(0.278391\pi\) | |||||||
\(810\) | −6.11034e6 | −0.327230 | ||||||||
\(811\) | −2.78099e6 | −0.148473 | −0.0742366 | − | 0.997241i | \(-0.523652\pi\) | ||||
−0.0742366 | + | 0.997241i | \(0.523652\pi\) | |||||||
\(812\) | 372456. | 0.0198237 | ||||||||
\(813\) | 2.00621e7 | 1.06451 | ||||||||
\(814\) | −1.31596e6 | −0.0696114 | ||||||||
\(815\) | −1.21505e7 | −0.640767 | ||||||||
\(816\) | 3.53605e6 | 0.185906 | ||||||||
\(817\) | 4.29477e7 | 2.25105 | ||||||||
\(818\) | −1.79997e7 | −0.940551 | ||||||||
\(819\) | 1.36954e6 | 0.0713454 | ||||||||
\(820\) | −4.07170e6 | −0.211467 | ||||||||
\(821\) | −1.59900e7 | −0.827925 | −0.413963 | − | 0.910294i | \(-0.635856\pi\) | ||||
−0.413963 | + | 0.910294i | \(0.635856\pi\) | |||||||
\(822\) | −1.25726e7 | −0.648999 | ||||||||
\(823\) | 3.19956e7 | 1.64661 | 0.823304 | − | 0.567600i | \(-0.192128\pi\) | ||||
0.823304 | + | 0.567600i | \(0.192128\pi\) | |||||||
\(824\) | −1.61917e6 | −0.0830758 | ||||||||
\(825\) | −6.02963e6 | −0.308429 | ||||||||
\(826\) | −613946. | −0.0313098 | ||||||||
\(827\) | −2.56186e7 | −1.30254 | −0.651271 | − | 0.758846i | \(-0.725764\pi\) | ||||
−0.651271 | + | 0.758846i | \(0.725764\pi\) | |||||||
\(828\) | 1.98252e6 | 0.100494 | ||||||||
\(829\) | 2.44926e7 | 1.23779 | 0.618897 | − | 0.785473i | \(-0.287580\pi\) | ||||
0.618897 | + | 0.785473i | \(0.287580\pi\) | |||||||
\(830\) | 925019. | 0.0466075 | ||||||||
\(831\) | 1.26487e7 | 0.635395 | ||||||||
\(832\) | 3.21632e6 | 0.161084 | ||||||||
\(833\) | −1.05918e7 | −0.528880 | ||||||||
\(834\) | 3.78113e6 | 0.188238 | ||||||||
\(835\) | 1.20989e7 | 0.600522 | ||||||||
\(836\) | −1.47333e7 | −0.729093 | ||||||||
\(837\) | 79783.8 | 0.00393642 | ||||||||
\(838\) | 2.29963e7 | 1.13122 | ||||||||
\(839\) | −3.75328e7 | −1.84080 | −0.920398 | − | 0.390982i | \(-0.872136\pi\) | ||||
−0.920398 | + | 0.390982i | \(0.872136\pi\) | |||||||
\(840\) | 260267. | 0.0127268 | ||||||||
\(841\) | −1.07379e7 | −0.523514 | ||||||||
\(842\) | −2.89849e6 | −0.140894 | ||||||||
\(843\) | 2.86127e7 | 1.38672 | ||||||||
\(844\) | 1.03629e7 | 0.500754 | ||||||||
\(845\) | 6.13252e6 | 0.295459 | ||||||||
\(846\) | −1.63597e7 | −0.785867 | ||||||||
\(847\) | 252991. | 0.0121170 | ||||||||
\(848\) | −7.75901e6 | −0.370524 | ||||||||
\(849\) | 8.47647e6 | 0.403595 | ||||||||
\(850\) | 1.58072e6 | 0.0750425 | ||||||||
\(851\) | 394085. | 0.0186538 | ||||||||
\(852\) | −1.89513e7 | −0.894418 | ||||||||
\(853\) | −2.48528e7 | −1.16951 | −0.584754 | − | 0.811210i | \(-0.698809\pi\) | ||||
−0.584754 | + | 0.811210i | \(0.698809\pi\) | |||||||
\(854\) | 195186. | 0.00915808 | ||||||||
\(855\) | 1.22099e7 | 0.571212 | ||||||||
\(856\) | −8.74929e6 | −0.408120 | ||||||||
\(857\) | −1.82652e7 | −0.849516 | −0.424758 | − | 0.905307i | \(-0.639641\pi\) | ||||
