Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(132.316651346\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 271 x^{8} + 309 x^{7} + 24456 x^{6} - 33410 x^{5} - 822204 x^{4} + 1367872 x^{3} + \cdots - 7036608 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-3.54519\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.54519 | 0.626707 | 0.313354 | − | 0.949637i | \(-0.398548\pi\) | ||||
0.313354 | + | 0.949637i | \(0.398548\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −19.4316 | −0.607238 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 31.9067 | 0.361829 | ||||||||
\(7\) | 15.4153 | 0.118907 | 0.0594534 | − | 0.998231i | \(-0.481064\pi\) | ||||
0.0594534 | + | 0.998231i | \(0.481064\pi\) | |||||||
\(8\) | −182.335 | −1.00727 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −174.885 | −0.350589 | ||||||||
\(13\) | −9.16464 | −0.0150403 | −0.00752016 | − | 0.999972i | \(-0.502394\pi\) | ||||
−0.00752016 | + | 0.999972i | \(0.502394\pi\) | |||||||
\(14\) | 54.6502 | 0.0745198 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −24.6000 | −0.0240234 | ||||||||
\(17\) | −1481.22 | −1.24308 | −0.621539 | − | 0.783383i | \(-0.713492\pi\) | ||||
−0.621539 | + | 0.783383i | \(0.713492\pi\) | |||||||
\(18\) | 287.160 | 0.208902 | ||||||||
\(19\) | 1058.30 | 0.672549 | 0.336275 | − | 0.941764i | \(-0.390833\pi\) | ||||
0.336275 | + | 0.941764i | \(0.390833\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 138.738 | 0.0686509 | ||||||||
\(22\) | 428.968 | 0.188959 | ||||||||
\(23\) | −3006.99 | −1.18526 | −0.592629 | − | 0.805476i | \(-0.701910\pi\) | ||||
−0.592629 | + | 0.805476i | \(0.701910\pi\) | |||||||
\(24\) | −1641.01 | −0.581546 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −32.4904 | −0.00942587 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −299.544 | −0.0722048 | ||||||||
\(29\) | 3763.09 | 0.830901 | 0.415450 | − | 0.909616i | \(-0.363624\pi\) | ||||
0.415450 | + | 0.909616i | \(0.363624\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1375.47 | 0.257067 | 0.128534 | − | 0.991705i | \(-0.458973\pi\) | ||||
0.128534 | + | 0.991705i | \(0.458973\pi\) | |||||||
\(32\) | 5747.51 | 0.992212 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | −5251.22 | −0.779046 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1573.96 | −0.202413 | ||||||||
\(37\) | 2015.66 | 0.242055 | 0.121027 | − | 0.992649i | \(-0.461381\pi\) | ||||
0.121027 | + | 0.992649i | \(0.461381\pi\) | |||||||
\(38\) | 3751.87 | 0.421491 | ||||||||
\(39\) | −82.4818 | −0.00868353 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16545.7 | 1.53719 | 0.768593 | − | 0.639738i | \(-0.220957\pi\) | ||||
0.768593 | + | 0.639738i | \(0.220957\pi\) | |||||||
\(42\) | 491.852 | 0.0430240 | ||||||||
\(43\) | −13647.3 | −1.12558 | −0.562790 | − | 0.826600i | \(-0.690272\pi\) | ||||
−0.562790 | + | 0.826600i | \(0.690272\pi\) | |||||||
\(44\) | −2351.23 | −0.183089 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10660.4 | −0.742809 | ||||||||
\(47\) | 6638.58 | 0.438360 | 0.219180 | − | 0.975684i | \(-0.429662\pi\) | ||||
0.219180 | + | 0.975684i | \(0.429662\pi\) | |||||||
\(48\) | −221.400 | −0.0138699 | ||||||||
\(49\) | −16569.4 | −0.985861 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13331.0 | −0.717691 | ||||||||
\(52\) | 178.084 | 0.00913306 | ||||||||
\(53\) | −7719.83 | −0.377501 | −0.188751 | − | 0.982025i | \(-0.560444\pi\) | ||||
−0.188751 | + | 0.982025i | \(0.560444\pi\) | |||||||
\(54\) | 2584.44 | 0.120610 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2810.75 | −0.119771 | ||||||||
\(57\) | 9524.68 | 0.388296 | ||||||||
\(58\) | 13340.9 | 0.520731 | ||||||||
\(59\) | 39159.4 | 1.46455 | 0.732277 | − | 0.681007i | \(-0.238458\pi\) | ||||
0.732277 | + | 0.681007i | \(0.238458\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8220.98 | −0.282878 | −0.141439 | − | 0.989947i | \(-0.545173\pi\) | ||||
−0.141439 | + | 0.989947i | \(0.545173\pi\) | |||||||
\(62\) | 4876.30 | 0.161106 | ||||||||
\(63\) | 1248.64 | 0.0396356 | ||||||||
\(64\) | 21163.2 | 0.645850 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3860.71 | 0.109096 | ||||||||
\(67\) | 38209.1 | 1.03987 | 0.519936 | − | 0.854205i | \(-0.325956\pi\) | ||||
0.519936 | + | 0.854205i | \(0.325956\pi\) | |||||||
\(68\) | 28782.6 | 0.754845 | ||||||||
\(69\) | −27062.9 | −0.684308 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −48470.8 | −1.14113 | −0.570564 | − | 0.821253i | \(-0.693275\pi\) | ||||
−0.570564 | + | 0.821253i | \(0.693275\pi\) | |||||||
\(72\) | −14769.1 | −0.335756 | ||||||||
\(73\) | 49320.4 | 1.08323 | 0.541613 | − | 0.840628i | \(-0.317814\pi\) | ||||
0.541613 | + | 0.840628i | \(0.317814\pi\) | |||||||
\(74\) | 7145.91 | 0.151698 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20564.5 | −0.408398 | ||||||||
\(77\) | 1865.25 | 0.0358518 | ||||||||
\(78\) | −292.414 | −0.00544203 | ||||||||
\(79\) | 16423.9 | 0.296079 | 0.148040 | − | 0.988981i | \(-0.452704\pi\) | ||||
0.148040 | + | 0.988981i | \(0.452704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 58657.8 | 0.963365 | ||||||||
\(83\) | −419.670 | −0.00668671 | −0.00334336 | − | 0.999994i | \(-0.501064\pi\) | ||||
−0.00334336 | + | 0.999994i | \(0.501064\pi\) | |||||||
\(84\) | −2695.90 | −0.0416875 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −48382.3 | −0.705409 | ||||||||
\(87\) | 33867.8 | 0.479721 | ||||||||
\(88\) | −22062.5 | −0.303703 | ||||||||
\(89\) | −17081.2 | −0.228583 | −0.114291 | − | 0.993447i | \(-0.536460\pi\) | ||||
−0.114291 | + | 0.993447i | \(0.536460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −141.276 | −0.00178840 | ||||||||
\(92\) | 58430.7 | 0.719733 | ||||||||
\(93\) | 12379.2 | 0.148418 | ||||||||
\(94\) | 23535.0 | 0.274723 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 51727.5 | 0.572854 | ||||||||
\(97\) | −3464.57 | −0.0373870 | −0.0186935 | − | 0.999825i | \(-0.505951\pi\) | ||||
−0.0186935 | + | 0.999825i | \(0.505951\pi\) | |||||||
\(98\) | −58741.6 | −0.617846 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 118690. | 1.15774 | 0.578868 | − | 0.815421i | \(-0.303495\pi\) | ||||
0.578868 | + | 0.815421i | \(0.303495\pi\) | |||||||
\(102\) | −47261.0 | −0.449782 | ||||||||
\(103\) | 107513. | 0.998544 | 0.499272 | − | 0.866445i | \(-0.333601\pi\) | ||||
0.499272 | + | 0.866445i | \(0.333601\pi\) | |||||||
\(104\) | 1671.03 | 0.0151496 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27368.3 | −0.236583 | ||||||||
\(107\) | 187147. | 1.58024 | 0.790120 | − | 0.612952i | \(-0.210018\pi\) | ||||
0.790120 | + | 0.612952i | \(0.210018\pi\) | |||||||
\(108\) | −14165.7 | −0.116863 | ||||||||
\(109\) | −496.203 | −0.00400031 | −0.00200015 | − | 0.999998i | \(-0.500637\pi\) | ||||
−0.00200015 | + | 0.999998i | \(0.500637\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18141.0 | 0.139750 | ||||||||
\(112\) | −379.216 | −0.00285655 | ||||||||
\(113\) | −109520. | −0.806859 | −0.403429 | − | 0.915011i | \(-0.632182\pi\) | ||||
