Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,6,Mod(449,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.449");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.e (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(112.268673869\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 998x^{4} + 249001x^{2} + 44100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(-22.5458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.449 |
Dual form | 700.6.e.g.449.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 24.5458i | − 1.57462i | −0.616560 | − | 0.787308i | \(-0.711474\pi\) | ||||
0.616560 | − | 0.787308i | \(-0.288526\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −359.498 | −1.47941 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 90.2356 | 0.224852 | 0.112426 | − | 0.993660i | \(-0.464138\pi\) | ||||
0.112426 | + | 0.993660i | \(0.464138\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.4413i | 0.0237000i | 0.999930 | + | 0.0118500i | \(0.00377206\pi\) | ||||
−0.999930 | + | 0.0118500i | \(0.996228\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 407.384i | 0.341886i | 0.985281 | + | 0.170943i | \(0.0546814\pi\) | ||||
−0.985281 | + | 0.170943i | \(0.945319\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2289.19 | −1.45478 | −0.727391 | − | 0.686223i | \(-0.759268\pi\) | ||||
−0.727391 | + | 0.686223i | \(0.759268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1202.75 | 0.595149 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 505.976i | 0.199439i | 0.995016 | + | 0.0997197i | \(0.0317946\pi\) | ||||
−0.995016 | + | 0.0997197i | \(0.968205\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2859.53i | 0.754893i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3164.56 | 0.698745 | 0.349373 | − | 0.936984i | \(-0.386395\pi\) | ||||
0.349373 | + | 0.936984i | \(0.386395\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6231.43 | −1.16462 | −0.582309 | − | 0.812968i | \(-0.697851\pi\) | ||||
−0.582309 | + | 0.812968i | \(0.697851\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2214.91i | − 0.354055i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5388.70i | 0.647113i | 0.946209 | + | 0.323556i | \(0.104879\pi\) | ||||
−0.946209 | + | 0.323556i | \(0.895121\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 354.474 | 0.0373184 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11764.3 | 1.09297 | 0.546484 | − | 0.837469i | \(-0.315966\pi\) | ||||
0.546484 | + | 0.837469i | \(0.315966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5824.58i | 0.480390i | 0.970725 | + | 0.240195i | \(0.0772113\pi\) | ||||
−0.970725 | + | 0.240195i | \(0.922789\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7349.38i | 0.485295i | 0.970114 | + | 0.242648i | \(0.0780159\pi\) | ||||
−0.970114 | + | 0.242648i | \(0.921984\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2401.00 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9999.57 | 0.538339 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 14971.6i | − 0.732114i | −0.930592 | − | 0.366057i | \(-0.880707\pi\) | ||||
0.930592 | − | 0.366057i | \(-0.119293\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 56190.1i | 2.29072i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 47153.5 | 1.76353 | 0.881767 | − | 0.471685i | \(-0.156354\pi\) | ||||
0.881767 | + | 0.471685i | \(0.156354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4289.61 | −0.147602 | −0.0738011 | − | 0.997273i | \(-0.523513\pi\) | ||||
−0.0738011 | + | 0.997273i | \(0.523513\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 17615.4i | − 0.559166i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 48898.3i | 1.33078i | 0.746496 | + | 0.665390i | \(0.231735\pi\) | ||||
−0.746496 | + | 0.665390i | \(0.768265\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12419.6 | 0.314040 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 58567.6 | 1.37883 | 0.689417 | − | 0.724365i | \(-0.257867\pi\) | ||||
0.689417 | + | 0.724365i | \(0.257867\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1599.07i | 0.0351206i | 0.999846 | + | 0.0175603i | \(0.00558990\pi\) | ||||
−0.999846 | + | 0.0175603i | \(0.994410\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4421.54i | 0.0849859i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 79121.1 | 1.42634 | 0.713172 | − | 0.700989i | \(-0.247258\pi\) | ||||
0.713172 | + | 0.700989i | \(0.247258\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −17168.4 | −0.290748 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 71472.1i | 1.13878i | 0.822066 | + | 0.569392i | \(0.192821\pi\) | ||||
−0.822066 | + | 0.569392i | \(0.807179\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 77676.9i | − 1.10026i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 77165.9 | 1.03264 | 0.516322 | − | 0.856395i | \(-0.327301\pi\) | ||||
0.516322 | + | 0.856395i | \(0.327301\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −707.624 | −0.00895775 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 152956.i | 1.83383i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11559.6i | 0.124743i | 0.998053 | + | 0.0623713i | \(0.0198663\pi\) | ||||
−0.998053 | + | 0.0623713i | \(0.980134\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −32439.5 | −0.332649 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −171423. | −1.67211 | −0.836057 | − | 0.548642i | \(-0.815145\pi\) | ||||
−0.836057 | + | 0.548642i | \(0.815145\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 182469.i | 1.69471i | 0.531024 | + | 0.847357i | \(0.321807\pi\) | ||||
−0.531024 | + | 0.847357i | \(0.678193\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 76696.7i | − 0.647616i | −0.946123 | − | 0.323808i | \(-0.895037\pi\) | ||||
