Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,4,Mod(324,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.324");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.d (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: | \(19.1756207519\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 324.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.324 |
Dual form | 325.4.d.a.324.2 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.00000 | −1.06066 | −0.530330 | − | 0.847791i | \(-0.677932\pi\) | ||||
−0.530330 | + | 0.847791i | \(0.677932\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.192450i | −0.995360 | − | 0.0962250i | \(-0.969323\pi\) | ||
0.995360 | − | 0.0962250i | \(-0.0306768\pi\) | |||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.00000i | 0.204124i | ||||||||
\(7\) | 15.0000 | 0.809924 | 0.404962 | − | 0.914334i | \(-0.367285\pi\) | ||||
0.404962 | + | 0.914334i | \(0.367285\pi\) | |||||||
\(8\) | 21.0000 | 0.928078 | ||||||||
\(9\) | 26.0000 | 0.962963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 48.0000i | − | 1.31569i | −0.753155 | − | 0.657843i | \(-0.771469\pi\) | ||
0.753155 | − | 0.657843i | \(-0.228531\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.0240563i | ||||||
\(13\) | −39.0000 | + | 26.0000i | −0.832050 | + | 0.554700i | ||||
\(14\) | −45.0000 | −0.859054 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | 45.0000i | 0.642006i | 0.947078 | + | 0.321003i | \(0.104020\pi\) | ||||
−0.947078 | + | 0.321003i | \(0.895980\pi\) | |||||||
\(18\) | −78.0000 | −1.02138 | ||||||||
\(19\) | 6.00000i | 0.0724471i | 0.999344 | + | 0.0362235i | \(0.0115328\pi\) | ||||
−0.999344 | + | 0.0362235i | \(0.988467\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 15.0000i | − | 0.155870i | ||||||
\(22\) | 144.000i | 1.39550i | ||||||||
\(23\) | 162.000i | 1.46867i | 0.678789 | + | 0.734333i | \(0.262505\pi\) | ||||
−0.678789 | + | 0.734333i | \(0.737495\pi\) | |||||||
\(24\) | − | 21.0000i | − | 0.178609i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 117.000 | − | 78.0000i | 0.882523 | − | 0.588348i | ||||
\(27\) | − | 53.0000i | − | 0.377772i | ||||||
\(28\) | 15.0000 | 0.101240 | ||||||||
\(29\) | 144.000 | 0.922073 | 0.461037 | − | 0.887381i | \(-0.347478\pi\) | ||||
0.461037 | + | 0.887381i | \(0.347478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 264.000i | − | 1.52954i | −0.644302 | − | 0.764771i | \(-0.722852\pi\) | ||
0.644302 | − | 0.764771i | \(-0.277148\pi\) | |||||||
\(32\) | 45.0000 | 0.248592 | ||||||||
\(33\) | −48.0000 | −0.253204 | ||||||||
\(34\) | − | 135.000i | − | 0.680950i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 26.0000 | 0.120370 | ||||||||
\(37\) | 303.000 | 1.34629 | 0.673147 | − | 0.739509i | \(-0.264942\pi\) | ||||
0.673147 | + | 0.739509i | \(0.264942\pi\) | |||||||
\(38\) | − | 18.0000i | − | 0.0768417i | ||||||
\(39\) | 26.0000 | + | 39.0000i | 0.106752 | + | 0.160128i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 192.000i | 0.731350i | 0.930743 | + | 0.365675i | \(0.119162\pi\) | ||||
−0.930743 | + | 0.365675i | \(0.880838\pi\) | |||||||
\(42\) | 45.0000i | 0.165325i | ||||||||
\(43\) | − | 97.0000i | − | 0.344008i | −0.985096 | − | 0.172004i | \(-0.944976\pi\) | ||
0.985096 | − | 0.172004i | \(-0.0550243\pi\) | |||||||
\(44\) | − | 48.0000i | − | 0.164461i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 486.000i | − | 1.55776i | ||||||
\(47\) | 111.000 | 0.344490 | 0.172245 | − | 0.985054i | \(-0.444898\pi\) | ||||
0.172245 | + | 0.985054i | \(0.444898\pi\) | |||||||
\(48\) | 71.0000i | 0.213499i | ||||||||
\(49\) | −118.000 | −0.344023 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 45.0000 | 0.123554 | ||||||||
\(52\) | −39.0000 | + | 26.0000i | −0.104006 | + | 0.0693375i | ||||
\(53\) | − | 414.000i | − | 1.07297i | −0.843911 | − | 0.536484i | \(-0.819752\pi\) | ||
0.843911 | − | 0.536484i | \(-0.180248\pi\) | |||||||
\(54\) | 159.000i | 0.400688i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 315.000 | 0.751672 | ||||||||
\(57\) | 6.00000 | 0.0139424 | ||||||||
\(58\) | −432.000 | −0.978007 | ||||||||
\(59\) | − | 522.000i | − | 1.15184i | −0.817506 | − | 0.575920i | \(-0.804644\pi\) | ||
0.817506 | − | 0.575920i | \(-0.195356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 376.000 | 0.789211 | 0.394605 | − | 0.918851i | \(-0.370881\pi\) | ||||
0.394605 | + | 0.918851i | \(0.370881\pi\) | |||||||
\(62\) | 792.000i | 1.62232i | ||||||||
\(63\) | 390.000 | 0.779927 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 144.000 | 0.268563 | ||||||||
\(67\) | 36.0000 | 0.0656433 | 0.0328216 | − | 0.999461i | \(-0.489551\pi\) | ||||
0.0328216 | + | 0.999461i | \(0.489551\pi\) | |||||||
\(68\) | 45.0000i | 0.0802508i | ||||||||
\(69\) | 162.000 | 0.282645 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 357.000i | − | 0.596734i | −0.954451 | − | 0.298367i | \(-0.903558\pi\) | ||
0.954451 | − | 0.298367i | \(-0.0964419\pi\) | |||||||
\(72\) | 546.000 | 0.893704 | ||||||||
\(73\) | 1098.00 | 1.76043 | 0.880214 | − | 0.474578i | \(-0.157399\pi\) | ||||
0.880214 | + | 0.474578i | \(0.157399\pi\) | |||||||
\(74\) | −909.000 | −1.42796 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000i | 0.00905588i | ||||||||
\(77\) | − | 720.000i | − | 1.06561i | ||||||
\(78\) | −78.0000 | − | 117.000i | −0.113228 | − | 0.169842i | ||||
\(79\) | 830.000 | 1.18205 | 0.591027 | − | 0.806652i | \(-0.298723\pi\) | ||||
0.591027 | + | 0.806652i | \(0.298723\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | − | 576.000i | − | 0.775714i | ||||||
\(83\) | −438.000 | −0.579238 | −0.289619 | − | 0.957142i | \(-0.593529\pi\) | ||||
−0.289619 | + | 0.957142i | \(0.593529\pi\) | |||||||
\(84\) | − | 15.0000i | − | 0.0194837i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 291.000i | 0.364876i | ||||||||
\(87\) | − | 144.000i | − | 0.177453i | ||||||
\(88\) | − | 1008.00i | − | 1.22106i | ||||||
\(89\) | 438.000i | 0.521662i | 0.965384 | + | 0.260831i | \(0.0839965\pi\) | ||||