−0.403429 | + | 0.915011i | \(0.632182\pi\) | |||||||
\(114\) | 33766.8 | 0.243348 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −73122.9 | −0.504555 | ||||||||
\(117\) | −742.336 | −0.00501344 | ||||||||
\(118\) | 138827. | 0.917847 | ||||||||
\(119\) | −22833.5 | −0.147811 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −29144.9 | −0.177281 | ||||||||
\(123\) | 148912. | 0.887495 | ||||||||
\(124\) | −26727.6 | −0.156101 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4426.66 | 0.0248399 | ||||||||
\(127\) | 1438.91 | 0.00791634 | 0.00395817 | − | 0.999992i | \(-0.498740\pi\) | ||||
0.00395817 | + | 0.999992i | \(0.498740\pi\) | |||||||
\(128\) | −108893. | −0.587453 | ||||||||
\(129\) | −122826. | −0.649854 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 289785. | 1.47536 | 0.737680 | − | 0.675151i | \(-0.235921\pi\) | ||||
0.737680 | + | 0.675151i | \(0.235921\pi\) | |||||||
\(132\) | −21161.0 | −0.105707 | ||||||||
\(133\) | 16314.0 | 0.0799707 | ||||||||
\(134\) | 135459. | 0.651695 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 270079. | 1.25211 | ||||||||
\(137\) | 283421. | 1.29012 | 0.645062 | − | 0.764130i | \(-0.276832\pi\) | ||||
0.645062 | + | 0.764130i | \(0.276832\pi\) | |||||||
\(138\) | −95943.2 | −0.428861 | ||||||||
\(139\) | 200510. | 0.880238 | 0.440119 | − | 0.897940i | \(-0.354936\pi\) | ||||
0.440119 | + | 0.897940i | \(0.354936\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 59747.3 | 0.253087 | ||||||||
\(142\) | −171838. | −0.715153 | ||||||||
\(143\) | −1108.92 | −0.00453483 | ||||||||
\(144\) | −1992.60 | −0.00800780 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 174850. | 0.678865 | ||||||||
\(147\) | −149124. | −0.569187 | ||||||||
\(148\) | −39167.6 | −0.146985 | ||||||||
\(149\) | 350853. | 1.29467 | 0.647336 | − | 0.762205i | \(-0.275883\pi\) | ||||
0.647336 | + | 0.762205i | \(0.275883\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −66420.6 | −0.237061 | −0.118531 | − | 0.992950i | \(-0.537818\pi\) | ||||
−0.118531 | + | 0.992950i | \(0.537818\pi\) | |||||||
\(152\) | −192965. | −0.677437 | ||||||||
\(153\) | −119979. | −0.414359 | ||||||||
\(154\) | 6612.67 | 0.0224686 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1602.75 | 0.00527297 | ||||||||
\(157\) | 507303. | 1.64255 | 0.821275 | − | 0.570533i | \(-0.193263\pi\) | ||||
0.821275 | + | 0.570533i | \(0.193263\pi\) | |||||||
\(158\) | 58225.8 | 0.185555 | ||||||||
\(159\) | −69478.5 | −0.217950 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −46353.7 | −0.140935 | ||||||||
\(162\) | 23260.0 | 0.0696341 | ||||||||
\(163\) | −402141. | −1.18552 | −0.592761 | − | 0.805379i | \(-0.701962\pi\) | ||||
−0.592761 | + | 0.805379i | \(0.701962\pi\) | |||||||
\(164\) | −321511. | −0.933438 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1487.81 | −0.00419061 | ||||||||
\(167\) | 293252. | 0.813672 | 0.406836 | − | 0.913501i | \(-0.366632\pi\) | ||||
0.406836 | + | 0.913501i | \(0.366632\pi\) | |||||||
\(168\) | −25296.7 | −0.0691498 | ||||||||
\(169\) | −371209. | −0.999774 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 85722.2 | 0.224183 | ||||||||
\(172\) | 265190. | 0.683495 | ||||||||
\(173\) | −69667.0 | −0.176975 | −0.0884875 | − | 0.996077i | \(-0.528203\pi\) | ||||
−0.0884875 | + | 0.996077i | \(0.528203\pi\) | |||||||
\(174\) | 120068. | 0.300644 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2976.60 | −0.00724333 | ||||||||
\(177\) | 352434. | 0.845561 | ||||||||
\(178\) | −60556.1 | −0.143254 | ||||||||
\(179\) | 137994. | 0.321904 | 0.160952 | − | 0.986962i | \(-0.448544\pi\) | ||||
0.160952 | + | 0.986962i | \(0.448544\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 365502. | 0.829264 | 0.414632 | − | 0.909989i | \(-0.363910\pi\) | ||||
0.414632 | + | 0.909989i | \(0.363910\pi\) | |||||||
\(182\) | −500.849 | −0.00112080 | ||||||||
\(183\) | −73988.8 | −0.163320 | ||||||||
\(184\) | 548279. | 1.19387 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 43886.7 | 0.0930145 | ||||||||
\(187\) | −179228. | −0.374802 | ||||||||
\(188\) | −128998. | −0.266189 | ||||||||
\(189\) | 11237.8 | 0.0228836 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 339173. | 0.672725 | 0.336363 | − | 0.941733i | \(-0.390803\pi\) | ||||
0.336363 | + | 0.941733i | \(0.390803\pi\) | |||||||
\(192\) | 190469. | 0.372881 | ||||||||
\(193\) | −84815.0 | −0.163900 | −0.0819500 | − | 0.996636i | \(-0.526115\pi\) | ||||
−0.0819500 | + | 0.996636i | \(0.526115\pi\) | |||||||
\(194\) | −12282.6 | −0.0234307 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 321970. | 0.598653 | ||||||||
\(197\) | −15771.8 | −0.0289545 | −0.0144772 | − | 0.999895i | \(-0.504608\pi\) | ||||
−0.0144772 | + | 0.999895i | \(0.504608\pi\) | |||||||
\(198\) | 34746.4 | 0.0629864 | ||||||||
\(199\) | 937964. | 1.67901 | 0.839505 | − | 0.543351i | \(-0.182845\pi\) | ||||
0.839505 | + | 0.543351i | \(0.182845\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 343882. | 0.600371 | ||||||||
\(202\) | 420777. | 0.725561 | ||||||||
\(203\) | 58009.1 | 0.0987998 | ||||||||
\(204\) | 259043. | 0.435810 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 381154. | 0.625795 | ||||||||
\(207\) | −243566. | −0.395086 | ||||||||
\(208\) | 225.450 | 0.000361320 0 | ||||||||
\(209\) | 128054. | 0.202781 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −680076. | −1.05160 | −0.525801 | − | 0.850608i | \(-0.676234\pi\) | ||||
−0.525801 | + | 0.850608i | \(0.676234\pi\) | |||||||
\(212\) | 150009. | 0.229233 | ||||||||
\(213\) | −436237. | −0.658831 | ||||||||
\(214\) | 663471. | 0.990348 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −132922. | −0.193849 | ||||||||
\(217\) | 21203.3 | 0.0305671 | ||||||||
\(218\) | −1759.14 | −0.00250702 | ||||||||
\(219\) | 443883. | 0.625401 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13574.9 | 0.0186963 | ||||||||
\(222\) | 64313.2 | 0.0875826 | ||||||||
\(223\) | 398926. | 0.537193 | 0.268596 | − | 0.963253i | \(-0.413440\pi\) | ||||
0.268596 | + | 0.963253i | \(0.413440\pi\) | |||||||
\(224\) | 88599.5 | 0.117981 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −388269. | −0.505664 | ||||||||
\(227\) | 327010. | 0.421208 | 0.210604 | − | 0.977571i | \(-0.432457\pi\) | ||||
0.210604 | + | 0.977571i | \(0.432457\pi\) | |||||||
\(228\) | −185080. | −0.235788 | ||||||||
\(229\) | 855131. | 1.07757 | 0.538783 | − | 0.842445i | \(-0.318884\pi\) | ||||
0.538783 | + | 0.842445i | \(0.318884\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16787.3 | 0.0206990 | ||||||||
\(232\) | −686142. | −0.836940 | ||||||||
\(233\) | −1.30246e6 | −1.57172 | −0.785858 | − | 0.618407i | \(-0.787778\pi\) | ||||
−0.785858 | + | 0.618407i | \(0.787778\pi\) | |||||||
\(234\) | −2631.72 | −0.00314196 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −760930. | −0.889333 | ||||||||
\(237\) | 147815. | 0.170941 | ||||||||
\(238\) | −80949.2 | −0.0926339 | ||||||||