0.946123 | − | 0.323808i | \(-0.104963\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13146.0 | 0.105981 | 0.0529904 | − | 0.998595i | \(-0.483125\pi\) | ||||
0.0529904 | + | 0.998595i | \(0.483125\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 132270. | 1.01895 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 5996.97i | − 0.0441811i | −0.999756 | − | 0.0220905i | \(-0.992968\pi\) | ||||
0.999756 | − | 0.0220905i | \(-0.00703221\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 5191.61i | − 0.0350621i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19961.8 | −0.129221 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −152909. | −0.949442 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 288765.i | − 1.72101i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 109534.i | − 0.602613i | −0.953527 | − | 0.301306i | \(-0.902577\pi\) | ||||
0.953527 | − | 0.301306i | \(-0.0974227\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 142969. | 0.756429 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 385186. | 1.96107 | 0.980533 | − | 0.196354i | \(-0.0629101\pi\) | ||||
0.980533 | + | 0.196354i | \(0.0629101\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 112170.i | − 0.549856i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 315816.i | − 1.43758i | −0.695226 | − | 0.718791i | \(-0.744696\pi\) | ||||
0.695226 | − | 0.718791i | \(-0.255304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −95433.5 | −0.418952 | −0.209476 | − | 0.977814i | \(-0.567176\pi\) | ||||
−0.209476 | + | 0.977814i | \(0.567176\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 180397. | 0.764154 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1303.12i | 0.00532898i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 58934.5i | 0.224945i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 151387. | 0.558629 | 0.279315 | − | 0.960200i | \(-0.409893\pi\) | ||||
0.279315 | + | 0.960200i | \(0.409893\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 300641. | 1.07301 | 0.536507 | − | 0.843896i | \(-0.319743\pi\) | ||||
0.536507 | + | 0.843896i | \(0.319743\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 146453.i | − 0.505791i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 306110.i | − 0.991125i | −0.868572 | − | 0.495563i | \(-0.834962\pi\) | ||||
0.868572 | − | 0.495563i | \(-0.165038\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −367491. | −1.15280 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24792.8 | −0.0753810 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 373022.i | − 1.09968i | −0.835271 | − | 0.549839i | \(-0.814689\pi\) | ||||
0.835271 | − | 0.549839i | \(-0.185311\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 317441.i | − 0.880789i | −0.897804 | − | 0.440394i | \(-0.854839\pi\) | ||||
0.897804 | − | 0.440394i | \(-0.145161\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 371084. | 0.999438 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 822959. | 2.15223 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 354815.i | 0.901335i | 0.892692 | + | 0.450668i | \(0.148814\pi\) | ||||
−0.892692 | + | 0.450668i | \(0.851186\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1.15742e6i | − 2.77689i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −356294. | −0.831144 | −0.415572 | − | 0.909560i | \(-0.636419\pi\) | ||||
−0.415572 | + | 0.909560i | \(0.636419\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9772.82 | 0.0221729 | 0.0110865 | − | 0.999939i | \(-0.496471\pi\) | ||||
0.0110865 | + | 0.999939i | \(0.496471\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 105292.i | 0.232417i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 36760.5i | 0.0768736i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −140117. | −0.285323 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −302267. | −0.599525 | −0.299762 | − | 0.954014i | \(-0.596907\pi\) | ||||
−0.299762 | + | 0.954014i | \(0.596907\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 267712.i | − 0.517339i | −0.965966 | − | 0.258669i | \(-0.916716\pi\) | ||||
0.965966 | − | 0.258669i | \(-0.0832840\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 151930.i | − 0.278920i | −0.990228 | − | 0.139460i | \(-0.955463\pi\) | ||||
0.990228 | − | 0.139460i | \(-0.0445366\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −825686. | −1.47803 | −0.739013 | − | 0.673691i | \(-0.764708\pi\) | ||||
−0.739013 | + | 0.673691i | \(0.764708\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.20025e6 | 2.09547 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 155064.i | 0.264101i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 181897.i | − 0.295053i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −206567. | −0.327110 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 972289. | 1.50345 | 0.751726 | − | 0.659476i | \(-0.229222\pi\) | ||||
0.751726 | + | 0.659476i | \(0.229222\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.43759e6i | − 2.17113i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 305340.i | − 0.440184i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39250.6 | 0.0553014 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5883.15 | −0.00810269 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.35209e6i | 1.82073i | 0.413811 | + | 0.910363i | \(0.364197\pi\) | ||||
−0.413811 | + | 0.910363i | \(0.635803\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 876401.i | 1.12885i | 0.825483 | + | 0.564427i | \(0.190903\pi\) | ||||
−0.825483 | + | 0.564427i | \(0.809097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.10402e6 | −1.39119 | −0.695597 | − | 0.718433i | \(-0.744860\pi\) | ||||
