Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [464,6,Mod(1,464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(464, 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("464.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 464 = 2^{4} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 464.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: | \(74.4180923932\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3257317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 34x^{2} - 27x + 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.10057\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 464.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 17.5258 | 1.12428 | 0.562141 | − | 0.827041i | \(-0.309978\pi\) | ||||
0.562141 | + | 0.827041i | \(0.309978\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 32.5670 | 0.582577 | 0.291289 | − | 0.956635i | \(-0.405916\pi\) | ||||
0.291289 | + | 0.956635i | \(0.405916\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 220.793 | 1.70310 | 0.851551 | − | 0.524272i | \(-0.175663\pi\) | ||||
0.851551 | + | 0.524272i | \(0.175663\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 64.1549 | 0.264012 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 85.7296 | 0.213623 | 0.106812 | − | 0.994279i | \(-0.465936\pi\) | ||||
0.106812 | + | 0.994279i | \(0.465936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1034.02 | 1.69695 | 0.848475 | − | 0.529235i | \(-0.177521\pi\) | ||||
0.848475 | + | 0.529235i | \(0.177521\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 570.765 | 0.654981 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −313.020 | −0.262694 | −0.131347 | − | 0.991336i | \(-0.541930\pi\) | ||||
−0.131347 | + | 0.991336i | \(0.541930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −458.534 | −0.291398 | −0.145699 | − | 0.989329i | \(-0.546543\pi\) | ||||
−0.145699 | + | 0.989329i | \(0.546543\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3869.58 | 1.91477 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3448.84 | 1.35942 | 0.679709 | − | 0.733482i | \(-0.262106\pi\) | ||||
0.679709 | + | 0.733482i | \(0.262106\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2064.39 | −0.660604 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3134.41 | −0.827459 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −841.000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7983.23 | 1.49202 | 0.746009 | − | 0.665936i | \(-0.231967\pi\) | ||||
0.746009 | + | 0.665936i | \(0.231967\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1502.48 | 0.240173 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7190.58 | 0.992188 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 152.624 | 0.0183282 | 0.00916409 | − | 0.999958i | \(-0.497083\pi\) | ||||
0.00916409 | + | 0.999958i | \(0.497083\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18122.0 | 1.90785 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18492.2 | −1.71802 | −0.859011 | − | 0.511957i | \(-0.828921\pi\) | ||||
−0.859011 | + | 0.511957i | \(0.828921\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2072.84 | −0.170960 | −0.0854799 | − | 0.996340i | \(-0.527242\pi\) | ||||
−0.0854799 | + | 0.996340i | \(0.527242\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2089.33 | 0.153807 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −15845.6 | −1.04632 | −0.523159 | − | 0.852235i | \(-0.675247\pi\) | ||||
−0.523159 | + | 0.852235i | \(0.675247\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 31942.6 | 1.90055 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5485.94 | −0.295343 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9240.52 | 0.451863 | 0.225931 | − | 0.974143i | \(-0.427457\pi\) | ||||
0.225931 | + | 0.974143i | \(0.427457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2791.96 | 0.124452 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8036.19 | −0.327614 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14323.2 | 0.535686 | 0.267843 | − | 0.963463i | \(-0.413689\pi\) | ||||
0.267843 | + | 0.963463i | \(0.413689\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −19580.2 | −0.673739 | −0.336870 | − | 0.941551i | \(-0.609368\pi\) | ||||
−0.336870 | + | 0.941551i | \(0.609368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14165.0 | 0.449639 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 33674.9 | 0.988604 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9193.70 | 0.250209 | 0.125105 | − | 0.992144i | \(-0.460073\pi\) | ||||
0.125105 | + | 0.992144i | \(0.460073\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 60443.8 | 1.52837 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 19374.7 | 0.456131 | 0.228066 | − | 0.973646i | \(-0.426760\pi\) | ||||
0.228066 | + | 0.973646i | \(0.426760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −56912.4 | −1.24997 | −0.624985 | − | 0.780637i | \(-0.714895\pi\) | ||||
−0.624985 | + | 0.780637i | \(0.714895\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −36180.1 | −0.742706 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18928.5 | 0.363822 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −51573.6 | −0.929736 | −0.464868 | − | 0.885380i | \(-0.653898\pi\) | ||||
−0.464868 | + | 0.885380i | \(0.653898\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −70522.8 | −1.19431 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −19978.1 | −0.318317 | −0.159158 | − | 0.987253i | \(-0.550878\pi\) | ||||
−0.159158 | + | 0.987253i | \(0.550878\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10194.2 | −0.153040 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14739.2 | −0.208774 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 130663. | 1.74855 | 0.874274 | − | 0.485432i | \(-0.161338\pi\) | ||||
0.874274 | + | 0.485432i | \(0.161338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 228304. | 2.89008 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 139913. | 1.67745 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14933.1 | −0.169762 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 43603.5 | 0.470535 | 0.235268 | − | 0.971931i | \(-0.424403\pi\) | ||||
0.235268 | + | 0.971931i | \(0.424403\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5499.97 | 0.0563991 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −56686.0 | −0.552933 | −0.276467 | − | 0.961024i | \(-0.589164\pi\) | ||||
−0.276467 | + | 0.961024i | \(0.589164\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 111450. | 1.03511 | 0.517556 | − | 0.855649i | \(-0.326842\pi\) | ||||