\(239\) | −887999. | −1.00558 | −0.502791 | − | 0.864408i | \(-0.667694\pi\) | ||||
−0.502791 | + | 0.864408i | \(0.667694\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 787905. | 0.873838 | 0.436919 | − | 0.899501i | \(-0.356070\pi\) | ||||
0.436919 | + | 0.899501i | \(0.356070\pi\) | |||||||
\(242\) | 51905.1 | 0.0569734 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 159747. | 0.171774 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 527920. | 0.556199 | ||||||||
\(247\) | −9698.92 | −0.0101154 | ||||||||
\(248\) | −250796. | −0.258936 | ||||||||
\(249\) | −3777.03 | −0.00386057 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.07431e6 | −1.07633 | −0.538167 | − | 0.842838i | \(-0.680883\pi\) | ||||
−0.538167 | + | 0.842838i | \(0.680883\pi\) | |||||||
\(252\) | −24263.1 | −0.0240683 | ||||||||
\(253\) | −363846. | −0.357368 | ||||||||
\(254\) | 5101.21 | 0.00496123 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.06327e6 | −1.01401 | ||||||||
\(257\) | 183068. | 0.172894 | 0.0864471 | − | 0.996256i | \(-0.472449\pi\) | ||||
0.0864471 | + | 0.996256i | \(0.472449\pi\) | |||||||
\(258\) | −435441. | −0.407268 | ||||||||
\(259\) | 31072.1 | 0.0287820 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 304810. | 0.276967 | ||||||||
\(262\) | 1.02734e6 | 0.924618 | ||||||||
\(263\) | −1.79693e6 | −1.60193 | −0.800963 | − | 0.598714i | \(-0.795679\pi\) | ||||
−0.800963 | + | 0.598714i | \(0.795679\pi\) | |||||||
\(264\) | −198563. | −0.175343 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 57836.2 | 0.0501182 | ||||||||
\(267\) | −153731. | −0.131972 | ||||||||
\(268\) | −742465. | −0.631450 | ||||||||
\(269\) | −198575. | −0.167319 | −0.0836593 | − | 0.996494i | \(-0.526661\pi\) | ||||
−0.0836593 | + | 0.996494i | \(0.526661\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.09316e6 | 1.73133 | 0.865663 | − | 0.500627i | \(-0.166897\pi\) | ||||
0.865663 | + | 0.500627i | \(0.166897\pi\) | |||||||
\(272\) | 36438.1 | 0.0298630 | ||||||||
\(273\) | −1271.48 | −0.00103253 | ||||||||
\(274\) | 1.00478e6 | 0.808530 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 525876. | 0.415538 | ||||||||
\(277\) | 634155. | 0.496588 | 0.248294 | − | 0.968685i | \(-0.420130\pi\) | ||||
0.248294 | + | 0.968685i | \(0.420130\pi\) | |||||||
\(278\) | 710848. | 0.551651 | ||||||||
\(279\) | 111413. | 0.0856891 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 724201. | 0.547133 | 0.273567 | − | 0.961853i | \(-0.411797\pi\) | ||||
0.273567 | + | 0.961853i | \(0.411797\pi\) | |||||||
\(282\) | 211815. | 0.158612 | ||||||||
\(283\) | −2.42288e6 | −1.79831 | −0.899157 | − | 0.437626i | \(-0.855819\pi\) | ||||
−0.899157 | + | 0.437626i | \(0.855819\pi\) | |||||||
\(284\) | 941867. | 0.692937 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3931.34 | −0.00284201 | ||||||||
\(287\) | 255058. | 0.182782 | ||||||||
\(288\) | 465548. | 0.330737 | ||||||||
\(289\) | 774167. | 0.545243 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −31181.2 | −0.0215854 | ||||||||
\(292\) | −958375. | −0.657776 | ||||||||
\(293\) | −742942. | −0.505575 | −0.252788 | − | 0.967522i | \(-0.581347\pi\) | ||||
−0.252788 | + | 0.967522i | \(0.581347\pi\) | |||||||
\(294\) | −528674. | −0.356714 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −367526. | −0.243814 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | 1.24384e6 | 0.811379 | ||||||||
\(299\) | 27558.0 | 0.0178266 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −210378. | −0.133839 | ||||||||
\(302\) | −235474. | −0.148568 | ||||||||
\(303\) | 1.06821e6 | 0.668419 | ||||||||
\(304\) | −26034.1 | −0.0161569 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −425349. | −0.259682 | ||||||||
\(307\) | −1.25868e6 | −0.762203 | −0.381102 | − | 0.924533i | \(-0.624455\pi\) | ||||
−0.381102 | + | 0.924533i | \(0.624455\pi\) | |||||||
\(308\) | −36244.9 | −0.0217706 | ||||||||
\(309\) | 967616. | 0.576510 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.71512e6 | −1.00553 | −0.502763 | − | 0.864424i | \(-0.667683\pi\) | ||||
−0.502763 | + | 0.864424i | \(0.667683\pi\) | |||||||
\(312\) | 15039.3 | 0.00874664 | ||||||||
\(313\) | 2.85909e6 | 1.64956 | 0.824778 | − | 0.565457i | \(-0.191300\pi\) | ||||
0.824778 | + | 0.565457i | \(0.191300\pi\) | |||||||
\(314\) | 1.79849e6 | 1.02940 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −319143. | −0.179791 | ||||||||
\(317\) | 1.60936e6 | 0.899510 | 0.449755 | − | 0.893152i | \(-0.351511\pi\) | ||||
0.449755 | + | 0.893152i | \(0.351511\pi\) | |||||||
\(318\) | −246315. | −0.136591 | ||||||||
\(319\) | 455334. | 0.250526 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.68432e6 | 0.912352 | ||||||||
\(322\) | −164333. | −0.0883251 | ||||||||
\(323\) | −1.56758e6 | −0.836031 | ||||||||
\(324\) | −127491. | −0.0674709 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.42567e6 | −0.742975 | ||||||||
\(327\) | −4465.83 | −0.00230958 | ||||||||
\(328\) | −3.01687e6 | −1.54836 | ||||||||
\(329\) | 102336. | 0.0521240 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.21843e6 | −0.611264 | −0.305632 | − | 0.952150i | \(-0.598868\pi\) | ||||
−0.305632 | + | 0.952150i | \(0.598868\pi\) | |||||||
\(332\) | 8154.87 | 0.00406043 | ||||||||
\(333\) | 163269. | 0.0806850 | ||||||||
\(334\) | 1.03963e6 | 0.509934 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3412.94 | −0.00164923 | ||||||||
\(337\) | −1.59524e6 | −0.765160 | −0.382580 | − | 0.923922i | \(-0.624964\pi\) | ||||
−0.382580 | + | 0.923922i | \(0.624964\pi\) | |||||||
\(338\) | −1.31601e6 | −0.626565 | ||||||||
\(339\) | −985681. | −0.465840 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 166432. | 0.0775087 | ||||||||
\(342\) | 303901. | 0.140497 | ||||||||
\(343\) | −514507. | −0.236133 | ||||||||
\(344\) | 2.48838e6 | 1.13376 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −246983. | −0.110911 | ||||||||
\(347\) | 2.98284e6 | 1.32986 | 0.664930 | − | 0.746906i | \(-0.268462\pi\) | ||||
0.664930 | + | 0.746906i | \(0.268462\pi\) | |||||||
\(348\) | −658106. | −0.291305 | ||||||||
\(349\) | 1.45121e6 | 0.637775 | 0.318887 | − | 0.947793i | \(-0.396691\pi\) | ||||
0.318887 | + | 0.947793i | \(0.396691\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6681.02 | −0.00289451 | ||||||||
\(352\) | 695448. | 0.299163 | ||||||||
\(353\) | 373296. | 0.159447 | 0.0797235 | − | 0.996817i | \(-0.474596\pi\) | ||||
0.0797235 | + | 0.996817i | \(0.474596\pi\) | |||||||
\(354\) | 1.24945e6 | 0.529919 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 331915. | 0.138804 | ||||||||
\(357\) | −205502. | −0.0853384 | ||||||||
\(358\) | 489213. | 0.201739 | ||||||||
\(359\) | 1.59973e6 | 0.655103 | 0.327551 | − | 0.944833i | \(-0.393777\pi\) | ||||
0.327551 | + | 0.944833i | \(0.393777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.35610e6 | −0.547678 | ||||||||
\(362\) | 1.29577e6 | 0.519706 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 2745.22 | 0.00108598 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −262304. | −0.102354 | ||||||||
