Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,4,Mod(379,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.379");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.g (of order \(2\), degree \(1\), 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: | \(37.1712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.379 |
Dual form | 630.4.g.a.379.1 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −10.0000 | + | 5.00000i | −0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.0000 | − | 20.0000i | −0.316228 | − | 0.632456i | ||||
\(11\) | 37.0000 | 1.01417 | 0.507087 | − | 0.861895i | \(-0.330722\pi\) | ||||
0.507087 | + | 0.861895i | \(0.330722\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 51.0000i | 1.08807i | 0.839064 | + | 0.544033i | \(0.183103\pi\) | ||||
−0.839064 | + | 0.544033i | \(0.816897\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 41.0000i | 0.584939i | 0.956275 | + | 0.292469i | \(0.0944770\pi\) | ||||
−0.956275 | + | 0.292469i | \(0.905523\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 108.000 | 1.30405 | 0.652024 | − | 0.758199i | \(-0.273920\pi\) | ||||
0.652024 | + | 0.758199i | \(0.273920\pi\) | |||||||
\(20\) | 40.0000 | − | 20.0000i | 0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 74.0000i | 0.717130i | ||||||||
\(23\) | 70.0000i | 0.634609i | 0.948324 | + | 0.317305i | \(0.102778\pi\) | ||||
−0.948324 | + | 0.317305i | \(0.897222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 75.0000 | − | 100.000i | 0.600000 | − | 0.800000i | ||||
\(26\) | −102.000 | −0.769379 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 28.0000i | 0.188982i | ||||||||
\(29\) | −249.000 | −1.59442 | −0.797209 | − | 0.603703i | \(-0.793691\pi\) | ||||
−0.797209 | + | 0.603703i | \(0.793691\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −134.000 | −0.776358 | −0.388179 | − | 0.921584i | \(-0.626896\pi\) | ||||
−0.388179 | + | 0.921584i | \(0.626896\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −82.0000 | −0.413614 | ||||||||
\(35\) | 35.0000 | + | 70.0000i | 0.169031 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 334.000i | 1.48403i | 0.670381 | + | 0.742017i | \(0.266131\pi\) | ||||
−0.670381 | + | 0.742017i | \(0.733869\pi\) | |||||||
\(38\) | 216.000i | 0.922101i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 40.0000 | + | 80.0000i | 0.158114 | + | 0.316228i | ||||
\(41\) | −206.000 | −0.784678 | −0.392339 | − | 0.919821i | \(-0.628334\pi\) | ||||
−0.392339 | + | 0.919821i | \(0.628334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 376.000i | − | 1.33348i | −0.745292 | − | 0.666738i | \(-0.767690\pi\) | ||
0.745292 | − | 0.666738i | \(-0.232310\pi\) | |||||||
\(44\) | −148.000 | −0.507087 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −140.000 | −0.448736 | ||||||||
\(47\) | − | 287.000i | − | 0.890708i | −0.895355 | − | 0.445354i | \(-0.853078\pi\) | ||
0.895355 | − | 0.445354i | \(-0.146922\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 200.000 | + | 150.000i | 0.565685 | + | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 204.000i | − | 0.544033i | ||||||
\(53\) | 6.00000i | 0.0155503i | 0.999970 | + | 0.00777513i | \(0.00247492\pi\) | ||||
−0.999970 | + | 0.00777513i | \(0.997525\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −370.000 | + | 185.000i | −0.907105 | + | 0.453553i | ||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 498.000i | − | 1.12742i | ||||||
\(59\) | −2.00000 | −0.00441318 | −0.00220659 | − | 0.999998i | \(-0.500702\pi\) | ||||
−0.00220659 | + | 0.999998i | \(0.500702\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −940.000 | −1.97303 | −0.986514 | − | 0.163679i | \(-0.947664\pi\) | ||||
−0.986514 | + | 0.163679i | \(0.947664\pi\) | |||||||
\(62\) | − | 268.000i | − | 0.548968i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −255.000 | − | 510.000i | −0.486598 | − | 0.973196i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 106.000i | − | 0.193283i | −0.995319 | − | 0.0966415i | \(-0.969190\pi\) | ||
0.995319 | − | 0.0966415i | \(-0.0308100\pi\) | |||||||
\(68\) | − | 164.000i | − | 0.292469i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −140.000 | + | 70.0000i | −0.239046 | + | 0.119523i | ||||
\(71\) | −456.000 | −0.762215 | −0.381107 | − | 0.924531i | \(-0.624457\pi\) | ||||
−0.381107 | + | 0.924531i | \(0.624457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 650.000i | 1.04215i | 0.853512 | + | 0.521074i | \(0.174468\pi\) | ||||
−0.853512 | + | 0.521074i | \(0.825532\pi\) | |||||||
\(74\) | −668.000 | −1.04937 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −432.000 | −0.652024 | ||||||||
\(77\) | − | 259.000i | − | 0.383322i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1239.00 | 1.76454 | 0.882268 | − | 0.470747i | \(-0.156016\pi\) | ||||
0.882268 | + | 0.470747i | \(0.156016\pi\) | |||||||
\(80\) | −160.000 | + | 80.0000i | −0.223607 | + | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 412.000i | − | 0.554851i | ||||||
\(83\) | − | 428.000i | − | 0.566013i | −0.959118 | − | 0.283007i | \(-0.908668\pi\) | ||
0.959118 | − | 0.283007i | \(-0.0913319\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −205.000 | − | 410.000i | −0.261593 | − | 0.523185i | ||||
\(86\) | 752.000 | 0.942910 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 296.000i | − | 0.358565i | ||||||
\(89\) | −220.000 | −0.262022 | −0.131011 | − | 0.991381i | \(-0.541822\pi\) | ||||
−0.131011 | + | 0.991381i | \(0.541822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 357.000 | 0.411250 | ||||||||
\(92\) | − | 280.000i | − | 0.317305i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 574.000 | 0.629825 | ||||||||
\(95\) | −1080.00 | + | 540.000i | −1.16638 | + | 0.583188i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1055.00i | 1.10432i | 0.833738 | + | 0.552160i | \(0.186196\pi\) | ||||
−0.833738 | + | 0.552160i | \(0.813804\pi\) | |||||||
\(98\) | − | 98.0000i | − | 0.101015i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −300.000 | + | 400.000i | −0.300000 | + | 0.400000i | ||||
\(101\) | −1960.00 | −1.93096 | −0.965482 | − | 0.260471i | \(-0.916122\pi\) | ||||
−0.965482 | + | 0.260471i | \(0.916122\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1825.00i | 1.74585i | 0.487854 | + | 0.872925i | \(0.337780\pi\) | ||||
−0.487854 | + | 0.872925i | \(0.662220\pi\) | |||||||
\(104\) | 408.000 | 0.384689 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −0.0109957 | ||||||||
\(107\) | − | 144.000i | − | 0.130103i | −0.997882 | − | 0.0650514i | \(-0.979279\pi\) | ||
0.997882 | − | 0.0650514i | \(-0.0207211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1681.00 | −1.47716 | −0.738581 | − | 0.674165i | \(-0.764504\pi\) | ||||
−0.738581 | + | 0.674165i | \(0.764504\pi\) | |||||||
\(110\) | −370.000 | − | 740.000i | −0.320710 | − | 0.641420i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 112.000i | − | 0.0944911i | ||||||
\(113\) | − | 798.000i | − | 0.664332i | −0.943221 | − | 0.332166i | \(-0.892221\pi\) | ||
0.943221 | − | 0.332166i | \(-0.107779\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −350.000 | − | 700.000i | −0.283806 | − | 0.567612i | ||||
\(116\) | 996.000 | 0.797209 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4.00000i | − | 0.00312059i | ||||||