0.517556 | + | 0.855649i | \(0.326842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 126021. | 1.11550 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −189434. | −1.59955 | −0.799775 | − | 0.600300i | \(-0.795048\pi\) | ||||
−0.799775 | + | 0.600300i | \(0.795048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 100232. | 0.808054 | 0.404027 | − | 0.914747i | \(-0.367610\pi\) | ||||
0.404027 | + | 0.914747i | \(0.367610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2674.87 | 0.0206061 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −103444. | −0.762092 | −0.381046 | − | 0.924556i | \(-0.624436\pi\) | ||||
−0.381046 | + | 0.924556i | \(0.624436\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 112318. | 0.791966 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 66337.2 | 0.448015 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −69112.8 | −0.447395 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −153701. | −0.954365 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −324091. | −1.93154 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −169003. | −0.967430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 247538. | 1.36186 | 0.680930 | − | 0.732349i | \(-0.261576\pi\) | ||||
0.680930 | + | 0.732349i | \(0.261576\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −36328.2 | −0.192207 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −198458. | −1.01040 | −0.505198 | − | 0.863004i | \(-0.668580\pi\) | ||||
−0.505198 | + | 0.863004i | \(0.668580\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −101241. | −0.496281 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −102078. | −0.482059 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 141442. | 0.643839 | 0.321920 | − | 0.946767i | \(-0.395672\pi\) | ||||
0.321920 | + | 0.946767i | \(0.395672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 325330. | 1.42819 | 0.714097 | − | 0.700047i | \(-0.246838\pi\) | ||||
0.714097 | + | 0.700047i | \(0.246838\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −277707. | −1.17636 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 88645.8 | 0.362508 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −27388.9 | −0.108182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 559821. | 2.13676 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −391462. | −1.44452 | −0.722261 | − | 0.691621i | \(-0.756897\pi\) | ||||
−0.722261 | + | 0.691621i | \(0.756897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 216585. | 0.773013 | 0.386507 | − | 0.922287i | \(-0.373682\pi\) | ||||
0.386507 | + | 0.922287i | \(0.373682\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20081.8 | −0.0693544 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 259990. | 0.869216 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 564396. | 1.82740 | 0.913702 | − | 0.406385i | \(-0.133211\pi\) | ||||
0.913702 | + | 0.406385i | \(0.133211\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 161948. | 0.508022 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 761480. | 2.31523 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −476986. | −1.40617 | −0.703083 | − | 0.711108i | \(-0.748194\pi\) | ||||
−0.703083 | + | 0.711108i | \(0.748194\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 48931.4 | 0.139919 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 203397. | 0.564357 | 0.282178 | − | 0.959362i | \(-0.408943\pi\) | ||||
0.282178 | + | 0.959362i | \(0.408943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 697898. | 1.87964 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29417.2 | −0.0769327 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −95409.0 | −0.242367 | −0.121184 | − | 0.992630i | \(-0.538669\pi\) | ||||
−0.121184 | + | 0.992630i | \(0.538669\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −455803. | −1.12508 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 251026. | 0.602263 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 327011. | 0.762833 | 0.381416 | − | 0.924403i | \(-0.375436\pi\) | ||||
0.381416 | + | 0.924403i | \(0.375436\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 108581. | 0.246353 | 0.123177 | − | 0.992385i | \(-0.460692\pi\) | ||||
0.123177 | + | 0.992385i | \(0.460692\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −343159. | −0.757473 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4970.52 | 0.0106776 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26835.1 | −0.0561176 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −692056. | −1.40925 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 315738. | 0.626244 | 0.313122 | − | 0.949713i | \(-0.398625\pi\) | ||||
0.313122 | + | 0.949713i | \(0.398625\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 41432.1 | 0.0800651 | 0.0400326 | − | 0.999198i | \(-0.487254\pi\) | ||||
0.0400326 | + | 0.999198i | \(0.487254\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 590180. | 1.11147 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 354739. | 0.651243 | 0.325622 | − | 0.945500i | \(-0.394426\pi\) | ||||
0.325622 | + | 0.945500i | \(0.394426\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 949129. | 1.69900 | 0.849498 | − | 0.527591i | \(-0.176905\pi\) | ||||
0.849498 | + | 0.527591i | \(0.176905\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 161127. | 0.281306 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −185687. | −0.316258 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −602236. | −1.00088 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 221260. | 0.358903 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −39309.9 | −0.0622495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 380574. | 0.588481 | 0.294241 | − | 0.955731i | \(-0.404933\pi\) | ||||
0.294241 | + | 0.955731i | \(0.404933\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 339558. | 0.512820 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −67506.2 | −0.0995973 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.76264e6 | 2.54106 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −997437. | −1.40532 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −323668. | −0.445779 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 68362.6 | 0.0920569 | 0.0460284 | − | 0.998940i | \(-0.485344\pi\) | ||||
0.0460284 | + | 0.998940i | \(0.485344\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −132441. | −0.174407 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.07914e6 | 1.39000 | 0.694998 | − | 0.719012i | \(-0.255405\pi\) | ||||
0.694998 | + | 0.719012i | \(0.255405\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −724221. | −0.912604 | −0.456302 | − | 0.889825i | \(-0.650826\pi\) | ||||