−0.695597 | + | 0.718433i | \(0.744860\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 108530. | 0.133820 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 81858.7i | − 0.0987814i | −0.998780 | − | 0.0493907i | \(-0.984272\pi\) | ||||
0.998780 | − | 0.0493907i | \(-0.0157279\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.94209e6i | − 2.24594i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.45239e6 | 1.64471 | 0.822354 | − | 0.568977i | \(-0.192661\pi\) | ||||
0.822354 | + | 0.568977i | \(0.192661\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.11432e6 | 1.23586 | 0.617929 | − | 0.786234i | \(-0.287972\pi\) | ||||
0.617929 | + | 0.786234i | \(0.287972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.11628e6i | 1.21271i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 33058.9i | − 0.0344783i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.75434e6 | 1.79315 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −157265. | −0.157560 | −0.0787801 | − | 0.996892i | \(-0.525102\pi\) | ||||
−0.0787801 | + | 0.996892i | \(0.525102\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 45657.1i | 0.0448443i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 655000.i | 0.618598i | 0.950965 | + | 0.309299i | \(0.100094\pi\) | ||||
−0.950965 | + | 0.309299i | \(0.899906\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −264046. | −0.244586 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.13765e6 | −1.03373 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 498514.i | 0.444414i | 0.975000 | + | 0.222207i | \(0.0713261\pi\) | ||||
−0.975000 | + | 0.222207i | \(0.928674\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.89410e6i | − 1.62602i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.00547e6 | 0.847202 | 0.423601 | − | 0.905849i | \(-0.360766\pi\) | ||||
0.423601 | + | 0.905849i | \(0.360766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 93641.4 | 0.0774541 | 0.0387271 | − | 0.999250i | \(-0.487670\pi\) | ||||
0.0387271 | + | 0.999250i | \(0.487670\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17369.2i | 0.0141050i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12211.8i | 0.00956271i | 0.999989 | + | 0.00478135i | \(0.00152196\pi\) | ||||
−0.999989 | + | 0.00478135i | \(0.998478\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.24018e6 | 1.72295 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −389424. | −0.294210 | −0.147105 | − | 0.989121i | \(-0.546996\pi\) | ||||
−0.147105 | + | 0.989121i | \(0.546996\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.23856e6i | − 0.919283i | −0.888105 | − | 0.459642i | \(-0.847978\pi\) | ||||
0.888105 | − | 0.459642i | \(-0.152022\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 576452.i | 0.413103i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.25390e6 | 0.883114 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 283741. | 0.196422 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.36915e6i | 0.931716i | 0.884860 | + | 0.465858i | \(0.154254\pi\) | ||||
−0.884860 | + | 0.465858i | \(0.845746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 258032.i | 0.169739i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7306.96 | −0.00472671 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −285404. | −0.181570 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.20772e6i | 2.63294i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.15266e6i | 1.30356i | 0.758409 | + | 0.651778i | \(0.225977\pi\) | ||||
−0.758409 | + | 0.651778i | \(0.774023\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.47885e6 | 2.66852 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.58326e6 | 1.51449 | 0.757245 | − | 0.653131i | \(-0.226545\pi\) | ||||
0.757245 | + | 0.653131i | \(0.226545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 3.07474e6i | − 1.77398i | −0.461793 | − | 0.886988i | \(-0.652794\pi\) | ||||
0.461793 | − | 0.886988i | \(-0.347206\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.04850e6i | − 0.586031i | −0.956108 | − | 0.293015i | \(-0.905341\pi\) | ||||
0.956108 | − | 0.293015i | \(-0.0946587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 285556. | 0.157114 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.88258e6 | −1.01975 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 932579.i | − 0.497370i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 322680.i | − 0.166879i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −360120. | −0.183424 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.26689e6 | 1.13726 | 0.568631 | − | 0.822592i | \(-0.307473\pi\) | ||||
0.568631 | + | 0.822592i | \(0.307473\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1.93723e6i | − 0.957348i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.78963e6i | 1.33805i | 0.743240 | + | 0.669024i | \(0.233288\pi\) | ||||
−0.743240 | + | 0.669024i | \(0.766712\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −147201. | −0.0695682 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −562297. | −0.261866 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 117649.i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.74629e6i | 0.778562i | 0.921119 | + | 0.389281i | \(0.127277\pi\) | ||||
−0.921119 | + | 0.389281i | \(0.872723\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.21671e6 | −1.41367 | −0.706836 | − | 0.707377i | \(-0.749878\pi\) | ||||
−0.706836 | + | 0.707377i | \(0.749878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −41295.4 | −0.0178910 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 507518.i | − 0.216778i | −0.994109 | − | 0.108389i | \(-0.965431\pi\) | ||||
0.994109 | − | 0.108389i | \(-0.0345691\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 489979.i | 0.203473i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −804256. | −0.329350 | −0.164675 | − | 0.986348i | \(-0.552658\pi\) | ||||