\(119\) | 287.000 | 0.221086 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 38.0000 | 0.0285500 | ||||||||
\(122\) | − | 1880.00i | − | 1.39514i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 536.000 | 0.388179 | ||||||||
\(125\) | −250.000 | + | 1375.00i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 434.000i | − | 0.303238i | −0.988439 | − | 0.151619i | \(-0.951551\pi\) | ||
0.988439 | − | 0.151619i | \(-0.0484487\pi\) | |||||||
\(128\) | − | 128.000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1020.00 | − | 510.000i | 0.688153 | − | 0.344077i | ||||
\(131\) | 1290.00 | 0.860365 | 0.430183 | − | 0.902742i | \(-0.358449\pi\) | ||||
0.430183 | + | 0.902742i | \(0.358449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 756.000i | − | 0.492884i | ||||||
\(134\) | 212.000 | 0.136672 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 328.000 | 0.206807 | ||||||||
\(137\) | 192.000i | 0.119735i | 0.998206 | + | 0.0598674i | \(0.0190678\pi\) | ||||
−0.998206 | + | 0.0598674i | \(0.980932\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1402.00 | −0.855511 | −0.427756 | − | 0.903894i | \(-0.640696\pi\) | ||||
−0.427756 | + | 0.903894i | \(0.640696\pi\) | |||||||
\(140\) | −140.000 | − | 280.000i | −0.0845154 | − | 0.169031i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 912.000i | − | 0.538967i | ||||||
\(143\) | 1887.00i | 1.10349i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2490.00 | − | 1245.00i | 1.42609 | − | 0.713046i | ||||
\(146\) | −1300.00 | −0.736909 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1336.00i | − | 0.742017i | ||||||
\(149\) | −302.000 | −0.166046 | −0.0830228 | − | 0.996548i | \(-0.526457\pi\) | ||||
−0.0830228 | + | 0.996548i | \(0.526457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3167.00 | −1.70680 | −0.853400 | − | 0.521257i | \(-0.825463\pi\) | ||||
−0.853400 | + | 0.521257i | \(0.825463\pi\) | |||||||
\(152\) | − | 864.000i | − | 0.461050i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 518.000 | 0.271050 | ||||||||
\(155\) | 1340.00 | − | 670.000i | 0.694396 | − | 0.347198i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 470.000i | 0.238918i | 0.992839 | + | 0.119459i | \(0.0381160\pi\) | ||||
−0.992839 | + | 0.119459i | \(0.961884\pi\) | |||||||
\(158\) | 2478.00i | 1.24772i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −160.000 | − | 320.000i | −0.0790569 | − | 0.158114i | ||||
\(161\) | 490.000 | 0.239860 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2390.00i | − | 1.14846i | −0.818693 | − | 0.574231i | \(-0.805301\pi\) | ||
0.818693 | − | 0.574231i | \(-0.194699\pi\) | |||||||
\(164\) | 824.000 | 0.392339 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 856.000 | 0.400232 | ||||||||
\(167\) | − | 2631.00i | − | 1.21912i | −0.792740 | − | 0.609560i | \(-0.791346\pi\) | ||
0.792740 | − | 0.609560i | \(-0.208654\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −404.000 | −0.183887 | ||||||||
\(170\) | 820.000 | − | 410.000i | 0.369948 | − | 0.184974i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1504.00i | 0.666738i | ||||||||
\(173\) | 2243.00i | 0.985735i | 0.870104 | + | 0.492867i | \(0.164051\pi\) | ||||
−0.870104 | + | 0.492867i | \(0.835949\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −700.000 | − | 525.000i | −0.302372 | − | 0.226779i | ||||
\(176\) | 592.000 | 0.253544 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 440.000i | − | 0.185277i | ||||||
\(179\) | 52.0000 | 0.0217132 | 0.0108566 | − | 0.999941i | \(-0.496544\pi\) | ||||
0.0108566 | + | 0.999941i | \(0.496544\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2462.00 | 1.01104 | 0.505522 | − | 0.862814i | \(-0.331300\pi\) | ||||
0.505522 | + | 0.862814i | \(0.331300\pi\) | |||||||
\(182\) | 714.000i | 0.290798i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 560.000 | 0.224368 | ||||||||
\(185\) | −1670.00 | − | 3340.00i | −0.663680 | − | 1.32736i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1517.00i | 0.593230i | ||||||||
\(188\) | 1148.00i | 0.445354i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1080.00 | − | 2160.00i | −0.412376 | − | 0.824752i | ||||
\(191\) | −3159.00 | −1.19674 | −0.598370 | − | 0.801220i | \(-0.704185\pi\) | ||||
−0.598370 | + | 0.801220i | \(0.704185\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2060.00i | 0.768301i | 0.923271 | + | 0.384150i | \(0.125506\pi\) | ||||
−0.923271 | + | 0.384150i | \(0.874494\pi\) | |||||||
\(194\) | −2110.00 | −0.780872 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 1738.00i | 0.628565i | 0.949329 | + | 0.314283i | \(0.101764\pi\) | ||||
−0.949329 | + | 0.314283i | \(0.898236\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 894.000 | 0.318462 | 0.159231 | − | 0.987241i | \(-0.449099\pi\) | ||||
0.159231 | + | 0.987241i | \(0.449099\pi\) | |||||||
\(200\) | −800.000 | − | 600.000i | −0.282843 | − | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3920.00i | − | 1.36540i | ||||||
\(203\) | 1743.00i | 0.602634i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2060.00 | − | 1030.00i | 0.701837 | − | 0.350919i | ||||
\(206\) | −3650.00 | −1.23450 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 816.000i | 0.272016i | ||||||||
\(209\) | 3996.00 | 1.32253 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4083.00 | −1.33216 | −0.666079 | − | 0.745881i | \(-0.732029\pi\) | ||||
−0.666079 | + | 0.745881i | \(0.732029\pi\) | |||||||
\(212\) | − | 24.0000i | − | 0.00777513i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 288.000 | 0.0919966 | ||||||||
\(215\) | 1880.00 | + | 3760.00i | 0.596349 | + | 1.19270i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 938.000i | 0.293436i | ||||||||
\(218\) | − | 3362.00i | − | 1.04451i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1480.00 | − | 740.000i | 0.453553 | − | 0.226776i | ||||
\(221\) | −2091.00 | −0.636452 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 377.000i | 0.113210i | 0.998397 | + | 0.0566049i | \(0.0180275\pi\) | ||||
−0.998397 | + | 0.0566049i | \(0.981972\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1596.00 | 0.469754 | ||||||||
\(227\) | − | 2551.00i | − | 0.745885i | −0.927855 | − | 0.372942i | \(-0.878349\pi\) | ||
0.927855 | − | 0.372942i | \(-0.121651\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −74.0000 | −0.0213540 | −0.0106770 | − | 0.999943i | \(-0.503399\pi\) | ||||
−0.0106770 | + | 0.999943i | \(0.503399\pi\) | |||||||
\(230\) | 1400.00 | − | 700.000i | 0.401362 | − | 0.200681i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1992.00i | 0.563712i | ||||||||
\(233\) | − | 1888.00i | − | 0.530845i | −0.964132 | − | 0.265423i | \(-0.914488\pi\) | ||
0.964132 | − | 0.265423i | \(-0.0855115\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1435.00 | + | 2870.00i | 0.398337 | + | 0.796673i | ||||
\(236\) | 8.00000 | 0.00220659 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 574.000i | 0.156331i | ||||||||
\(239\) | 4997.00 | 1.35242 | 0.676211 | − | 0.736708i | \(-0.263621\pi\) | ||||
0.676211 | + | 0.736708i | \(0.263621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3830.00 | −1.02370 | −0.511851 | − | 0.859074i | \(-0.671040\pi\) | ||||
−0.511851 | + | 0.859074i | \(0.671040\pi\) | |||||||
\(242\) | 76.0000i | 0.0201879i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3760.00 | 0.986514 | ||||||||