\(367\) | −3.67213e6 | −1.42316 | −0.711578 | − | 0.702607i | \(-0.752019\pi\) | ||||
−0.711578 | + | 0.702607i | \(0.752019\pi\) | |||||||
\(368\) | 73971.9 | 0.0284739 | ||||||||
\(369\) | 1.34020e6 | 0.512395 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −119004. | −0.0448875 | ||||||||
\(372\) | −240549. | −0.0901250 | ||||||||
\(373\) | −290636. | −0.108163 | −0.0540814 | − | 0.998537i | \(-0.517223\pi\) | ||||
−0.0540814 | + | 0.998537i | \(0.517223\pi\) | |||||||
\(374\) | −635398. | −0.234891 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.21045e6 | −0.441546 | ||||||||
\(377\) | −34487.3 | −0.0124970 | ||||||||
\(378\) | 39840.0 | 0.0143413 | ||||||||
\(379\) | 4.72607e6 | 1.69006 | 0.845031 | − | 0.534718i | \(-0.179582\pi\) | ||||
0.845031 | + | 0.534718i | \(0.179582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12950.2 | 0.00457050 | ||||||||
\(382\) | 1.20243e6 | 0.421602 | ||||||||
\(383\) | 1.69814e6 | 0.591531 | 0.295766 | − | 0.955261i | \(-0.404425\pi\) | ||||
0.295766 | + | 0.955261i | \(0.404425\pi\) | |||||||
\(384\) | −980033. | −0.339166 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −300685. | −0.102717 | ||||||||
\(387\) | −1.10543e6 | −0.375193 | ||||||||
\(388\) | 67322.3 | 0.0227028 | ||||||||
\(389\) | −614215. | −0.205800 | −0.102900 | − | 0.994692i | \(-0.532812\pi\) | ||||
−0.102900 | + | 0.994692i | \(0.532812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.45403e6 | 1.47337 | ||||||||
\(392\) | 3.02117e6 | 0.993026 | ||||||||
\(393\) | 2.60807e6 | 0.851799 | ||||||||
\(394\) | −55914.0 | −0.0181460 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −190449. | −0.0610297 | ||||||||
\(397\) | 151925. | 0.0483786 | 0.0241893 | − | 0.999707i | \(-0.492300\pi\) | ||||
0.0241893 | + | 0.999707i | \(0.492300\pi\) | |||||||
\(398\) | 3.32526e6 | 1.05225 | ||||||||
\(399\) | 146826. | 0.0461711 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −411747. | −0.127870 | −0.0639350 | − | 0.997954i | \(-0.520365\pi\) | ||||
−0.0639350 | + | 0.997954i | \(0.520365\pi\) | |||||||
\(402\) | 1.21913e6 | 0.376256 | ||||||||
\(403\) | −12605.7 | −0.00386637 | ||||||||
\(404\) | −2.30633e6 | −0.703021 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 205653. | 0.0619186 | ||||||||
\(407\) | 243895. | 0.0729823 | ||||||||
\(408\) | 2.43071e6 | 0.722907 | ||||||||
\(409\) | −522118. | −0.154334 | −0.0771668 | − | 0.997018i | \(-0.524587\pi\) | ||||
−0.0771668 | + | 0.997018i | \(0.524587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.55079e6 | 0.744853 | ||||||||
\(412\) | −2.08915e6 | −0.606354 | ||||||||
\(413\) | 603653. | 0.174146 | ||||||||
\(414\) | −863489. | −0.247603 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −52673.8 | −0.0149232 | ||||||||
\(417\) | 1.80459e6 | 0.508205 | ||||||||
\(418\) | 453976. | 0.127084 | ||||||||
\(419\) | 4.42421e6 | 1.23112 | 0.615561 | − | 0.788090i | \(-0.288930\pi\) | ||||
0.615561 | + | 0.788090i | \(0.288930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 41986.3 | 0.0115452 | 0.00577261 | − | 0.999983i | \(-0.498163\pi\) | ||||
0.00577261 | + | 0.999983i | \(0.498163\pi\) | |||||||
\(422\) | −2.41100e6 | −0.659047 | ||||||||
\(423\) | 537725. | 0.146120 | ||||||||
\(424\) | 1.40760e6 | 0.380245 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.54654e6 | −0.412894 | ||||||||
\(427\) | −126729. | −0.0336361 | ||||||||
\(428\) | −3.63657e6 | −0.959582 | ||||||||
\(429\) | −9980.29 | −0.00261818 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.90650e6 | 0.753664 | 0.376832 | − | 0.926282i | \(-0.377013\pi\) | ||||
0.376832 | + | 0.926282i | \(0.377013\pi\) | |||||||
\(432\) | −17933.4 | −0.00462331 | ||||||||
\(433\) | −1.49232e6 | −0.382508 | −0.191254 | − | 0.981541i | \(-0.561255\pi\) | ||||
−0.191254 | + | 0.981541i | \(0.561255\pi\) | |||||||
\(434\) | 75169.7 | 0.0191566 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9642.04 | 0.00242914 | ||||||||
\(437\) | −3.18229e6 | −0.797144 | ||||||||
\(438\) | 1.57365e6 | 0.391943 | ||||||||
\(439\) | −6.08351e6 | −1.50658 | −0.753291 | − | 0.657687i | \(-0.771535\pi\) | ||||
−0.753291 | + | 0.657687i | \(0.771535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.34212e6 | −0.328620 | ||||||||
\(442\) | 48125.5 | 0.0117171 | ||||||||
\(443\) | 1.20270e6 | 0.291171 | 0.145586 | − | 0.989346i | \(-0.453493\pi\) | ||||
0.145586 | + | 0.989346i | \(0.453493\pi\) | |||||||
\(444\) | −352509. | −0.0848618 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.41427e6 | 0.336662 | ||||||||
\(447\) | 3.15768e6 | 0.747479 | ||||||||
\(448\) | 326237. | 0.0767960 | ||||||||
\(449\) | −935321. | −0.218950 | −0.109475 | − | 0.993990i | \(-0.534917\pi\) | ||||
−0.109475 | + | 0.993990i | \(0.534917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00203e6 | 0.463479 | ||||||||
\(452\) | 2.12815e6 | 0.489956 | ||||||||
\(453\) | −597786. | −0.136867 | ||||||||
\(454\) | 1.15931e6 | 0.263974 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.73668e6 | −0.391118 | ||||||||
\(457\) | −530855. | −0.118901 | −0.0594504 | − | 0.998231i | \(-0.518935\pi\) | ||||
−0.0594504 | + | 0.998231i | \(0.518935\pi\) | |||||||
\(458\) | 3.03160e6 | 0.675318 | ||||||||
\(459\) | −1.07981e6 | −0.239230 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.26064e6 | 0.495426 | 0.247713 | − | 0.968833i | \(-0.420321\pi\) | ||||
0.247713 | + | 0.968833i | \(0.420321\pi\) | |||||||
\(462\) | 59514.1 | 0.0129722 | ||||||||
\(463\) | 3.48143e6 | 0.754753 | 0.377376 | − | 0.926060i | \(-0.376826\pi\) | ||||
0.377376 | + | 0.926060i | \(0.376826\pi\) | |||||||
\(464\) | −92571.8 | −0.0199611 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.61746e6 | −0.985006 | ||||||||
\(467\) | 6.14838e6 | 1.30457 | 0.652287 | − | 0.757972i | \(-0.273810\pi\) | ||||
0.652287 | + | 0.757972i | \(0.273810\pi\) | |||||||
\(468\) | 14424.8 | 0.00304435 | ||||||||
\(469\) | 589005. | 0.123648 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.56573e6 | 0.948326 | ||||||||
\(472\) | −7.14012e6 | −1.47520 | ||||||||
\(473\) | −1.65133e6 | −0.339375 | ||||||||
\(474\) | 524032. | 0.107130 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 443692. | 0.0897562 | ||||||||
\(477\) | −625307. | −0.125834 | ||||||||
\(478\) | −3.14813e6 | −0.630206 | ||||||||
\(479\) | −5.92932e6 | −1.18077 | −0.590386 | − | 0.807121i | \(-0.701024\pi\) | ||||
−0.590386 | + | 0.807121i | \(0.701024\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18472.8 | −0.00364058 | ||||||||
\(482\) | 2.79327e6 | 0.547641 | ||||||||
\(483\) | −417183. | −0.0813690 | ||||||||
\(484\) | −284498. | −0.0552035 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 209340. | 0.0402033 | ||||||||
\(487\) | −8.99316e6 | −1.71826 | −0.859132 | − | 0.511754i | \(-0.828996\pi\) | ||||
−0.859132 | + | 0.511754i | \(0.828996\pi\) | |||||||
\(488\) | 1.49897e6 | 0.284934 | ||||||||