−0.164675 | + | 0.986348i | \(0.552658\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.76430e6 | 1.11639 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.75327e6i | 1.49501i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.60921e6i | 0.623658i | 0.950138 | + | 0.311829i | \(0.100942\pi\) | ||||
−0.950138 | + | 0.311829i | \(0.899058\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.22925e6 | −1.61695 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 733609. | 0.276713 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.19298e6i | 1.93261i | 0.257397 | + | 0.966306i | \(0.417135\pi\) | ||||
−0.257397 | + | 0.966306i | \(0.582865\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 45700.4i | 0.0165603i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 114187. | 0.0408337 | 0.0204169 | − | 0.999792i | \(-0.493501\pi\) | ||||
0.0204169 | + | 0.999792i | \(0.493501\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.68859e6 | −0.948884 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.03725e6i | 1.05799i | 0.848624 | + | 0.528997i | \(0.177432\pi\) | ||||
−0.848624 | + | 0.528997i | \(0.822568\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2.09392e6i | − 0.710695i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.75485e6 | −0.587985 | −0.293993 | − | 0.955808i | \(-0.594984\pi\) | ||||
−0.293993 | + | 0.955808i | \(0.594984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −206127. | −0.0681855 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 9.45471e6i | − 3.08793i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 411623.i | − 0.131076i | −0.997850 | − | 0.0655380i | \(-0.979124\pi\) | ||||
0.997850 | − | 0.0655380i | \(-0.0208764\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.75332e6 | −0.865812 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.34807e6 | −1.03976 | −0.519881 | − | 0.854238i | \(-0.674024\pi\) | ||||
−0.519881 | + | 0.854238i | \(0.674024\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 89990.0i | − 0.0276014i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 486253.i | 0.145504i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.67438e6 | 0.494933 | 0.247467 | − | 0.968896i | \(-0.420402\pi\) | ||||
0.247467 | + | 0.968896i | \(0.420402\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.75197e6 | −2.26364 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.31052e6i | 0.666553i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.34249e6i | 0.659688i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.61117e6 | −0.726608 | −0.363304 | − | 0.931671i | \(-0.618351\pi\) | ||||
−0.363304 | + | 0.931671i | \(0.618351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.20146e6 | 0.880324 | 0.440162 | − | 0.897918i | \(-0.354921\pi\) | ||||
0.440162 | + | 0.897918i | \(0.354921\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 2.64209e6i | − 0.717953i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 210191.i | − 0.0557884i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31986.1 | 0.00839109 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.57601e6 | 1.44587 | 0.722937 | − | 0.690914i | \(-0.242792\pi\) | ||||
0.722937 | + | 0.690914i | \(0.242792\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 5.12039e6i | − 1.31245i | −0.754564 | − | 0.656226i | \(-0.772152\pi\) | ||||
0.754564 | − | 0.656226i | \(-0.227848\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.15828e6i | − 0.290141i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.83173e6 | −0.948930 | −0.474465 | − | 0.880274i | \(-0.657358\pi\) | ||||
−0.474465 | + | 0.880274i | \(0.657358\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 863154. | 0.211345 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.70686e6i | 0.655325i | 0.944795 | + | 0.327662i | \(0.106261\pi\) | ||||
−0.944795 | + | 0.327662i | \(0.893739\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 3.71592e6i | − 0.879626i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.55860e6 | 1.76940 | 0.884699 | − | 0.466164i | \(-0.154364\pi\) | ||||
0.884699 | + | 0.466164i | \(0.154364\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.06156e6 | 0.245756 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 7.37948e6i | − 1.68959i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 2.67340e6i | − 0.598790i | −0.954129 | − | 0.299395i | \(-0.903215\pi\) | ||||
0.954129 | − | 0.299395i | \(-0.0967848\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.16493e6 | −0.258087 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −792744. | −0.173732 | −0.0868661 | − | 0.996220i | \(-0.527685\pi\) | ||||
−0.0868661 | + | 0.996220i | \(0.527685\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6.72717e6i | − 1.45841i | −0.684294 | − | 0.729206i | \(-0.739890\pi\) | ||||
0.684294 | − | 0.729206i | \(-0.260110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 7.79719e6i | − 1.65442i | −0.561892 | − | 0.827211i | \(-0.689926\pi\) | ||||
0.561892 | − | 0.827211i | \(-0.310074\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.39601e6 | −0.502988 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.51373e6 | −1.56064 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 525584.i | 0.108016i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.38226e6i | 1.08310i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.99000e6 | 0.595433 | 0.297717 | − | 0.954654i | \(-0.403775\pi\) | ||||
0.297717 | + | 0.954654i | \(0.403775\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −77819.9 | −0.0153366 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 608561.i | 0.118696i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.01844e7i | 1.94587i | 0.231082 | + | 0.972934i | \(0.425774\pi\) | ||||