−0.424758 | + | 0.905307i | \(0.639641\pi\) | |||||||
\(858\) | −3.03019e7 | −1.40524 | ||||||||
\(859\) | 3.03679e7 | 1.40421 | 0.702104 | − | 0.712075i | \(-0.252244\pi\) | ||||
0.702104 | + | 0.712075i | \(0.252244\pi\) | |||||||
\(860\) | 8.23888e6 | 0.379859 | ||||||||
\(861\) | −1.65583e6 | −0.0761214 | ||||||||
\(862\) | 1.16082e6 | 0.0532106 | ||||||||
\(863\) | 6.46938e6 | 0.295689 | 0.147845 | − | 0.989011i | \(-0.452766\pi\) | ||||
0.147845 | + | 0.989011i | \(0.452766\pi\) | |||||||
\(864\) | −196203. | −0.00894172 | ||||||||
\(865\) | 4.05540e6 | 0.184287 | ||||||||
\(866\) | −1.24691e7 | −0.564991 | ||||||||
\(867\) | −2.22840e7 | −1.00681 | ||||||||
\(868\) | −49609.5 | −0.00223494 | ||||||||
\(869\) | −4.38570e7 | −1.97011 | ||||||||
\(870\) | 6.82942e6 | 0.305904 | ||||||||
\(871\) | 2.31754e7 | 1.03510 | ||||||||
\(872\) | 5.45608e6 | 0.242991 | ||||||||
\(873\) | −1.28614e7 | −0.571154 | ||||||||
\(874\) | 4.41212e6 | 0.195375 | ||||||||
\(875\) | 116347. | 0.00513730 | ||||||||
\(876\) | −2.84235e7 | −1.25146 | ||||||||
\(877\) | 7.87858e6 | 0.345899 | 0.172949 | − | 0.984931i | \(-0.444670\pi\) | ||||
0.172949 | + | 0.984931i | \(0.444670\pi\) | |||||||
\(878\) | 4.04007e6 | 0.176869 | ||||||||
\(879\) | 3.16672e7 | 1.38241 | ||||||||
\(880\) | −2.82636e6 | −0.123033 | ||||||||
\(881\) | 1.58782e7 | 0.689227 | 0.344614 | − | 0.938745i | \(-0.388010\pi\) | ||||
0.344614 | + | 0.938745i | \(0.388010\pi\) | |||||||
\(882\) | −1.56948e7 | −0.679336 | ||||||||
\(883\) | −3.52265e7 | −1.52044 | −0.760218 | − | 0.649668i | \(-0.774908\pi\) | ||||
−0.760218 | + | 0.649668i | \(0.774908\pi\) | |||||||
\(884\) | 7.94391e6 | 0.341903 | ||||||||
\(885\) | −1.12574e7 | −0.483148 | ||||||||
\(886\) | −1.26219e7 | −0.540185 | ||||||||
\(887\) | 3.57175e6 | 0.152431 | 0.0762154 | − | 0.997091i | \(-0.475716\pi\) | ||||
0.0762154 | + | 0.997091i | \(0.475716\pi\) | |||||||
\(888\) | 1.04154e6 | 0.0443247 | ||||||||
\(889\) | −1.27088e6 | −0.0539325 | ||||||||
\(890\) | 2.29889e6 | 0.0972844 | ||||||||
\(891\) | 2.69844e7 | 1.13872 | ||||||||
\(892\) | −8.54653e6 | −0.359648 | ||||||||
\(893\) | −3.64087e7 | −1.52784 | ||||||||
\(894\) | −3.24861e7 | −1.35942 | ||||||||
\(895\) | −7.14540e6 | −0.298173 | ||||||||
\(896\) | 121999. | 0.00507674 | ||||||||
\(897\) | 9.07442e6 | 0.376563 | ||||||||
\(898\) | −1.25914e7 | −0.521056 | ||||||||
\(899\) | −1.30176e6 | −0.0537193 | ||||||||
\(900\) | 2.34229e6 | 0.0963906 | ||||||||
\(901\) | −1.91638e7 | −0.786446 | ||||||||
\(902\) | 1.79814e7 | 0.735880 | ||||||||
\(903\) | 3.35048e6 | 0.136737 | ||||||||
\(904\) | 622621. | 0.0253398 | ||||||||
\(905\) | 1.17480e6 | 0.0476808 | ||||||||
\(906\) | −1.96013e7 | −0.793349 | ||||||||