−0.456302 | + | 0.889825i | \(0.650826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 331738. | 0.409039 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.37311e6 | 1.65697 | 0.828486 | − | 0.560009i | \(-0.189203\pi\) | ||||
0.828486 | + | 0.560009i | \(0.189203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −516044. | −0.609561 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −903870. | −1.04529 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.11446e6 | −1.26204 | −0.631018 | − | 0.775769i | \(-0.717362\pi\) | ||||
−0.631018 | + | 0.775769i | \(0.717362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.47058e6 | −1.63097 | −0.815486 | − | 0.578776i | \(-0.803530\pi\) | ||||
−0.815486 | + | 0.578776i | \(0.803530\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −474309. | −0.515283 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.04028e6 | 1.10722 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −474132. | −0.494489 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −350133. | −0.357878 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −375105. | −0.375810 | −0.187905 | − | 0.982187i | \(-0.560170\pi\) | ||||
−0.187905 | + | 0.982187i | \(0.560170\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 295667. | 0.290404 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −178661. | −0.172060 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −471074. | −0.444894 | −0.222447 | − | 0.974945i | \(-0.571404\pi\) | ||||
−0.222447 | + | 0.974945i | \(0.571404\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33698.4 | 0.0312147 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −53954.3 | −0.0490258 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.11373e6 | −0.992865 | −0.496433 | − | 0.868075i | \(-0.665357\pi\) | ||||
−0.496433 | + | 0.868075i | \(0.665357\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 300936. | 0.263245 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.28998e6 | 1.96586 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −381568. | −0.321508 | −0.160754 | − | 0.986995i | \(-0.551393\pi\) | ||||
−0.160754 | + | 0.986995i | \(0.551393\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.08834e6 | −0.900208 | −0.450104 | − | 0.892976i | \(-0.648613\pi\) | ||||
−0.450104 | + | 0.892976i | \(0.648613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00121e6 | 3.24927 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −176979. | −0.141120 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.18958e6 | −1.71459 | −0.857295 | − | 0.514825i | \(-0.827857\pi\) | ||||
−0.857295 | + | 0.514825i | \(0.827857\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 512163. | 0.393911 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.02712e6 | −0.775992 | −0.387996 | − | 0.921661i | \(-0.626833\pi\) | ||||
−0.387996 | + | 0.921661i | \(0.626833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −889156. | −0.659952 | −0.329976 | − | 0.943989i | \(-0.607041\pi\) | ||||
−0.329976 | + | 0.943989i | \(0.607041\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −261715. | −0.190861 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.08295e6 | −2.92597 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.32188e6 | −0.930992 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 764188. | 0.529015 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −482000. | −0.328003 | −0.164001 | − | 0.986460i | \(-0.552440\pi\) | ||||
−0.164001 | + | 0.986460i | \(0.552440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 466465. | 0.312079 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −268712. | −0.176765 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.56616e6 | 2.30687 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −457668. | −0.291162 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −993470. | −0.621653 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −637668. | −0.392505 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −229158. | −0.138768 | −0.0693839 | − | 0.997590i | \(-0.522103\pi\) | ||||
−0.0693839 | + | 0.997590i | \(0.522103\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.95326e6 | 1.16376 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.49699e6 | −1.46392 | −0.731958 | − | 0.681350i | \(-0.761393\pi\) | ||||
−0.731958 | + | 0.681350i | \(0.761393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.78111e6 | −1.60457 | −0.802283 | − | 0.596944i | \(-0.796381\pi\) | ||||
−0.802283 | + | 0.596944i | \(0.796381\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 461311. | 0.261949 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.94375e6 | 1.08641 | 0.543203 | − | 0.839602i | \(-0.317212\pi\) | ||||
0.543203 | + | 0.839602i | \(0.317212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −72098.6 | −0.0396689 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.31998e6 | −1.79835 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 143530. | 0.0765487 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.13461e6 | −1.12101 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.75665e6 | 0.908481 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.49860e6 | −1.78199 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 60445.1 | 0.0303243 | 0.0151622 | − | 0.999885i | \(-0.495174\pi\) | ||||
0.0151622 | + | 0.999885i | \(0.495174\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9791.59 | 0.00483886 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 299412. | 0.145766 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.72999e6 | −0.829791 | −0.414895 | − | 0.909869i | \(-0.636182\pi\) | ||||
−0.414895 | + | 0.909869i | \(0.636182\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.81294e6 | −0.856807 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 684398. | 0.318730 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.34184e6 | 1.53373 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.96847e6 | 0.890394 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.17667e6 | −0.524605 | −0.262303 | − | 0.964986i | \(-0.584482\pi\) | ||||
−0.262303 | + | 0.964986i | \(0.584482\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.20893e6 | 0.531297 | 0.265648 | − | 0.964070i | \(-0.414414\pi\) | ||||
0.265648 | + | 0.964070i | \(0.414414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.24103e6 | −1.40416 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.00723e6 | 0.430223 | 0.215111 | − | 0.976589i | \(-0.430989\pi\) | ||||