\(245\) | 490.000 | − | 245.000i | 0.127775 | − | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5508.00i | 1.41889i | ||||||||
\(248\) | 1072.00i | 0.274484i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2750.00 | − | 500.000i | −0.695701 | − | 0.126491i | ||||
\(251\) | 3390.00 | 0.852490 | 0.426245 | − | 0.904608i | \(-0.359836\pi\) | ||||
0.426245 | + | 0.904608i | \(0.359836\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2590.00i | 0.643604i | ||||||||
\(254\) | 868.000 | 0.214422 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 7170.00i | 1.74028i | 0.492803 | + | 0.870141i | \(0.335972\pi\) | ||||
−0.492803 | + | 0.870141i | \(0.664028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2338.00 | 0.560912 | ||||||||
\(260\) | 1020.00 | + | 2040.00i | 0.243299 | + | 0.486598i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2580.00i | 0.608370i | ||||||||
\(263\) | 7672.00i | 1.79877i | 0.437160 | + | 0.899384i | \(0.355984\pi\) | ||||
−0.437160 | + | 0.899384i | \(0.644016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.0000 | − | 60.0000i | −0.00695428 | − | 0.0139086i | ||||
\(266\) | 1512.00 | 0.348521 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 424.000i | 0.0966415i | ||||||||
\(269\) | −54.0000 | −0.0122395 | −0.00611977 | − | 0.999981i | \(-0.501948\pi\) | ||||
−0.00611977 | + | 0.999981i | \(0.501948\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2932.00 | 0.657219 | 0.328609 | − | 0.944466i | \(-0.393420\pi\) | ||||
0.328609 | + | 0.944466i | \(0.393420\pi\) | |||||||
\(272\) | 656.000i | 0.146235i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −384.000 | −0.0846653 | ||||||||
\(275\) | 2775.00 | − | 3700.00i | 0.608505 | − | 0.811340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3254.00i | − | 0.705826i | −0.935656 | − | 0.352913i | \(-0.885191\pi\) | ||
0.935656 | − | 0.352913i | \(-0.114809\pi\) | |||||||
\(278\) | − | 2804.00i | − | 0.604938i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 560.000 | − | 280.000i | 0.119523 | − | 0.0597614i | ||||
\(281\) | −3327.00 | −0.706307 | −0.353153 | − | 0.935565i | \(-0.614891\pi\) | ||||
−0.353153 | + | 0.935565i | \(0.614891\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4627.00i | 0.971896i | 0.873988 | + | 0.485948i | \(0.161526\pi\) | ||||
−0.873988 | + | 0.485948i | \(0.838474\pi\) | |||||||
\(284\) | 1824.00 | 0.381107 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3774.00 | −0.780284 | ||||||||
\(287\) | 1442.00i | 0.296580i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3232.00 | 0.657847 | ||||||||
\(290\) | 2490.00 | + | 4980.00i | 0.504199 | + | 1.00840i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 2600.00i | − | 0.521074i | ||||||
\(293\) | 4083.00i | 0.814100i | 0.913406 | + | 0.407050i | \(0.133443\pi\) | ||||
−0.913406 | + | 0.407050i | \(0.866557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.0000 | − | 10.0000i | 0.00394727 | − | 0.00197364i | ||||
\(296\) | 2672.00 | 0.524685 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 604.000i | − | 0.117412i | ||||||
\(299\) | −3570.00 | −0.690496 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2632.00 | −0.504007 | ||||||||
\(302\) | − | 6334.00i | − | 1.20689i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1728.00 | 0.326012 | ||||||||
\(305\) | 9400.00 | − | 4700.00i | 1.76473 | − | 0.882365i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4089.00i | 0.760168i | 0.924952 | + | 0.380084i | \(0.124105\pi\) | ||||
−0.924952 | + | 0.380084i | \(0.875895\pi\) | |||||||
\(308\) | 1036.00i | 0.191661i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1340.00 | + | 2680.00i | 0.245506 | + | 0.491012i | ||||
\(311\) | 4008.00 | 0.730781 | 0.365390 | − | 0.930854i | \(-0.380935\pi\) | ||||
0.365390 | + | 0.930854i | \(0.380935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7355.00i | 1.32821i | 0.747640 | + | 0.664104i | \(0.231187\pi\) | ||||
−0.747640 | + | 0.664104i | \(0.768813\pi\) | |||||||
\(314\) | −940.000 | −0.168940 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4956.00 | −0.882268 | ||||||||
\(317\) | − | 1684.00i | − | 0.298369i | −0.988809 | − | 0.149184i | \(-0.952335\pi\) | ||
0.988809 | − | 0.149184i | \(-0.0476648\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9213.00 | −1.61702 | ||||||||
\(320\) | 640.000 | − | 320.000i | 0.111803 | − | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 980.000i | 0.169606i | ||||||||
\(323\) | 4428.00i | 0.762788i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5100.00 | + | 3825.00i | 0.870453 | + | 0.652839i | ||||
\(326\) | 4780.00 | 0.812085 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1648.00i | 0.277426i | ||||||||
\(329\) | −2009.00 | −0.336656 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1460.00 | −0.242444 | −0.121222 | − | 0.992625i | \(-0.538681\pi\) | ||||
−0.121222 | + | 0.992625i | \(0.538681\pi\) | |||||||
\(332\) | 1712.00i | 0.283007i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5262.00 | 0.862047 | ||||||||
\(335\) | 530.000 | + | 1060.00i | 0.0864388 | + | 0.172878i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7514.00i | − | 1.21458i | −0.794480 | − | 0.607290i | \(-0.792256\pi\) | ||
0.794480 | − | 0.607290i | \(-0.207744\pi\) | |||||||
\(338\) | − | 808.000i | − | 0.130028i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 820.000 | + | 1640.00i | 0.130796 | + | 0.261593i | ||||
\(341\) | −4958.00 | −0.787363 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | −3008.00 | −0.471455 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4486.00 | −0.697020 | ||||||||
\(347\) | − | 2862.00i | − | 0.442767i | −0.975187 | − | 0.221384i | \(-0.928943\pi\) | ||
0.975187 | − | 0.221384i | \(-0.0710573\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6368.00 | 0.976708 | 0.488354 | − | 0.872646i | \(-0.337597\pi\) | ||||
0.488354 | + | 0.872646i | \(0.337597\pi\) | |||||||
\(350\) | 1050.00 | − | 1400.00i | 0.160357 | − | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1184.00i | 0.179282i | ||||||||
\(353\) | 3635.00i | 0.548078i | 0.961719 | + | 0.274039i | \(0.0883597\pi\) | ||||
−0.961719 | + | 0.274039i | \(0.911640\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4560.00 | − | 2280.00i | 0.681746 | − | 0.340873i | ||||
\(356\) | 880.000 | 0.131011 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 104.000i | 0.0153535i | ||||||||
\(359\) | 7116.00 | 1.04615 | 0.523075 | − | 0.852286i | \(-0.324785\pi\) | ||||
0.523075 | + | 0.852286i | \(0.324785\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4805.00 | 0.700539 | ||||||||
\(362\) | 4924.00i | 0.714916i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1428.00 | −0.205625 | ||||||||
\(365\) | −3250.00 | − | 6500.00i | −0.466062 | − | 0.932125i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 319.000i | 0.0453724i | 0.999743 | + | 0.0226862i | \(0.00722186\pi\) | ||||
−0.999743 | + | 0.0226862i | \(0.992778\pi\) | |||||||
\(368\) | 1120.00i | 0.158652i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6680.00 | − | 3340.00i | 0.938586 | − | 0.469293i | ||||
\(371\) | 42.0000 | 0.00587744 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 11652.0i | − | 1.61747i | −0.588171 | − | 0.808737i | \(-0.700152\pi\) | ||