−0.965384 | + | 0.260831i | \(0.916003\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −585.000 | + | 390.000i | −0.673897 | + | 0.449265i | ||||
\(92\) | 162.000i | 0.183583i | ||||||||
\(93\) | −264.000 | −0.294360 | ||||||||
\(94\) | −333.000 | −0.365386 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 45.0000i | − | 0.0478416i | ||||||
\(97\) | 852.000 | 0.891830 | 0.445915 | − | 0.895075i | \(-0.352878\pi\) | ||||
0.445915 | + | 0.895075i | \(0.352878\pi\) | |||||||
\(98\) | 354.000 | 0.364892 | ||||||||
\(99\) | − | 1248.00i | − | 1.26696i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 396.000 | 0.390133 | 0.195067 | − | 0.980790i | \(-0.437508\pi\) | ||||
0.195067 | + | 0.980790i | \(0.437508\pi\) | |||||||
\(102\) | −135.000 | −0.131049 | ||||||||
\(103\) | 182.000i | 0.174107i | 0.996204 | + | 0.0870534i | \(0.0277451\pi\) | ||||
−0.996204 | + | 0.0870534i | \(0.972255\pi\) | |||||||
\(104\) | −819.000 | + | 546.000i | −0.772207 | + | 0.514805i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1242.00i | 1.13805i | ||||||||
\(107\) | 612.000i | 0.552937i | 0.961023 | + | 0.276469i | \(0.0891642\pi\) | ||||
−0.961023 | + | 0.276469i | \(0.910836\pi\) | |||||||
\(108\) | − | 53.0000i | − | 0.0472215i | ||||||
\(109\) | 1083.00i | 0.951675i | 0.879533 | + | 0.475838i | \(0.157855\pi\) | ||||
−0.879533 | + | 0.475838i | \(0.842145\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 303.000i | − | 0.259094i | ||||||
\(112\) | −1065.00 | −0.898509 | ||||||||
\(113\) | 90.0000i | 0.0749247i | 0.999298 | + | 0.0374623i | \(0.0119274\pi\) | ||||
−0.999298 | + | 0.0374623i | \(0.988073\pi\) | |||||||
\(114\) | −18.0000 | −0.0147882 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 144.000 | 0.115259 | ||||||||
\(117\) | −1014.00 | + | 676.000i | −0.801234 | + | 0.534156i | ||||
\(118\) | 1566.00i | 1.22171i | ||||||||
\(119\) | 675.000i | 0.519976i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −973.000 | −0.731029 | ||||||||
\(122\) | −1128.00 | −0.837085 | ||||||||
\(123\) | 192.000 | 0.140748 | ||||||||
\(124\) | − | 264.000i | − | 0.191193i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1170.00 | −0.827237 | ||||||||
\(127\) | − | 2086.00i | − | 1.45750i | −0.684780 | − | 0.728750i | \(-0.740102\pi\) | ||
0.684780 | − | 0.728750i | \(-0.259898\pi\) | |||||||
\(128\) | −1659.00 | −1.14560 | ||||||||
\(129\) | −97.0000 | −0.0662044 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1467.00 | −0.978415 | −0.489208 | − | 0.872167i | \(-0.662714\pi\) | ||||
−0.489208 | + | 0.872167i | \(0.662714\pi\) | |||||||
\(132\) | −48.0000 | −0.0316505 | ||||||||
\(133\) | 90.0000i | 0.0586766i | ||||||||
\(134\) | −108.000 | −0.0696252 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 945.000i | 0.595831i | ||||||||
\(137\) | −414.000 | −0.258178 | −0.129089 | − | 0.991633i | \(-0.541205\pi\) | ||||
−0.129089 | + | 0.991633i | \(0.541205\pi\) | |||||||
\(138\) | −486.000 | −0.299790 | ||||||||
\(139\) | 2419.00 | 1.47609 | 0.738046 | − | 0.674750i | \(-0.235749\pi\) | ||||
0.738046 | + | 0.674750i | \(0.235749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 111.000i | − | 0.0662971i | ||||||
\(142\) | 1071.00i | 0.632932i | ||||||||
\(143\) | 1248.00 | + | 1872.00i | 0.729811 | + | 1.09472i | ||||
\(144\) | −1846.00 | −1.06829 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3294.00 | −1.86721 | ||||||||
\(147\) | 118.000i | 0.0662073i | ||||||||
\(148\) | 303.000 | 0.168287 | ||||||||
\(149\) | − | 930.000i | − | 0.511333i | −0.966765 | − | 0.255666i | \(-0.917705\pi\) | ||
0.966765 | − | 0.255666i | \(-0.0822948\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1683.00i | − | 0.907024i | −0.891250 | − | 0.453512i | \(-0.850171\pi\) | ||
0.891250 | − | 0.453512i | \(-0.149829\pi\) | |||||||
\(152\) | 126.000i | 0.0672365i | ||||||||
\(153\) | 1170.00i | 0.618228i | ||||||||
\(154\) | 2160.00i | 1.13025i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 26.0000 | + | 39.0000i | 0.0133440 | + | 0.0200160i | ||||
\(157\) | − | 1874.00i | − | 0.952621i | −0.879277 | − | 0.476310i | \(-0.841974\pi\) | ||
0.879277 | − | 0.476310i | \(-0.158026\pi\) | |||||||
\(158\) | −2490.00 | −1.25376 | ||||||||
\(159\) | −414.000 | −0.206493 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2430.00i | 1.18951i | ||||||||
\(162\) | −1947.00 | −0.944264 | ||||||||
\(163\) | 1194.00 | 0.573750 | 0.286875 | − | 0.957968i | \(-0.407384\pi\) | ||||
0.286875 | + | 0.957968i | \(0.407384\pi\) | |||||||
\(164\) | 192.000i | 0.0914188i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1314.00 | 0.614375 | ||||||||
\(167\) | −2388.00 | −1.10652 | −0.553260 | − | 0.833008i | \(-0.686617\pi\) | ||||
−0.553260 | + | 0.833008i | \(0.686617\pi\) | |||||||
\(168\) | − | 315.000i | − | 0.144659i | ||||||
\(169\) | 845.000 | − | 2028.00i | 0.384615 | − | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 156.000i | 0.0697638i | ||||||||
\(172\) | − | 97.0000i | − | 0.0430011i | ||||||
\(173\) | − | 1566.00i | − | 0.688213i | −0.938931 | − | 0.344106i | \(-0.888182\pi\) | ||
0.938931 | − | 0.344106i | \(-0.111818\pi\) | |||||||
\(174\) | 432.000i | 0.188217i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3408.00i | 1.45959i | ||||||||
\(177\) | −522.000 | −0.221672 | ||||||||
\(178\) | − | 1314.00i | − | 0.553306i | ||||||
\(179\) | 657.000 | 0.274338 | 0.137169 | − | 0.990548i | \(-0.456200\pi\) | ||||
0.137169 | + | 0.990548i | \(0.456200\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1222.00 | −0.501826 | −0.250913 | − | 0.968010i | \(-0.580731\pi\) | ||||
−0.250913 | + | 0.968010i | \(0.580731\pi\) | |||||||
\(182\) | 1755.00 | − | 1170.00i | 0.714776 | − | 0.476517i | ||||
\(183\) | − | 376.000i | − | 0.151884i | ||||||
\(184\) | 3402.00i | 1.36304i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 792.000 | 0.312216 | ||||||||
\(187\) | 2160.00 | 0.844678 | ||||||||
\(188\) | 111.000 | 0.0430612 | ||||||||