0.215111 | + | 0.976589i | \(0.430989\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 630978. | 0.265732 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.21126e6 | −0.502998 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.10145e6 | −0.451055 | −0.225527 | − | 0.974237i | \(-0.572411\pi\) | ||||
−0.225527 | + | 0.974237i | \(0.572411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.26585e6 | −0.915087 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.69375e6 | −1.07298 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.85347e6 | −0.728204 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.99288e6 | −1.15991 | −0.579955 | − | 0.814648i | \(-0.696930\pi\) | ||||
−0.579955 | + | 0.814648i | \(0.696930\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.18636e6 | −0.453578 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.04024e6 | 0.769568 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.23178e6 | 1.57489 | 0.787446 | − | 0.616384i | \(-0.211403\pi\) | ||||
0.787446 | + | 0.616384i | \(0.211403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.96192e6 | −1.08766 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −869608. | −0.315116 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.06268e6 | −0.380018 | −0.190009 | − | 0.981782i | \(-0.560852\pi\) | ||||
−0.190009 | + | 0.981782i | \(0.560852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.33831e6 | 1.53112 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.75736e6 | 1.30884 | 0.654418 | − | 0.756133i | \(-0.272913\pi\) | ||||
0.654418 | + | 0.756133i | \(0.272913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 616445. | 0.211955 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −132983. | −0.0451354 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.88561e6 | −1.30192 | −0.650961 | − | 0.759112i | \(-0.725634\pi\) | ||||
−0.650961 | + | 0.759112i | \(0.725634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.07956e6 | −0.357111 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.47815e6 | −1.13597 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.67960e6 | −0.541643 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 719537. | 0.229127 | 0.114564 | − | 0.993416i | \(-0.463453\pi\) | ||||
0.114564 | + | 0.993416i | \(0.463453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.77433e6 | −0.557960 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.57519e6 | −0.489185 | −0.244592 | − | 0.969626i | \(-0.578654\pi\) | ||||
−0.244592 | + | 0.969626i | \(0.578654\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.25479e6 | 2.53188 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.29672e6 | −0.695777 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13084.4 | 0.00391533 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.35355e6 | −0.991279 | −0.495639 | − | 0.868528i | \(-0.665066\pi\) | ||||
−0.495639 | + | 0.868528i | \(0.665066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.47889e6 | 0.723857 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.16247e6 | 0.912328 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −650628. | −0.185444 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.70168e6 | 1.60569 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.79853e6 | −1.89182 | −0.945911 | − | 0.324427i | \(-0.894829\pi\) | ||||
−0.945911 | + | 0.324427i | \(0.894829\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.77259e6 | −0.487420 | −0.243710 | − | 0.969848i | \(-0.578365\pi\) | ||||
−0.243710 | + | 0.969848i | \(0.578365\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.01657e6 | −0.276241 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 646196. | 0.173537 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.32317e6 | −1.14745 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.55359e6 | 0.407562 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.30221e6 | −0.337666 | −0.168833 | − | 0.985645i | \(-0.554000\pi\) | ||||
−0.168833 | + | 0.985645i | \(0.554000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.15386e6 | 0.552074 | 0.276037 | − | 0.961147i | \(-0.410979\pi\) | ||||
0.276037 | + | 0.961147i | \(0.410979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −480013. | −0.121627 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.58141e6 | −0.396133 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.81916e6 | 1.44112 | 0.720558 | − | 0.693394i | \(-0.243886\pi\) | ||||
0.720558 | + | 0.693394i | \(0.243886\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.04927e6 | 0.501769 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.34332e6 | −1.05151 | −0.525754 | − | 0.850637i | \(-0.676217\pi\) | ||||
−0.525754 | + | 0.850637i | \(0.676217\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.25531e6 | 1.01866 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.86070e6 | −1.62405 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.68108e6 | 0.627615 | 0.313807 | − | 0.949487i | \(-0.398395\pi\) | ||||
0.313807 | + | 0.949487i | \(0.398395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.58533e6 | −0.367010 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.79584e6 | 0.869086 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.43518e6 | 1.68369 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.29834e6 | −0.962743 | −0.481371 | − | 0.876517i | \(-0.659861\pi\) | ||||
−0.481371 | + | 0.876517i | \(0.659861\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 981134. | 0.217369 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.28441e6 | 0.500636 | 0.250318 | − | 0.968164i | \(-0.419465\pi\) | ||||
0.250318 | + | 0.968164i | \(0.419465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.51960e6 | −0.329440 | −0.164720 | − | 0.986340i | \(-0.552672\pi\) | ||||
−0.164720 | + | 0.986340i | \(0.552672\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.55654e6 | 0.977244 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.71846e6 | 1.00117 | 0.500585 | − | 0.865687i | \(-0.333118\pi\) | ||||
0.500585 | + | 0.865687i | \(0.333118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.02991e6 | 0.426132 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.89151e6 | 2.05452 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −177703. | −0.0365210 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 946591. | 0.192499 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 592824. | 0.119297 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.85157e6 | −1.16529 | −0.582644 | − | 0.812727i | \(-0.697982\pi\) | ||||