0.588171 | − | 0.808737i | \(-0.299848\pi\) | |||||||
\(374\) | −3034.00 | −0.419477 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2296.00 | −0.314913 | ||||||||
\(377\) | − | 12699.0i | − | 1.73483i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7748.00 | −1.05010 | −0.525050 | − | 0.851071i | \(-0.675953\pi\) | ||||
−0.525050 | + | 0.851071i | \(0.675953\pi\) | |||||||
\(380\) | 4320.00 | − | 2160.00i | 0.583188 | − | 0.291594i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 6318.00i | − | 0.846223i | ||||||
\(383\) | − | 8680.00i | − | 1.15803i | −0.815315 | − | 0.579017i | \(-0.803436\pi\) | ||
0.815315 | − | 0.579017i | \(-0.196564\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1295.00 | + | 2590.00i | 0.171427 | + | 0.342854i | ||||
\(386\) | −4120.00 | −0.543271 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 4220.00i | − | 0.552160i | ||||||
\(389\) | −1711.00 | −0.223011 | −0.111505 | − | 0.993764i | \(-0.535567\pi\) | ||||
−0.111505 | + | 0.993764i | \(0.535567\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2870.00 | −0.371208 | ||||||||
\(392\) | 392.000i | 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3476.00 | −0.444463 | ||||||||
\(395\) | −12390.0 | + | 6195.00i | −1.57825 | + | 0.789125i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1589.00i | − | 0.200881i | −0.994943 | − | 0.100440i | \(-0.967975\pi\) | ||
0.994943 | − | 0.100440i | \(-0.0320252\pi\) | |||||||
\(398\) | 1788.00i | 0.225187i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1200.00 | − | 1600.00i | 0.150000 | − | 0.200000i | ||||
\(401\) | 5147.00 | 0.640970 | 0.320485 | − | 0.947254i | \(-0.396154\pi\) | ||||
0.320485 | + | 0.947254i | \(0.396154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6834.00i | − | 0.844729i | ||||||
\(404\) | 7840.00 | 0.965482 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3486.00 | −0.426126 | ||||||||
\(407\) | 12358.0i | 1.50507i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9100.00 | 1.10016 | 0.550081 | − | 0.835111i | \(-0.314597\pi\) | ||||
0.550081 | + | 0.835111i | \(0.314597\pi\) | |||||||
\(410\) | 2060.00 | + | 4120.00i | 0.248137 | + | 0.496274i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 7300.00i | − | 0.872925i | ||||||
\(413\) | 14.0000i | 0.00166803i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2140.00 | + | 4280.00i | 0.253129 | + | 0.506258i | ||||
\(416\) | −1632.00 | −0.192345 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7992.00i | 0.935171i | ||||||||
\(419\) | 2618.00 | 0.305245 | 0.152623 | − | 0.988285i | \(-0.451228\pi\) | ||||
0.152623 | + | 0.988285i | \(0.451228\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3695.00 | −0.427751 | −0.213876 | − | 0.976861i | \(-0.568609\pi\) | ||||
−0.213876 | + | 0.976861i | \(0.568609\pi\) | |||||||
\(422\) | − | 8166.00i | − | 0.941978i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 48.0000 | 0.00549784 | ||||||||
\(425\) | 4100.00 | + | 3075.00i | 0.467951 | + | 0.350963i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6580.00i | 0.745734i | ||||||||
\(428\) | 576.000i | 0.0650514i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7520.00 | + | 3760.00i | −0.843364 | + | 0.421682i | ||||
\(431\) | −15779.0 | −1.76345 | −0.881726 | − | 0.471762i | \(-0.843618\pi\) | ||||
−0.881726 | + | 0.471762i | \(0.843618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7238.00i | 0.803317i | 0.915790 | + | 0.401658i | \(0.131566\pi\) | ||||
−0.915790 | + | 0.401658i | \(0.868434\pi\) | |||||||
\(434\) | −1876.00 | −0.207491 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6724.00 | 0.738581 | ||||||||
\(437\) | 7560.00i | 0.827560i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2646.00 | 0.287669 | 0.143834 | − | 0.989602i | \(-0.454057\pi\) | ||||
0.143834 | + | 0.989602i | \(0.454057\pi\) | |||||||
\(440\) | 1480.00 | + | 2960.00i | 0.160355 | + | 0.320710i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 4182.00i | − | 0.450039i | ||||||
\(443\) | − | 5688.00i | − | 0.610034i | −0.952347 | − | 0.305017i | \(-0.901338\pi\) | ||
0.952347 | − | 0.305017i | \(-0.0986621\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2200.00 | − | 1100.00i | 0.234360 | − | 0.117180i | ||||
\(446\) | −754.000 | −0.0800514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 448.000i | 0.0472456i | ||||||||
\(449\) | −3285.00 | −0.345276 | −0.172638 | − | 0.984985i | \(-0.555229\pi\) | ||||
−0.172638 | + | 0.984985i | \(0.555229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7622.00 | −0.795800 | ||||||||
\(452\) | 3192.00i | 0.332166i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5102.00 | 0.527420 | ||||||||
\(455\) | −3570.00 | + | 1785.00i | −0.367833 | + | 0.183917i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14834.0i | − | 1.51839i | −0.650862 | − | 0.759196i | \(-0.725592\pi\) | ||
0.650862 | − | 0.759196i | \(-0.274408\pi\) | |||||||
\(458\) | − | 148.000i | − | 0.0150995i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1400.00 | + | 2800.00i | 0.141903 | + | 0.283806i | ||||
\(461\) | 9972.00 | 1.00747 | 0.503734 | − | 0.863859i | \(-0.331959\pi\) | ||||
0.503734 | + | 0.863859i | \(0.331959\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9096.00i | − | 0.913017i | −0.889719 | − | 0.456509i | \(-0.849100\pi\) | ||
0.889719 | − | 0.456509i | \(-0.150900\pi\) | |||||||
\(464\) | −3984.00 | −0.398605 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3776.00 | 0.375364 | ||||||||
\(467\) | 15867.0i | 1.57224i | 0.618072 | + | 0.786121i | \(0.287914\pi\) | ||||
−0.618072 | + | 0.786121i | \(0.712086\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −742.000 | −0.0730541 | ||||||||
\(470\) | −5740.00 | + | 2870.00i | −0.563333 | + | 0.281666i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.0000i | 0.00156030i | ||||||||
\(473\) | − | 13912.0i | − | 1.35238i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8100.00 | − | 10800.0i | 0.782428 | − | 1.04324i | ||||
\(476\) | −1148.00 | −0.110543 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9994.00i | 0.956307i | ||||||||
\(479\) | 242.000 | 0.0230841 | 0.0115420 | − | 0.999933i | \(-0.496326\pi\) | ||||
0.0115420 | + | 0.999933i | \(0.496326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17034.0 | −1.61473 | ||||||||
\(482\) | − | 7660.00i | − | 0.723866i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −152.000 | −0.0142750 | ||||||||
\(485\) | −5275.00 | − | 10550.0i | −0.493867 | − | 0.987734i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3558.00i | 0.331064i | 0.986204 | + | 0.165532i | \(0.0529342\pi\) | ||||
−0.986204 | + | 0.165532i | \(0.947066\pi\) | |||||||
\(488\) | 7520.00i | 0.697571i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 490.000 | + | 980.000i | 0.0451754 | + | 0.0903508i | ||||
\(491\) | −1473.00 | −0.135388 | −0.0676941 | − | 0.997706i | \(-0.521564\pi\) | ||||
−0.0676941 | + | 0.997706i | \(0.521564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 10209.0i | − | 0.932637i | ||||||
\(494\) | −11016.0 | −1.00331 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2144.00 | −0.194090 | ||||||||
\(497\) | 3192.00i | 0.288090i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −603.000 | −0.0540962 | −0.0270481 | − | 0.999634i | \(-0.508611\pi\) | ||||
−0.0270481 | + | 0.999634i | \(0.508611\pi\) | |||||||
\(500\) | 1000.00 | − | 5500.00i | 0.0894427 | − | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6780.00i | 0.602801i | ||||||||
\(503\) | − | 18387.0i | − | 1.62989i | −0.579537 | − | 0.814946i | \(-0.696766\pi\) | ||
0.579537 | − | 0.814946i | \(-0.303234\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19600.0 | − | 9800.00i | 1.72711 | − | 0.863553i | ||||
\(506\) | −5180.00 | −0.455097 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1736.00i | 0.151619i | ||||||||
\(509\) | 9018.00 | 0.785296 | 0.392648 | − | 0.919689i | \(-0.371559\pi\) | ||||
0.392648 | + | 0.919689i | \(0.371559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4550.00 | 0.393895 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14340.0 | −1.23056 | ||||||||
\(515\) | −9125.00 | − | 18250.0i | −0.780768 | − | 1.56154i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10619.0i | − | 0.903333i | ||||||
\(518\) | 4676.00i | 0.396625i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4080.00 | + | 2040.00i | −0.344077 | + | 0.172038i | ||||
\(521\) | −4624.00 | −0.388831 | −0.194416 | − | 0.980919i | \(-0.562281\pi\) | ||||
−0.194416 | + | 0.980919i | \(0.562281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5876.00i | − | 0.491280i | −0.969361 | − | 0.245640i | \(-0.921002\pi\) | ||
0.969361 | − | 0.245640i | \(-0.0789981\pi\) | |||||||
\(524\) | −5160.00 | −0.430183 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15344.0 | −1.27192 | ||||||||
\(527\) | − | 5494.00i | − | 0.454122i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7267.00 | 0.597271 | ||||||||
\(530\) | 120.000 | − | 60.0000i | 0.00983484 | − | 0.00491742i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3024.00i | 0.246442i | ||||||||
\(533\) | − | 10506.0i | − | 0.853781i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 720.000 | + | 1440.00i | 0.0581838 | + | 0.116368i | ||||
\(536\) | −848.000 | −0.0683359 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 108.000i | − | 0.00865467i | ||||||
\(539\) | −1813.00 | −0.144882 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8537.00 | −0.678437 | −0.339218 | − | 0.940708i | \(-0.610163\pi\) | ||||
−0.339218 | + | 0.940708i | \(0.610163\pi\) | |||||||
\(542\) | 5864.00i | 0.464724i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1312.00 | −0.103404 | ||||||||
\(545\) | 16810.0 | − | 8405.00i | 1.32121 | − | 0.660607i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13060.0i | 1.02085i | 0.859922 | + | 0.510425i | \(0.170512\pi\) | ||||
−0.859922 | + | 0.510425i | \(0.829488\pi\) | |||||||
\(548\) | − | 768.000i | − | 0.0598674i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7400.00 | + | 5550.00i | 0.573704 | + | 0.430278i | ||||
\(551\) | −26892.0 | −2.07920 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8673.00i | − | 0.666932i | ||||||
\(554\) | 6508.00 | 0.499095 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5608.00 | 0.427756 | ||||||||
\(557\) | 21372.0i | 1.62578i | 0.582416 | + | 0.812891i | \(0.302108\pi\) | ||||
−0.582416 | + | 0.812891i | \(0.697892\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19176.0 | 1.45091 | ||||||||
\(560\) | 560.000 | + | 1120.00i | 0.0422577 | + | 0.0845154i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 6654.00i | − | 0.499434i | ||||||
\(563\) | 12704.0i | 0.950994i | 0.879717 | + | 0.475497i | \(0.157732\pi\) | ||||
−0.879717 | + | 0.475497i | \(0.842268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3990.00 | + | 7980.00i | 0.297098 | + | 0.594197i | ||||
\(566\) | −9254.00 | −0.687234 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3648.00i | 0.269484i | ||||||||
\(569\) | 8762.00 | 0.645557 | 0.322779 | − | 0.946474i | \(-0.395383\pi\) | ||||
0.322779 | + | 0.946474i | \(0.395383\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24764.0 | −1.81496 | −0.907479 | − | 0.420097i | \(-0.861996\pi\) | ||||
−0.907479 | + | 0.420097i | \(0.861996\pi\) | |||||||
\(572\) | − | 7548.00i | − | 0.551744i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2884.00 | −0.209714 | ||||||||
\(575\) | 7000.00 | + | 5250.00i | 0.507687 | + | 0.380765i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1811.00i | − | 0.130664i | −0.997864 | − | 0.0653318i | \(-0.979189\pi\) | ||
0.997864 | − | 0.0653318i | \(-0.0208106\pi\) | |||||||
\(578\) | 6464.00i | 0.465168i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9960.00 | + | 4980.00i | −0.713046 | + | 0.356523i | ||||
\(581\) | −2996.00 | −0.213933 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 222.000i | 0.0157707i | ||||||||
\(584\) | 5200.00 | 0.368455 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8166.00 | −0.575656 | ||||||||
\(587\) | 10548.0i | 0.741674i | 0.928698 | + | 0.370837i | \(0.120929\pi\) | ||||
−0.928698 | + | 0.370837i | \(0.879071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14472.0 | −1.01241 | ||||||||
\(590\) | 20.0000 | + | 40.0000i | 0.00139557 | + | 0.00279114i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5344.00i | 0.371009i | ||||||||
\(593\) | − | 17439.0i | − | 1.20765i | −0.797119 | − | 0.603823i | \(-0.793643\pi\) | ||
0.797119 | − | 0.603823i | \(-0.206357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2870.00 | + | 1435.00i | −0.197745 | + | 0.0988727i | ||||
\(596\) | 1208.00 | 0.0830228 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 7140.00i | − | 0.488255i | ||||||
\(599\) | 2451.00 | 0.167187 | 0.0835936 | − | 0.996500i | \(-0.473360\pi\) | ||||
0.0835936 | + | 0.996500i | \(0.473360\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7792.00 | −0.528856 | −0.264428 | − | 0.964405i | \(-0.585183\pi\) | ||||
−0.264428 | + | 0.964405i | \(0.585183\pi\) | |||||||
\(602\) | − | 5264.00i | − | 0.356386i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12668.0 | 0.853400 | ||||||||
\(605\) | −380.000 | + | 190.000i | −0.0255359 | + | 0.0127679i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1937.00i | 0.129523i | 0.997901 | + | 0.0647615i | \(0.0206286\pi\) | ||||
−0.997901 | + | 0.0647615i | \(0.979371\pi\) | |||||||
\(608\) | 3456.00i | 0.230525i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9400.00 | + | 18800.0i | 0.623926 | + | 1.24785i | ||||
\(611\) | 14637.0 | 0.969148 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5036.00i | 0.331814i | 0.986141 | + | 0.165907i | \(0.0530552\pi\) | ||||
−0.986141 | + | 0.165907i | \(0.946945\pi\) | |||||||
\(614\) | −8178.00 | −0.537520 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2072.00 | −0.135525 | ||||||||
\(617\) | − | 27286.0i | − | 1.78038i | −0.455592 | − | 0.890189i | \(-0.650572\pi\) | ||
0.455592 | − | 0.890189i | \(-0.349428\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28538.0 | −1.85305 | −0.926526 | − | 0.376231i | \(-0.877220\pi\) | ||||
−0.926526 | + | 0.376231i | \(0.877220\pi\) | |||||||
\(620\) | −5360.00 | + | 2680.00i | −0.347198 | + | 0.173599i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8016.00i | 0.516740i | ||||||||
\(623\) | 1540.00i | 0.0990350i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4375.00 | − | 15000.0i | −0.280000 | − | 0.960000i | ||||
\(626\) | −14710.0 | −0.939185 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 1880.00i | − | 0.119459i | ||||||