\(189\) | − | 795.000i | − | 0.305967i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1260.00 | 0.477332 | 0.238666 | − | 0.971102i | \(-0.423290\pi\) | ||||
0.238666 | + | 0.971102i | \(0.423290\pi\) | |||||||
\(192\) | − | 433.000i | − | 0.162756i | ||||||
\(193\) | −342.000 | −0.127553 | −0.0637764 | − | 0.997964i | \(-0.520314\pi\) | ||||
−0.0637764 | + | 0.997964i | \(0.520314\pi\) | |||||||
\(194\) | −2556.00 | −0.945928 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −118.000 | −0.0430029 | ||||||||
\(197\) | −81.0000 | −0.0292945 | −0.0146472 | − | 0.999893i | \(-0.504663\pi\) | ||||
−0.0146472 | + | 0.999893i | \(0.504663\pi\) | |||||||
\(198\) | 3744.00i | 1.34381i | ||||||||
\(199\) | −1996.00 | −0.711019 | −0.355509 | − | 0.934673i | \(-0.615693\pi\) | ||||
−0.355509 | + | 0.934673i | \(0.615693\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 36.0000i | − | 0.0126331i | ||||||
\(202\) | −1188.00 | −0.413799 | ||||||||
\(203\) | 2160.00 | 0.746809 | ||||||||
\(204\) | 45.0000 | 0.0154443 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 546.000i | − | 0.184668i | ||||||
\(207\) | 4212.00i | 1.41427i | ||||||||
\(208\) | 2769.00 | − | 1846.00i | 0.923056 | − | 0.615371i | ||||
\(209\) | 288.000 | 0.0953176 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2833.00 | 0.924321 | 0.462161 | − | 0.886796i | \(-0.347074\pi\) | ||||
0.462161 | + | 0.886796i | \(0.347074\pi\) | |||||||
\(212\) | − | 414.000i | − | 0.134121i | ||||||
\(213\) | −357.000 | −0.114841 | ||||||||
\(214\) | − | 1836.00i | − | 0.586478i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1113.00i | − | 0.350602i | ||||||
\(217\) | − | 3960.00i | − | 1.23881i | ||||||
\(218\) | − | 3249.00i | − | 1.00940i | ||||||
\(219\) | − | 1098.00i | − | 0.338794i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1170.00 | − | 1755.00i | −0.356121 | − | 0.534181i | ||||
\(222\) | 909.000i | 0.274811i | ||||||||
\(223\) | −3507.00 | −1.05312 | −0.526561 | − | 0.850138i | \(-0.676519\pi\) | ||||
−0.526561 | + | 0.850138i | \(0.676519\pi\) | |||||||
\(224\) | 675.000 | 0.201341 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 270.000i | − | 0.0794696i | ||||||
\(227\) | 228.000 | 0.0666647 | 0.0333324 | − | 0.999444i | \(-0.489388\pi\) | ||||
0.0333324 | + | 0.999444i | \(0.489388\pi\) | |||||||
\(228\) | 6.00000 | 0.00174281 | ||||||||
\(229\) | − | 5493.00i | − | 1.58510i | −0.609808 | − | 0.792549i | \(-0.708753\pi\) | ||
0.609808 | − | 0.792549i | \(-0.291247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −720.000 | −0.205076 | ||||||||
\(232\) | 3024.00 | 0.855756 | ||||||||
\(233\) | 3627.00i | 1.01980i | 0.860235 | + | 0.509898i | \(0.170317\pi\) | ||||
−0.860235 | + | 0.509898i | \(0.829683\pi\) | |||||||
\(234\) | 3042.00 | − | 2028.00i | 0.849837 | − | 0.566558i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 522.000i | − | 0.143980i | ||||||
\(237\) | − | 830.000i | − | 0.227486i | ||||||
\(238\) | − | 2025.00i | − | 0.551518i | ||||||
\(239\) | 6075.00i | 1.64418i | 0.569357 | + | 0.822090i | \(0.307192\pi\) | ||||
−0.569357 | + | 0.822090i | \(0.692808\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 210.000i | 0.0561298i | 0.999606 | + | 0.0280649i | \(0.00893451\pi\) | ||||
−0.999606 | + | 0.0280649i | \(0.991065\pi\) | |||||||
\(242\) | 2919.00 | 0.775374 | ||||||||
\(243\) | − | 2080.00i | − | 0.549103i | ||||||
\(244\) | 376.000 | 0.0986514 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −576.000 | −0.149286 | ||||||||
\(247\) | −156.000 | − | 234.000i | −0.0401864 | − | 0.0602796i | ||||
\(248\) | − | 5544.00i | − | 1.41953i | ||||||
\(249\) | 438.000i | 0.111474i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7092.00 | 1.78344 | 0.891719 | − | 0.452589i | \(-0.149499\pi\) | ||||
0.891719 | + | 0.452589i | \(0.149499\pi\) | |||||||
\(252\) | 390.000 | 0.0974908 | ||||||||
\(253\) | 7776.00 | 1.93230 | ||||||||
\(254\) | 6258.00i | 1.54591i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | 5805.00i | 1.40897i | 0.709718 | + | 0.704486i | \(0.248823\pi\) | ||||
−0.709718 | + | 0.704486i | \(0.751177\pi\) | |||||||
\(258\) | 291.000 | 0.0702204 | ||||||||
\(259\) | 4545.00 | 1.09040 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3744.00 | 0.887923 | ||||||||
\(262\) | 4401.00 | 1.03777 | ||||||||
\(263\) | 792.000i | 0.185691i | 0.995681 | + | 0.0928457i | \(0.0295963\pi\) | ||||
−0.995681 | + | 0.0928457i | \(0.970404\pi\) | |||||||
\(264\) | −1008.00 | −0.234993 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 270.000i | − | 0.0622359i | ||||||
\(267\) | 438.000 | 0.100394 | ||||||||
\(268\) | 36.0000 | 0.00820541 | ||||||||
\(269\) | −5472.00 | −1.24027 | −0.620137 | − | 0.784493i | \(-0.712923\pi\) | ||||
−0.620137 | + | 0.784493i | \(0.712923\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2331.00i | 0.522502i | 0.965271 | + | 0.261251i | \(0.0841351\pi\) | ||||
−0.965271 | + | 0.261251i | \(0.915865\pi\) | |||||||
\(272\) | − | 3195.00i | − | 0.712225i | ||||||
\(273\) | 390.000 | + | 585.000i | 0.0864611 | + | 0.129692i | ||||
\(274\) | 1242.00 | 0.273839 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 162.000 | 0.0353306 | ||||||||
\(277\) | 1384.00i | 0.300204i | 0.988671 | + | 0.150102i | \(0.0479602\pi\) | ||||
−0.988671 | + | 0.150102i | \(0.952040\pi\) | |||||||
\(278\) | −7257.00 | −1.56563 | ||||||||
\(279\) | − | 6864.00i | − | 1.47289i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4062.00i | − | 0.862344i | −0.902270 | − | 0.431172i | \(-0.858100\pi\) | ||
0.902270 | − | 0.431172i | \(-0.141900\pi\) | |||||||
\(282\) | 333.000i | 0.0703187i | ||||||||
\(283\) | − | 3764.00i | − | 0.790624i | −0.918547 | − | 0.395312i | \(-0.870636\pi\) | ||
0.918547 | − | 0.395312i | \(-0.129364\pi\) | |||||||
\(284\) | − | 357.000i | − | 0.0745917i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3744.00 | − | 5616.00i | −0.774082 | − | 1.16112i | ||||
\(287\) | 2880.00i | 0.592338i | ||||||||
\(288\) | 1170.00 | 0.239385 | ||||||||