−0.582644 | + | 0.812727i | \(0.697982\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 157816. | 0.0311020 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.33456e7 | 2.60297 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.42004e6 | 0.274123 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.83575e6 | −0.350745 | −0.175372 | − | 0.984502i | \(-0.556113\pi\) | ||||
−0.175372 | + | 0.984502i | \(0.556113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.35958e6 | −1.58093 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.75635e6 | 1.07757 | 0.538783 | − | 0.842445i | \(-0.318884\pi\) | ||||
0.538783 | + | 0.842445i | \(0.318884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 263250. | 0.0487811 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 179118. | 0.0328568 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.27781e6 | 0.776838 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.10166e6 | −0.737409 | −0.368705 | − | 0.929547i | \(-0.620199\pi\) | ||||
−0.368705 | + | 0.929547i | \(0.620199\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.56471e6 | 0.634497 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.12157e6 | 0.197654 | 0.0988270 | − | 0.995105i | \(-0.468491\pi\) | ||||
0.0988270 | + | 0.995105i | \(0.468491\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.84610e6 | −0.322126 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.22312e7 | 2.11325 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.68902e6 | −0.460045 | −0.230023 | − | 0.973185i | \(-0.573880\pi\) | ||||
−0.230023 | + | 0.973185i | \(0.573880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.25659e7 | −2.12883 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.43723e6 | 0.241120 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.62960e6 | 0.603033 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.35844e6 | −0.223518 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.67212e6 | −0.272489 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.88911e6 | 0.466305 | 0.233152 | − | 0.972440i | \(-0.425096\pi\) | ||||
0.233152 | + | 0.972440i | \(0.425096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.40417e6 | 0.224474 | 0.112237 | − | 0.993681i | \(-0.464198\pi\) | ||||
0.112237 | + | 0.993681i | \(0.464198\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.98832e6 | −1.26490 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.49891e6 | −0.391945 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.45814e6 | 0.848019 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 918904. | 0.141428 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.91212e7 | −2.91540 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.16930e6 | −0.931861 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.73113e6 | 0.857640 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.73843e6 | 0.406003 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −211154. | −0.0310174 | −0.0155087 | − | 0.999880i | \(-0.504937\pi\) | ||||
−0.0155087 | + | 0.999880i | \(0.504937\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.90298e6 | 0.276971 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.26426e6 | 0.470754 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.61571e6 | 0.659584 | 0.329792 | − | 0.944054i | \(-0.393021\pi\) | ||||
0.329792 | + | 0.944054i | \(0.393021\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.25616e6 | −0.177875 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 385627. | 0.0541113 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.13871e7 | −1.58343 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 87112.5 | 0.0120046 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.01209e7 | 1.38223 | 0.691114 | − | 0.722746i | \(-0.257120\pi\) | ||||
0.691114 | + | 0.722746i | \(0.257120\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.14335e6 | −0.290110 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −470308. | −0.0630921 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.84774e6 | −0.511604 | −0.255802 | − | 0.966729i | \(-0.582340\pi\) | ||||
−0.255802 | + | 0.966729i | \(0.582340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.36885e6 | −0.443978 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.55709e7 | −2.03403 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.38443e6 | 0.567718 | 0.283859 | − | 0.958866i | \(-0.408385\pi\) | ||||
0.283859 | + | 0.958866i | \(0.408385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.61241e6 | −0.335313 | −0.167656 | − | 0.985845i | \(-0.553620\pi\) | ||||
−0.167656 | + | 0.985845i | \(0.553620\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.53357e6 | 0.704075 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.11974e6 | −0.898037 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.06124e6 | −0.882961 | −0.441480 | − | 0.897271i | \(-0.645547\pi\) | ||||
−0.441480 | + | 0.897271i | \(0.645547\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 726132. | 0.0900159 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.41103e6 | −0.542125 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 792186. | 0.0965285 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.16041e6 | 0.261003 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.18957e6 | 0.980993 | 0.490496 | − | 0.871443i | \(-0.336815\pi\) | ||||
0.490496 | + | 0.871443i | \(0.336815\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.66058e6 | −0.434772 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.21710e6 | 0.732182 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.78828e6 | −1.14306 | −0.571531 | − | 0.820580i | \(-0.693650\pi\) | ||||
−0.571531 | + | 0.820580i | \(0.693650\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.25080e6 | −0.260642 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.66343e7 | 1.91015 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.44247e6 | −0.505892 | −0.252946 | − | 0.967480i | \(-0.581400\pi\) | ||||
−0.252946 | + | 0.967480i | \(0.581400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 248973. | 0.0281168 | 0.0140584 | − | 0.999901i | \(-0.495525\pi\) | ||||
0.0140584 | + | 0.999901i | \(0.495525\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 589821. | 0.0660582 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00560e6 | −0.555991 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.61487e6 | 0.618540 | 0.309270 | − | 0.950974i | \(-0.399915\pi\) | ||||
0.309270 | + | 0.950974i | \(0.399915\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.25432e6 | −0.355563 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.63846e7 | −1.77555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.11213e6 | 0.764449 | 0.382225 | − | 0.924069i | \(-0.375158\pi\) | ||||