\(629\) | −13694.0 | −0.868069 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25007.0 | 1.57768 | 0.788838 | − | 0.614602i | \(-0.210683\pi\) | ||||
0.788838 | + | 0.614602i | \(0.210683\pi\) | |||||||
\(632\) | − | 9912.00i | − | 0.623858i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3368.00 | 0.210978 | ||||||||
\(635\) | 2170.00 | + | 4340.00i | 0.135612 | + | 0.271225i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2499.00i | − | 0.155438i | ||||||
\(638\) | − | 18426.0i | − | 1.14340i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 640.000 | + | 1280.00i | 0.0395285 | + | 0.0790569i | ||||
\(641\) | 12130.0 | 0.747436 | 0.373718 | − | 0.927542i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927542i | \(0.378083\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14385.0i | 0.882254i | 0.897445 | + | 0.441127i | \(0.145421\pi\) | ||||
−0.897445 | + | 0.441127i | \(0.854579\pi\) | |||||||
\(644\) | −1960.00 | −0.119930 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8856.00 | −0.539373 | ||||||||
\(647\) | − | 2208.00i | − | 0.134166i | −0.997747 | − | 0.0670830i | \(-0.978631\pi\) | ||
0.997747 | − | 0.0670830i | \(-0.0213692\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −74.0000 | −0.00447574 | ||||||||
\(650\) | −7650.00 | + | 10200.0i | −0.461627 | + | 0.615503i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9560.00i | 0.574231i | ||||||||
\(653\) | − | 22448.0i | − | 1.34527i | −0.739977 | − | 0.672633i | \(-0.765163\pi\) | ||
0.739977 | − | 0.672633i | \(-0.234837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12900.0 | + | 6450.00i | −0.769534 | + | 0.384767i | ||||
\(656\) | −3296.00 | −0.196169 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 4018.00i | − | 0.238052i | ||||||
\(659\) | 8791.00 | 0.519649 | 0.259825 | − | 0.965656i | \(-0.416335\pi\) | ||||
0.259825 | + | 0.965656i | \(0.416335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13180.0 | −0.775556 | −0.387778 | − | 0.921753i | \(-0.626757\pi\) | ||||
−0.387778 | + | 0.921753i | \(0.626757\pi\) | |||||||
\(662\) | − | 2920.00i | − | 0.171434i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3424.00 | −0.200116 | ||||||||
\(665\) | 3780.00 | + | 7560.00i | 0.220424 | + | 0.440848i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 17430.0i | − | 1.01183i | ||||||
\(668\) | 10524.0i | 0.609560i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2120.00 | + | 1060.00i | −0.122243 | + | 0.0611215i | ||||
\(671\) | −34780.0 | −2.00099 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 7164.00i | − | 0.410330i | −0.978727 | − | 0.205165i | \(-0.934227\pi\) | ||
0.978727 | − | 0.205165i | \(-0.0657731\pi\) | |||||||
\(674\) | 15028.0 | 0.858838 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1616.00 | 0.0919436 | ||||||||
\(677\) | 12335.0i | 0.700255i | 0.936702 | + | 0.350127i | \(0.113862\pi\) | ||||
−0.936702 | + | 0.350127i | \(0.886138\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7385.00 | 0.417394 | ||||||||
\(680\) | −3280.00 | + | 1640.00i | −0.184974 | + | 0.0924870i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 9916.00i | − | 0.556750i | ||||||
\(683\) | 15436.0i | 0.864776i | 0.901688 | + | 0.432388i | \(0.142329\pi\) | ||||
−0.901688 | + | 0.432388i | \(0.857671\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −960.000 | − | 1920.00i | −0.0535470 | − | 0.107094i | ||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 6016.00i | − | 0.333369i | ||||||
\(689\) | −306.000 | −0.0169197 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19184.0 | −1.05614 | −0.528071 | − | 0.849200i | \(-0.677084\pi\) | ||||
−0.528071 | + | 0.849200i | \(0.677084\pi\) | |||||||
\(692\) | − | 8972.00i | − | 0.492867i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5724.00 | 0.313084 | ||||||||
\(695\) | 14020.0 | − | 7010.00i | 0.765193 | − | 0.382596i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8446.00i | − | 0.458989i | ||||||
\(698\) | 12736.0i | 0.690637i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2800.00 | + | 2100.00i | 0.151186 | + | 0.113389i | ||||
\(701\) | −32975.0 | −1.77667 | −0.888337 | − | 0.459192i | \(-0.848139\pi\) | ||||
−0.888337 | + | 0.459192i | \(0.848139\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36072.0i | 1.93525i | ||||||||
\(704\) | −2368.00 | −0.126772 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7270.00 | −0.387550 | ||||||||
\(707\) | 13720.0i | 0.729836i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31497.0 | 1.66840 | 0.834199 | − | 0.551463i | \(-0.185930\pi\) | ||||
0.834199 | + | 0.551463i | \(0.185930\pi\) | |||||||
\(710\) | 4560.00 | + | 9120.00i | 0.241033 | + | 0.482067i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1760.00i | 0.0926387i | ||||||||
\(713\) | − | 9380.00i | − | 0.492684i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9435.00 | − | 18870.0i | −0.493495 | − | 0.986990i | ||||
\(716\) | −208.000 | −0.0108566 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14232.0i | 0.739740i | ||||||||
\(719\) | −18610.0 | −0.965279 | −0.482640 | − | 0.875819i | \(-0.660322\pi\) | ||||
−0.482640 | + | 0.875819i | \(0.660322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12775.0 | 0.659869 | ||||||||
\(722\) | 9610.00i | 0.495356i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9848.00 | −0.505522 | ||||||||
\(725\) | −18675.0 | + | 24900.0i | −0.956651 | + | 1.27553i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17508.0i | 0.893172i | 0.894741 | + | 0.446586i | \(0.147360\pi\) | ||||
−0.894741 | + | 0.446586i | \(0.852640\pi\) | |||||||
\(728\) | − | 2856.00i | − | 0.145399i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13000.0 | − | 6500.00i | 0.659112 | − | 0.329556i | ||||
\(731\) | 15416.0 | 0.780002 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4685.00i | − | 0.236077i | −0.993009 | − | 0.118038i | \(-0.962339\pi\) | ||
0.993009 | − | 0.118038i | \(-0.0376606\pi\) | |||||||
\(734\) | −638.000 | −0.0320831 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2240.00 | −0.112184 | ||||||||
\(737\) | − | 3922.00i | − | 0.196023i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25925.0 | 1.29048 | 0.645241 | − | 0.763979i | \(-0.276757\pi\) | ||||
0.645241 | + | 0.763979i | \(0.276757\pi\) | |||||||
\(740\) | 6680.00 | + | 13360.0i | 0.331840 | + | 0.663680i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 84.0000i | 0.00415598i | ||||||||
\(743\) | − | 25578.0i | − | 1.26294i | −0.775400 | − | 0.631471i | \(-0.782452\pi\) | ||
0.775400 | − | 0.631471i | \(-0.217548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3020.00 | − | 1510.00i | 0.148516 | − | 0.0742579i | ||||
\(746\) | 23304.0 | 1.14373 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 6068.00i | − | 0.296615i | ||||||
\(749\) | −1008.00 | −0.0491743 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4291.00 | −0.208496 | −0.104248 | − | 0.994551i | \(-0.533244\pi\) | ||||
−0.104248 | + | 0.994551i | \(0.533244\pi\) | |||||||
\(752\) | − | 4592.00i | − | 0.222677i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25398.0 | 1.22671 | ||||||||
\(755\) | 31670.0 | − | 15835.0i | 1.52661 | − | 0.763304i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31528.0i | 1.51374i | 0.653563 | + | 0.756872i | \(0.273274\pi\) | ||||
