Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,6,Mod(1,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.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: | \(51.9643576194\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 110x^{3} + 39x^{2} + 2214x - 1944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{7} \) |
Twist minimal: | no (minimal twist has level 36) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-7.49663\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −110.399 | −1.97488 | −0.987441 | − | 0.157988i | \(-0.949499\pi\) | ||||
−0.987441 | + | 0.157988i | \(0.949499\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 101.745 | 0.784814 | 0.392407 | − | 0.919792i | \(-0.371642\pi\) | ||||
0.392407 | + | 0.919792i | \(0.371642\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 150.312 | 0.374552 | 0.187276 | − | 0.982307i | \(-0.440034\pi\) | ||||
0.187276 | + | 0.982307i | \(0.440034\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 635.424 | 1.04281 | 0.521405 | − | 0.853309i | \(-0.325408\pi\) | ||||
0.521405 | + | 0.853309i | \(0.325408\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1498.54 | −1.25761 | −0.628806 | − | 0.777562i | \(-0.716456\pi\) | ||||
−0.628806 | + | 0.777562i | \(0.716456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1437.69 | 0.913651 | 0.456825 | − | 0.889556i | \(-0.348986\pi\) | ||||
0.456825 | + | 0.889556i | \(0.348986\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1264.11 | 0.498269 | 0.249134 | − | 0.968469i | \(-0.419854\pi\) | ||||
0.249134 | + | 0.968469i | \(0.419854\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9063.00 | 2.90016 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2777.50 | 0.613280 | 0.306640 | − | 0.951826i | \(-0.400795\pi\) | ||||
0.306640 | + | 0.951826i | \(0.400795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6968.68 | −1.30241 | −0.651203 | − | 0.758904i | \(-0.725735\pi\) | ||||
−0.651203 | + | 0.758904i | \(0.725735\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11232.5 | −1.54992 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7950.71 | −0.954776 | −0.477388 | − | 0.878693i | \(-0.658416\pi\) | ||||
−0.477388 | + | 0.878693i | \(0.658416\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2027.53 | 0.188369 | 0.0941843 | − | 0.995555i | \(-0.469976\pi\) | ||||
0.0941843 | + | 0.995555i | \(0.469976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12523.3 | −1.03288 | −0.516438 | − | 0.856325i | \(-0.672742\pi\) | ||||
−0.516438 | + | 0.856325i | \(0.672742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6482.34 | 0.428043 | 0.214021 | − | 0.976829i | \(-0.431344\pi\) | ||||
0.214021 | + | 0.976829i | \(0.431344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6455.01 | −0.384067 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9827.54 | −0.480568 | −0.240284 | − | 0.970703i | \(-0.577241\pi\) | ||||
−0.240284 | + | 0.970703i | \(0.577241\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16594.3 | −0.739696 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −47087.9 | −1.76108 | −0.880541 | − | 0.473970i | \(-0.842821\pi\) | ||||
−0.880541 | + | 0.473970i | \(0.842821\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8337.84 | 0.286899 | 0.143450 | − | 0.989658i | \(-0.454181\pi\) | ||||
0.143450 | + | 0.989658i | \(0.454181\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −70150.3 | −2.05943 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7260.89 | −0.197607 | −0.0988036 | − | 0.995107i | \(-0.531502\pi\) | ||||
−0.0988036 | + | 0.995107i | \(0.531502\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3582.33 | −0.0843372 | −0.0421686 | − | 0.999111i | \(-0.513427\pi\) | ||||
−0.0421686 | + | 0.999111i | \(0.513427\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58077.5 | 1.27556 | 0.637780 | − | 0.770218i | \(-0.279853\pi\) | ||||
0.637780 | + | 0.770218i | \(0.279853\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15293.5 | 0.293954 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −63742.8 | −1.14912 | −0.574558 | − | 0.818464i | \(-0.694826\pi\) | ||||
−0.574558 | + | 0.818464i | \(0.694826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −82846.5 | −1.32002 | −0.660008 | − | 0.751259i | \(-0.729447\pi\) | ||||
−0.660008 | + | 0.751259i | \(0.729447\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 165438. | 2.48363 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3861.51 | 0.0516752 | 0.0258376 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258376 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 64651.0 | 0.818412 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −158720. | −1.80435 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 69277.2 | 0.747585 | 0.373793 | − | 0.927512i | \(-0.378057\pi\) | ||||
0.373793 | + | 0.927512i | \(0.378057\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 25445.7 | 0.248205 | 0.124103 | − | 0.992269i | \(-0.460395\pi\) | ||||
0.124103 | + | 0.992269i | \(0.460395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −63387.8 | −0.588725 | −0.294363 | − | 0.955694i | \(-0.595107\pi\) | ||||
−0.294363 | + | 0.955694i | \(0.595107\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 61158.9 | 0.516417 | 0.258208 | − | 0.966089i | \(-0.416868\pi\) | ||||
0.258208 | + | 0.966089i | \(0.416868\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −124036. | −0.999957 | −0.499979 | − | 0.866038i | \(-0.666659\pi\) | ||||
−0.499979 | + | 0.866038i | \(0.666659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −117437. | −0.865185 | −0.432592 | − | 0.901590i | \(-0.642401\pi\) | ||||
−0.432592 | + | 0.901590i | \(0.642401\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −139556. | −0.984022 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −152469. | −0.986991 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −138457. | −0.859711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −655551. | −3.75259 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −29838.6 | −0.164161 | −0.0820803 | − | 0.996626i | \(-0.526156\pi\) | ||||
−0.0820803 | + | 0.996626i | \(0.526156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 172058. | 0.875983 | 0.437992 | − | 0.898979i | \(-0.355690\pi\) | ||||
0.437992 | + | 0.898979i | \(0.355690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 146277. | 0.717046 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −190361. | −0.866518 | −0.433259 | − | 0.901270i | \(-0.642636\pi\) | ||||
−0.433259 | + | 0.901270i | \(0.642636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −337063. | −1.47970 | −0.739852 | − | 0.672770i | \(-0.765104\pi\) | ||||
−0.739852 | + | 0.672770i | \(0.765104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 95511.9 | 0.390586 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −306634. | −1.21115 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 55098.7 | 0.203318 | 0.101659 | − | 0.994819i | \(-0.467585\pi\) | ||||
0.101659 | + | 0.994819i | \(0.467585\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 334064. | 1.19230 | 0.596152 | − | 0.802872i | \(-0.296696\pi\) | ||||
0.596152 | + | 0.802872i | \(0.296696\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 769337. | 2.57210 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −120107. | −0.388882 | −0.194441 | − | 0.980914i | \(-0.562289\pi\) | ||||
−0.194441 | + | 0.980914i | \(0.562289\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 128616. | 0.391048 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 367083. | 1.08217 | 0.541085 | − | 0.840968i | \(-0.318014\pi\) | ||||
0.541085 | + | 0.840968i | \(0.318014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −589448. | −1.63552 | −0.817758 | − | 0.575563i | \(-0.804783\pi\) | ||||
−0.817758 | + | 0.575563i | \(0.804783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32470.6 | 0.0874527 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −436457. | −1.10873 | −0.554366 | − | 0.832273i | \(-0.687039\pi\) | ||||
−0.554366 | + | 0.832273i | \(0.687039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 922112. | 2.27609 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −241064. | −0.562341 | −0.281171 | − | 0.959658i | \(-0.590723\pi\) | ||||
−0.281171 | + | 0.959658i | \(0.590723\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 27128.8 | 0.0615510 | 0.0307755 | − | 0.999526i | \(-0.490202\pi\) | ||||
0.0307755 | + | 0.999526i | \(0.490202\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 877752. | 1.88557 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −225249. | −0.471041 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 56072.5 | 0.111216 | 0.0556079 | − | 0.998453i | \(-0.482290\pi\) | ||||
0.0556079 | + | 0.998453i | \(0.482290\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 354483. | 0.685019 | 0.342510 | − | 0.939514i | \(-0.388723\pi\) | ||||
0.342510 | + | 0.939514i | \(0.388723\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 816895. | 1.49969 | 0.749844 | − | 0.661615i | \(-0.230129\pi\) | ||||
0.749844 | + | 0.661615i | \(0.230129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 860396. | 1.54016 | 0.770079 | − | 0.637948i | \(-0.220217\pi\) | ||||
0.770079 | + | 0.637948i | \(0.220217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 282596. | 0.481310 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −223838. | −0.372006 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 216102. | 0.342210 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −387171. | −0.598683 | −0.299341 | − | 0.954146i | \(-0.596767\pi\) | ||||
−0.299341 | + | 0.954146i | \(0.596767\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.38256e6 | 2.03981 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −709026. | −1.02215 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −952209. | −1.31145 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −294994. | −0.397238 | −0.198619 | − | 0.980077i | \(-0.563646\pi\) | ||||
−0.198619 | + | 0.980077i | \(0.563646\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −687980. | −0.886158 | −0.443079 | − | 0.896483i | \(-0.646114\pi\) | ||||
−0.443079 | + | 0.896483i | \(0.646114\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.08647e6 | −1.36908 | −0.684538 | − | 0.728977i | \(-0.739996\pi\) | ||||
−0.684538 | + | 0.728977i | \(0.739996\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −168058. | −0.202801 | −0.101400 | − | 0.994846i | \(-0.532332\pi\) | ||||
−0.101400 | + | 0.994846i | \(0.532332\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −715646. | −0.845334 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.54628e6 | 1.75102 | 0.875512 | − | 0.483197i | \(-0.160524\pi\) | ||||
0.875512 | + | 0.483197i | \(0.160524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.15373e6 | −1.27956 | −0.639782 | − | 0.768557i | \(-0.720975\pi\) | ||||
−0.639782 | + | 0.768557i | \(0.720975\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 712629. | 0.758487 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 913541. | 0.952764 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 586711. | 0.587814 | 0.293907 | − | 0.955834i | \(-0.405044\pi\) | ||||
0.293907 | + | 0.955834i | \(0.405044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 190010. | 0.186628 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −108342. | −0.102321 | −0.0511604 | − | 0.998690i | \(-0.516292\pi\) | ||||
−0.0511604 | + | 0.998690i | \(0.516292\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −808942. | −0.749321 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.73671e6 | 1.54823 | 0.774117 | − | 0.633042i | \(-0.218194\pi\) | ||||
0.774117 | + | 0.633042i | \(0.218194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.08495e6 | 0.949065 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18297.3 | −0.0154172 | −0.00770860 | − | 0.999970i | \(-0.502454\pi\) | ||||
−0.00770860 | + | 0.999970i | \(0.502454\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7105.09 | 0.00587688 | 0.00293844 | − | 0.999996i | \(-0.499065\pi\) | ||||
0.00293844 | + | 0.999996i | \(0.499065\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.36228e6 | 1.08626 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 710403. | 0.556296 | 0.278148 | − | 0.960538i | \(-0.410280\pi\) | ||||
0.278148 | + | 0.960538i | \(0.410280\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.02845e6 | 0.776991 | 0.388496 | − | 0.921451i | \(-0.372995\pi\) | ||||
0.388496 | + | 0.921451i | \(0.372995\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.84463e6 | −1.36913 | −0.684564 | − | 0.728953i | \(-0.740007\pi\) | ||||
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 206291. | 0.147834 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 825769. | 0.581586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −940972. | −0.640336 | −0.320168 | − | 0.947361i | \(-0.603739\pi\) | ||||
−0.320168 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.19847e6 | 3.47793 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 803243. | 0.519600 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.27418e6 | −0.810615 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −920492. | −0.566592 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.93094e6 | −1.77485 | −0.887425 | − | 0.460952i | \(-0.847508\pi\) | ||||
−0.887425 | + | 0.460952i | \(0.847508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.28251e6 | 1.33817 | 0.669086 | − | 0.743185i | \(-0.266686\pi\) | ||||
0.669086 | + | 0.743185i | \(0.266686\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 802648. | 0.463089 | 0.231544 | − | 0.972824i | \(-0.425622\pi\) | ||||
0.231544 | + | 0.972824i | \(0.425622\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.11196e6 | −0.621502 | −0.310751 | − | 0.950491i | \(-0.600581\pi\) | ||||
−0.310751 | + | 0.950491i | \(0.600581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 417491. | 0.229705 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.15443e6 | −1.14902 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.75885e6 | 3.02432 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 659544. | 0.335934 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.22658e6 | −0.615355 | −0.307678 | − | 0.951491i | \(-0.599552\pi\) | ||||
−0.307678 | + | 0.951491i | \(0.599552\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 801597. | 0.390251 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.30128e6 | 1.10381 | 0.551907 | − | 0.833906i | \(-0.313900\pi\) | ||||
0.551907 | + | 0.833906i | \(0.313900\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.04748e6 | −0.487818 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.36679e6 | −1.08624 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.61930e6 | −0.721945 | −0.360973 | − | 0.932576i | \(-0.617555\pi\) | ||||
−0.360973 | + | 0.932576i | \(0.617555\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −278614. | −0.122445 | −0.0612223 | − | 0.998124i | \(-0.519500\pi\) | ||||
−0.0612223 | + | 0.998124i | \(0.519500\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.36993e6 | −1.43941 | −0.719704 | − | 0.694281i | \(-0.755723\pi\) | ||||
−0.719704 | + | 0.694281i | \(0.755723\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 395486. | 0.166556 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −272571. | −0.111621 | −0.0558103 | − | 0.998441i | \(-0.517774\pi\) | ||||
−0.0558103 | + | 0.998441i | \(0.517774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −409156. | −0.165242 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.41172e6 | −2.51908 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.95765e6 | −1.53381 | −0.766906 | − | 0.641759i | \(-0.778205\pi\) | ||||
−0.766906 | + | 0.641759i | \(0.778205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −999900. | −0.377157 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.92388e6 | −0.715987 | −0.357994 | − | 0.933724i | \(-0.616539\pi\) | ||||
−0.357994 | + | 0.933724i | \(0.616539\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.76489e6 | 0.639534 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.11015e6 | −1.11220 | −0.556101 | − | 0.831115i | \(-0.687703\pi\) | ||||
−0.556101 | + | 0.831115i | \(0.687703\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.83421e6 | 0.987269 | 0.493634 | − | 0.869670i | \(-0.335668\pi\) | ||||
0.493634 | + | 0.869670i | \(0.335668\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.68839e6 | −0.580524 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.05383e6 | 0.688162 | 0.344081 | − | 0.938940i | \(-0.388190\pi\) | ||||
0.344081 | + | 0.938940i | \(0.388190\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.89431e6 | −0.626628 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.03716e6 | 2.26937 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.82167e6 | −1.21696 | −0.608480 | − | 0.793569i | \(-0.708220\pi\) | ||||
−0.608480 | + | 0.793569i | \(0.708220\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.31729e6 | −1.65131 | −0.825656 | − | 0.564173i | \(-0.809195\pi\) | ||||
−0.825656 | + | 0.564173i | \(0.809195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.42807e6 | −1.35816 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.19509e6 | −0.357613 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.15843e6 | 0.933605 | 0.466803 | − | 0.884362i | \(-0.345406\pi\) | ||||
0.466803 | + | 0.884362i | \(0.345406\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.79095e6 | −1.38212 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.14620e6 | 2.60688 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.61564e6 | 1.00612 | 0.503060 | − | 0.864251i | \(-0.332207\pi\) | ||||
0.503060 | + | 0.864251i | \(0.332207\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.02889e6 | 0.282920 | 0.141460 | − | 0.989944i | \(-0.454820\pi\) | ||||
0.141460 | + | 0.989944i | \(0.454820\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.35813e7 | −3.64727 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 848331. | 0.225162 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.21668e6 | −1.61200 | −0.806001 | − | 0.591914i | \(-0.798372\pi\) | ||||
−0.806001 | + | 0.591914i | \(0.798372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −598070. | −0.153297 | −0.0766483 | − | 0.997058i | \(-0.524422\pi\) | ||||
−0.0766483 | + | 0.997058i | \(0.524422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.81739e6 | 0.455244 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −493097. | −0.122115 | −0.0610577 | − | 0.998134i | \(-0.519447\pi\) | ||||
−0.0610577 | + | 0.998134i | \(0.519447\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 195512. | 0.0473329 | 0.0236665 | − | 0.999720i | \(-0.492466\pi\) | ||||
0.0236665 | + | 0.999720i | \(0.492466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −426308. | −0.102053 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.51225e6 | 0.354004 | 0.177002 | − | 0.984210i | \(-0.443360\pi\) | ||||
0.177002 | + | 0.984210i | \(0.443360\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 304763. | 0.0705538 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.13743e6 | −1.61627 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.56472e6 | 0.574445 | 0.287223 | − | 0.957864i | \(-0.407268\pi\) | ||||
0.287223 | + | 0.957864i | \(0.407268\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.36673e6 | 1.17613 | 0.588067 | − | 0.808812i | \(-0.299889\pi\) | ||||
0.588067 | + | 0.808812i | \(0.299889\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.50215e6 | 1.19283 | 0.596417 | − | 0.802675i | \(-0.296591\pi\) | ||||
0.596417 | + | 0.802675i | \(0.296591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −964114. | −0.204567 | −0.102284 | − | 0.994755i | \(-0.532615\pi\) | ||||
−0.102284 | + | 0.994755i | \(0.532615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −738757. | −0.155085 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.88240e6 | −0.386865 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.30298e7 | 2.64973 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 562534. | 0.112024 | 0.0560118 | − | 0.998430i | \(-0.482162\pi\) | ||||
0.0560118 | + | 0.998430i | \(0.482162\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.05207e6 | −0.995650 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.64815e6 | −1.47639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.14185e6 | 0.600292 | 0.300146 | − | 0.953893i | \(-0.402965\pi\) | ||||
0.300146 | + | 0.953893i | \(0.402965\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.73361e6 | −1.07331 | −0.536654 | − | 0.843802i | \(-0.680312\pi\) | ||||
−0.536654 | + | 0.843802i | \(0.680312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.16219e6 | −0.771267 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −364483. | −0.0661890 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.71562e6 | 0.308439 | 0.154220 | − | 0.988037i | \(-0.450714\pi\) | ||||
0.154220 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.15229e6 | 0.907989 | 0.453995 | − | 0.891004i | \(-0.349999\pi\) | ||||
0.453995 | + | 0.891004i | \(0.349999\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.80919e6 | −0.490176 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.04256e6 | 0.178364 | 0.0891819 | − | 0.996015i | \(-0.471575\pi\) | ||||
0.0891819 | + | 0.996015i | \(0.471575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.90908e6 | 1.00108 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.99796e6 | 1.16266 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 974374. | 0.160324 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.52239e6 | −1.53692 | −0.768461 | − | 0.639897i | \(-0.778977\pi\) | ||||
−0.768461 | + | 0.639897i | \(0.778977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.97573e6 | −0.475706 | −0.237853 | − | 0.971301i | \(-0.576444\pi\) | ||||
−0.237853 | + | 0.971301i | \(0.576444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.04429e7 | 1.63792 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.83838e6 | −0.751728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.28834e6 | 0.196433 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.75190e6 | −1.01986 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −970266. | −0.143853 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.80579e6 | 0.265261 | 0.132631 | − | 0.991166i | \(-0.457658\pi\) | ||||
0.132631 | + | 0.991166i | \(0.457658\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.36935e7 | 1.97480 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.36973e6 | −1.33893 | −0.669466 | − | 0.742843i | \(-0.733477\pi\) | ||||
−0.669466 | + | 0.742843i | \(0.733477\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.99317e6 | 0.560323 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.48550e6 | −0.901842 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.53733e6 | −0.483101 | −0.241550 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241550 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.95761e6 | −1.07709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.78060e6 | −0.369716 | −0.184858 | − | 0.982765i | \(-0.559182\pi\) | ||||
−0.184858 | + | 0.982765i | \(0.559182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.29650e7 | 1.70864 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.35293e6 | −0.952094 | −0.476047 | − | 0.879420i | \(-0.657931\pi\) | ||||
−0.476047 | + | 0.879420i | \(0.657931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.75171e6 | −0.738255 | −0.369128 | − | 0.929379i | \(-0.620343\pi\) | ||||
−0.369128 | + | 0.929379i | \(0.620343\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.14566e7 | 1.44506 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.30488e7 | −1.63167 | −0.815835 | − | 0.578285i | \(-0.803722\pi\) | ||||
−0.815835 | + | 0.578285i | \(0.803722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.42920e6 | −1.03597 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.47720e6 | −0.179998 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.24724e6 | −0.149401 | −0.0747005 | − | 0.997206i | \(-0.523800\pi\) | ||||
−0.0747005 | + | 0.997206i | \(0.523800\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.00188e7 | −1.18994 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.32769e7 | 1.55045 | 0.775226 | − | 0.631684i | \(-0.217636\pi\) | ||||
0.775226 | + | 0.631684i | \(0.217636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.68324e7 | 1.94919 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.04914e6 | −0.461101 | −0.230551 | − | 0.973060i | \(-0.574053\pi\) | ||||
−0.230551 | + | 0.973060i | \(0.574053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.83714e6 | −0.772126 | −0.386063 | − | 0.922472i | \(-0.626165\pi\) | ||||
−0.386063 | + | 0.922472i | \(0.626165\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.52856e7 | 1.69783 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 696200. | 0.0766941 | 0.0383471 | − | 0.999264i | \(-0.487791\pi\) | ||||
0.0383471 | + | 0.999264i | \(0.487791\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.11904e6 | 0.446367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.42785e6 | −0.153473 | −0.0767363 | − | 0.997051i | \(-0.524450\pi\) | ||||
−0.0767363 | + | 0.997051i | \(0.524450\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50335e7 | 1.58982 | 0.794908 | − | 0.606730i | \(-0.207519\pi\) | ||||
0.794908 | + | 0.606730i | \(0.207519\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.16303e6 | −0.751398 | −0.375699 | − | 0.926742i | \(-0.622597\pi\) | ||||
−0.375699 | + | 0.926742i | \(0.622597\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 392889. | 0.0405555 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.40504e7 | 4.51076 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.19145e7 | 1.20074 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.38021e7 | 1.37998 | 0.689989 | − | 0.723820i | \(-0.257615\pi\) | ||||
0.689989 | + | 0.723820i | \(0.257615\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.29416e6 | 0.324198 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.10167e6 | −0.400509 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.04659e6 | 0.388995 | 0.194497 | − | 0.980903i | \(-0.437692\pi\) | ||||
0.194497 | + | 0.980903i | \(0.437692\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.08876e7 | 1.03850 | 0.519249 | − | 0.854623i | \(-0.326212\pi\) | ||||
0.519249 | + | 0.854623i | \(0.326212\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.45797e6 | 0.794339 | 0.397169 | − | 0.917745i | \(-0.369993\pi\) | ||||
0.397169 | + | 0.917745i | \(0.369993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.07788e6 | −0.659617 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.95548e6 | −0.454782 | −0.227391 | − | 0.973804i | \(-0.573020\pi\) | ||||
−0.227391 | + | 0.973804i | \(0.573020\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.89950e7 | −1.72996 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.67430e7 | −1.50183 | −0.750915 | − | 0.660398i | \(-0.770387\pi\) | ||||
−0.750915 | + | 0.660398i | \(0.770387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.50798e7 | −1.34243 | −0.671217 | − | 0.741260i | \(-0.734228\pi\) | ||||
−0.671217 | + | 0.741260i | \(0.734228\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.61489e7 | −1.41608 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.51105e6 | 0.305578 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.25328e6 | 0.107459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.41419e7 | 1.20357 | 0.601784 | − | 0.798659i | \(-0.294457\pi\) | ||||
0.601784 | + | 0.798659i | \(0.294457\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.45879e7 | −1.22327 | −0.611635 | − | 0.791140i | \(-0.709488\pi\) | ||||
−0.611635 | + | 0.791140i | \(0.709488\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.04859e6 | 0.586715 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.10096e7 | 0.903065 | 0.451532 | − | 0.892255i | \(-0.350878\pi\) | ||||
0.451532 | + | 0.892255i | \(0.350878\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.10158e7 | 1.71127 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.24465e6 | −0.501141 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.10359e7 | 0.879247 | 0.439623 | − | 0.898182i | \(-0.355112\pi\) | ||||
0.439623 | + | 0.898182i | \(0.355112\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.72116e7 | 2.92224 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.03834e6 | −0.236894 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.51294e7 | 1.93146 | 0.965732 | − | 0.259542i | \(-0.0835717\pi\) | ||||
0.965732 | + | 0.259542i | \(0.0835717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.14306e7 | −0.872332 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.58896e6 | 0.194795 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.25301e7 | 0.936137 | 0.468068 | − | 0.883692i | \(-0.344950\pi\) | ||||
0.468068 | + | 0.883692i | \(0.344950\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.80915e6 | −0.648948 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.05444e7 | −0.771362 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.72246e6 | 0.124258 | 0.0621292 | − | 0.998068i | \(-0.480211\pi\) | ||||
0.0621292 | + | 0.998068i | \(0.480211\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.44937e6 | −0.462040 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.51724e7 | 1.77861 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.98849e6 | 0.490397 | 0.245198 | − | 0.969473i | \(-0.421147\pi\) | ||||
0.245198 | + | 0.969473i | \(0.421147\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.87667e7 | 1.29896 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.92609e6 | −0.407388 | −0.203694 | − | 0.979035i | \(-0.565295\pi\) | ||||
−0.203694 | + | 0.979035i | \(0.565295\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.09140e6 | −0.0740142 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.06632e7 | −0.718254 | −0.359127 | − | 0.933289i | \(-0.616925\pi\) | ||||
−0.359127 | + | 0.933289i | \(0.616925\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.84986e7 | 1.22933 | 0.614664 | − | 0.788789i | \(-0.289292\pi\) | ||||
0.614664 | + | 0.788789i | \(0.289292\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.08286e6 | −0.401529 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.22259e6 | 0.405291 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.61247e7 | −1.69025 | −0.845127 | − | 0.534566i | \(-0.820475\pi\) | ||||
−0.845127 | + | 0.534566i | \(0.820475\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.68804e7 | −2.35466 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.49174e7 | 1.58039 | 0.790193 | − | 0.612858i | \(-0.209980\pi\) | ||||
0.790193 | + | 0.612858i | \(0.209980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.12439e7 | −0.703808 | −0.351904 | − | 0.936036i | \(-0.614466\pi\) | ||||
−0.351904 | + | 0.936036i | \(0.614466\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.26200e7 | −0.784781 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.99208e7 | −1.83647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.67461e6 | 0.528974 | 0.264487 | − | 0.964389i | \(-0.414797\pi\) | ||||
0.264487 | + | 0.964389i | \(0.414797\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.17066e7 | −1.30660 | −0.653300 | − | 0.757099i | \(-0.726616\pi\) | ||||
−0.653300 | + | 0.757099i | \(0.726616\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.31571e7 | −3.77718 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.91496e6 | 0.172103 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −538467. | −0.0315887 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.32597e7 | 0.767997 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.86429e6 | 0.452609 | 0.226304 | − | 0.974057i | \(-0.427336\pi\) | ||||
0.226304 | + | 0.974057i | \(0.427336\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.19486e7 | −0.679009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.29807e6 | 0.299181 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.89618e7 | −1.05739 | −0.528693 | − | 0.848813i | \(-0.677318\pi\) | ||||
−0.528693 | + | 0.848813i | \(0.677318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.71406e6 | −0.538312 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.72975e6 | 0.477764 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.41991e7 | −0.772274 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.09408e7 | 1.12492 | 0.562459 | − | 0.826825i | \(-0.309855\pi\) | ||||
0.562459 | + | 0.826825i | \(0.309855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.21466e7 | 1.71626 | 0.858130 | − | 0.513432i | \(-0.171626\pi\) | ||||
0.858130 | + | 0.513432i | \(0.171626\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.05257e7 | −2.13716 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.80046e7 | −0.943687 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.97605e7 | 1.54093 | 0.770463 | − | 0.637485i | \(-0.220025\pi\) | ||||
0.770463 | + | 0.637485i | \(0.220025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.65220e7 | −0.850284 | −0.425142 | − | 0.905127i | \(-0.639776\pi\) | ||||
−0.425142 | + | 0.905127i | \(0.639776\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.49588e7 | −1.26900 | −0.634498 | − | 0.772925i | \(-0.718793\pi\) | ||||
−0.634498 | + | 0.772925i | \(0.718793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.92909e7 | −1.48029 | −0.740145 | − | 0.672447i | \(-0.765243\pi\) | ||||
−0.740145 | + | 0.672447i | \(0.765243\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.67311e6 | 0.483007 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.50747e7 | 3.22995 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.74835e7 | −1.83838 | −0.919189 | − | 0.393817i | \(-0.871155\pi\) | ||||
−0.919189 | + | 0.393817i | \(0.871155\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.27967e7 | −0.623888 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.58473e6 | −0.172709 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.40873e7 | −0.674713 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.00505e7 | −0.475735 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.48271e7 | 0.697726 | 0.348863 | − | 0.937174i | \(-0.386568\pi\) | ||||
0.348863 | + | 0.937174i | \(0.386568\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.32370e6 | −0.247606 | −0.123803 | − | 0.992307i | \(-0.539509\pi\) | ||||
−0.123803 | + | 0.992307i | \(0.539509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.68868e7 | 1.24324 | 0.621621 | − | 0.783318i | \(-0.286474\pi\) | ||||
0.621621 | + | 0.783318i | \(0.286474\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.21441e6 | 0.101212 | 0.0506060 | − | 0.998719i | \(-0.483885\pi\) | ||||
0.0506060 | + | 0.998719i | \(0.483885\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.81846e7 | 2.18961 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.58131e6 | −0.430403 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.61374e6 | −0.206067 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.66988e7 | −2.94509 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.24646e7 | 1.42531 | 0.712657 | − | 0.701513i | \(-0.247492\pi\) | ||||
0.712657 | + | 0.701513i | \(0.247492\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.78418e6 | −0.337888 | −0.168944 | − | 0.985626i | \(-0.554036\pi\) | ||||
−0.168944 | + | 0.985626i | \(0.554036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.71890e7 | 0.741906 | 0.370953 | − | 0.928652i | \(-0.379031\pi\) | ||||
0.370953 | + | 0.928652i | \(0.379031\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.63433e7 | 1.55101 | 0.775506 | − | 0.631340i | \(-0.217495\pi\) | ||||
0.775506 | + | 0.631340i | \(0.217495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.03592e6 | −0.128836 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.31958e6 | 0.391082 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.66133e7 | 1.11056 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.93555e7 | −0.798739 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.47270e7 | 0.604368 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.99500e6 | −0.121556 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.78418e6 | −0.354555 | −0.177277 | − | 0.984161i | \(-0.556729\pi\) | ||||
−0.177277 | + | 0.984161i | \(0.556729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.67006e6 | 0.146513 | 0.0732566 | − | 0.997313i | \(-0.476661\pi\) | ||||
0.0732566 | + | 0.997313i | \(0.476661\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.24528e7 | −0.494414 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.75060e7 | 0.687484 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.38118e7 | 1.32063 | 0.660313 | − | 0.750990i | \(-0.270424\pi\) | ||||
0.660313 | + | 0.750990i | \(0.270424\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.27630e6 | −0.0879477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.20572e7 | −2.76900 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.17835e7 | 0.447954 | 0.223977 | − | 0.974594i | \(-0.428096\pi\) | ||||
0.223977 | + | 0.974594i | \(0.428096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.28029e6 | −0.350903 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.48673e7 | 0.930250 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.78550e7 | −1.40856 | −0.704278 | − | 0.709924i | \(-0.748729\pi\) | ||||
−0.704278 | + | 0.709924i | \(0.748729\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.56271e7 | −1.67977 | −0.839884 | − | 0.542766i | \(-0.817377\pi\) | ||||
−0.839884 | + | 0.542766i | \(0.817377\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.56302e6 | 0.0938582 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.15884e7 | −1.50694 | −0.753472 | − | 0.657480i | \(-0.771622\pi\) | ||||
−0.753472 | + | 0.657480i | \(0.771622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.69039e7 | 1.33017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.40042e7 | 1.92617 | 0.963087 | − | 0.269190i | \(-0.0867560\pi\) | ||||
0.963087 | + | 0.269190i | \(0.0867560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.19036e6 | −0.219638 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.93683e7 | −0.680055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.99334e7 | 0.696261 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.91347e7 | −1.35283 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.72935e7 | 0.594724 | 0.297362 | − | 0.954765i | \(-0.403893\pi\) | ||||
0.297362 | + | 0.954765i | \(0.403893\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.55169e7 | −1.54926 | −0.774630 | − | 0.632415i | \(-0.782064\pi\) | ||||
−0.774630 | + | 0.632415i | \(0.782064\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.42944e7 | −1.16129 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.59652e6 | −0.221095 | −0.110547 | − | 0.993871i | \(-0.535260\pi\) | ||||
−0.110547 | + | 0.993871i | \(0.535260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 580432. | 0.0193551 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.69457e7 | 1.21950 | 0.609748 | − | 0.792595i | \(-0.291271\pi\) | ||||
0.609748 | + | 0.792595i | \(0.291271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.01846e7 | −2.96171 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.58308e7 | −0.514649 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.56015e6 | −0.244538 | −0.122269 | − | 0.992497i | \(-0.539017\pi\) | ||||
−0.122269 | + | 0.992497i | \(0.539017\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.49870e7 | −3.04163 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.56153e7 | −0.497521 | −0.248761 | − | 0.968565i | \(-0.580023\pi\) | ||||
−0.248761 | + | 0.968565i | \(0.580023\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 324.6.a.d.1.1 | 5 | ||
3.2 | odd | 2 | 324.6.a.e.1.5 | 5 | |||
9.2 | odd | 6 | 36.6.e.a.13.5 | ✓ | 10 | ||
9.4 | even | 3 | 108.6.e.a.73.5 | 10 | |||
9.5 | odd | 6 | 36.6.e.a.25.5 | yes | 10 | ||
9.7 | even | 3 | 108.6.e.a.37.5 | 10 | |||
36.7 | odd | 6 | 432.6.i.d.145.5 | 10 | |||
36.11 | even | 6 | 144.6.i.d.49.1 | 10 | |||
36.23 | even | 6 | 144.6.i.d.97.1 | 10 | |||
36.31 | odd | 6 | 432.6.i.d.289.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.e.a.13.5 | ✓ | 10 | 9.2 | odd | 6 | ||
36.6.e.a.25.5 | yes | 10 | 9.5 | odd | 6 | ||
108.6.e.a.37.5 | 10 | 9.7 | even | 3 | |||
108.6.e.a.73.5 | 10 | 9.4 | even | 3 | |||
144.6.i.d.49.1 | 10 | 36.11 | even | 6 | |||
144.6.i.d.97.1 | 10 | 36.23 | even | 6 | |||
324.6.a.d.1.1 | 5 | 1.1 | even | 1 | trivial | ||
324.6.a.e.1.5 | 5 | 3.2 | odd | 2 | |||
432.6.i.d.145.5 | 10 | 36.7 | odd | 6 | |||
432.6.i.d.289.5 | 10 | 36.31 | odd | 6 |