−0.231082 | + | 0.972934i | \(0.574226\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.15614e6 | −1.73157 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.36159e6 | −0.442079 | −0.221040 | − | 0.975265i | \(-0.570945\pi\) | ||||
−0.221040 | + | 0.975265i | \(0.570945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.28919e6i | 0.238891i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.86981e6i | 0.521150i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.04692e7 | −1.88219 | −0.941096 | − | 0.338141i | \(-0.890202\pi\) | ||||
−0.941096 | + | 0.338141i | \(0.890202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.79185e6 | −1.38690 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.05909e6i | 0.891565i | 0.895141 | + | 0.445782i | \(0.147074\pi\) | ||||
−0.895141 | + | 0.445782i | \(0.852926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9.10858e6i | − 1.57373i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.22380e6 | −1.40695 | −0.703474 | − | 0.710721i | \(-0.748369\pi\) | ||||
−0.703474 | + | 0.710721i | \(0.748369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −78354.6 | −0.0132743 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 6.54602e6i | − 1.09821i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 663176.i | 0.109119i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.70922e6 | 1.41926 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.91440e6 | 0.308985 | 0.154493 | − | 0.987994i | \(-0.450626\pi\) | ||||
0.154493 | + | 0.987994i | \(0.450626\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.13982e7i | 1.82215i | 0.412245 | + | 0.911073i | \(0.364745\pi\) | ||||
−0.412245 | + | 0.911073i | \(0.635255\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.53858e6i | − 0.398167i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.18033e6 | 0.960224 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.69516e7 | −2.60900 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 169892.i | 0.0259033i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.74554e6i | 1.30873i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −216656. | −0.0321217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.18345e6 | −0.320738 | −0.160369 | − | 0.987057i | \(-0.551268\pi\) | ||||
−0.160369 | + | 0.987057i | \(0.551268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 239882.i | − 0.0349139i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.45056e6i | − 0.493084i | −0.969132 | − | 0.246542i | \(-0.920706\pi\) | ||||
0.969132 | − | 0.246542i | \(-0.0792944\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.54210e6 | 0.218365 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.24430e6 | −1.01652 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.87693e6i | 0.539108i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.17331e7i | − 1.60241i | −0.598391 | − | 0.801204i | \(-0.704193\pi\) | ||||
0.598391 | − | 0.801204i | \(-0.295807\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −84114.5 | −0.0113852 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 902317. | 0.121046 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 604258.i | 0.0803436i | 0.999193 | + | 0.0401718i | \(0.0127905\pi\) | ||||
−0.999193 | + | 0.0401718i | \(0.987209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 841250.i | − 0.109892i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.22306e6 | −0.158368 | −0.0791842 | − | 0.996860i | \(-0.525232\pi\) | ||||
−0.0791842 | + | 0.996860i | \(0.525232\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.34785e6 | −0.814772 | −0.407386 | − | 0.913256i | \(-0.633560\pi\) | ||||
−0.407386 | + | 0.913256i | \(0.633560\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.41939e6i | 0.944021i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.02896e6i | 0.628838i | 0.949284 | + | 0.314419i | \(0.101810\pi\) | ||||
−0.949284 | + | 0.314419i | \(0.898190\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.57122e6 | −0.814610 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.50213e6 | −0.430420 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.35097e6i | − 0.164617i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.24089e7i | 1.48641i | 0.669063 | + | 0.743206i | \(0.266696\pi\) | ||||
−0.669063 | + | 0.743206i | \(0.733304\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.42649e7 | 1.69427 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.72926e6 | −0.439191 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.60941e7i | 1.87945i | 0.341932 | + | 0.939725i | \(0.388919\pi\) | ||||
−0.341932 | + | 0.939725i | \(0.611081\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.02671e7i | 2.32732i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.42343e6 | −0.275971 | −0.137986 | − | 0.990434i | \(-0.544063\pi\) | ||||
−0.137986 | + | 0.990434i | \(0.544063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.84941e6 | 0.886443 | 0.443222 | − | 0.896412i | \(-0.353835\pi\) | ||||
0.443222 | + | 0.896412i | \(0.353835\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.75788e7i | − 1.96878i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.84175e6i | 0.753695i | 0.926275 | + | 0.376847i | \(0.122992\pi\) | ||||
−0.926275 | + | 0.376847i | \(0.877008\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.80617e6 | 0.415858 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −106135. | −0.0115015 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.16723e6i | 0.125460i | 0.998031 | + | 0.0627302i | \(0.0199808\pi\) | ||||
−0.998031 | + | 0.0627302i | \(0.980019\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.05925e6i | 0.852279i | 0.904657 | + | 0.426140i | \(0.140127\pi\) | ||||