\(289\) | 2888.00 | 0.587828 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 852.000i | − | 0.171633i | ||||||
\(292\) | 1098.00 | 0.220053 | ||||||||
\(293\) | −4227.00 | −0.842812 | −0.421406 | − | 0.906872i | \(-0.638463\pi\) | ||||
−0.421406 | + | 0.906872i | \(0.638463\pi\) | |||||||
\(294\) | − | 354.000i | − | 0.0702235i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6363.00 | 1.24947 | ||||||||
\(297\) | −2544.00 | −0.497030 | ||||||||
\(298\) | 2790.00i | 0.542350i | ||||||||
\(299\) | −4212.00 | − | 6318.00i | −0.814670 | − | 1.22200i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1455.00i | − | 0.278621i | ||||||
\(302\) | 5049.00i | 0.962044i | ||||||||
\(303\) | − | 396.000i | − | 0.0750812i | ||||||
\(304\) | − | 426.000i | − | 0.0803710i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 3510.00i | − | 0.655730i | ||||||
\(307\) | 306.000 | 0.0568871 | 0.0284436 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284436 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(308\) | − | 720.000i | − | 0.133201i | ||||||
\(309\) | 182.000 | 0.0335069 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2106.00 | −0.383988 | −0.191994 | − | 0.981396i | \(-0.561495\pi\) | ||||
−0.191994 | + | 0.981396i | \(0.561495\pi\) | |||||||
\(312\) | 546.000 | + | 819.000i | 0.0990742 | + | 0.148611i | ||||
\(313\) | 10051.0i | 1.81507i | 0.419979 | + | 0.907534i | \(0.362037\pi\) | ||||
−0.419979 | + | 0.907534i | \(0.637963\pi\) | |||||||
\(314\) | 5622.00i | 1.01041i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 830.000 | 0.147757 | ||||||||
\(317\) | 2154.00 | 0.381643 | 0.190821 | − | 0.981625i | \(-0.438885\pi\) | ||||
0.190821 | + | 0.981625i | \(0.438885\pi\) | |||||||
\(318\) | 1242.00 | 0.219019 | ||||||||
\(319\) | − | 6912.00i | − | 1.21316i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 612.000 | 0.106413 | ||||||||
\(322\) | − | 7290.00i | − | 1.26166i | ||||||
\(323\) | −270.000 | −0.0465115 | ||||||||
\(324\) | 649.000 | 0.111283 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3582.00 | −0.608554 | ||||||||
\(327\) | 1083.00 | 0.183150 | ||||||||
\(328\) | 4032.00i | 0.678750i | ||||||||
\(329\) | 1665.00 | 0.279010 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10770.0i | − | 1.78844i | −0.447630 | − | 0.894219i | \(-0.647732\pi\) | ||
0.447630 | − | 0.894219i | \(-0.352268\pi\) | |||||||
\(332\) | −438.000 | −0.0724047 | ||||||||
\(333\) | 7878.00 | 1.29643 | ||||||||
\(334\) | 7164.00 | 1.17364 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1065.00i | 0.172918i | ||||||||
\(337\) | 2171.00i | 0.350926i | 0.984486 | + | 0.175463i | \(0.0561422\pi\) | ||||
−0.984486 | + | 0.175463i | \(0.943858\pi\) | |||||||
\(338\) | −2535.00 | + | 6084.00i | −0.407946 | + | 0.979071i | ||||
\(339\) | 90.0000 | 0.0144193 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12672.0 | −2.01240 | ||||||||
\(342\) | − | 468.000i | − | 0.0739957i | ||||||
\(343\) | −6915.00 | −1.08856 | ||||||||
\(344\) | − | 2037.00i | − | 0.319267i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4698.00i | 0.729960i | ||||||||
\(347\) | 7047.00i | 1.09021i | 0.838368 | + | 0.545105i | \(0.183510\pi\) | ||||
−0.838368 | + | 0.545105i | \(0.816490\pi\) | |||||||
\(348\) | − | 144.000i | − | 0.0221816i | ||||||
\(349\) | 6873.00i | 1.05416i | 0.849814 | + | 0.527082i | \(0.176714\pi\) | ||||
−0.849814 | + | 0.527082i | \(0.823286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1378.00 | + | 2067.00i | 0.209550 | + | 0.314326i | ||||
\(352\) | − | 2160.00i | − | 0.327069i | ||||||
\(353\) | −9318.00 | −1.40495 | −0.702475 | − | 0.711709i | \(-0.747922\pi\) | ||||
−0.702475 | + | 0.711709i | \(0.747922\pi\) | |||||||
\(354\) | 1566.00 | 0.235119 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 438.000i | 0.0652077i | ||||||||
\(357\) | 675.000 | 0.100069 | ||||||||
\(358\) | −1971.00 | −0.290979 | ||||||||
\(359\) | − | 4128.00i | − | 0.606873i | −0.952852 | − | 0.303437i | \(-0.901866\pi\) | ||
0.952852 | − | 0.303437i | \(-0.0981341\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6823.00 | 0.994751 | ||||||||
\(362\) | 3666.00 | 0.532267 | ||||||||
\(363\) | 973.000i | 0.140687i | ||||||||
\(364\) | −585.000 | + | 390.000i | −0.0842372 | + | 0.0561581i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1128.00i | 0.161097i | ||||||||
\(367\) | 2536.00i | 0.360703i | 0.983602 | + | 0.180352i | \(0.0577236\pi\) | ||||
−0.983602 | + | 0.180352i | \(0.942276\pi\) | |||||||
\(368\) | − | 11502.0i | − | 1.62930i | ||||||
\(369\) | 4992.00i | 0.704263i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6210.00i | − | 0.869022i | ||||||
\(372\) | −264.000 | −0.0367951 | ||||||||
\(373\) | − | 92.0000i | − | 0.0127710i | −0.999980 | − | 0.00638550i | \(-0.997967\pi\) | ||
0.999980 | − | 0.00638550i | \(-0.00203258\pi\) | |||||||
\(374\) | −6480.00 | −0.895917 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2331.00 | 0.319713 | ||||||||
\(377\) | −5616.00 | + | 3744.00i | −0.767211 | + | 0.511474i | ||||
\(378\) | 2385.00i | 0.324527i | ||||||||
\(379\) | 10182.0i | 1.37998i | 0.723817 | + | 0.689992i | \(0.242386\pi\) | ||||
−0.723817 | + | 0.689992i | \(0.757614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2086.00 | −0.280496 | ||||||||
\(382\) | −3780.00 | −0.506287 | ||||||||
\(383\) | −579.000 | −0.0772468 | −0.0386234 | − | 0.999254i | \(-0.512297\pi\) | ||||
−0.0386234 | + | 0.999254i | \(0.512297\pi\) | |||||||
\(384\) | 1659.00i | 0.220470i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1026.00 | 0.135290 | ||||||||
\(387\) | − | 2522.00i | − | 0.331267i | ||||||
\(388\) | 852.000 | 0.111479 | ||||||||
\(389\) | −2106.00 | −0.274495 | −0.137247 | − | 0.990537i | \(-0.543826\pi\) | ||||
−0.137247 | + | 0.990537i | \(0.543826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7290.00 | −0.942893 | ||||||||
\(392\) | −2478.00 | −0.319280 | ||||||||
\(393\) | 1467.00i | 0.188296i | ||||||||