\(489\) | −3.61927e6 | −0.684461 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.74306e6 | −0.513489 | −0.256745 | − | 0.966479i | \(-0.582650\pi\) | ||||
−0.256745 | + | 0.966479i | \(0.582650\pi\) | |||||||
\(492\) | −2.89359e6 | −0.538921 | ||||||||
\(493\) | −5.57397e6 | −1.03287 | ||||||||
\(494\) | −34384.5 | −0.00633936 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −33836.5 | −0.00617563 | ||||||||
\(497\) | −747192. | −0.135688 | ||||||||
\(498\) | −13390.3 | −0.00241945 | ||||||||
\(499\) | −6.85332e6 | −1.23211 | −0.616055 | − | 0.787703i | \(-0.711270\pi\) | ||||
−0.616055 | + | 0.787703i | \(0.711270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.63927e6 | 0.469774 | ||||||||
\(502\) | −3.80865e6 | −0.674546 | ||||||||
\(503\) | −3.53279e6 | −0.622583 | −0.311292 | − | 0.950314i | \(-0.600762\pi\) | ||||
−0.311292 | + | 0.950314i | \(0.600762\pi\) | |||||||
\(504\) | −227671. | −0.0399237 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.28990e6 | −0.223965 | ||||||||
\(507\) | −3.34088e6 | −0.577220 | ||||||||
\(508\) | −27960.4 | −0.00480711 | ||||||||
\(509\) | −8.42114e6 | −1.44071 | −0.720354 | − | 0.693606i | \(-0.756021\pi\) | ||||
−0.720354 | + | 0.693606i | \(0.756021\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 760288. | 0.128803 | ||||||||
\(512\) | −284922. | −0.0480343 | ||||||||
\(513\) | 771499. | 0.129432 | ||||||||
\(514\) | 649012. | 0.108354 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.38671e6 | 0.394616 | ||||||||
\(517\) | 803269. | 0.132170 | ||||||||
\(518\) | 110156. | 0.0180379 | ||||||||
\(519\) | −627003. | −0.102177 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.11375e6 | 0.179761 | 0.0898804 | − | 0.995953i | \(-0.471352\pi\) | ||||
0.0898804 | + | 0.995953i | \(0.471352\pi\) | |||||||
\(522\) | 1.08061e6 | 0.173577 | ||||||||
\(523\) | −1.22565e6 | −0.195935 | −0.0979674 | − | 0.995190i | \(-0.531234\pi\) | ||||
−0.0979674 | + | 0.995190i | \(0.531234\pi\) | |||||||
\(524\) | −5.63100e6 | −0.895895 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.37047e6 | −1.00394 | ||||||||
\(527\) | −2.03738e6 | −0.319555 | ||||||||
\(528\) | −26789.4 | −0.00418194 | ||||||||
\(529\) | 2.60565e6 | 0.404834 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.17191e6 | 0.488185 | ||||||||
\(532\) | −317007. | −0.0485613 | ||||||||
\(533\) | −151636. | −0.0231198 | ||||||||
\(534\) | −545005. | −0.0827080 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.96686e6 | −1.04743 | ||||||||
\(537\) | 1.24194e6 | 0.185851 | ||||||||
\(538\) | −703987. | −0.104860 | ||||||||
\(539\) | −2.00489e6 | −0.297248 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −47884.8 | −0.00703403 | −0.00351701 | − | 0.999994i | \(-0.501120\pi\) | ||||
−0.00351701 | + | 0.999994i | \(0.501120\pi\) | |||||||
\(542\) | 7.42065e6 | 1.08503 | ||||||||
\(543\) | 3.28951e6 | 0.478776 | ||||||||
\(544\) | −8.51334e6 | −1.23340 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4507.64 | −0.000647095 0 | ||||||||
\(547\) | 1.04705e6 | 0.149624 | 0.0748118 | − | 0.997198i | \(-0.476164\pi\) | ||||
0.0748118 | + | 0.997198i | \(0.476164\pi\) | |||||||
\(548\) | −5.50734e6 | −0.783412 | ||||||||
\(549\) | −665899. | −0.0942926 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.98247e6 | 0.558822 | ||||||||
\(552\) | 4.93451e6 | 0.689282 | ||||||||
\(553\) | 253179. | 0.0352059 | ||||||||
\(554\) | 2.24820e6 | 0.311215 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.89624e6 | −0.534514 | ||||||||
\(557\) | 8.54477e6 | 1.16698 | 0.583488 | − | 0.812121i | \(-0.301687\pi\) | ||||
0.583488 | + | 0.812121i | \(0.301687\pi\) | |||||||
\(558\) | 394980. | 0.0537020 | ||||||||
\(559\) | 125073. | 0.0169291 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.61305e6 | −0.216392 | ||||||||
\(562\) | 2.56743e6 | 0.342892 | ||||||||
\(563\) | 3.21883e6 | 0.427984 | 0.213992 | − | 0.976835i | \(-0.431353\pi\) | ||||
0.213992 | + | 0.976835i | \(0.431353\pi\) | |||||||
\(564\) | −1.16099e6 | −0.153684 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.58957e6 | −1.12702 | ||||||||
\(567\) | 101140. | 0.0132119 | ||||||||
\(568\) | 8.83792e6 | 1.14942 | ||||||||
\(569\) | −9.31971e6 | −1.20676 | −0.603381 | − | 0.797453i | \(-0.706180\pi\) | ||||
−0.603381 | + | 0.797453i | \(0.706180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.38799e7 | 1.78154 | 0.890769 | − | 0.454457i | \(-0.150167\pi\) | ||||
0.890769 | + | 0.454457i | \(0.150167\pi\) | |||||||
\(572\) | 21548.1 | 0.00275372 | ||||||||
\(573\) | 3.05256e6 | 0.388398 | ||||||||
\(574\) | 904228. | 0.114551 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.71422e6 | 0.215283 | ||||||||
\(577\) | −4.91293e6 | −0.614330 | −0.307165 | − | 0.951656i | \(-0.599380\pi\) | ||||
−0.307165 | + | 0.951656i | \(0.599380\pi\) | |||||||
\(578\) | 2.74457e6 | 0.341708 | ||||||||
\(579\) | −763335. | −0.0946278 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6469.34 | −0.000795096 0 | ||||||||
\(582\) | −110543. | −0.0135277 | ||||||||
\(583\) | −934100. | −0.113821 | ||||||||
\(584\) | −8.99282e6 | −1.09110 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.63387e6 | −0.316848 | ||||||||
\(587\) | 5.36479e6 | 0.642624 | 0.321312 | − | 0.946973i | \(-0.395876\pi\) | ||||
0.321312 | + | 0.946973i | \(0.395876\pi\) | |||||||
\(588\) | 2.89773e6 | 0.345632 | ||||||||
\(589\) | 1.45566e6 | 0.172890 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −141946. | −0.0167169 | ||||||||
\(592\) | −49585.3 | −0.00581498 | ||||||||
\(593\) | 8.86855e6 | 1.03566 | 0.517829 | − | 0.855484i | \(-0.326741\pi\) | ||||
0.517829 | + | 0.855484i | \(0.326741\pi\) | |||||||
\(594\) | 312718. | 0.0363652 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.81764e6 | −0.786174 | ||||||||
\(597\) | 8.44168e6 | 0.969377 | ||||||||
\(598\) | 97698.3 | 0.0111721 | ||||||||
\(599\) | −1.10799e7 | −1.26174 | −0.630869 | − | 0.775889i | \(-0.717302\pi\) | ||||
−0.630869 | + | 0.775889i | \(0.717302\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.50666e6 | −0.621873 | −0.310937 | − | 0.950431i | \(-0.600643\pi\) | ||||
−0.310937 | + | 0.950431i | \(0.600643\pi\) | |||||||
\(602\) | −745828. | −0.0838779 | ||||||||
\(603\) | 3.09494e6 | 0.346624 | ||||||||
\(604\) | 1.29066e6 | 0.143953 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.78700e6 | 0.418903 | ||||||||
\(607\) | −1.29430e7 | −1.42581 | −0.712906 | − | 0.701259i | \(-0.752621\pi\) | ||||
−0.712906 | + | 0.701259i | \(0.752621\pi\) | |||||||
\(608\) | 6.08257e6 | 0.667311 | ||||||||
\(609\) | 522082. | 0.0570421 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −60840.2 | −0.00659307 | ||||||||
\(612\) | 2.33139e6 | 0.251615 | ||||||||
\(613\) | −3.41360e6 | −0.366911 | −0.183456 | − | 0.983028i | \(-0.558728\pi\) | ||||
−0.183456 | + | 0.983028i | \(0.558728\pi\) | |||||||
\(614\) | −4.46227e6 | −0.477678 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −340100. | −0.0361123 | ||||||||
\(617\) | −1.36370e7 | −1.44213 | −0.721067 | − | 0.692865i | \(-0.756348\pi\) | ||||