−0.904657 | + | 0.426140i | \(0.859873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.10346e6 | −0.535350 | −0.267675 | − | 0.963509i | \(-0.586255\pi\) | ||||
−0.267675 | + | 0.963509i | \(0.586255\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.44686e6 | −0.150555 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.78113e6i | 0.390303i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.07035e6i | 0.515073i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.19527e6 | −0.221239 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.01731e6 | 0.601630 | 0.300815 | − | 0.953683i | \(-0.402741\pi\) | ||||
0.300815 | + | 0.953683i | \(0.402741\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 2.38656e7i | − 2.36736i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 34673.6i | − 0.00338571i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.10549e7 | −2.03987 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.28323e6 | 0.604002 | 0.302001 | − | 0.953308i | \(-0.402345\pi\) | ||||
0.302001 | + | 0.953308i | \(0.402345\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.65315e6i | 0.729983i | 0.931011 | + | 0.364991i | \(0.118928\pi\) | ||||
−0.931011 | + | 0.364991i | \(0.881072\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.00172e7i | 1.87994i | 0.341260 | + | 0.939969i | \(0.389146\pi\) | ||||
−0.341260 | + | 0.939969i | \(0.610854\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.25492e6 | 0.396534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.49483e6 | −0.693121 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.94459e6i | 0.270236i | 0.990830 | + | 0.135118i | \(0.0431413\pi\) | ||||
−0.990830 | + | 0.135118i | \(0.956859\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 574863.i | − 0.0519579i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.11116e6 | 0.548164 | 0.274082 | − | 0.961706i | \(-0.411626\pi\) | ||||
0.274082 | + | 0.961706i | \(0.411626\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.81315e6 | 0.606518 | 0.303259 | − | 0.952908i | \(-0.401925\pi\) | ||||
0.303259 | + | 0.952908i | \(0.401925\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 144407.i | 0.0127586i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.60120e6i | 0.139357i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.31882e7 | 2.86694 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −387075. | −0.0331886 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.02171e7i | 0.869540i | 0.900541 | + | 0.434770i | \(0.143170\pi\) | ||||
−0.900541 | + | 0.434770i | \(0.856830\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.09917e6i | 0.259881i | 0.991522 | + | 0.129940i | \(0.0414786\pi\) | ||||
−0.991522 | + | 0.129940i | \(0.958521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −566422. | −0.0471483 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.15120e7 | 1.77751 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.08480e7i | − 0.889814i | −0.895577 | − | 0.444907i | \(-0.853237\pi\) | ||||
0.895577 | − | 0.444907i | \(-0.146763\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.70990e7i | 2.19059i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 216210. | 0.0173511 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.27049e6 | 0.101222 | 0.0506112 | − | 0.998718i | \(-0.483883\pi\) | ||||
0.0506112 | + | 0.998718i | \(0.483883\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.58953e6i | − 0.125729i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.79260e6i | 0.373671i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.00929e6 | −0.155543 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.34177e6 | 0.179990 | 0.0899952 | − | 0.995942i | \(-0.471315\pi\) | ||||
0.0899952 | + | 0.995942i | \(0.471315\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.23358e7i | − 0.941408i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 8.39973e6i | − 0.632000i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.30501e6 | 0.545764 | 0.272882 | − | 0.962048i | \(-0.412023\pi\) | ||||
0.272882 | + | 0.962048i | \(0.412023\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.84438e7 | −2.11015 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 3.15296e6i | − 0.232271i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 3.56501e7i | − 2.58978i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.26261e7 | −0.910850 | −0.455425 | − | 0.890274i | \(-0.650513\pi\) | ||||
−0.455425 | + | 0.890274i | \(0.650513\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.94098e6 | −0.640541 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.73520e7i | − 1.94600i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.43022e7i | 1.00361i | 0.864980 | + | 0.501806i | \(0.167331\pi\) | ||||
−0.864980 | + | 0.501806i | \(0.832669\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.32281e7 | 1.61880 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.37284e6 | −0.164238 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.32911e7i | 1.60114i | 0.599237 | + | 0.800572i | \(0.295471\pi\) | ||||
−0.599237 | + | 0.800572i | \(0.704529\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.41236e6i | 0.299228i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.00700e7 | 0.678293 | 0.339146 | − | 0.940734i | \(-0.389862\pi\) | ||||
0.339146 | + | 0.940734i | \(0.389862\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −811458. | −0.0542901 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.66744e7i | 1.10810i | 0.832484 | + | 0.554049i | \(0.186918\pi\) | ||||