\(394\) | 243.000 | 0.0310715 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − | 1248.00i | − | 0.158370i | ||||||
\(397\) | −1974.00 | −0.249552 | −0.124776 | − | 0.992185i | \(-0.539821\pi\) | ||||
−0.124776 | + | 0.992185i | \(0.539821\pi\) | |||||||
\(398\) | 5988.00 | 0.754149 | ||||||||
\(399\) | 90.0000 | 0.0112923 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11886.0i | 1.48020i | 0.672499 | + | 0.740098i | \(0.265221\pi\) | ||||
−0.672499 | + | 0.740098i | \(0.734779\pi\) | |||||||
\(402\) | 108.000i | 0.0133994i | ||||||||
\(403\) | 6864.00 | + | 10296.0i | 0.848437 | + | 1.27266i | ||||
\(404\) | 396.000 | 0.0487667 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6480.00 | −0.792111 | ||||||||
\(407\) | − | 14544.0i | − | 1.77130i | ||||||
\(408\) | 945.000 | 0.114668 | ||||||||
\(409\) | 1254.00i | 0.151605i | 0.997123 | + | 0.0758023i | \(0.0241518\pi\) | ||||
−0.997123 | + | 0.0758023i | \(0.975848\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 414.000i | 0.0496864i | ||||||||
\(412\) | 182.000i | 0.0217633i | ||||||||
\(413\) | − | 7830.00i | − | 0.932903i | ||||||
\(414\) | − | 12636.0i | − | 1.50006i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1755.00 | + | 1170.00i | −0.206841 | + | 0.137894i | ||||
\(417\) | − | 2419.00i | − | 0.284074i | ||||||
\(418\) | −864.000 | −0.101100 | ||||||||
\(419\) | −5823.00 | −0.678931 | −0.339466 | − | 0.940618i | \(-0.610246\pi\) | ||||
−0.339466 | + | 0.940618i | \(0.610246\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7341.00i | 0.849830i | 0.905233 | + | 0.424915i | \(0.139696\pi\) | ||||
−0.905233 | + | 0.424915i | \(0.860304\pi\) | |||||||
\(422\) | −8499.00 | −0.980391 | ||||||||
\(423\) | 2886.00 | 0.331731 | ||||||||
\(424\) | − | 8694.00i | − | 0.995797i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1071.00 | 0.121808 | ||||||||
\(427\) | 5640.00 | 0.639201 | ||||||||
\(428\) | 612.000i | 0.0691171i | ||||||||
\(429\) | 1872.00 | − | 1248.00i | 0.210678 | − | 0.140452i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7485.00i | 0.836519i | 0.908328 | + | 0.418260i | \(0.137360\pi\) | ||||
−0.908328 | + | 0.418260i | \(0.862640\pi\) | |||||||
\(432\) | 3763.00i | 0.419091i | ||||||||
\(433\) | − | 15203.0i | − | 1.68732i | −0.536878 | − | 0.843660i | \(-0.680396\pi\) | ||
0.536878 | − | 0.843660i | \(-0.319604\pi\) | |||||||
\(434\) | 11880.0i | 1.31396i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1083.00i | 0.118959i | ||||||||
\(437\) | −972.000 | −0.106401 | ||||||||
\(438\) | 3294.00i | 0.359346i | ||||||||
\(439\) | 1762.00 | 0.191562 | 0.0957809 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957809 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3068.00 | −0.331282 | ||||||||
\(442\) | 3510.00 | + | 5265.00i | 0.377723 | + | 0.566585i | ||||
\(443\) | − | 7317.00i | − | 0.784743i | −0.919807 | − | 0.392372i | \(-0.871655\pi\) | ||
0.919807 | − | 0.392372i | \(-0.128345\pi\) | |||||||
\(444\) | − | 303.000i | − | 0.0323868i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10521.0 | 1.11700 | ||||||||
\(447\) | −930.000 | −0.0984060 | ||||||||
\(448\) | 6495.00 | 0.684955 | ||||||||
\(449\) | 5016.00i | 0.527215i | 0.964630 | + | 0.263608i | \(0.0849124\pi\) | ||||
−0.964630 | + | 0.263608i | \(0.915088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9216.00 | 0.962227 | ||||||||
\(452\) | 90.0000i | 0.00936558i | ||||||||
\(453\) | −1683.00 | −0.174557 | ||||||||
\(454\) | −684.000 | −0.0707086 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 126.000 | 0.0129397 | ||||||||
\(457\) | −9870.00 | −1.01028 | −0.505141 | − | 0.863037i | \(-0.668560\pi\) | ||||
−0.505141 | + | 0.863037i | \(0.668560\pi\) | |||||||
\(458\) | 16479.0i | 1.68125i | ||||||||
\(459\) | 2385.00 | 0.242532 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14541.0i | 1.46907i | 0.678570 | + | 0.734536i | \(0.262600\pi\) | ||||
−0.678570 | + | 0.734536i | \(0.737400\pi\) | |||||||
\(462\) | 2160.00 | 0.217516 | ||||||||
\(463\) | 2112.00 | 0.211993 | 0.105997 | − | 0.994366i | \(-0.466197\pi\) | ||||
0.105997 | + | 0.994366i | \(0.466197\pi\) | |||||||
\(464\) | −10224.0 | −1.02293 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 10881.0i | − | 1.08166i | ||||||
\(467\) | − | 3276.00i | − | 0.324615i | −0.986740 | − | 0.162307i | \(-0.948106\pi\) | ||
0.986740 | − | 0.162307i | \(-0.0518936\pi\) | |||||||
\(468\) | −1014.00 | + | 676.000i | −0.100154 | + | 0.0667695i | ||||
\(469\) | 540.000 | 0.0531661 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1874.00 | −0.183332 | ||||||||
\(472\) | − | 10962.0i | − | 1.06900i | ||||||
\(473\) | −4656.00 | −0.452607 | ||||||||
\(474\) | 2490.00i | 0.241286i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 675.000i | 0.0649970i | ||||||||
\(477\) | − | 10764.0i | − | 1.03323i | ||||||
\(478\) | − | 18225.0i | − | 1.74392i | ||||||
\(479\) | 15453.0i | 1.47404i | 0.675870 | + | 0.737020i | \(0.263768\pi\) | ||||
−0.675870 | + | 0.737020i | \(0.736232\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11817.0 | + | 7878.00i | −1.12018 | + | 0.746790i | ||||
\(482\) | − | 630.000i | − | 0.0595347i | ||||||
\(483\) | 2430.00 | 0.228921 | ||||||||
\(484\) | −973.000 | −0.0913787 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6240.00i | 0.582412i | ||||||||
\(487\) | 3660.00 | 0.340555 | 0.170278 | − | 0.985396i | \(-0.445534\pi\) | ||||
0.170278 | + | 0.985396i | \(0.445534\pi\) | |||||||
\(488\) | 7896.00 | 0.732449 | ||||||||
\(489\) | − | 1194.00i | − | 0.110418i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 747.000 | 0.0686591 | 0.0343296 | − | 0.999411i | \(-0.489070\pi\) | ||||
0.0343296 | + | 0.999411i | \(0.489070\pi\) | |||||||
\(492\) | 192.000 | 0.0175936 | ||||||||
\(493\) | 6480.00i | 0.591977i | ||||||||
\(494\) | 468.000 | + | 702.000i | 0.0426241 | + | 0.0639362i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18744.0i | 1.69684i | ||||||||
\(497\) | − | 5355.00i | − | 0.483309i | ||||||