\(907\) | −4.42353e7 | −1.78546 | −0.892732 | − | 0.450588i | \(-0.851214\pi\) | ||||
−0.892732 | + | 0.450588i | \(0.851214\pi\) | |||||||
\(908\) | −3.29486e6 | −0.132624 | ||||||||
\(909\) | 4.43093e7 | 1.77863 | ||||||||
\(910\) | 584702. | 0.0234062 | ||||||||
\(911\) | −3.38099e7 | −1.34973 | −0.674867 | − | 0.737939i | \(-0.735799\pi\) | ||||
−0.674867 | + | 0.737939i | \(0.735799\pi\) | |||||||
\(912\) | 1.16610e7 | 0.464246 | ||||||||
\(913\) | −4.08506e6 | −0.162189 | ||||||||
\(914\) | −5.60499e6 | −0.221927 | ||||||||
\(915\) | 3.57897e6 | 0.141320 | ||||||||
\(916\) | −1.49447e7 | −0.588504 | ||||||||
\(917\) | 979755. | 0.0384764 | ||||||||
\(918\) | −484596. | −0.0189790 | ||||||||
\(919\) | −2.23014e7 | −0.871052 | −0.435526 | − | 0.900176i | \(-0.643438\pi\) | ||||
−0.435526 | + | 0.900176i | \(0.643438\pi\) | |||||||
\(920\) | 846400. | 0.0329690 | ||||||||
\(921\) | 4.98688e7 | 1.93722 | ||||||||
\(922\) | −1.59855e7 | −0.619298 | ||||||||
\(923\) | −4.25751e7 | −1.64495 | ||||||||
\(924\) | −1.14939e6 | −0.0442880 | ||||||||
\(925\) | 465602. | 0.0178921 | ||||||||
\(926\) | 1.87051e7 | 0.716856 | ||||||||
\(927\) | −5.92589e6 | −0.226493 | ||||||||
\(928\) | 3.20125e6 | 0.122025 | ||||||||
\(929\) | −3.58441e7 | −1.36263 | −0.681316 | − | 0.731989i | \(-0.738592\pi\) | ||||
−0.681316 | + | 0.731989i | \(0.738592\pi\) | |||||||
\(930\) | −909647. | −0.0344878 | ||||||||
\(931\) | −3.49290e7 | −1.32073 | ||||||||
\(932\) | −8.47741e6 | −0.319686 | ||||||||
\(933\) | 4.78781e7 | 1.80067 | ||||||||
\(934\) | 1.99804e6 | 0.0749439 | ||||||||
\(935\) | −6.98075e6 | −0.261140 | ||||||||
\(936\) | 1.17712e7 | 0.439168 | ||||||||
\(937\) | 1.21031e7 | 0.450348 | 0.225174 | − | 0.974319i | \(-0.427705\pi\) | ||||
0.225174 | + | 0.974319i | \(0.427705\pi\) | |||||||
\(938\) | 879070. | 0.0326224 | ||||||||
\(939\) | 5.38279e7 | 1.99225 | ||||||||
\(940\) | −6.98448e6 | −0.257819 | ||||||||
\(941\) | −4.13064e7 | −1.52070 | −0.760350 | − | 0.649513i | \(-0.774973\pi\) | ||||
−0.760350 | + | 0.649513i | \(0.774973\pi\) | |||||||
\(942\) | −2.76389e7 | −1.01483 | ||||||||
\(943\) | −5.38483e6 | −0.197194 | ||||||||
\(944\) | −5.27685e6 | −0.192728 | ||||||||
\(945\) | −35668.1 | −0.00129927 | ||||||||
\(946\) | −3.63844e7 | −1.32187 | ||||||||
\(947\) | −5.16814e6 | −0.187266 | −0.0936331 | − | 0.995607i | \(-0.529848\pi\) | ||||
−0.0936331 | + | 0.995607i | \(0.529848\pi\) | |||||||
\(948\) | 3.47117e7 | 1.25445 | ||||||||
\(949\) | −6.38547e7 | −2.30159 | ||||||||
\(950\) | 5.21281e6 | 0.187397 | ||||||||
\(951\) | 4.92072e7 | 1.76432 | ||||||||
\(952\) | 301321. | 0.0107755 | ||||||||
\(953\) | 3.52996e7 | 1.25903 | 0.629516 | − | 0.776987i | \(-0.283253\pi\) | ||||