−0.832484 | + | 0.554049i | \(0.813082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 2.56940e7i | − 1.68473i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.75814e6 | 0.244776 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39313.6 | 0.00254356 | 0.00127178 | − | 0.999999i | \(-0.499595\pi\) | ||||
0.00127178 | + | 0.999999i | \(0.499595\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.86019e6i | 0.248097i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.77082e6i | − 0.302589i | −0.988489 | − | 0.151295i | \(-0.951656\pi\) | ||||
0.988489 | − | 0.151295i | \(-0.0483442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.12069e6 | 0.0706125 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.58376e7 | 0.991350 | 0.495675 | − | 0.868508i | \(-0.334921\pi\) | ||||
0.495675 | + | 0.868508i | \(0.334921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 644154.i | 0.0400570i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 680958.i | 0.0417957i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.80265e7 | −1.09925 | −0.549624 | − | 0.835412i | \(-0.685229\pi\) | ||||
−0.549624 | + | 0.835412i | \(0.685229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.60775e7 | 0.974055 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.60103e6i | 0.457534i | 0.973481 | + | 0.228767i | \(0.0734694\pi\) | ||||
−0.973481 | + | 0.228767i | \(0.926531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.48124e6i | 0.385128i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.69308e7 | −1.59003 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.28488e6 | 0.310033 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.04917e6i | 0.527478i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.13160e7i | − 1.80231i | −0.433498 | − | 0.901155i | \(-0.642721\pi\) | ||||
0.433498 | − | 0.901155i | \(-0.357279\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.22364e7 | 0.699781 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 293852. | 0.0166989 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 61947.5i | − 0.00349817i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.51589e6i | 0.419117i | 0.977796 | + | 0.209558i | \(0.0672026\pi\) | ||||
−0.977796 | + | 0.209558i | \(0.932797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.99402e6 | −0.165916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.77410e7 | −1.52771 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 144293.i | 0.00789691i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.46800e7i | − 1.33402i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.23042e7 | −1.73535 | −0.867676 | − | 0.497130i | \(-0.834387\pi\) | ||||
−0.867676 | + | 0.497130i | \(0.834387\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.53053e7 | 1.88490 | 0.942448 | − | 0.334354i | \(-0.108518\pi\) | ||||
0.942448 | + | 0.334354i | \(0.108518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.29851e6i | − 0.121960i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 1.33336e7i | − 0.698862i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 254389. | 0.0132522 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.06861e7 | 0.553299 | 0.276650 | − | 0.960971i | \(-0.410776\pi\) | ||||
0.276650 | + | 0.960971i | \(0.410776\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.14692e7i | 0.590246i | 0.955459 | + | 0.295123i | \(0.0953607\pi\) | ||||
−0.955459 | + | 0.295123i | \(0.904639\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.29781e6i | − 0.167673i | −0.996480 | − | 0.0838363i | \(-0.973283\pi\) | ||||
0.996480 | − | 0.0838363i | \(-0.0267173\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.63786e6 | 0.385998 | 0.192999 | − | 0.981199i | \(-0.438179\pi\) | ||||
0.192999 | + | 0.981199i | \(0.438179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 299749. | 0.0150576 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 978128.i | − 0.0488408i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.78190e7i | − 0.879162i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.15181e6 | −0.105536 | −0.0527678 | − | 0.998607i | \(-0.516804\pi\) | ||||
−0.0527678 | + | 0.998607i | \(0.516804\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.04967e7 | −0.511755 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.55874e6i | 0.463267i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 7.49252e6i | − 0.358855i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.04014e7 | −1.44752 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.72656e6 | −0.129060 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 6.77711e6i | − 0.318913i | −0.987205 | − | 0.159456i | \(-0.949026\pi\) | ||||
0.987205 | − | 0.159456i | \(-0.0509741\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 2.76782e7i | − 1.28732i | −0.765313 | − | 0.643658i | \(-0.777416\pi\) | ||||
0.765313 | − | 0.643658i | \(-0.222584\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.64843e6 | −0.446143 | −0.223071 | − | 0.974802i | \(-0.571608\pi\) | ||||
−0.223071 | + | 0.974802i | \(0.571608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.41495e7 | 0.650479 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.44710e7i | 0.661413i | 0.943734 | + | 0.330707i | \(0.107287\pi\) | ||||
−0.943734 | + | 0.330707i | \(0.892713\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 3.07779e7i | − 1.39057i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.13954e6 | 0.320716 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −706154. | −0.0315395 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 4.15566e6i | − 0.184546i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.65012e7i | − 0.724463i | −0.932088 | − | 0.362231i | \(-0.882015\pi\) | ||||
0.932088 | − | 0.362231i | \(-0.117985\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.36070e7 | 1.46709 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.14305e7 | 0.930236 | 0.465118 | − | 0.885249i | \(-0.346012\pi\) | ||||