−0.721067 | + | 0.692865i | \(0.756348\pi\) | |||||||
\(618\) | 3.43038e6 | 0.361303 | ||||||||
\(619\) | −6.21254e6 | −0.651692 | −0.325846 | − | 0.945423i | \(-0.605649\pi\) | ||||
−0.325846 | + | 0.945423i | \(0.605649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.19210e6 | −0.228103 | ||||||||
\(622\) | −6.08042e6 | −0.630170 | ||||||||
\(623\) | −263312. | −0.0271801 | ||||||||
\(624\) | 2029.05 | 0.000208608 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.01360e7 | 1.03379 | ||||||||
\(627\) | 1.15249e6 | 0.117076 | ||||||||
\(628\) | −9.85772e6 | −0.997419 | ||||||||
\(629\) | −2.98565e6 | −0.300893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.32349e6 | −0.332293 | −0.166146 | − | 0.986101i | \(-0.553132\pi\) | ||||
−0.166146 | + | 0.986101i | \(0.553132\pi\) | |||||||
\(632\) | −2.99465e6 | −0.298231 | ||||||||
\(633\) | −6.12069e6 | −0.607143 | ||||||||
\(634\) | 5.70550e6 | 0.563729 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.35008e6 | 0.132348 | ||||||||
\(637\) | 151852. | 0.0148277 | ||||||||
\(638\) | 1.61424e6 | 0.157006 | ||||||||
\(639\) | −3.92614e6 | −0.380376 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.81780e6 | −0.174744 | −0.0873720 | − | 0.996176i | \(-0.527847\pi\) | ||||
−0.0873720 | + | 0.996176i | \(0.527847\pi\) | |||||||
\(642\) | 5.97124e6 | 0.571777 | ||||||||
\(643\) | −421961. | −0.0402481 | −0.0201240 | − | 0.999797i | \(-0.506406\pi\) | ||||
−0.0201240 | + | 0.999797i | \(0.506406\pi\) | |||||||
\(644\) | 900727. | 0.0855813 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.55736e6 | −0.523947 | ||||||||
\(647\) | −5.62498e6 | −0.528275 | −0.264138 | − | 0.964485i | \(-0.585087\pi\) | ||||
−0.264138 | + | 0.964485i | \(0.585087\pi\) | |||||||
\(648\) | −1.19630e6 | −0.111919 | ||||||||
\(649\) | 4.73828e6 | 0.441580 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 190830. | 0.0176479 | ||||||||
\(652\) | 7.81426e6 | 0.719894 | ||||||||
\(653\) | 1.69247e7 | 1.55324 | 0.776619 | − | 0.629970i | \(-0.216933\pi\) | ||||
0.776619 | + | 0.629970i | \(0.216933\pi\) | |||||||
\(654\) | −15832.2 | −0.00144743 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −407025. | −0.0369285 | ||||||||
\(657\) | 3.99495e6 | 0.361075 | ||||||||
\(658\) | 362800. | 0.0326665 | ||||||||
\(659\) | −480657. | −0.0431144 | −0.0215572 | − | 0.999768i | \(-0.506862\pi\) | ||||
−0.0215572 | + | 0.999768i | \(0.506862\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.53510e7 | −1.36657 | −0.683285 | − | 0.730151i | \(-0.739449\pi\) | ||||
−0.683285 | + | 0.730151i | \(0.739449\pi\) | |||||||
\(662\) | −4.31955e6 | −0.383083 | ||||||||
\(663\) | 122174. | 0.0107943 | ||||||||
\(664\) | 76520.5 | 0.00673531 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 578819. | 0.0505658 | ||||||||
\(667\) | −1.13156e7 | −0.984831 | ||||||||
\(668\) | −5.69836e6 | −0.494093 | ||||||||
\(669\) | 3.59033e6 | 0.310148 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −994738. | −0.0852909 | ||||||||
\(672\) | 797396. | 0.0681163 | ||||||||
\(673\) | −3.83589e6 | −0.326459 | −0.163229 | − | 0.986588i | \(-0.552191\pi\) | ||||
−0.163229 | + | 0.986588i | \(0.552191\pi\) | |||||||
\(674\) | −5.65545e6 | −0.479531 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.21319e6 | 0.607101 | ||||||||
\(677\) | −5.74417e6 | −0.481676 | −0.240838 | − | 0.970565i | \(-0.577422\pi\) | ||||
−0.240838 | + | 0.970565i | \(0.577422\pi\) | |||||||
\(678\) | −3.49443e6 | −0.291945 | ||||||||
\(679\) | −53407.5 | −0.00444557 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.94309e6 | 0.243185 | ||||||||
\(682\) | 590033. | 0.0485753 | ||||||||
\(683\) | 2.11651e7 | 1.73608 | 0.868038 | − | 0.496498i | \(-0.165381\pi\) | ||||
0.868038 | + | 0.496498i | \(0.165381\pi\) | |||||||
\(684\) | −1.66572e6 | −0.136133 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.82402e6 | −0.147986 | ||||||||
\(687\) | 7.69618e6 | 0.622133 | ||||||||
\(688\) | 335724. | 0.0270403 | ||||||||
\(689\) | 70749.5 | 0.00567774 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.20475e7 | −1.75657 | −0.878283 | − | 0.478142i | \(-0.841311\pi\) | ||||
−0.878283 | + | 0.478142i | \(0.841311\pi\) | |||||||
\(692\) | 1.35374e6 | 0.107466 | ||||||||
\(693\) | 151085. | 0.0119506 | ||||||||
\(694\) | 1.05747e7 | 0.833432 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.17528e6 | −0.483207 | ||||||||
\(697\) | −2.45079e7 | −1.91084 | ||||||||
\(698\) | 5.14482e6 | 0.399698 | ||||||||
\(699\) | −1.17221e7 | −0.907431 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.26680e7 | 0.973676 | 0.486838 | − | 0.873492i | \(-0.338150\pi\) | ||||
0.486838 | + | 0.873492i | \(0.338150\pi\) | |||||||
\(702\) | −23685.5 | −0.00181401 | ||||||||
\(703\) | 2.13317e6 | 0.162794 | ||||||||
\(704\) | 2.56075e6 | 0.194731 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.32341e6 | 0.0999266 | ||||||||
\(707\) | 1.82964e6 | 0.137663 | ||||||||
\(708\) | −6.84837e6 | −0.513457 | ||||||||
\(709\) | −6.24919e6 | −0.466883 | −0.233441 | − | 0.972371i | \(-0.574999\pi\) | ||||
−0.233441 | + | 0.972371i | \(0.574999\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.33033e6 | 0.0986931 | ||||||||
\(712\) | 3.11450e6 | 0.230244 | ||||||||
\(713\) | −4.13603e6 | −0.304691 | ||||||||
\(714\) | −728542. | −0.0534822 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.68144e6 | −0.195472 | ||||||||
\(717\) | −7.99199e6 | −0.580573 | ||||||||
\(718\) | 5.67133e6 | 0.410558 | ||||||||
\(719\) | 2.29008e6 | 0.165207 | 0.0826036 | − | 0.996582i | \(-0.473676\pi\) | ||||
0.0826036 | + | 0.996582i | \(0.473676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.65734e6 | 0.118734 | ||||||||
\(722\) | −4.80765e6 | −0.343233 | ||||||||
\(723\) | 7.09114e6 | 0.504511 | ||||||||
\(724\) | −7.10229e6 | −0.503561 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 467146. | 0.0328936 | ||||||||
\(727\) | −5.32482e6 | −0.373653 | −0.186827 | − | 0.982393i | \(-0.559820\pi\) | ||||
−0.186827 | + | 0.982393i | \(0.559820\pi\) | |||||||
\(728\) | 25759.5 | 0.00180139 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.02147e7 | 1.39918 | ||||||||
\(732\) | 1.43772e6 | 0.0991739 | ||||||||
\(733\) | 2.07826e7 | 1.42870 | 0.714348 | − | 0.699790i | \(-0.246723\pi\) | ||||
0.714348 | + | 0.699790i | \(0.246723\pi\) | |||||||
\(734\) | −1.30184e7 | −0.891902 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.72827e7 | −1.17603 | ||||||||
\(737\) | 4.62330e6 | 0.313533 | ||||||||
\(738\) | 4.75128e6 | 0.321122 | ||||||||
\(739\) | 1.24923e7 | 0.841454 | 0.420727 | − | 0.907187i | \(-0.361775\pi\) | ||||
0.420727 | + | 0.907187i | \(0.361775\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −87290.3 | −0.00584010 | ||||||||
\(742\) | −421890. | −0.0281313 | ||||||||
\(743\) | −2.39696e7 | −1.59290 | −0.796450 | − | 0.604705i | \(-0.793291\pi\) | ||||
−0.796450 | + | 0.604705i | \(0.793291\pi\) | |||||||