−0.653563 | + | 0.756872i | \(0.726726\pi\) | |||||||
\(758\) | − | 15496.0i | − | 0.742533i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4320.00 | + | 8640.00i | 0.206188 | + | 0.412376i | ||||
\(761\) | 23154.0 | 1.10293 | 0.551466 | − | 0.834197i | \(-0.314068\pi\) | ||||
0.551466 | + | 0.834197i | \(0.314068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11767.0i | 0.558315i | ||||||||
\(764\) | 12636.0 | 0.598370 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17360.0 | 0.818854 | ||||||||
\(767\) | − | 102.000i | − | 0.00480183i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13992.0 | −0.656131 | −0.328065 | − | 0.944655i | \(-0.606397\pi\) | ||||
−0.328065 | + | 0.944655i | \(0.606397\pi\) | |||||||
\(770\) | −5180.00 | + | 2590.00i | −0.242434 | + | 0.121217i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 8240.00i | − | 0.384150i | ||||||
\(773\) | 21681.0i | 1.00881i | 0.863467 | + | 0.504406i | \(0.168288\pi\) | ||||
−0.863467 | + | 0.504406i | \(0.831712\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10050.0 | + | 13400.0i | −0.465815 | + | 0.621087i | ||||
\(776\) | 8440.00 | 0.390436 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 3422.00i | − | 0.157692i | ||||||
\(779\) | −22248.0 | −1.02326 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16872.0 | −0.773019 | ||||||||
\(782\) | − | 5740.00i | − | 0.262483i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −784.000 | −0.0357143 | ||||||||
\(785\) | −2350.00 | − | 4700.00i | −0.106847 | − | 0.213695i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16903.0i | 0.765600i | 0.923831 | + | 0.382800i | \(0.125040\pi\) | ||||
−0.923831 | + | 0.382800i | \(0.874960\pi\) | |||||||
\(788\) | − | 6952.00i | − | 0.314283i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12390.0 | − | 24780.0i | −0.557995 | − | 1.11599i | ||||
\(791\) | −5586.00 | −0.251094 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 47940.0i | − | 2.14678i | ||||||
\(794\) | 3178.00 | 0.142044 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3576.00 | −0.159231 | ||||||||
\(797\) | 18905.0i | 0.840213i | 0.907475 | + | 0.420106i | \(0.138007\pi\) | ||||
−0.907475 | + | 0.420106i | \(0.861993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11767.0 | 0.521009 | ||||||||
\(800\) | 3200.00 | + | 2400.00i | 0.141421 | + | 0.106066i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10294.0i | 0.453234i | ||||||||
\(803\) | 24050.0i | 1.05692i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4900.00 | + | 2450.00i | −0.214537 | + | 0.107269i | ||||
\(806\) | 13668.0 | 0.597314 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15680.0i | 0.682699i | ||||||||
\(809\) | −5571.00 | −0.242109 | −0.121054 | − | 0.992646i | \(-0.538628\pi\) | ||||
−0.121054 | + | 0.992646i | \(0.538628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10894.0 | 0.471689 | 0.235845 | − | 0.971791i | \(-0.424214\pi\) | ||||
0.235845 | + | 0.971791i | \(0.424214\pi\) | |||||||
\(812\) | − | 6972.00i | − | 0.301317i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24716.0 | −1.06424 | ||||||||
\(815\) | 11950.0 | + | 23900.0i | 0.513608 | + | 1.02722i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 40608.0i | − | 1.73892i | ||||||
\(818\) | 18200.0i | 0.777932i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8240.00 | + | 4120.00i | −0.350919 | + | 0.175459i | ||||
\(821\) | 30731.0 | 1.30636 | 0.653179 | − | 0.757204i | \(-0.273435\pi\) | ||||
0.653179 | + | 0.757204i | \(0.273435\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1038.00i | 0.0439640i | 0.999758 | + | 0.0219820i | \(0.00699766\pi\) | ||||
−0.999758 | + | 0.0219820i | \(0.993002\pi\) | |||||||
\(824\) | 14600.0 | 0.617251 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.0000 | −0.00117947 | ||||||||
\(827\) | 7958.00i | 0.334615i | 0.985905 | + | 0.167308i | \(0.0535073\pi\) | ||||
−0.985905 | + | 0.167308i | \(0.946493\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30666.0 | 1.28477 | 0.642385 | − | 0.766382i | \(-0.277945\pi\) | ||||
0.642385 | + | 0.766382i | \(0.277945\pi\) | |||||||
\(830\) | −8560.00 | + | 4280.00i | −0.357978 | + | 0.178989i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 3264.00i | − | 0.136008i | ||||||
\(833\) | − | 2009.00i | − | 0.0835627i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13155.0 | + | 26310.0i | 0.545207 | + | 1.09041i | ||||
\(836\) | −15984.0 | −0.661266 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5236.00i | 0.215841i | ||||||||
\(839\) | −5354.00 | −0.220311 | −0.110155 | − | 0.993914i | \(-0.535135\pi\) | ||||
−0.110155 | + | 0.993914i | \(0.535135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37612.0 | 1.54217 | ||||||||
\(842\) | − | 7390.00i | − | 0.302466i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16332.0 | 0.666079 | ||||||||
\(845\) | 4040.00 | − | 2020.00i | 0.164474 | − | 0.0822368i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 266.000i | − | 0.0107909i | ||||||
\(848\) | 96.0000i | 0.00388756i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6150.00 | + | 8200.00i | −0.248169 | + | 0.330891i | ||||
\(851\) | −23380.0 | −0.941782 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42890.0i | − | 1.72160i | −0.508943 | − | 0.860800i | \(-0.669963\pi\) | ||
0.508943 | − | 0.860800i | \(-0.330037\pi\) | |||||||
\(854\) | −13160.0 | −0.527314 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1152.00 | −0.0459983 | ||||||||
\(857\) | 22950.0i | 0.914769i | 0.889269 | + | 0.457385i | \(0.151214\pi\) | ||||
−0.889269 | + | 0.457385i | \(0.848786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2824.00 | 0.112170 | 0.0560848 | − | 0.998426i | \(-0.482138\pi\) | ||||
0.0560848 | + | 0.998426i | \(0.482138\pi\) | |||||||
\(860\) | −7520.00 | − | 15040.0i | −0.298174 | − | 0.596349i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 31558.0i | − | 1.24695i | ||||||
\(863\) | 4866.00i | 0.191936i | 0.995384 | + | 0.0959679i | \(0.0305946\pi\) | ||||
−0.995384 | + | 0.0959679i | \(0.969405\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11215.0 | − | 22430.0i | −0.440834 | − | 0.881668i | ||||
\(866\) | −14476.0 | −0.568031 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 3752.00i | − | 0.146718i | ||||||
\(869\) | 45843.0 | 1.78955 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5406.00 | 0.210305 | ||||||||
\(872\) | 13448.0i | 0.522255i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15120.0 | −0.585173 | ||||||||
\(875\) | 9625.00 | + | 1750.00i | 0.371868 | + | 0.0676123i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10676.0i | 0.411064i | 0.978650 | + | 0.205532i | \(0.0658924\pi\) | ||||
−0.978650 | + | 0.205532i | \(0.934108\pi\) | |||||||
\(878\) | 5292.00i | 0.203413i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5920.00 | + | 2960.00i | −0.226776 | + | 0.113388i | ||||
\(881\) | 29856.0 | 1.14174 | 0.570871 | − | 0.821040i | \(-0.306606\pi\) | ||||
0.570871 | + | 0.821040i | \(0.306606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1944.00i | − | 0.0740893i | −0.999314 | − | 0.0370446i | \(-0.988206\pi\) | ||
0.999314 | − | 0.0370446i | \(-0.0117944\pi\) | |||||||
\(884\) | 8364.00 | 0.318226 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11376.0 | 0.431359 | ||||||||