0.465118 | + | 0.885249i | \(0.346012\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.06482e7i | − 0.891213i | −0.895229 | − | 0.445606i | \(-0.852988\pi\) | ||||
0.895229 | − | 0.445606i | \(-0.147012\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 2.33225e7i | − 0.995326i | −0.867370 | − | 0.497663i | \(-0.834192\pi\) | ||||
0.867370 | − | 0.497663i | \(-0.165808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.36715e6 | 0.227766 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.54920e6 | −0.0653751 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.68241e7i | − 0.705999i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 179355.i | 0.00744275i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.97198e7 | −0.813772 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.09919e6 | 0.250300 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.00549e6i | 0.285903i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.53172e6i | 0.142550i | 0.997457 | + | 0.0712752i | \(0.0227069\pi\) | ||||
−0.997457 | + | 0.0712752i | \(0.977293\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.16262e7 | 2.47375 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.09852e7 | 1.63618 | 0.818091 | − | 0.575089i | \(-0.195033\pi\) | ||||
0.818091 | + | 0.575089i | \(0.195033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.44932e6i | 0.256057i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.88741e7i | 0.741213i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.53948e7 | 1.77304 | 0.886518 | − | 0.462693i | \(-0.153117\pi\) | ||||
0.886518 | + | 0.462693i | \(0.153117\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.28389e7 | 2.05260 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 845793.i | 0.0326783i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 6.55972e7i | − 2.50718i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.26640e7 | 1.24174 | 0.620869 | − | 0.783914i | \(-0.286780\pi\) | ||||
0.620869 | + | 0.783914i | \(0.286780\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.49635e6 | 0.207826 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 6.34082e7i | − 2.38474i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.27944e7i | 0.476068i | 0.971257 | + | 0.238034i | \(0.0765030\pi\) | ||||
−0.971257 | + | 0.238034i | \(0.923497\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.54720e7 | −2.79333 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.71929e7 | 0.632957 | 0.316479 | − | 0.948600i | \(-0.397499\pi\) | ||||
0.316479 | + | 0.948600i | \(0.397499\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.95248e6i | 0.217981i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.33455e7i | − 1.57061i | −0.619107 | − | 0.785307i | \(-0.712505\pi\) | ||||
0.619107 | − | 0.785307i | \(-0.287495\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23092.7 | −0.000832356 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.57363e7 | −0.922773 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.85588e6i | 0.244529i | 0.992498 | + | 0.122265i | \(0.0390157\pi\) | ||||
−0.992498 | + | 0.122265i | \(0.960984\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 7.00922e6i | − 0.247394i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.54750e7 | 0.543355 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.02016e7 | 0.356335 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.75723e7i | 0.958092i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.81761e7i | 0.625080i | 0.949905 | + | 0.312540i | \(0.101180\pi\) | ||||
−0.949905 | + | 0.312540i | \(0.898820\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.28909e7 | −0.783166 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.09710e7 | −0.713790 | −0.356895 | − | 0.934144i | \(-0.616165\pi\) | ||||
−0.356895 | + | 0.934144i | \(0.616165\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.67624e6i | − 0.158349i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.72323e7i | 0.912742i | 0.889790 | + | 0.456371i | \(0.150851\pi\) | ||||
−0.889790 | + | 0.456371i | \(0.849149\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.96311e6 | 0.232192 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.72596e6 | −0.156790 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.97759e7i | 1.31291i | 0.754363 | + | 0.656457i | \(0.227946\pi\) | ||||
−0.754363 | + | 0.656457i | \(0.772054\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.83944e6i | 0.288823i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.94710e6 | −0.0958086 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.12673e6 | −0.295210 | −0.147605 | − | 0.989046i | \(-0.547156\pi\) | ||||
−0.147605 | + | 0.989046i | \(0.547156\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 5.56427e7i | − 1.79075i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.68299e7i | − 0.536221i | −0.963388 | − | 0.268110i | \(-0.913601\pi\) | ||||
0.963388 | − | 0.268110i | \(-0.0863992\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.54092e7 | −0.488501 |
(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 | 700.6.e.g.449.1 | 6 | ||
5.2 | odd | 4 | 700.6.a.i.1.1 | 3 | |||
5.3 | odd | 4 | 140.6.a.d.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 700.6.e.g.449.6 | 6 | ||
20.3 | even | 4 | 560.6.a.t.1.1 | 3 | |||
35.13 | even | 4 | 980.6.a.h.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.6.a.d.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
560.6.a.t.1.1 | 3 | 20.3 | even | 4 | |||
700.6.a.i.1.1 | 3 | 5.2 | odd | 4 | |||
700.6.e.g.449.1 | 6 | 1.1 | even | 1 | trivial | ||
700.6.e.g.449.6 | 6 | 5.4 | even | 2 | inner | ||
980.6.a.h.1.1 | 3 | 35.13 | even | 4 |