0.382225 | + | 0.924069i | \(0.375158\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.05547e7 | −1.12527 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 872669. | 0.0922862 | 0.0461431 | − | 0.998935i | \(-0.485307\pi\) | ||||
0.0461431 | + | 0.998935i | \(0.485307\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.40244e6 | 0.986312 | 0.493156 | − | 0.869941i | \(-0.335843\pi\) | ||||
0.493156 | + | 0.869941i | \(0.335843\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.08101e7 | −1.12486 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.88495e7 | 2.97796 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 947282. | 0.0970017 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −688939. | −0.0699861 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −47774.5 | −0.00481470 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.90990e7 | 1.90957 | 0.954786 | − | 0.297293i | \(-0.0960838\pi\) | ||||
0.954786 | + | 0.297293i | \(0.0960838\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.66987e6 | 0.661619 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.06158e6 | 0.793388 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.30292e7 | 3.22515 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.24298e6 | 0.120424 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.06757e6 | −0.391012 | −0.195506 | − | 0.980703i | \(-0.562635\pi\) | ||||
−0.195506 | + | 0.980703i | \(0.562635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00899e6 | 0.0962410 | 0.0481205 | − | 0.998842i | \(-0.484677\pi\) | ||||
0.0481205 | + | 0.998842i | \(0.484677\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.18310e6 | −0.111975 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.99986e7 | −1.87819 | −0.939095 | − | 0.343657i | \(-0.888334\pi\) | ||||
−0.939095 | + | 0.343657i | \(0.888334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.22792e6 | 0.114435 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.08918e7 | 2.85687 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.16599e7 | −1.07007 | −0.535035 | − | 0.844830i | \(-0.679702\pi\) | ||||
−0.535035 | + | 0.844830i | \(0.679702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.46320e6 | −0.588633 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.65121e6 | −0.330007 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.40204e7 | −1.25761 | −0.628806 | − | 0.777562i | \(-0.716456\pi\) | ||||
−0.628806 | + | 0.777562i | \(0.716456\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.39932e6 | 0.480657 | 0.240328 | − | 0.970692i | \(-0.422745\pi\) | ||||
0.240328 | + | 0.970692i | \(0.422745\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.67256e6 | −0.501182 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.29712e6 | −0.289122 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.90047e6 | −0.252438 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.19811e6 | 0.103498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.67860e6 | −0.143926 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.37236e6 | 0.201903 | 0.100951 | − | 0.994891i | \(-0.467811\pi\) | ||||
0.100951 | + | 0.994891i | \(0.467811\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.47064e6 | 0.546623 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.48279e7 | 1.24339 | 0.621695 | − | 0.783260i | \(-0.286444\pi\) | ||||
0.621695 | + | 0.783260i | \(0.286444\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.62736e6 | 0.801369 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.89128e7 | 1.56275 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.45710e7 | 1.19519 | 0.597594 | − | 0.801799i | \(-0.296123\pi\) | ||||
0.597594 | + | 0.801799i | \(0.296123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.60635e6 | 0.375086 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.26926e7 | −1.02603 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.55485e6 | 0.766789 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.39101e6 | 0.190496 | 0.0952480 | − | 0.995454i | \(-0.469636\pi\) | ||||
0.0952480 | + | 0.995454i | \(0.469636\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.21436e6 | 0.0960534 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.05950e7 | 0.832033 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.78844e6 | 0.451315 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.40649e7 | 1.86291 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.67685e6 | −0.205745 | −0.102872 | − | 0.994695i | \(-0.532803\pi\) | ||||
−0.102872 | + | 0.994695i | \(0.532803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −69983.4 | −0.00534080 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.04411e6 | −0.685319 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.25159e7 | −0.941701 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.61177e7 | 1.20417 | 0.602085 | − | 0.798432i | \(-0.294337\pi\) | ||||
0.602085 | + | 0.798432i | \(0.294337\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.30870e6 | −0.245461 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.75329e7 | 2.02828 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.88693e6 | 0.211189 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.95319e7 | −1.41888 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.74012e7 | −1.97673 | −0.988363 | − | 0.152111i | \(-0.951393\pi\) | ||||
−0.988363 | + | 0.152111i | \(0.951393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.46074e7 | 1.76290 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.57732e7 | −1.83367 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.73615e6 | 0.122671 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.44905e7 | 1.01683 | 0.508413 | − | 0.861113i | \(-0.330232\pi\) | ||||
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.82438e6 | 0.614986 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 648840. | 0.0449101 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.24243e6 | 0.635370 | 0.317685 | − | 0.948196i | \(-0.397095\pi\) | ||||
0.317685 | + | 0.948196i | \(0.397095\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.82317e7 | 1.24483 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 788172. | 0.0534505 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 270924. | 0.0182489 | 0.00912445 | − | 0.999958i | \(-0.497096\pi\) | ||||
0.00912445 | + | 0.999958i | \(0.497096\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.30955e6 | −0.555945 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.56128e7 | −1.03755 | −0.518776 | − | 0.854910i | \(-0.673612\pi\) | ||||