\(498\) | − | 1314.00i | − | 0.118236i | ||||||
\(499\) | − | 15804.0i | − | 1.41780i | −0.705307 | − | 0.708902i | \(-0.749191\pi\) | ||
0.705307 | − | 0.708902i | \(-0.250809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2388.00i | 0.212950i | ||||||||
\(502\) | −21276.0 | −1.89162 | ||||||||
\(503\) | − | 12078.0i | − | 1.07064i | −0.844650 | − | 0.535319i | \(-0.820191\pi\) | ||
0.844650 | − | 0.535319i | \(-0.179809\pi\) | |||||||
\(504\) | 8190.00 | 0.723833 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −23328.0 | −2.04952 | ||||||||
\(507\) | −2028.00 | − | 845.000i | −0.177646 | − | 0.0740193i | ||||
\(508\) | − | 2086.00i | − | 0.182188i | ||||||
\(509\) | 16110.0i | 1.40287i | 0.712731 | + | 0.701437i | \(0.247458\pi\) | ||||
−0.712731 | + | 0.701437i | \(0.752542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16470.0 | 1.42581 | ||||||||
\(512\) | 8733.00 | 0.753804 | ||||||||
\(513\) | 318.000 | 0.0273685 | ||||||||
\(514\) | − | 17415.0i | − | 1.49444i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −97.0000 | −0.00827556 | ||||||||
\(517\) | − | 5328.00i | − | 0.453240i | ||||||
\(518\) | −13635.0 | −1.15654 | ||||||||
\(519\) | −1566.00 | −0.132447 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3915.00 | 0.329212 | 0.164606 | − | 0.986359i | \(-0.447365\pi\) | ||||
0.164606 | + | 0.986359i | \(0.447365\pi\) | |||||||
\(522\) | −11232.0 | −0.941784 | ||||||||
\(523\) | 16184.0i | 1.35311i | 0.736392 | + | 0.676555i | \(0.236528\pi\) | ||||
−0.736392 | + | 0.676555i | \(0.763472\pi\) | |||||||
\(524\) | −1467.00 | −0.122302 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 2376.00i | − | 0.196955i | ||||||
\(527\) | 11880.0 | 0.981975 | ||||||||
\(528\) | 3408.00 | 0.280898 | ||||||||
\(529\) | −14077.0 | −1.15698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 13572.0i | − | 1.10918i | ||||||
\(532\) | 90.0000i | 0.00733458i | ||||||||
\(533\) | −4992.00 | − | 7488.00i | −0.405680 | − | 0.608520i | ||||
\(534\) | −1314.00 | −0.106484 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 756.000 | 0.0609221 | ||||||||
\(537\) | − | 657.000i | − | 0.0527964i | ||||||
\(538\) | 16416.0 | 1.31551 | ||||||||
\(539\) | 5664.00i | 0.452627i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 7923.00i | − | 0.629642i | −0.949151 | − | 0.314821i | \(-0.898055\pi\) | ||
0.949151 | − | 0.314821i | \(-0.101945\pi\) | |||||||
\(542\) | − | 6993.00i | − | 0.554198i | ||||||
\(543\) | 1222.00i | 0.0965765i | ||||||||
\(544\) | 2025.00i | 0.159598i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1170.00 | − | 1755.00i | −0.0917058 | − | 0.137559i | ||||
\(547\) | 14389.0i | 1.12473i | 0.826888 | + | 0.562367i | \(0.190109\pi\) | ||||
−0.826888 | + | 0.562367i | \(0.809891\pi\) | |||||||
\(548\) | −414.000 | −0.0322723 | ||||||||
\(549\) | 9776.00 | 0.759981 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 864.000i | 0.0668015i | ||||||||
\(552\) | 3402.00 | 0.262317 | ||||||||
\(553\) | 12450.0 | 0.957374 | ||||||||
\(554\) | − | 4152.00i | − | 0.318414i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2419.00 | 0.184512 | ||||||||
\(557\) | −10383.0 | −0.789842 | −0.394921 | − | 0.918715i | \(-0.629228\pi\) | ||||
−0.394921 | + | 0.918715i | \(0.629228\pi\) | |||||||
\(558\) | 20592.0i | 1.56224i | ||||||||
\(559\) | 2522.00 | + | 3783.00i | 0.190822 | + | 0.286232i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 2160.00i | − | 0.162558i | ||||||
\(562\) | 12186.0i | 0.914654i | ||||||||
\(563\) | − | 16425.0i | − | 1.22954i | −0.788706 | − | 0.614770i | \(-0.789249\pi\) | ||
0.788706 | − | 0.614770i | \(-0.210751\pi\) | |||||||
\(564\) | − | 111.000i | − | 0.00828713i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11292.0i | 0.838583i | ||||||||
\(567\) | 9735.00 | 0.721043 | ||||||||
\(568\) | − | 7497.00i | − | 0.553815i | ||||||
\(569\) | −12213.0 | −0.899817 | −0.449908 | − | 0.893075i | \(-0.648543\pi\) | ||||
−0.449908 | + | 0.893075i | \(0.648543\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6383.00 | −0.467811 | −0.233906 | − | 0.972259i | \(-0.575151\pi\) | ||||
−0.233906 | + | 0.972259i | \(0.575151\pi\) | |||||||
\(572\) | 1248.00 | + | 1872.00i | 0.0912264 | + | 0.136840i | ||||
\(573\) | − | 1260.00i | − | 0.0918626i | ||||||
\(574\) | − | 8640.00i | − | 0.628269i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 11258.0 | 0.814381 | ||||||||
\(577\) | −6426.00 | −0.463636 | −0.231818 | − | 0.972759i | \(-0.574467\pi\) | ||||
−0.231818 | + | 0.972759i | \(0.574467\pi\) | |||||||
\(578\) | −8664.00 | −0.623486 | ||||||||
\(579\) | 342.000i | 0.0245476i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6570.00 | −0.469139 | ||||||||
\(582\) | 2556.00i | 0.182044i | ||||||||
\(583\) | −19872.0 | −1.41169 | ||||||||
\(584\) | 23058.0 | 1.63381 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12681.0 | 0.893937 | ||||||||
\(587\) | 21330.0 | 1.49980 | 0.749901 | − | 0.661551i | \(-0.230101\pi\) | ||||
0.749901 | + | 0.661551i | \(0.230101\pi\) | |||||||
\(588\) | 118.000i | 0.00827591i | ||||||||
\(589\) | 1584.00 | 0.110811 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 81.0000i | 0.00563772i | ||||||||
\(592\) | −21513.0 | −1.49355 | ||||||||
\(593\) | −12084.0 | −0.836813 | −0.418407 | − | 0.908260i | \(-0.637411\pi\) | ||||
−0.418407 | + | 0.908260i | \(0.637411\pi\) | |||||||
\(594\) | 7632.00 | 0.527180 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 930.000i | − | 0.0639166i | ||||||
\(597\) | 1996.00i | 0.136836i | ||||||||
\(598\) | 12636.0 | + | 18954.0i | 0.864088 | + | 1.29613i | ||||
\(599\) | −2394.00 | −0.163299 | −0.0816496 | − | 0.996661i | \(-0.526019\pi\) | ||||
−0.0816496 | + | 0.996661i | \(0.526019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21971.0 | −1.49121 | −0.745604 | − | 0.666389i | \(-0.767839\pi\) | ||||
−0.745604 | + | 0.666389i | \(0.767839\pi\) | |||||||
\(602\) | 4365.00i | 0.295522i | ||||||||
\(603\) | 936.000 | 0.0632121 | ||||||||