0.629516 | + | 0.776987i | \(0.283253\pi\) | |||||||
\(954\) | −2.83966e7 | −1.01017 | ||||||||
\(955\) | −1.27861e7 | −0.453658 | ||||||||
\(956\) | −1.27441e7 | −0.450988 | ||||||||
\(957\) | −3.01600e7 | −1.06451 | ||||||||
\(958\) | −2.90827e7 | −1.02381 | ||||||||
\(959\) | −1.07136e6 | −0.0376174 | ||||||||
\(960\) | 2.23699e6 | 0.0783403 | ||||||||
\(961\) | −2.84558e7 | −0.993944 | ||||||||
\(962\) | 2.33988e6 | 0.0815185 | ||||||||
\(963\) | −3.20209e7 | −1.11267 | ||||||||
\(964\) | 7.87249e6 | 0.272847 | ||||||||
\(965\) | −1.25711e7 | −0.434565 | ||||||||
\(966\) | 344203. | 0.0118678 | ||||||||
\(967\) | 2.21489e7 | 0.761704 | 0.380852 | − | 0.924636i | \(-0.375631\pi\) | ||||
0.380852 | + | 0.924636i | \(0.375631\pi\) | |||||||
\(968\) | 2.17445e6 | 0.0745868 | ||||||||
\(969\) | 2.88011e7 | 0.985372 | ||||||||
\(970\) | −5.49095e6 | −0.187378 | ||||||||
\(971\) | −272621. | −0.00927922 | −0.00463961 | − | 0.999989i | \(-0.501477\pi\) | ||||
−0.00463961 | + | 0.999989i | \(0.501477\pi\) | |||||||
\(972\) | −2.06125e7 | −0.699784 | ||||||||
\(973\) | 322206. | 0.0109107 | ||||||||
\(974\) | 1.75927e7 | 0.594204 | ||||||||
\(975\) | 1.07212e7 | 0.361187 | ||||||||
\(976\) | 1.67762e6 | 0.0563728 | ||||||||
\(977\) | 2.78738e7 | 0.934244 | 0.467122 | − | 0.884193i | \(-0.345291\pi\) | ||||
0.467122 | + | 0.884193i | \(0.345291\pi\) | |||||||
\(978\) | −4.24695e7 | −1.41981 | ||||||||
\(979\) | −1.01523e7 | −0.338539 | ||||||||
\(980\) | −6.70062e6 | −0.222869 | ||||||||
\(981\) | 1.99683e7 | 0.662475 | ||||||||
\(982\) | 2.69458e7 | 0.891688 | ||||||||
\(983\) | −3.91324e7 | −1.29167 | −0.645837 | − | 0.763475i | \(-0.723492\pi\) | ||||
−0.645837 | + | 0.763475i | \(0.723492\pi\) | |||||||
\(984\) | −1.42318e7 | −0.468567 | ||||||||
\(985\) | 1.28655e7 | 0.422511 | ||||||||
\(986\) | 7.90669e6 | 0.259002 | ||||||||
\(987\) | −2.84035e6 | −0.0928068 | ||||||||
\(988\) | 2.61970e7 | 0.853805 | ||||||||
\(989\) | 1.08959e7 | 0.354220 | ||||||||
\(990\) | −1.03440e7 | −0.335429 | ||||||||
\(991\) | −2.03186e7 | −0.657217 | −0.328608 | − | 0.944466i | \(-0.606580\pi\) | ||||
−0.328608 | + | 0.944466i | \(0.606580\pi\) | |||||||
\(992\) | −426393. | −0.0137572 | ||||||||
\(993\) | 1.62443e7 | 0.522791 | ||||||||
\(994\) | −1.61492e6 | −0.0518424 | ||||||||
\(995\) | 1.06712e7 | 0.341708 | ||||||||
\(996\) | 3.23321e6 | 0.103273 | ||||||||
\(997\) | 2.54600e7 | 0.811186 | 0.405593 | − | 0.914054i | \(-0.367065\pi\) | ||||
0.405593 | + | 0.914054i | \(0.367065\pi\) | |||||||
\(998\) | 2.04284e7 | 0.649243 | ||||||||
\(999\) | −142738. | −0.00452508 |
(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.h.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.6.a.h.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial |