Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,6,Mod(1,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("280.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.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: | \(44.9074695476\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 232x^{2} + 60x + 5808 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-13.3078\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.1 |
$q$-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 | ||||||||
\(3\) | −15.6617 | −1.00470 | −0.502350 | − | 0.864664i | \(-0.667531\pi\) | ||||
−0.502350 | + | 0.864664i | \(0.667531\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.28996 | 0.00942368 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −541.846 | −1.35019 | −0.675093 | − | 0.737732i | \(-0.735897\pi\) | ||||
−0.675093 | + | 0.737732i | \(0.735897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 762.537 | 1.25142 | 0.625709 | − | 0.780056i | \(-0.284810\pi\) | ||||
0.625709 | + | 0.780056i | \(0.284810\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −391.543 | −0.449316 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 734.092 | 0.616067 | 0.308034 | − | 0.951375i | \(-0.400329\pi\) | ||||
0.308034 | + | 0.951375i | \(0.400329\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1106.05 | 0.702897 | 0.351448 | − | 0.936207i | \(-0.385689\pi\) | ||||
0.351448 | + | 0.936207i | \(0.385689\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −767.425 | −0.379741 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4521.40 | −1.78219 | −0.891093 | − | 0.453821i | \(-0.850061\pi\) | ||||
−0.891093 | + | 0.453821i | \(0.850061\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3769.94 | 0.995233 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4034.79 | −0.890893 | −0.445447 | − | 0.895308i | \(-0.646955\pi\) | ||||
−0.445447 | + | 0.895308i | \(0.646955\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9248.86 | 1.72856 | 0.864279 | − | 0.503013i | \(-0.167775\pi\) | ||||
0.864279 | + | 0.503013i | \(0.167775\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8486.24 | 1.35653 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11490.0 | 1.37980 | 0.689900 | − | 0.723904i | \(-0.257654\pi\) | ||||
0.689900 | + | 0.723904i | \(0.257654\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11942.7 | −1.25730 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11025.2 | −1.02430 | −0.512148 | − | 0.858897i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858897i | \(0.671150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8340.65 | −0.687905 | −0.343953 | − | 0.938987i | \(-0.611766\pi\) | ||||
−0.343953 | + | 0.938987i | \(0.611766\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 57.2489 | 0.00421440 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1060.61 | −0.0700342 | −0.0350171 | − | 0.999387i | \(-0.511149\pi\) | ||||
−0.0350171 | + | 0.999387i | \(0.511149\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11497.2 | −0.618963 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5213.92 | 0.254961 | 0.127481 | − | 0.991841i | \(-0.459311\pi\) | ||||
0.127481 | + | 0.991841i | \(0.459311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13546.1 | −0.603822 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17322.7 | −0.706201 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −50307.0 | −1.88147 | −0.940737 | − | 0.339136i | \(-0.889865\pi\) | ||||
−0.940737 | + | 0.339136i | \(0.889865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12131.6 | −0.417441 | −0.208721 | − | 0.977975i | \(-0.566930\pi\) | ||||
−0.208721 | + | 0.977975i | \(0.566930\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 112.208 | 0.00356182 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19063.4 | 0.559652 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −66799.4 | −1.81796 | −0.908982 | − | 0.416835i | \(-0.863139\pi\) | ||||
−0.908982 | + | 0.416835i | \(0.863139\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 70812.9 | 1.79056 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −60509.7 | −1.42455 | −0.712277 | − | 0.701899i | \(-0.752336\pi\) | ||||
−0.712277 | + | 0.701899i | \(0.752336\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −66790.8 | −1.46693 | −0.733465 | − | 0.679727i | \(-0.762098\pi\) | ||||
−0.733465 | + | 0.679727i | \(0.762098\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9788.58 | −0.200940 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −26550.4 | −0.510323 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61795.8 | 1.11402 | 0.557008 | − | 0.830507i | \(-0.311949\pi\) | ||||
0.557008 | + | 0.830507i | \(0.311949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −59600.2 | −1.00933 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −123891. | −1.97399 | −0.986995 | − | 0.160753i | \(-0.948608\pi\) | ||||
−0.986995 | + | 0.160753i | \(0.948608\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18352.3 | 0.275514 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 63191.8 | 0.895081 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 25976.4 | 0.347620 | 0.173810 | − | 0.984779i | \(-0.444392\pi\) | ||||
0.173810 | + | 0.984779i | \(0.444392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 37364.3 | 0.472992 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −144853. | −1.73668 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27651.3 | 0.314345 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −68019.8 | −0.734017 | −0.367008 | − | 0.930218i | \(-0.619618\pi\) | ||||
−0.367008 | + | 0.930218i | \(0.619618\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1240.80 | −0.0127237 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −27324.6 | −0.266533 | −0.133266 | − | 0.991080i | \(-0.542547\pi\) | ||||
−0.133266 | + | 0.991080i | \(0.542547\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14070.9 | −0.130686 | −0.0653429 | − | 0.997863i | \(-0.520814\pi\) | ||||
−0.0653429 | + | 0.997863i | \(0.520814\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −19185.6 | −0.169825 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −186019. | −1.57072 | −0.785358 | − | 0.619042i | \(-0.787521\pi\) | ||||
−0.785358 | + | 0.619042i | \(0.787521\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 57760.5 | 0.465655 | 0.232828 | − | 0.972518i | \(-0.425202\pi\) | ||||
0.232828 | + | 0.972518i | \(0.425202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −179954. | −1.38629 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 232262. | 1.71113 | 0.855563 | − | 0.517698i | \(-0.173211\pi\) | ||||
0.855563 | + | 0.517698i | \(0.173211\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −113035. | −0.797018 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1746.18 | 0.0117930 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 35970.5 | 0.232852 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 132546. | 0.823005 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 172673. | 1.02911 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 155827. | 0.857302 | 0.428651 | − | 0.903470i | \(-0.358989\pi\) | ||||
0.428651 | + | 0.903470i | \(0.358989\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 130629. | 0.691139 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 276458. | 1.40751 | 0.703755 | − | 0.710443i | \(-0.251505\pi\) | ||||
0.703755 | + | 0.710443i | \(0.251505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 54196.5 | 0.265670 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 94248.4 | 0.445082 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −206689. | −0.940840 | −0.470420 | − | 0.882443i | \(-0.655898\pi\) | ||||
−0.470420 | + | 0.882443i | \(0.655898\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −121060. | −0.531451 | −0.265725 | − | 0.964049i | \(-0.585611\pi\) | ||||
−0.265725 | + | 0.964049i | \(0.585611\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16611.0 | 0.0703634 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −413178. | −1.68965 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −100870. | −0.398420 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −37603.8 | −0.143529 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 213540. | 0.787976 | 0.393988 | − | 0.919116i | \(-0.371095\pi\) | ||||
0.393988 | + | 0.919116i | \(0.371095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −306833. | −1.09512 | −0.547558 | − | 0.836768i | \(-0.684442\pi\) | ||||
−0.547558 | + | 0.836768i | \(0.684442\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1681.04 | 0.00580562 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 231221. | 0.773034 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −113475. | −0.367410 | −0.183705 | − | 0.982981i | \(-0.558809\pi\) | ||||
−0.183705 | + | 0.982981i | \(0.558809\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −81659.0 | −0.256160 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −221548. | −0.673603 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −519473. | −1.53142 | −0.765709 | − | 0.643187i | \(-0.777612\pi\) | ||||
−0.765709 | + | 0.643187i | \(0.777612\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 212156. | 0.606660 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 57730.3 | 0.160182 | 0.0800908 | − | 0.996788i | \(-0.474479\pi\) | ||||
0.0800908 | + | 0.996788i | \(0.474479\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 210170. | 0.566049 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2532.81 | 0.00662388 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 298815. | 0.759080 | 0.379540 | − | 0.925175i | \(-0.376082\pi\) | ||||
0.379540 | + | 0.925175i | \(0.376082\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30625.0 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 787895. | 1.89032 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 112965. | 0.263519 | 0.131760 | − | 0.991282i | \(-0.457937\pi\) | ||||
0.131760 | + | 0.991282i | \(0.457937\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −163008. | −0.369840 | −0.184920 | − | 0.982754i | \(-0.559203\pi\) | ||||
−0.184920 | + | 0.982754i | \(0.559203\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 190003. | 0.419403 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 287250. | 0.617066 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −397765. | −0.831806 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 184727. | 0.376163 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 414125. | 0.821387 | 0.410693 | − | 0.911773i | \(-0.365287\pi\) | ||||
0.410693 | + | 0.911773i | \(0.365287\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −782850. | −1.51281 | −0.756407 | − | 0.654102i | \(-0.773047\pi\) | ||||
−0.756407 | + | 0.654102i | \(0.773047\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −298566. | −0.562282 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −435399. | −0.799322 | −0.399661 | − | 0.916663i | \(-0.630872\pi\) | ||||
−0.399661 | + | 0.916663i | \(0.630872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.02204e6 | 1.82950 | 0.914752 | − | 0.404016i | \(-0.132386\pi\) | ||||
0.914752 | + | 0.404016i | \(0.132386\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.04619e6 | 1.82651 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −197705. | −0.336726 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −275629. | −0.458079 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10353.8 | −0.0167948 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −599309. | −0.949042 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −628212. | −0.971404 | −0.485702 | − | 0.874124i | \(-0.661436\pi\) | ||||
−0.485702 | + | 0.874124i | \(0.661436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 947686. | 1.43125 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −208516. | −0.307641 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 453194. | 0.653333 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.04606e6 | 1.47383 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 559773. | 0.770958 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −371528. | −0.500299 | −0.250149 | − | 0.968207i | \(-0.580480\pi\) | ||||
−0.250149 | + | 0.968207i | \(0.580480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1431.22 | 0.00188474 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.32477e6 | −1.70638 | −0.853189 | − | 0.521602i | \(-0.825335\pi\) | ||||
−0.853189 | + | 0.521602i | \(0.825335\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.08203e6 | 1.36349 | 0.681746 | − | 0.731589i | \(-0.261221\pi\) | ||||
0.681746 | + | 0.731589i | \(0.261221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 415826. | 0.512722 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.12343e6 | 1.35568 | 0.677839 | − | 0.735210i | \(-0.262916\pi\) | ||||
0.677839 | + | 0.735210i | \(0.262916\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26515.2 | −0.0313202 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −967830. | −1.11925 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −438692. | −0.496781 | −0.248391 | − | 0.968660i | \(-0.579902\pi\) | ||||
−0.248391 | + | 0.968660i | \(0.579902\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.55676e6 | −1.72655 | −0.863276 | − | 0.504731i | \(-0.831592\pi\) | ||||
−0.863276 | + | 0.504731i | \(0.831592\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17348.1 | 0.0188467 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 843406. | 0.879618 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.94035e6 | 1.98327 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 110717. | 0.110926 | 0.0554628 | − | 0.998461i | \(-0.482337\pi\) | ||||
0.0554628 | + | 0.998461i | \(0.482337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.44990e6 | 2.40628 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −287429. | −0.276809 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.48151e6 | 1.39918 | 0.699589 | − | 0.714545i | \(-0.253366\pi\) | ||||
0.699589 | + | 0.714545i | \(0.253366\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 563011. | 0.521516 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9239.48 | −0.00839550 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 456663. | 0.407105 | 0.203553 | − | 0.979064i | \(-0.434751\pi\) | ||||
0.203553 | + | 0.979064i | \(0.434751\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 130348. | 0.114022 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −406836. | −0.349254 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 642686. | 0.541524 | 0.270762 | − | 0.962646i | \(-0.412724\pi\) | ||||
0.270762 | + | 0.962646i | \(0.412724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.17995e6 | 0.975975 | 0.487988 | − | 0.872851i | \(-0.337731\pi\) | ||||
0.487988 | + | 0.872851i | \(0.337731\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −585190. | −0.475215 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −338654. | −0.270037 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −998004. | −0.781507 | −0.390753 | − | 0.920495i | \(-0.627785\pi\) | ||||
−0.390753 | + | 0.920495i | \(0.627785\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21179.5 | 0.0162894 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −577449. | −0.436262 | −0.218131 | − | 0.975919i | \(-0.569996\pi\) | ||||
−0.218131 | + | 0.975919i | \(0.569996\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −67362.3 | −0.0499978 | −0.0249989 | − | 0.999687i | \(-0.507958\pi\) | ||||
−0.0249989 | + | 0.999687i | \(0.507958\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −433067. | −0.315823 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −540233. | −0.387147 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −880966. | −0.620461 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.06531e6 | 0.737467 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.10005e6 | −0.748591 | −0.374295 | − | 0.927310i | \(-0.622115\pi\) | ||||
−0.374295 | + | 0.927310i | \(0.622115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.25767e6 | −0.841421 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.04272e6 | −1.34375 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.44773e6 | −2.23026 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −408692. | −0.260004 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 427951. | 0.267786 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −303291. | −0.186685 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −49804.6 | −0.0301595 | −0.0150797 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150797 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 220374. | 0.131300 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −443921. | −0.260258 | −0.130129 | − | 0.991497i | \(-0.541539\pi\) | ||||
−0.130129 | + | 0.991497i | \(0.541539\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.26926e6 | 1.30925 | 0.654627 | − | 0.755952i | \(-0.272826\pi\) | ||||
0.654627 | + | 0.755952i | \(0.272826\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2805.20 | 0.00159289 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.21532e6 | −1.79712 | −0.898558 | − | 0.438855i | \(-0.855384\pi\) | ||||
−0.898558 | + | 0.438855i | \(0.855384\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.18623e6 | 1.20287 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.91338e6 | 1.57810 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 811944. | 0.433032 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 476586. | 0.250284 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −904629. | −0.467844 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −51969.8 | −0.0264704 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.64911e6 | 0.827330 | 0.413665 | − | 0.910429i | \(-0.364249\pi\) | ||||
0.413665 | + | 0.910429i | \(0.364249\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26311.6 | 0.0130028 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.66998e6 | −0.813018 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −940021. | −0.450882 | −0.225441 | − | 0.974257i | \(-0.572382\pi\) | ||||
−0.225441 | + | 0.974257i | \(0.572382\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.63763e6 | −1.71917 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.01145e6 | −2.33388 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.77032e6 | 0.800764 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 840254. | 0.374617 | 0.187308 | − | 0.982301i | \(-0.440024\pi\) | ||||
0.187308 | + | 0.982301i | \(0.440024\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.17991e6 | −1.39750 | −0.698748 | − | 0.715367i | \(-0.746259\pi\) | ||||
−0.698748 | + | 0.715367i | \(0.746259\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.87472e6 | 1.24545 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.44355e6 | 1.04372 | 0.521861 | − | 0.853030i | \(-0.325238\pi\) | ||||
0.521861 | + | 0.853030i | \(0.325238\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.51274e6 | −0.637080 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −563361. | −0.233946 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.33016e6 | 0.954224 | 0.477112 | − | 0.878842i | \(-0.341684\pi\) | ||||
0.477112 | + | 0.878842i | \(0.341684\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.25275e6 | −0.505936 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.07590e6 | −0.826874 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.66977e6 | −0.656031 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.32215e6 | 0.512408 | 0.256204 | − | 0.966623i | \(-0.417528\pi\) | ||||
0.256204 | + | 0.966623i | \(0.417528\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25247.1 | −0.00965264 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 255482. | 0.0963663 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.12859e6 | −1.53649 | −0.768246 | − | 0.640155i | \(-0.778870\pi\) | ||||
−0.768246 | + | 0.640155i | \(0.778870\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −244715. | −0.0898632 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.07668e6 | −1.11488 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.98173e6 | −0.708673 | −0.354336 | − | 0.935118i | \(-0.615293\pi\) | ||||
−0.354336 | + | 0.935118i | \(0.615293\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.44052e6 | −0.861332 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.08393e6 | 1.07426 | 0.537128 | − | 0.843501i | \(-0.319509\pi\) | ||||
0.537128 | + | 0.843501i | \(0.319509\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −663761. | −0.228223 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19099.7 | −0.00648260 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −573834. | −0.192270 | −0.0961351 | − | 0.995368i | \(-0.530648\pi\) | ||||
−0.0961351 | + | 0.995368i | \(0.530648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.31912e6 | −1.09795 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.32982e6 | −1.41413 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.54490e6 | 0.498203 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.35793e6 | −0.432414 | −0.216207 | − | 0.976348i | \(-0.569369\pi\) | ||||
−0.216207 | + | 0.976348i | \(0.569369\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −848812. | −0.266919 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.00515e6 | −0.933264 | −0.466632 | − | 0.884451i | \(-0.654533\pi\) | ||||
−0.466632 | + | 0.884451i | \(0.654533\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.05260e6 | 2.16315 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.49001e6 | −0.451388 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.22582e6 | −1.86299 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 71979.4 | 0.0212765 | 0.0106382 | − | 0.999943i | \(-0.496614\pi\) | ||||
0.0106382 | + | 0.999943i | \(0.496614\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.23711e6 | 0.945262 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.46504e6 | −0.711130 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.09728e6 | −0.882795 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.89601e6 | 0.533949 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.86991e6 | 1.63341 | 0.816707 | − | 0.577052i | \(-0.195797\pi\) | ||||
0.816707 | + | 0.577052i | \(0.195797\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.17367e6 | 0.597706 | 0.298853 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298853 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2428.74 | −0.000659980 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 458808. | 0.123213 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −594451. | −0.157778 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.47108e6 | 1.69759 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.95004e6 | 0.505649 | 0.252825 | − | 0.967512i | \(-0.418640\pi\) | ||||
0.252825 | + | 0.967512i | \(0.418640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 773400. | 0.198237 | 0.0991185 | − | 0.995076i | \(-0.468398\pi\) | ||||
0.0991185 | + | 0.995076i | \(0.468398\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.57979e6 | 0.400292 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.00090e6 | −1.25269 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.22946e6 | 0.799777 | 0.399888 | − | 0.916564i | \(-0.369049\pi\) | ||||
0.399888 | + | 0.916564i | \(0.369049\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5498.18 | 0.00134624 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 636374. | 0.154065 | 0.0770323 | − | 0.997029i | \(-0.475456\pi\) | ||||
0.0770323 | + | 0.997029i | \(0.475456\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 649411. | 0.155460 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.34440e6 | −0.791680 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.01084e6 | 0.470718 | 0.235359 | − | 0.971908i | \(-0.424373\pi\) | ||||
0.235359 | + | 0.971908i | \(0.424373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.97393e6 | 1.38299 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.80554e6 | 1.10026 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 934108. | 0.211528 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.48087e6 | −1.22761 | −0.613804 | − | 0.789459i | \(-0.710361\pi\) | ||||
−0.613804 | + | 0.789459i | \(0.710361\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.76748e6 | 0.613130 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.41469e6 | 0.310034 | 0.155017 | − | 0.987912i | \(-0.450457\pi\) | ||||
0.155017 | + | 0.987912i | \(0.450457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.34587e6 | −0.508571 | −0.254285 | − | 0.967129i | \(-0.581840\pi\) | ||||
−0.254285 | + | 0.967129i | \(0.581840\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.62133e6 | −0.776668 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.55705e6 | −0.754741 | −0.377370 | − | 0.926062i | \(-0.623172\pi\) | ||||
−0.377370 | + | 0.926062i | \(0.623172\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.27317e6 | −0.687126 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.77722e6 | 0.369137 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.51934e6 | 0.928801 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 691282. | 0.140579 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11939.6 | 0.00240267 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.54517e6 | 0.506848 | 0.253424 | − | 0.967355i | \(-0.418443\pi\) | ||||
0.253424 | + | 0.967355i | \(0.418443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.76157e6 | 1.72671 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.46983e6 | 0.676769 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.70049e6 | −0.328262 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.84424e6 | 0.352366 | 0.176183 | − | 0.984357i | \(-0.443625\pi\) | ||||
0.176183 | + | 0.984357i | \(0.443625\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.13585e6 | 1.53862 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.66566e6 | −1.62218 | −0.811088 | − | 0.584924i | \(-0.801124\pi\) | ||||
−0.811088 | + | 0.584924i | \(0.801124\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.96191e6 | −0.548850 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31020.1 | −0.00569023 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.96497e6 | −0.538431 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −195522. | −0.0351516 | −0.0175758 | − | 0.999846i | \(-0.505595\pi\) | ||||
−0.0175758 | + | 0.999846i | \(0.505595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −904156. | −0.160935 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.02277e7 | 1.80242 | 0.901210 | − | 0.433382i | \(-0.142680\pi\) | ||||
0.901210 | + | 0.433382i | \(0.142680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −683115. | −0.119197 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.29163e6 | −0.568710 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 437697. | 0.0748823 | 0.0374412 | − | 0.999299i | \(-0.488079\pi\) | ||||
0.0374412 | + | 0.999299i | \(0.488079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.27275e6 | −0.554448 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.16975e6 | 0.699546 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −351772. | −0.0584444 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 574686. | 0.0945593 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.67996e6 | −0.762648 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.08466e6 | −1.30487 | −0.652435 | − | 0.757845i | \(-0.726253\pi\) | ||||
−0.652435 | + | 0.757845i | \(0.726253\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.31342e6 | 0.689553 | 0.344777 | − | 0.938685i | \(-0.387955\pi\) | ||||
0.344777 | + | 0.938685i | \(0.387955\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −479641. | −0.0759482 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.78951e6 | 1.06491 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.40067e7 | 2.17619 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −115201. | −0.0177304 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.40709e6 | −1.28182 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.65047e6 | −0.702446 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.76923e6 | −0.264758 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.30097e6 | −0.192884 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.05370e7 | 1.54783 | 0.773913 | − | 0.633292i | \(-0.218297\pi\) | ||||
0.773913 | + | 0.633292i | \(0.218297\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.55299e6 | 0.371578 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.44401e6 | 0.208247 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.45511e6 | 0.207935 | 0.103968 | − | 0.994581i | \(-0.466846\pi\) | ||||
0.103968 | + | 0.994581i | \(0.466846\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27780.9 | −0.00393383 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.46268e6 | −0.626206 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.02800e6 | 0.421058 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.49884e6 | −0.619966 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.83282e6 | 0.660028 | 0.330014 | − | 0.943976i | \(-0.392946\pi\) | ||||
0.330014 | + | 0.943976i | \(0.392946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.36006e6 | −0.860858 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.22968e6 | 0.835716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.28765e7 | −1.71209 | −0.856047 | − | 0.516898i | \(-0.827086\pi\) | ||||
−0.856047 | + | 0.516898i | \(0.827086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.80655e6 | 0.765239 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.92041e6 | −0.381493 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.36290e6 | −0.435445 | −0.217722 | − | 0.976011i | \(-0.569863\pi\) | ||||
−0.217722 | + | 0.976011i | \(0.569863\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.12235e7 | 1.44058 | 0.720288 | − | 0.693675i | \(-0.244010\pi\) | ||||
0.720288 | + | 0.693675i | \(0.244010\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.48591e6 | −0.825248 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.82587e6 | −0.356437 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.07434e6 | 0.509468 | 0.254734 | − | 0.967011i | \(-0.418012\pi\) | ||||
0.254734 | + | 0.967011i | \(0.418012\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.22608e7 | 1.51992 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.07066e6 | −0.746098 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.82514e6 | −0.344245 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 43654.4 | 0.00527398 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.50426e6 | −0.539546 | −0.269773 | − | 0.962924i | \(-0.586949\pi\) | ||||
−0.269773 | + | 0.962924i | \(0.586949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.02297e7 | 1.21500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.81910e6 | 0.803079 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.53126e6 | −0.295597 | −0.147798 | − | 0.989018i | \(-0.547219\pi\) | ||||
−0.147798 | + | 0.989018i | \(0.547219\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 899263. | 0.104134 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.60069e7 | −1.83810 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.46047e6 | 0.394065 | 0.197033 | − | 0.980397i | \(-0.436869\pi\) | ||||
0.197033 | + | 0.980397i | \(0.436869\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.07573e7 | −1.21483 | −0.607416 | − | 0.794384i | \(-0.707794\pi\) | ||||
−0.607416 | + | 0.794384i | \(0.707794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −152968. | −0.0171319 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.31364e6 | 0.368059 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.74702e6 | 0.302614 | 0.151307 | − | 0.988487i | \(-0.451652\pi\) | ||||
0.151307 | + | 0.988487i | \(0.451652\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.09640e6 | 0.338309 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −808753. | −0.0876421 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.93872e6 | 0.423354 | 0.211677 | − | 0.977340i | \(-0.432107\pi\) | ||||
0.211677 | + | 0.977340i | \(0.432107\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.31683e6 | 0.460232 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.90587e6 | 0.730307 | 0.365153 | − | 0.930947i | \(-0.381017\pi\) | ||||
0.365153 | + | 0.930947i | \(0.381017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.92686e6 | 0.621725 | 0.310863 | − | 0.950455i | \(-0.399382\pi\) | ||||
0.310863 | + | 0.950455i | \(0.399382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.70454e7 | −1.77369 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.27285e6 | 0.131388 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.38623e6 | 0.953503 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.43473e6 | 0.850050 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.64774e6 | −0.664662 | −0.332331 | − | 0.943163i | \(-0.607835\pi\) | ||||
−0.332331 | + | 0.943163i | \(0.607835\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.83889e6 | 0.975971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.89568e6 | 0.383397 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.83085e6 | 0.178774 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −138564. | −0.0134245 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.08946e7 | 1.04729 | 0.523645 | − | 0.851936i | \(-0.324572\pi\) | ||||
0.523645 | + | 0.851936i | \(0.324572\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.48078e6 | 0.236625 | 0.118313 | − | 0.992976i | \(-0.462252\pi\) | ||||
0.118313 | + | 0.992976i | \(0.462252\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.26573e6 | 0.309087 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.46723e7 | −1.37796 | −0.688981 | − | 0.724779i | \(-0.741942\pi\) | ||||
−0.688981 | + | 0.724779i | \(0.741942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.72586e7 | 2.54034 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.09780e6 | −0.656404 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.88045e7 | −1.72576 | −0.862878 | − | 0.505413i | \(-0.831340\pi\) | ||||
−0.862878 | + | 0.505413i | \(0.831340\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.91146e6 | 0.629458 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −152948. | −0.0138239 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.22517e6 | −0.109896 | −0.0549482 | − | 0.998489i | \(-0.517499\pi\) | ||||
−0.0549482 | + | 0.998489i | \(0.517499\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.39727e7 | −1.24388 | −0.621940 | − | 0.783065i | \(-0.713655\pi\) | ||||
−0.621940 | + | 0.783065i | \(0.713655\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.76701e6 | −0.774582 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.35491e6 | 0.118811 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.82429e7 | 1.58774 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.81877e6 | 0.502651 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.57348e6 | 0.563623 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.48808e6 | −0.381964 | −0.190982 | − | 0.981594i | \(-0.561167\pi\) | ||||
−0.190982 | + | 0.981594i | \(0.561167\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.35621e6 | 0.199047 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.67787e6 | −0.140697 | −0.0703486 | − | 0.997522i | \(-0.522411\pi\) | ||||
−0.0703486 | + | 0.997522i | \(0.522411\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.33297e6 | −0.277432 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.07482e7 | 1.71440 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.68480e7 | 1.38197 | 0.690983 | − | 0.722871i | \(-0.257178\pi\) | ||||
0.690983 | + | 0.722871i | \(0.257178\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.16722e6 | −0.420756 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.69465e7 | −1.36990 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.97581e6 | 0.319063 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.49162e6 | −0.596871 | −0.298435 | − | 0.954430i | \(-0.596465\pi\) | ||||
−0.298435 | + | 0.954430i | \(0.596465\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −60799.3 | −0.00480912 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.02650e6 | −0.237672 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.09348e6 | −0.631035 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.75949e7 | −1.36205 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.73756e7 | 1.33550 | 0.667750 | − | 0.744386i | \(-0.267258\pi\) | ||||
0.667750 | + | 0.744386i | \(0.267258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.27086e7 | 0.969857 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 415274. | 0.0314675 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.33891e6 | −0.100740 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.80073e6 | −0.582800 | −0.291400 | − | 0.956601i | \(-0.594121\pi\) | ||||
−0.291400 | + | 0.956601i | \(0.594121\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 141510. | 0.0104981 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.18178e7 | −3.08061 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.03294e7 | −0.755634 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.87068e6 | 0.499116 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.74606e6 | 0.270242 | 0.135121 | − | 0.990829i | \(-0.456858\pi\) | ||||
0.135121 | + | 0.990829i | \(0.456858\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −689473. | −0.0493946 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.43816e7 | 1.73467 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.52174e6 | −0.178179 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.41411e6 | −0.520263 | −0.260131 | − | 0.965573i | \(-0.583766\pi\) | ||||
−0.260131 | + | 0.965573i | \(0.583766\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.42112e7 | 0.990400 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.12280e6 | −0.423796 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.73393e6 | −0.256688 | −0.128344 | − | 0.991730i | \(-0.540966\pi\) | ||||
−0.128344 | + | 0.991730i | \(0.540966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −940096. | −0.0641880 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.61950e7 | 2.45459 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.73088e7 | −1.83946 | −0.919732 | − | 0.392548i | \(-0.871594\pi\) | ||||
−0.919732 | + | 0.392548i | \(0.871594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.32092e7 | −0.883753 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.93553e6 | 0.195081 | 0.0975404 | − | 0.995232i | \(-0.468902\pi\) | ||||
0.0975404 | + | 0.995232i | \(0.468902\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.33849e6 | 0.352394 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −283705. | −0.0186023 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.11493e6 | −0.593675 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.23130e7 | 0.796640 | 0.398320 | − | 0.917246i | \(-0.369593\pi\) | ||||
0.398320 | + | 0.917246i | \(0.369593\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.73403e6 | −0.111447 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.67083e6 | −0.489751 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.45128e7 | −0.920473 | −0.460236 | − | 0.887796i | \(-0.652235\pi\) | ||||
−0.460236 | + | 0.887796i | \(0.652235\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.83697e7 | −2.41760 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.54961e6 | −0.284782 | −0.142391 | − | 0.989811i | \(-0.545479\pi\) | ||||
−0.142391 | + | 0.989811i | \(0.545479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.83026e6 | 0.176001 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 42025.9 | 0.00259635 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.83610e7 | −2.35451 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.17832e6 | 0.0718532 | 0.0359266 | − | 0.999354i | \(-0.488562\pi\) | ||||
0.0359266 | + | 0.999354i | \(0.488562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.32031e7 | −1.40576 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.52351e7 | −0.917055 | −0.458528 | − | 0.888680i | \(-0.651623\pi\) | ||||
−0.458528 | + | 0.888680i | \(0.651623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.78054e6 | 0.345711 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.81773e6 | −0.523967 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.21944e7 | −0.719974 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.27869e7 | 1.92341 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.52109e7 | −0.886646 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.83688e6 | −0.164311 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.26864e7 | −0.730131 | −0.365066 | − | 0.930982i | \(-0.618953\pi\) | ||||
−0.365066 | + | 0.930982i | \(0.618953\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.15214e6 | −0.409019 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.13808e7 | 0.646745 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.25083e6 | −0.522394 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.04147e6 | −0.114558 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.22399e7 | −0.682546 | −0.341273 | − | 0.939964i | \(-0.610858\pi\) | ||||
−0.341273 | + | 0.939964i | \(0.610858\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −778584. | −0.0431458 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 59484.9 | 0.00327586 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.61903e7 | 1.98063 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.53871e6 | −0.301244 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.00656e7 | −0.544070 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.87712e7 | 1.00837 | 0.504186 | − | 0.863595i | \(-0.331793\pi\) | ||||
0.504186 | + | 0.863595i | \(0.331793\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.49853e6 | −0.186781 | −0.0933906 | − | 0.995630i | \(-0.529771\pi\) | ||||
−0.0933906 | + | 0.995630i | \(0.529771\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.84800e7 | −0.980563 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.29868e7 | −0.684871 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.22519e6 | −0.483526 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 85562.6 | 0.00445733 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.45084e7 | −1.26899 | −0.634494 | − | 0.772928i | \(-0.718791\pi\) | ||||
−0.634494 | + | 0.772928i | \(0.718791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.94753e7 | 1.51691 | 0.758453 | − | 0.651728i | \(-0.225956\pi\) | ||||
0.758453 | + | 0.651728i | \(0.225956\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.30390e6 | 0.271307 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.52430e7 | 0.775008 | 0.387504 | − | 0.921868i | \(-0.373337\pi\) | ||||
0.387504 | + | 0.921868i | \(0.373337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.20806e7 | 0.610523 | 0.305262 | − | 0.952268i | \(-0.401256\pi\) | ||||
0.305262 | + | 0.952268i | \(0.401256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.56305e7 | 0.785180 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.76255e6 | 0.0880096 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.44326e6 | 0.0716354 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.48676e7 | 1.72032 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.25581e6 | −0.257771 | −0.128886 | − | 0.991659i | \(-0.541140\pi\) | ||||
−0.128886 | + | 0.991659i | \(0.541140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.23164e6 | −0.206309 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.04385e6 | 0.438313 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.25425e6 | 0.253145 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.49474e6 | 0.311067 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.05501e6 | 0.0502329 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.19509e7 | −2.45906 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.01496e7 | −0.477615 | −0.238808 | − | 0.971067i | \(-0.576757\pi\) | ||||
−0.238808 | + | 0.971067i | \(0.576757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 63320.2 | 0.00296229 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.47951e7 | −1.15323 | −0.576613 | − | 0.817018i | \(-0.695626\pi\) | ||||
−0.576613 | + | 0.817018i | \(0.695626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.93873e7 | −1.82127 | −0.910634 | − | 0.413214i | \(-0.864406\pi\) | ||||
−0.910634 | + | 0.413214i | \(0.864406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.46098e6 | 0.388967 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.66198e7 | −1.67374 | −0.836872 | − | 0.547398i | \(-0.815618\pi\) | ||||
−0.836872 | + | 0.547398i | \(0.815618\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.47038e6 | 0.339471 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.37975e7 | 0.623378 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.34838e7 | −1.50413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.09370e7 | −2.27504 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −155762. | −0.00691714 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.56298e7 | 0.686207 | 0.343104 | − | 0.939298i | \(-0.388522\pi\) | ||||
0.343104 | + | 0.939298i | \(0.388522\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.72287e7 | 0.752110 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.32549e7 | −0.575357 | −0.287678 | − | 0.957727i | \(-0.592883\pi\) | ||||
−0.287678 | + | 0.957727i | \(0.592883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.30665e7 | −1.85882 | −0.929411 | − | 0.369045i | \(-0.879685\pi\) | ||||
−0.929411 | + | 0.369045i | \(0.879685\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.96974e7 | 0.845376 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.62803e7 | 1.54832 | 0.774162 | − | 0.632987i | \(-0.218171\pi\) | ||||
0.774162 | + | 0.632987i | \(0.218171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.63553e6 | 0.324030 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.22941e7 | 1.36279 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.17309e6 | −0.0492268 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.82413e6 | 0.117849 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.39975e7 | 2.24075 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.73172e7 | −1.53996 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.82749e6 | 0.157073 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.40082e6 | 0.261226 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.07521e6 | −0.165397 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.15142e7 | 1.27200 | 0.636002 | − | 0.771688i | \(-0.280587\pi\) | ||||
0.636002 | + | 0.771688i | \(0.280587\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −62572.1 | −0.00251172 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.94324e7 | 1.57419 | 0.787096 | − | 0.616830i | \(-0.211584\pi\) | ||||
0.787096 | + | 0.616830i | \(0.211584\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.71298e7 | 2.66525 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.75007e6 | 0.187563 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.35465e7 | 0.531989 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.11238e7 | 0.434474 | 0.217237 | − | 0.976119i | \(-0.430296\pi\) | ||||
0.217237 | + | 0.976119i | \(0.430296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 780027. | 0.0303013 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.61409e7 | −1.78271 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.18126e6 | 0.275960 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32221.7 | −0.00123154 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.19210e7 | −1.59365 | −0.796823 | − | 0.604212i | \(-0.793488\pi\) | ||||
−0.796823 | + | 0.604212i | \(0.793488\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.65563e6 | 0.100414 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.95257e6 | 0.261482 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.94411e6 | −0.371995 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.80494e7 | 1.41579 | 0.707895 | − | 0.706318i | \(-0.249645\pi\) | ||||
0.707895 | + | 0.706318i | \(0.249645\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.55406e7 | −1.31541 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.85268e7 | −1.05022 | −0.525109 | − | 0.851035i | \(-0.675976\pi\) | ||||
−0.525109 | + | 0.851035i | \(0.675976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.98491e7 | 1.82548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.61817e6 | 0.168225 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.47030e7 | 0.895108 | 0.447554 | − | 0.894257i | \(-0.352295\pi\) | ||||
0.447554 | + | 0.894257i | \(0.352295\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.09305e7 | −1.83574 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.03575e7 | 1.80556 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.30722e7 | 0.822918 | 0.411459 | − | 0.911428i | \(-0.365019\pi\) | ||||
0.411459 | + | 0.911428i | \(0.365019\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.03531e7 | 0.367335 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.42402e7 | −1.20853 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.01278e7 | −0.355604 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.69122e7 | 1.98791 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −425975. | −0.0148019 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.95713e7 | −0.676551 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.88977e6 | −0.0993797 | −0.0496898 | − | 0.998765i | \(-0.515823\pi\) | ||||
−0.0496898 | + | 0.998765i | \(0.515823\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.27165e7 | −0.435067 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.27702e7 | 0.434660 | 0.217330 | − | 0.976098i | \(-0.430265\pi\) | ||||
0.217330 | + | 0.976098i | \(0.430265\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.93193e6 | −0.200870 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.46416e6 | −0.251460 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.52358e7 | 0.510657 | 0.255329 | − | 0.966854i | \(-0.417816\pi\) | ||||
0.255329 | + | 0.966854i | \(0.417816\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.40752e7 | −0.469352 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 132269. | 0.00438819 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.91000e7 | 1.29060 | 0.645301 | − | 0.763928i | \(-0.276732\pi\) | ||||
0.645301 | + | 0.763928i | \(0.276732\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.08850e7 | −0.357468 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 813937. | 0.0265949 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.77114e7 | 1.22598 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.15949e7 | −1.34541 | −0.672706 | − | 0.739910i | \(-0.734868\pi\) | ||||
−0.672706 | + | 0.739910i | \(0.734868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.58279e7 | −0.831219 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.55509e7 | 0.818179 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.76387e7 | 0.561989 | 0.280994 | − | 0.959709i | \(-0.409336\pi\) | ||||
0.280994 | + | 0.959709i | \(0.409336\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.33166e7 | 1.37322 |
(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 | 280.6.a.g.1.2 | ✓ | 4 | |
4.3 | odd | 2 | 560.6.a.x.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.6.a.g.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
560.6.a.x.1.3 | 4 | 4.3 | odd | 2 |