\(744\) | −2.25717e6 | −0.149497 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.03036e6 | −0.0677864 | ||||||||
\(747\) | −33993.3 | −0.00222890 | ||||||||
\(748\) | 3.48269e6 | 0.227594 | ||||||||
\(749\) | 2.88493e6 | 0.187901 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.76984e6 | 0.114508 | 0.0572539 | − | 0.998360i | \(-0.481766\pi\) | ||||
0.0572539 | + | 0.998360i | \(0.481766\pi\) | |||||||
\(752\) | −163309. | −0.0105309 | ||||||||
\(753\) | −9.66883e6 | −0.621422 | ||||||||
\(754\) | −122264. | −0.00783197 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −218368. | −0.0138958 | ||||||||
\(757\) | −1.88709e7 | −1.19689 | −0.598443 | − | 0.801165i | \(-0.704214\pi\) | ||||
−0.598443 | + | 0.801165i | \(0.704214\pi\) | |||||||
\(758\) | 1.67548e7 | 1.05917 | ||||||||
\(759\) | −3.27461e6 | −0.206327 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.56502e6 | 0.598721 | 0.299360 | − | 0.954140i | \(-0.403227\pi\) | ||||
0.299360 | + | 0.954140i | \(0.403227\pi\) | |||||||
\(762\) | 45910.9 | 0.00286437 | ||||||||
\(763\) | −7649.12 | −0.000475664 0 | ||||||||
\(764\) | −6.59068e6 | −0.408504 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.02025e6 | 0.370717 | ||||||||
\(767\) | −358881. | −0.0220274 | ||||||||
\(768\) | −9.56941e6 | −0.585439 | ||||||||
\(769\) | 2.63227e7 | 1.60514 | 0.802572 | − | 0.596556i | \(-0.203464\pi\) | ||||
0.802572 | + | 0.596556i | \(0.203464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.64761e6 | 0.0998205 | ||||||||
\(772\) | 1.64809e6 | 0.0995264 | ||||||||
\(773\) | −1.07241e7 | −0.645525 | −0.322762 | − | 0.946480i | \(-0.604611\pi\) | ||||
−0.322762 | + | 0.946480i | \(0.604611\pi\) | |||||||
\(774\) | −3.91897e6 | −0.235136 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 631713. | 0.0376587 | ||||||||
\(777\) | 279649. | 0.0166173 | ||||||||
\(778\) | −2.17751e6 | −0.128977 | ||||||||
\(779\) | 1.75103e7 | 1.03383 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.86497e6 | −0.344063 | ||||||||
\(782\) | 1.57904e7 | 0.923369 | ||||||||
\(783\) | 2.74329e6 | 0.159907 | ||||||||
\(784\) | 407606. | 0.0236837 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.24609e6 | 0.533829 | ||||||||
\(787\) | −2.31773e7 | −1.33391 | −0.666954 | − | 0.745099i | \(-0.732402\pi\) | ||||
−0.666954 | + | 0.745099i | \(0.732402\pi\) | |||||||
\(788\) | 306472. | 0.0175823 | ||||||||
\(789\) | −1.61724e7 | −0.924873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.68828e6 | −0.0959411 | ||||||||
\(792\) | −1.78706e6 | −0.101234 | ||||||||
\(793\) | 75342.3 | 0.00425457 | ||||||||
\(794\) | 538604. | 0.0303192 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.82262e7 | −1.01956 | ||||||||
\(797\) | 5.94831e6 | 0.331702 | 0.165851 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165851 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(798\) | 520526. | 0.0289358 | ||||||||
\(799\) | −9.83323e6 | −0.544916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.38358e6 | −0.0761942 | ||||||||
\(802\) | −1.45972e6 | −0.0801371 | ||||||||
\(803\) | 5.96776e6 | 0.326605 | ||||||||
\(804\) | −6.68219e6 | −0.364568 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −44689.6 | −0.00242308 | ||||||||
\(807\) | −1.78718e6 | −0.0966014 | ||||||||
\(808\) | −2.16413e7 | −1.16615 | ||||||||
\(809\) | 2.46026e6 | 0.132163 | 0.0660815 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660815 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.67473e7 | −0.894112 | −0.447056 | − | 0.894506i | \(-0.647528\pi\) | ||||
−0.447056 | + | 0.894506i | \(0.647528\pi\) | |||||||
\(812\) | −1.12721e6 | −0.0599950 | ||||||||
\(813\) | 1.88384e7 | 0.999582 | ||||||||
\(814\) | 864655. | 0.0457385 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 327943. | 0.0172414 | ||||||||
\(817\) | −1.44429e7 | −0.757008 | ||||||||
\(818\) | −1.85101e6 | −0.0967220 | ||||||||
\(819\) | −11443.3 | −0.000596132 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.04537e7 | 1.05904 | 0.529521 | − | 0.848297i | \(-0.322372\pi\) | ||||
0.529521 | + | 0.848297i | \(0.322372\pi\) | |||||||
\(822\) | 9.04305e6 | 0.466805 | ||||||||
\(823\) | 6.10386e6 | 0.314127 | 0.157063 | − | 0.987589i | \(-0.449797\pi\) | ||||
0.157063 | + | 0.987589i | \(0.449797\pi\) | |||||||
\(824\) | −1.96033e7 | −1.00580 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.14007e6 | 0.109138 | ||||||||
\(827\) | −1.25743e7 | −0.639321 | −0.319661 | − | 0.947532i | \(-0.603569\pi\) | ||||
−0.319661 | + | 0.947532i | \(0.603569\pi\) | |||||||
\(828\) | 4.73289e6 | 0.239911 | ||||||||
\(829\) | −3.64808e6 | −0.184365 | −0.0921824 | − | 0.995742i | \(-0.529384\pi\) | ||||
−0.0921824 | + | 0.995742i | \(0.529384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.70740e6 | 0.286705 | ||||||||
\(832\) | −193953. | −0.00971378 | ||||||||
\(833\) | 2.45429e7 | 1.22550 | ||||||||
\(834\) | 6.39763e6 | 0.318496 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.48830e6 | −0.123137 | ||||||||
\(837\) | 1.00272e6 | 0.0494726 | ||||||||
\(838\) | 1.56847e7 | 0.771552 | ||||||||
\(839\) | 3.98638e7 | 1.95512 | 0.977560 | − | 0.210657i | \(-0.0675602\pi\) | ||||
0.977560 | + | 0.210657i | \(0.0675602\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.35033e6 | −0.309604 | ||||||||
\(842\) | 148849. | 0.00723547 | ||||||||
\(843\) | 6.51781e6 | 0.315888 | ||||||||
\(844\) | 1.32150e7 | 0.638573 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.90634e6 | 0.0915744 | ||||||||
\(847\) | 225695. | 0.0108097 | ||||||||
\(848\) | 189908. | 0.00906886 | ||||||||
\(849\) | −2.18059e7 | −1.03826 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.06108e6 | −0.286897 | ||||||||
\(852\) | 8.47680e6 | 0.400067 | ||||||||
\(853\) | −7.03128e6 | −0.330873 | −0.165437 | − | 0.986220i | \(-0.552903\pi\) | ||||
−0.165437 | + | 0.986220i | \(0.552903\pi\) | |||||||
\(854\) | −449278. | −0.0210800 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.41234e7 | −1.59172 | ||||||||
\(857\) | 5.35026e6 | 0.248842 | 0.124421 | − | 0.992230i | \(-0.460293\pi\) | ||||
0.124421 | + | 0.992230i | \(0.460293\pi\) | |||||||
\(858\) | −35382.0 | −0.00164083 | ||||||||
\(859\) | 3.74127e7 | 1.72996 | 0.864981 | − | 0.501805i | \(-0.167331\pi\) | ||||
0.864981 | + | 0.501805i | \(0.167331\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.29552e6 | 0.105529 | ||||||||
\(862\) | 1.03041e7 | 0.472326 | ||||||||
\(863\) | −2.03619e7 | −0.930661 | −0.465331 | − | 0.885137i | \(-0.654065\pi\) | ||||
−0.465331 | + | 0.885137i | \(0.654065\pi\) | |||||||
\(864\) | 4.18993e6 | 0.190951 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.29054e6 | −0.239721 | ||||||||
\(867\) | 6.96750e6 | 0.314796 | ||||||||
\(868\) | −412014. | −0.0185615 | ||||||||
\(869\) | 1.98729e6 | 0.0892713 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −350173. | −0.0156400 | ||||||||
\(872\) | 90475.2 | 0.00402938 | ||||||||
\(873\) | −280630. | −0.0124623 | ||||||||
\(874\) | −1.12818e7 | −0.499576 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.62537e6 | −0.379767 | ||||||||