\(604\) | − | 1683.00i | − | 0.113378i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1188.00i | 0.0796356i | ||||||||
\(607\) | 15406.0i | 1.03017i | 0.857141 | + | 0.515083i | \(0.172239\pi\) | ||||
−0.857141 | + | 0.515083i | \(0.827761\pi\) | |||||||
\(608\) | 270.000i | 0.0180098i | ||||||||
\(609\) | − | 2160.00i | − | 0.143724i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4329.00 | + | 2886.00i | −0.286633 | + | 0.191088i | ||||
\(612\) | 1170.00i | 0.0772785i | ||||||||
\(613\) | −9630.00 | −0.634506 | −0.317253 | − | 0.948341i | \(-0.602760\pi\) | ||||
−0.317253 | + | 0.948341i | \(0.602760\pi\) | |||||||
\(614\) | −918.000 | −0.0603379 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 15120.0i | − | 0.988965i | ||||||
\(617\) | −14748.0 | −0.962289 | −0.481144 | − | 0.876641i | \(-0.659779\pi\) | ||||
−0.481144 | + | 0.876641i | \(0.659779\pi\) | |||||||
\(618\) | −546.000 | −0.0355394 | ||||||||
\(619\) | 3672.00i | 0.238433i | 0.992868 | + | 0.119217i | \(0.0380383\pi\) | ||||
−0.992868 | + | 0.119217i | \(0.961962\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8586.00 | 0.554822 | ||||||||
\(622\) | 6318.00 | 0.407281 | ||||||||
\(623\) | 6570.00i | 0.422506i | ||||||||
\(624\) | −1846.00 | − | 2769.00i | −0.118428 | − | 0.177642i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 30153.0i | − | 1.92517i | ||||||
\(627\) | − | 288.000i | − | 0.0183439i | ||||||
\(628\) | − | 1874.00i | − | 0.119078i | ||||||
\(629\) | 13635.0i | 0.864329i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19875.0i | − | 1.25390i | −0.779059 | − | 0.626950i | \(-0.784303\pi\) | ||
0.779059 | − | 0.626950i | \(-0.215697\pi\) | |||||||
\(632\) | 17430.0 | 1.09704 | ||||||||
\(633\) | − | 2833.00i | − | 0.177886i | ||||||
\(634\) | −6462.00 | −0.404793 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −414.000 | −0.0258116 | ||||||||
\(637\) | 4602.00 | − | 3068.00i | 0.286245 | − | 0.190830i | ||||
\(638\) | 20736.0i | 1.28675i | ||||||||
\(639\) | − | 9282.00i | − | 0.574633i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1710.00 | 0.105368 | 0.0526840 | − | 0.998611i | \(-0.483222\pi\) | ||||
0.0526840 | + | 0.998611i | \(0.483222\pi\) | |||||||
\(642\) | −1836.00 | −0.112868 | ||||||||
\(643\) | −16452.0 | −1.00903 | −0.504513 | − | 0.863404i | \(-0.668328\pi\) | ||||
−0.504513 | + | 0.863404i | \(0.668328\pi\) | |||||||
\(644\) | 2430.00i | 0.148689i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 810.000 | 0.0493329 | ||||||||
\(647\) | − | 25902.0i | − | 1.57390i | −0.617017 | − | 0.786950i | \(-0.711659\pi\) | ||
0.617017 | − | 0.786950i | \(-0.288341\pi\) | |||||||
\(648\) | 13629.0 | 0.826231 | ||||||||
\(649\) | −25056.0 | −1.51546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3960.00 | −0.238410 | ||||||||
\(652\) | 1194.00 | 0.0717188 | ||||||||
\(653\) | 18108.0i | 1.08518i | 0.839999 | + | 0.542589i | \(0.182556\pi\) | ||||
−0.839999 | + | 0.542589i | \(0.817444\pi\) | |||||||
\(654\) | −3249.00 | −0.194260 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 13632.0i | − | 0.811342i | ||||||
\(657\) | 28548.0 | 1.69523 | ||||||||
\(658\) | −4995.00 | −0.295935 | ||||||||
\(659\) | 32904.0 | 1.94500 | 0.972502 | − | 0.232894i | \(-0.0748195\pi\) | ||||
0.972502 | + | 0.232894i | \(0.0748195\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15318.0i | 0.901363i | 0.892685 | + | 0.450682i | \(0.148819\pi\) | ||||
−0.892685 | + | 0.450682i | \(0.851181\pi\) | |||||||
\(662\) | 32310.0i | 1.89692i | ||||||||
\(663\) | −1755.00 | + | 1170.00i | −0.102803 | + | 0.0685355i | ||||
\(664\) | −9198.00 | −0.537578 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23634.0 | −1.37507 | ||||||||
\(667\) | 23328.0i | 1.35422i | ||||||||
\(668\) | −2388.00 | −0.138315 | ||||||||
\(669\) | 3507.00i | 0.202673i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 18048.0i | − | 1.03835i | ||||||
\(672\) | − | 675.000i | − | 0.0387481i | ||||||
\(673\) | − | 7729.00i | − | 0.442691i | −0.975195 | − | 0.221346i | \(-0.928955\pi\) | ||
0.975195 | − | 0.221346i | \(-0.0710449\pi\) | |||||||
\(674\) | − | 6513.00i | − | 0.372213i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 845.000 | − | 2028.00i | 0.0480769 | − | 0.115385i | ||||
\(677\) | − | 19242.0i | − | 1.09236i | −0.837667 | − | 0.546182i | \(-0.816081\pi\) | ||
0.837667 | − | 0.546182i | \(-0.183919\pi\) | |||||||
\(678\) | −270.000 | −0.0152939 | ||||||||
\(679\) | 12780.0 | 0.722314 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 228.000i | − | 0.0128296i | ||||||
\(682\) | 38016.0 | 2.13447 | ||||||||
\(683\) | −22518.0 | −1.26153 | −0.630767 | − | 0.775973i | \(-0.717260\pi\) | ||||
−0.630767 | + | 0.775973i | \(0.717260\pi\) | |||||||
\(684\) | 156.000i | 0.00872048i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20745.0 | 1.15459 | ||||||||
\(687\) | −5493.00 | −0.305052 | ||||||||
\(688\) | 6887.00i | 0.381634i | ||||||||
\(689\) | 10764.0 | + | 16146.0i | 0.595175 | + | 0.892763i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9168.00i | − | 0.504728i | −0.967632 | − | 0.252364i | \(-0.918792\pi\) | ||
0.967632 | − | 0.252364i | \(-0.0812081\pi\) | |||||||
\(692\) | − | 1566.00i | − | 0.0860266i | ||||||
\(693\) | − | 18720.0i | − | 1.02614i | ||||||
\(694\) | − | 21141.0i | − | 1.15634i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 3024.00i | − | 0.164690i | ||||||
\(697\) | −8640.00 | −0.469531 | ||||||||
\(698\) | − | 20619.0i | − | 1.11811i | ||||||
\(699\) | 3627.00 | 0.196260 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1170.00 | 0.0630389 | 0.0315195 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315195 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(702\) | −4134.00 | − | 6201.00i | −0.222262 | − | 0.333393i | ||||
\(703\) | 1818.00i | 0.0975351i | ||||||||
\(704\) | − | 20784.0i | − | 1.11268i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27954.0 | 1.49017 | ||||||||
\(707\) | 5940.00 | 0.315978 | ||||||||