\(887\) | − | 14628.0i | − | 0.553732i | −0.960909 | − | 0.276866i | \(-0.910704\pi\) | ||
0.960909 | − | 0.276866i | \(-0.0892958\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3038.00 | −0.114613 | ||||||||
\(890\) | 2200.00 | + | 4400.00i | 0.0828586 | + | 0.165717i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 1508.00i | − | 0.0566049i | ||||||
\(893\) | − | 30996.0i | − | 1.16152i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −520.000 | + | 260.000i | −0.0194209 | + | 0.00971044i | ||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 6570.00i | − | 0.244147i | ||||||
\(899\) | 33366.0 | 1.23784 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −246.000 | −0.00909595 | ||||||||
\(902\) | − | 15244.0i | − | 0.562716i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6384.00 | −0.234877 | ||||||||
\(905\) | −24620.0 | + | 12310.0i | −0.904306 | + | 0.452153i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12858.0i | 0.470720i | 0.971908 | + | 0.235360i | \(0.0756269\pi\) | ||||
−0.971908 | + | 0.235360i | \(0.924373\pi\) | |||||||
\(908\) | 10204.0i | 0.372942i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3570.00 | − | 7140.00i | −0.130049 | − | 0.260097i | ||||
\(911\) | 18324.0 | 0.666412 | 0.333206 | − | 0.942854i | \(-0.391870\pi\) | ||||
0.333206 | + | 0.942854i | \(0.391870\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 15836.0i | − | 0.574036i | ||||||
\(914\) | 29668.0 | 1.07367 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 296.000 | 0.0106770 | ||||||||
\(917\) | − | 9030.00i | − | 0.325187i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14751.0 | 0.529478 | 0.264739 | − | 0.964320i | \(-0.414714\pi\) | ||||
0.264739 | + | 0.964320i | \(0.414714\pi\) | |||||||
\(920\) | −5600.00 | + | 2800.00i | −0.200681 | + | 0.100341i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19944.0i | 0.712387i | ||||||||
\(923\) | − | 23256.0i | − | 0.829340i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33400.0 | + | 25050.0i | 1.18723 | + | 0.890420i | ||||
\(926\) | 18192.0 | 0.645601 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 7968.00i | − | 0.281856i | ||||||
\(929\) | −47922.0 | −1.69243 | −0.846216 | − | 0.532840i | \(-0.821125\pi\) | ||||
−0.846216 | + | 0.532840i | \(0.821125\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5292.00 | −0.186292 | ||||||||
\(932\) | 7552.00i | 0.265423i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31734.0 | −1.11174 | ||||||||
\(935\) | −7585.00 | − | 15170.0i | −0.265301 | − | 0.530601i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44987.0i | 1.56848i | 0.620461 | + | 0.784238i | \(0.286946\pi\) | ||||
−0.620461 | + | 0.784238i | \(0.713054\pi\) | |||||||
\(938\) | − | 1484.00i | − | 0.0516571i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5740.00 | − | 11480.0i | −0.199168 | − | 0.398337i | ||||
\(941\) | 20356.0 | 0.705193 | 0.352597 | − | 0.935775i | \(-0.385299\pi\) | ||||
0.352597 | + | 0.935775i | \(0.385299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14420.0i | − | 0.497964i | ||||||
\(944\) | −32.0000 | −0.00110330 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27824.0 | 0.956275 | ||||||||
\(947\) | − | 27786.0i | − | 0.953457i | −0.879051 | − | 0.476728i | \(-0.841823\pi\) | ||
0.879051 | − | 0.476728i | \(-0.158177\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33150.0 | −1.13392 | ||||||||
\(950\) | 21600.0 | + | 16200.0i | 0.737681 | + | 0.553260i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 2296.00i | − | 0.0781657i | ||||||
\(953\) | 48674.0i | 1.65447i | 0.561859 | + | 0.827233i | \(0.310086\pi\) | ||||
−0.561859 | + | 0.827233i | \(0.689914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31590.0 | − | 15795.0i | 1.07040 | − | 0.535198i | ||||
\(956\) | −19988.0 | −0.676211 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 484.000i | 0.0163229i | ||||||||
\(959\) | 1344.00 | 0.0452555 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11835.0 | −0.397268 | ||||||||
\(962\) | − | 34068.0i | − | 1.14178i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15320.0 | 0.511851 | ||||||||
\(965\) | −10300.0 | − | 20600.0i | −0.343595 | − | 0.687189i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11168.0i | 0.371395i | 0.982607 | + | 0.185697i | \(0.0594544\pi\) | ||||
−0.982607 | + | 0.185697i | \(0.940546\pi\) | |||||||
\(968\) | − | 304.000i | − | 0.0100939i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21100.0 | − | 10550.0i | 0.698433 | − | 0.349217i | ||||
\(971\) | −20094.0 | −0.664106 | −0.332053 | − | 0.943261i | \(-0.607741\pi\) | ||||
−0.332053 | + | 0.943261i | \(0.607741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9814.00i | 0.323353i | ||||||||
\(974\) | −7116.00 | −0.234098 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15040.0 | −0.493257 | ||||||||
\(977\) | 49104.0i | 1.60796i | 0.594657 | + | 0.803980i | \(0.297288\pi\) | ||||
−0.594657 | + | 0.803980i | \(0.702712\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8140.00 | −0.265736 | ||||||||
\(980\) | −1960.00 | + | 980.000i | −0.0638877 | + | 0.0319438i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 2946.00i | − | 0.0957338i | ||||||
\(983\) | − | 27751.0i | − | 0.900427i | −0.892921 | − | 0.450213i | \(-0.851348\pi\) | ||
0.892921 | − | 0.450213i | \(-0.148652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8690.00 | − | 17380.0i | −0.281103 | − | 0.562206i | ||||
\(986\) | 20418.0 | 0.659474 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 22032.0i | − | 0.709445i | ||||||
\(989\) | 26320.0 | 0.846236 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37600.0 | 1.20525 | 0.602625 | − | 0.798024i | \(-0.294121\pi\) | ||||
0.602625 | + | 0.798024i | \(0.294121\pi\) | |||||||
\(992\) | − | 4288.00i | − | 0.137242i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6384.00 | −0.203710 | ||||||||
\(995\) | −8940.00 | + | 4470.00i | −0.284841 | + | 0.142421i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10911.0i | 0.346595i | 0.984870 | + | 0.173297i | \(0.0554422\pi\) | ||||
−0.984870 | + | 0.173297i | \(0.944558\pi\) | |||||||
\(998\) | − | 1206.00i | − | 0.0382518i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 630.4.g.a.379.2 | 2 | ||
3.2 | odd | 2 | 70.4.c.a.29.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 630.4.g.a.379.1 | 2 | ||
12.11 | even | 2 | 560.4.g.c.449.2 | 2 | |||
15.2 | even | 4 | 350.4.a.m.1.1 | 1 | |||
15.8 | even | 4 | 350.4.a.i.1.1 | 1 | |||
15.14 | odd | 2 | 70.4.c.a.29.2 | yes | 2 | ||
21.20 | even | 2 | 490.4.c.a.99.1 | 2 | |||
60.59 | even | 2 | 560.4.g.c.449.1 | 2 | |||
105.62 | odd | 4 | 2450.4.a.bn.1.1 | 1 | |||
105.83 | odd | 4 | 2450.4.a.c.1.1 | 1 | |||
105.104 | even | 2 | 490.4.c.a.99.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.c.a.29.1 | ✓ | 2 | 3.2 | odd | 2 | ||
70.4.c.a.29.2 | yes | 2 | 15.14 | odd | 2 | ||
350.4.a.i.1.1 | 1 | 15.8 | even | 4 | |||
350.4.a.m.1.1 | 1 | 15.2 | even | 4 | |||
490.4.c.a.99.1 | 2 | 21.20 | even | 2 | |||
490.4.c.a.99.2 | 2 | 105.104 | even | 2 | |||
560.4.g.c.449.1 | 2 | 60.59 | even | 2 | |||
560.4.g.c.449.2 | 2 | 12.11 | even | 2 | |||
630.4.g.a.379.1 | 2 | 5.4 | even | 2 | inner | ||
630.4.g.a.379.2 | 2 | 1.1 | even | 1 | trivial | ||
2450.4.a.c.1.1 | 1 | 105.83 | odd | 4 | |||
2450.4.a.bn.1.1 | 1 | 105.62 | odd | 4 |