\(877\) | −2.69907e7 | −1.18499 | −0.592497 | − | 0.805573i | \(-0.701858\pi\) | ||||
−0.592497 | + | 0.805573i | \(0.701858\pi\) | |||||||
\(878\) | −2.15672e7 | −0.944186 | ||||||||
\(879\) | −6.68648e6 | −0.291894 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.82848e6 | −0.252997 | −0.126499 | − | 0.991967i | \(-0.540374\pi\) | ||||
−0.126499 | + | 0.991967i | \(0.540374\pi\) | |||||||
\(882\) | −4.75807e6 | −0.205949 | ||||||||
\(883\) | 4.30317e6 | 0.185732 | 0.0928661 | − | 0.995679i | \(-0.470397\pi\) | ||||
0.0928661 | + | 0.995679i | \(0.470397\pi\) | |||||||
\(884\) | −263782. | −0.0113531 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.26381e6 | 0.182479 | ||||||||
\(887\) | 5.28627e6 | 0.225601 | 0.112800 | − | 0.993618i | \(-0.464018\pi\) | ||||
0.112800 | + | 0.993618i | \(0.464018\pi\) | |||||||
\(888\) | −3.30773e6 | −0.140766 | ||||||||
\(889\) | 22181.2 | 0.000941308 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −7.75178e6 | −0.326204 | ||||||||
\(893\) | 7.02560e6 | 0.294819 | ||||||||
\(894\) | 1.11946e7 | 0.468450 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.67861e6 | −0.0698522 | ||||||||
\(897\) | 248022. | 0.0102922 | ||||||||
\(898\) | −3.31589e6 | −0.137217 | ||||||||
\(899\) | 5.17601e6 | 0.213597 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14348e7 | 0.469263 | ||||||||
\(902\) | 7.09759e6 | 0.290466 | ||||||||
\(903\) | −1.89340e6 | −0.0772721 | ||||||||
\(904\) | 1.99693e7 | 0.812723 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.11926e6 | −0.0857758 | ||||||||
\(907\) | −1.24628e6 | −0.0503035 | −0.0251518 | − | 0.999684i | \(-0.508007\pi\) | ||||
−0.0251518 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(908\) | −6.35434e6 | −0.255774 | ||||||||
\(909\) | 9.61386e6 | 0.385912 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.11472e6 | −0.284028 | −0.142014 | − | 0.989865i | \(-0.545358\pi\) | ||||
−0.142014 | + | 0.989865i | \(0.545358\pi\) | |||||||
\(912\) | −234307. | −0.00932820 | ||||||||
\(913\) | −50780.1 | −0.00201612 | ||||||||
\(914\) | −1.88198e6 | −0.0745160 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.66166e7 | −0.654339 | ||||||||
\(917\) | 4.46713e6 | 0.175430 | ||||||||
\(918\) | −3.82814e6 | −0.149927 | ||||||||
\(919\) | 8.70813e6 | 0.340123 | 0.170061 | − | 0.985433i | \(-0.445603\pi\) | ||||
0.170061 | + | 0.985433i | \(0.445603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.13282e7 | −0.440058 | ||||||||
\(922\) | 8.01440e6 | 0.310487 | ||||||||
\(923\) | 444218. | 0.0171629 | ||||||||
\(924\) | −326204. | −0.0125692 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.23423e7 | 0.473009 | ||||||||
\(927\) | 8.70854e6 | 0.332848 | ||||||||
\(928\) | 2.16284e7 | 0.824430 | ||||||||
\(929\) | −1.65935e6 | −0.0630809 | −0.0315405 | − | 0.999502i | \(-0.510041\pi\) | ||||
−0.0315405 | + | 0.999502i | \(0.510041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.75353e7 | −0.663040 | ||||||||
\(932\) | 2.53089e7 | 0.954406 | ||||||||
\(933\) | −1.54361e7 | −0.580541 | ||||||||
\(934\) | 2.17972e7 | 0.817585 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 135354. | 0.00504987 | ||||||||
\(937\) | −3.17616e7 | −1.18183 | −0.590913 | − | 0.806735i | \(-0.701232\pi\) | ||||
−0.590913 | + | 0.806735i | \(0.701232\pi\) | |||||||
\(938\) | 2.08814e6 | 0.0774911 | ||||||||
\(939\) | 2.57318e7 | 0.952371 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.87851e7 | 1.79603 | 0.898014 | − | 0.439966i | \(-0.145010\pi\) | ||||
0.898014 | + | 0.439966i | \(0.145010\pi\) | |||||||
\(942\) | 1.61864e7 | 0.594323 | ||||||||
\(943\) | −4.97529e7 | −1.82196 | ||||||||
\(944\) | −963319. | −0.0351836 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.85426e6 | −0.212689 | ||||||||
\(947\) | −9.76025e6 | −0.353660 | −0.176830 | − | 0.984241i | \(-0.556584\pi\) | ||||
−0.176830 | + | 0.984241i | \(0.556584\pi\) | |||||||
\(948\) | −2.87228e6 | −0.103802 | ||||||||
\(949\) | −452003. | −0.0162921 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.44843e7 | 0.519332 | ||||||||
\(952\) | 4.16335e6 | 0.148885 | ||||||||
\(953\) | 3.78772e7 | 1.35097 | 0.675485 | − | 0.737374i | \(-0.263934\pi\) | ||||
0.675485 | + | 0.737374i | \(0.263934\pi\) | |||||||
\(954\) | −2.21683e6 | −0.0788609 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.72553e7 | 0.610628 | ||||||||
\(957\) | 4.09800e6 | 0.144641 | ||||||||
\(958\) | −2.10206e7 | −0.739998 | ||||||||
\(959\) | 4.36903e6 | 0.153405 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.67372e7 | −0.933916 | ||||||||
\(962\) | −65489.7 | −0.00228158 | ||||||||
\(963\) | 1.51589e7 | 0.526747 | ||||||||
\(964\) | −1.53103e7 | −0.530628 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.47899e6 | −0.0509945 | ||||||||
\(967\) | 1.59962e7 | 0.550113 | 0.275056 | − | 0.961428i | \(-0.411304\pi\) | ||||
0.275056 | + | 0.961428i | \(0.411304\pi\) | |||||||
\(968\) | −2.66957e6 | −0.0915698 | ||||||||
\(969\) | −1.41082e7 | −0.482683 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.23637e7 | 1.78231 | 0.891153 | − | 0.453703i | \(-0.149897\pi\) | ||||
0.891153 | + | 0.453703i | \(0.149897\pi\) | |||||||
\(972\) | −1.14742e6 | −0.0389544 | ||||||||
\(973\) | 3.09093e6 | 0.104666 | ||||||||
\(974\) | −3.18825e7 | −1.07685 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 202236. | 0.00679569 | ||||||||
\(977\) | 5.78033e6 | 0.193739 | 0.0968693 | − | 0.995297i | \(-0.469117\pi\) | ||||
0.0968693 | + | 0.995297i | \(0.469117\pi\) | |||||||
\(978\) | −1.28310e7 | −0.428957 | ||||||||
\(979\) | −2.06683e6 | −0.0689203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40192.5 | −0.00133344 | ||||||||
\(982\) | −9.72467e6 | −0.321807 | ||||||||
\(983\) | −2.58942e7 | −0.854709 | −0.427355 | − | 0.904084i | \(-0.640554\pi\) | ||||
−0.427355 | + | 0.904084i | \(0.640554\pi\) | |||||||
\(984\) | −2.71518e7 | −0.893945 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.97608e7 | −0.647310 | ||||||||
\(987\) | 921022. | 0.0300938 | ||||||||
\(988\) | 188466. | 0.00614243 | ||||||||
\(989\) | 4.10374e7 | 1.33410 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.10539e7 | 1.00446 | 0.502230 | − | 0.864734i | \(-0.332513\pi\) | ||||
0.502230 | + | 0.864734i | \(0.332513\pi\) | |||||||
\(992\) | 7.90552e6 | 0.255065 | ||||||||
\(993\) | −1.09658e7 | −0.352913 | ||||||||
\(994\) | −2.64894e6 | −0.0850366 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 73393.8 | 0.00234429 | ||||||||
\(997\) | 5.56862e7 | 1.77423 | 0.887115 | − | 0.461549i | \(-0.152706\pi\) | ||||
0.887115 | + | 0.461549i | \(0.152706\pi\) | |||||||
\(998\) | −2.42963e7 | −0.772172 | ||||||||
\(999\) | 1.46942e6 | 0.0465835 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 825.6.a.t.1.7 | ✓ | 10 | |
5.4 | even | 2 | 825.6.a.u.1.4 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.t.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial | |
825.6.a.u.1.4 | yes | 10 | 5.4 | even | 2 |