−0.518776 | + | 0.854910i | \(0.673612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.27488e7 | −0.841545 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.28169e6 | −0.0840394 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.18257e7 | −2.72420 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.81796e6 | −0.182320 | −0.0911600 | − | 0.995836i | \(-0.529057\pi\) | ||||
−0.0911600 | + | 0.995836i | \(0.529057\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.57403e6 | −0.422517 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.05355e6 | 0.450340 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.47622e6 | 0.0936293 | 0.0468146 | − | 0.998904i | \(-0.485093\pi\) | ||||
0.0468146 | + | 0.998904i | \(0.485093\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.18182e6 | 0.326496 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.59710e7 | −0.999700 | −0.499850 | − | 0.866112i | \(-0.666612\pi\) | ||||
−0.499850 | + | 0.866112i | \(0.666612\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.21305e7 | 1.37620 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −654005. | −0.0404043 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.48104e7 | 0.909033 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.69038e7 | −1.64058 | −0.820291 | − | 0.571947i | \(-0.806188\pi\) | ||||
−0.820291 | + | 0.571947i | \(0.806188\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.25597e6 | −0.500187 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.10506e7 | 1.26711 | 0.633556 | − | 0.773697i | \(-0.281595\pi\) | ||||
0.633556 | + | 0.773697i | \(0.281595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.64805e7 | −0.985633 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 590592. | 0.0350942 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.47930e6 | 0.500629 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.66099e6 | 0.0974403 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.63604e6 | 0.153655 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.83807e7 | 1.06460 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.46428e7 | 0.842728 | 0.421364 | − | 0.906892i | \(-0.361552\pi\) | ||||
0.421364 | + | 0.906892i | \(0.361552\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.95190e7 | −1.11626 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.28396e7 | −1.29792 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.02462e7 | −1.14330 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.27416e6 | 0.295962 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.53622e7 | −0.856660 | −0.428330 | − | 0.903622i | \(-0.640898\pi\) | ||||
−0.428330 | + | 0.903622i | \(0.640898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.96000e6 | 0.274862 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.38267e6 | 0.461638 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.87907e6 | −0.267023 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.47991e7 | 1.34880 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.68730e6 | −0.361466 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.26215e6 | −0.390116 | −0.195058 | − | 0.980792i | \(-0.562490\pi\) | ||||
−0.195058 | + | 0.980792i | \(0.562490\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.17728e6 | −0.223019 | −0.111510 | − | 0.993763i | \(-0.535569\pi\) | ||||
−0.111510 | + | 0.993763i | \(0.535569\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.90741e7 | −1.01209 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.55340e7 | −0.819200 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 950466. | 0.0498174 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.46468e7 | 0.763015 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.70285e7 | 1.39947 | 0.699736 | − | 0.714402i | \(-0.253301\pi\) | ||||
0.699736 | + | 0.714402i | \(0.253301\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.95032e6 | 0.357689 | 0.178844 | − | 0.983877i | \(-0.442764\pi\) | ||||
0.178844 | + | 0.983877i | \(0.442764\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.10171e6 | −0.158659 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 370060. | 0.0188152 | 0.00940759 | − | 0.999956i | \(-0.497005\pi\) | ||||
0.00940759 | + | 0.999956i | \(0.497005\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.38451e7 | 0.699698 | 0.349849 | − | 0.936806i | \(-0.386233\pi\) | ||||
0.349849 | + | 0.936806i | \(0.386233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.83741e7 | −1.92768 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.99869e6 | −0.499264 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.62405e6 | 0.328781 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.50227e7 | −1.23458 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.86174e7 | −0.913089 | −0.456544 | − | 0.889701i | \(-0.650913\pi\) | ||||
−0.456544 | + | 0.889701i | \(0.650913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 707281. | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.80012e7 | −0.872435 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.27285e7 | 1.09504 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.39362e7 | −1.62538 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.55832e7 | −0.741972 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 526376. | 0.0249157 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.15389e6 | 0.101356 | 0.0506782 | − | 0.998715i | \(-0.483862\pi\) | ||||
0.0506782 | + | 0.998715i | \(0.483862\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −958031. | −0.0448192 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.33513e7 | −1.55118 | −0.775588 | − | 0.631239i | \(-0.782547\pi\) | ||||
−0.775588 | + | 0.631239i | \(0.782547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.11061e7 | 1.43834 | 0.719171 | − | 0.694833i | \(-0.244522\pi\) | ||||
0.719171 | + | 0.694833i | \(0.244522\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.15571e7 | −3.28961 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.59387e7 | 0.728494 | 0.364247 | − | 0.931302i | \(-0.381326\pi\) | ||||
0.364247 | + | 0.931302i | \(0.381326\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.10719e6 | −0.141198 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.31670e7 | −1.04670 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.42138e6 | −0.198613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.50644e6 | 0.424593 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.79738e6 | 0.124227 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.73147e7 | −1.64763 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 666578. | 0.0292652 | 0.0146326 | − | 0.999893i | \(-0.495342\pi\) | ||||
0.0146326 | + | 0.999893i | \(0.495342\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.44745e6 | −0.368768 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.30910e7 | −1.00231 | −0.501155 | − | 0.865358i | \(-0.667091\pi\) | ||||
−0.501155 | + | 0.865358i | \(0.667091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.85060e6 | −0.166198 | −0.0830992 | − | 0.996541i | \(-0.526482\pi\) | ||||
−0.0830992 | + | 0.996541i | \(0.526482\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.17519e6 | 0.350864 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.14426e7 | 1.76863 | 0.884316 | − | 0.466889i | \(-0.154625\pi\) | ||||
0.884316 | + | 0.466889i | \(0.154625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.46547e7 | 2.31939 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.04589e6 | −0.255133 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.26574e6 | 0.304896 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.06498e7 | 0.444409 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.24999e7 | 2.59357 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.71389e6 | −0.277061 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.89247e6 | −0.118702 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.02102e6 | −0.327348 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.53617e6 | 0.143520 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.63163e7 | 1.86946 | 0.934729 | − | 0.355363i | \(-0.115643\pi\) | ||||
0.934729 | + | 0.355363i | \(0.115643\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.63669e6 | −0.145981 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.69515e6 | −0.107594 | −0.0537969 | − | 0.998552i | \(-0.517132\pi\) | ||||
−0.0537969 | + | 0.998552i | \(0.517132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.71272e6 | −0.0679999 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.11757e7 | −0.441286 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.38183e7 | −1.72081 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.39792e7 | −0.546000 | −0.273000 | − | 0.962014i | \(-0.588016\pi\) | ||||
−0.273000 | + | 0.962014i | \(0.588016\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.01618e6 | −0.156014 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.00338e7 | 0.774032 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −315076. | −0.0121077 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.15007e6 | 0.273282 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.25580e6 | −0.275833 | −0.137916 | − | 0.990444i | \(-0.544041\pi\) | ||||
−0.137916 | + | 0.990444i | \(0.544041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.46468e7 | −0.553819 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.37619e7 | −1.64586 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −873940. | −0.0326928 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.95850e6 | 0.147293 | 0.0736464 | − | 0.997284i | \(-0.476536\pi\) | ||||
0.0736464 | + | 0.997284i | \(0.476536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.87413e7 | −1.80399 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.07672e7 | −1.50085 | −0.750425 | − | 0.660956i | \(-0.770151\pi\) | ||||
−0.750425 | + | 0.660956i | \(0.770151\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.37766e7 | −2.33551 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.25382e7 | −0.820994 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.67878e7 | 0.970650 | 0.485325 | − | 0.874334i | \(-0.338701\pi\) | ||||
0.485325 | + | 0.874334i | \(0.338701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.88484e7 | −2.12114 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.40658e7 | 1.22143 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.81430e7 | −0.647107 | −0.323553 | − | 0.946210i | \(-0.604877\pi\) | ||||
−0.323553 | + | 0.946210i | \(0.604877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.02827e7 | 0.364835 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.26359e6 | −0.0445990 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.12294e7 | 1.09652 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.51028e7 | 1.22612 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.21531e7 | −0.422300 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.34932e6 | 0.0466441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.40529e7 | 0.483282 | 0.241641 | − | 0.970366i | \(-0.422314\pi\) | ||||
0.241641 | + | 0.970366i | \(0.422314\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.51549e6 | 0.0860624 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.77622e7 | −0.604573 | −0.302287 | − | 0.953217i | \(-0.597750\pi\) | ||||
−0.302287 | + | 0.953217i | \(0.597750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.18306e7 | 2.43236 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.74108e7 | −1.26034 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.66625e7 | −0.558474 | −0.279237 | − | 0.960222i | \(-0.590082\pi\) | ||||
−0.279237 | + | 0.960222i | \(0.590082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.12017e7 | 0.373531 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.43037e6 | 0.213336 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.28571e7 | 0.754461 | 0.377231 | − | 0.926119i | \(-0.376876\pi\) | ||||
0.377231 | + | 0.926119i | \(0.376876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.15528e7 | 0.379399 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.13159e7 | −2.00346 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.14888e6 | −0.232406 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.52864e7 | 0.817904 | 0.408952 | − | 0.912556i | \(-0.365894\pi\) | ||||
0.408952 | + | 0.912556i | \(0.365894\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.05935e6 | 0.0340931 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.09103e7 | 0.989796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.44014e7 | 1.41468 | 0.707340 | − | 0.706873i | \(-0.249895\pi\) | ||||
0.707340 | + | 0.706873i | \(0.249895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −478387. | −0.0151658 |
(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 | 464.6.a.i.1.3 | 4 | ||
4.3 | odd | 2 | 29.6.a.a.1.3 | ✓ | 4 | ||
12.11 | even | 2 | 261.6.a.a.1.2 | 4 | |||
20.19 | odd | 2 | 725.6.a.a.1.2 | 4 | |||
116.115 | odd | 2 | 841.6.a.a.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.a.a.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
261.6.a.a.1.2 | 4 | 12.11 | even | 2 | |||
464.6.a.i.1.3 | 4 | 1.1 | even | 1 | trivial | ||
725.6.a.a.1.2 | 4 | 20.19 | odd | 2 | |||
841.6.a.a.1.2 | 4 | 116.115 | odd | 2 |