\(708\) | −522.000 | −0.0277090 | ||||||||
\(709\) | 1662.00i | 0.0880363i | 0.999031 | + | 0.0440181i | \(0.0140159\pi\) | ||||
−0.999031 | + | 0.0440181i | \(0.985984\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21580.0 | 1.13827 | ||||||||
\(712\) | 9198.00i | 0.484143i | ||||||||
\(713\) | 42768.0 | 2.24639 | ||||||||
\(714\) | −2025.00 | −0.106140 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 657.000 | 0.0342922 | ||||||||
\(717\) | 6075.00 | 0.316423 | ||||||||
\(718\) | 12384.0i | 0.643686i | ||||||||
\(719\) | −30960.0 | −1.60586 | −0.802930 | − | 0.596073i | \(-0.796727\pi\) | ||||
−0.802930 | + | 0.596073i | \(0.796727\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2730.00i | 0.141013i | ||||||||
\(722\) | −20469.0 | −1.05509 | ||||||||
\(723\) | 210.000 | 0.0108022 | ||||||||
\(724\) | −1222.00 | −0.0627283 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 2919.00i | − | 0.149221i | ||||||
\(727\) | 8372.00i | 0.427098i | 0.976932 | + | 0.213549i | \(0.0685023\pi\) | ||||
−0.976932 | + | 0.213549i | \(0.931498\pi\) | |||||||
\(728\) | −12285.0 | + | 8190.00i | −0.625429 | + | 0.416953i | ||||
\(729\) | 15443.0 | 0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4365.00 | 0.220855 | ||||||||
\(732\) | − | 376.000i | − | 0.0189855i | ||||||
\(733\) | −2739.00 | −0.138018 | −0.0690091 | − | 0.997616i | \(-0.521984\pi\) | ||||
−0.0690091 | + | 0.997616i | \(0.521984\pi\) | |||||||
\(734\) | − | 7608.00i | − | 0.382584i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7290.00i | 0.365099i | ||||||||
\(737\) | − | 1728.00i | − | 0.0863659i | ||||||
\(738\) | − | 14976.0i | − | 0.746984i | ||||||
\(739\) | 6756.00i | 0.336297i | 0.985762 | + | 0.168148i | \(0.0537788\pi\) | ||||
−0.985762 | + | 0.168148i | \(0.946221\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −234.000 | + | 156.000i | −0.0116008 | + | 0.00773388i | ||||
\(742\) | 18630.0i | 0.921737i | ||||||||
\(743\) | 29643.0 | 1.46366 | 0.731828 | − | 0.681490i | \(-0.238668\pi\) | ||||
0.731828 | + | 0.681490i | \(0.238668\pi\) | |||||||
\(744\) | −5544.00 | −0.273189 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 276.000i | 0.0135457i | ||||||||
\(747\) | −11388.0 | −0.557785 | ||||||||
\(748\) | 2160.00 | 0.105585 | ||||||||
\(749\) | 9180.00i | 0.447837i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18128.0 | 0.880826 | 0.440413 | − | 0.897795i | \(-0.354832\pi\) | ||||
0.440413 | + | 0.897795i | \(0.354832\pi\) | |||||||
\(752\) | −7881.00 | −0.382168 | ||||||||
\(753\) | − | 7092.00i | − | 0.343223i | ||||||
\(754\) | 16848.0 | − | 11232.0i | 0.813751 | − | 0.542500i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 795.000i | − | 0.0382459i | ||||||
\(757\) | 6410.00i | 0.307761i | 0.988089 | + | 0.153881i | \(0.0491772\pi\) | ||||
−0.988089 | + | 0.153881i | \(0.950823\pi\) | |||||||
\(758\) | − | 30546.0i | − | 1.46369i | ||||||
\(759\) | − | 7776.00i | − | 0.371872i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28290.0i | 1.34758i | 0.738921 | + | 0.673792i | \(0.235336\pi\) | ||||
−0.738921 | + | 0.673792i | \(0.764664\pi\) | |||||||
\(762\) | 6258.00 | 0.297511 | ||||||||
\(763\) | 16245.0i | 0.770784i | ||||||||
\(764\) | 1260.00 | 0.0596665 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1737.00 | 0.0819326 | ||||||||
\(767\) | 13572.0 | + | 20358.0i | 0.638926 | + | 0.958390i | ||||
\(768\) | − | 1513.00i | − | 0.0710881i | ||||||
\(769\) | − | 27960.0i | − | 1.31114i | −0.755136 | − | 0.655568i | \(-0.772429\pi\) | ||
0.755136 | − | 0.655568i | \(-0.227571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5805.00 | 0.271157 | ||||||||
\(772\) | −342.000 | −0.0159441 | ||||||||
\(773\) | −5649.00 | −0.262847 | −0.131423 | − | 0.991326i | \(-0.541955\pi\) | ||||
−0.131423 | + | 0.991326i | \(0.541955\pi\) | |||||||
\(774\) | 7566.00i | 0.351362i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17892.0 | 0.827687 | ||||||||
\(777\) | − | 4545.00i | − | 0.209847i | ||||||
\(778\) | 6318.00 | 0.291146 | ||||||||
\(779\) | −1152.00 | −0.0529842 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17136.0 | −0.785114 | ||||||||
\(782\) | 21870.0 | 1.00009 | ||||||||
\(783\) | − | 7632.00i | − | 0.348334i | ||||||
\(784\) | 8378.00 | 0.381651 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 4401.00i | − | 0.199718i | ||||||
\(787\) | 756.000 | 0.0342420 | 0.0171210 | − | 0.999853i | \(-0.494550\pi\) | ||||
0.0171210 | + | 0.999853i | \(0.494550\pi\) | |||||||
\(788\) | −81.0000 | −0.00366181 | ||||||||
\(789\) | 792.000 | 0.0357363 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1350.00i | 0.0606833i | ||||||||
\(792\) | − | 26208.0i | − | 1.17583i | ||||||
\(793\) | −14664.0 | + | 9776.00i | −0.656663 | + | 0.437775i | ||||
\(794\) | 5922.00 | 0.264690 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1996.00 | −0.0888773 | ||||||||
\(797\) | − | 31194.0i | − | 1.38638i | −0.720753 | − | 0.693192i | \(-0.756204\pi\) | ||
0.720753 | − | 0.693192i | \(-0.243796\pi\) | |||||||
\(798\) | −270.000 | −0.0119773 | ||||||||
\(799\) | 4995.00i | 0.221164i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11388.0i | 0.502341i | ||||||||
\(802\) | − | 35658.0i | − | 1.56998i | ||||||
\(803\) | − | 52704.0i | − | 2.31617i | ||||||
\(804\) | − | 36.0000i | − | 0.00157913i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20592.0 | − | 30888.0i | −0.899904 | − | 1.34986i | ||||
\(807\) | 5472.00i | 0.238691i | ||||||||
\(808\) | 8316.00 | 0.362074 | ||||||||
\(809\) | −17055.0 | −0.741189 | −0.370594 | − | 0.928795i | \(-0.620846\pi\) | ||||
−0.370594 | + | 0.928795i | \(0.620846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35520.0i | − | 1.53795i | −0.639280 | − | 0.768974i | \(-0.720768\pi\) | ||
0.639280 | − | 0.768974i | \(-0.279232\pi\) | |||||||
\(812\) | 2160.00 | 0.0933512 | ||||||||
\(813\) | 2331.00 | 0.100556 | ||||||||
\(814\) | 43632.0i | 1.87875i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3195.00 | −0.137068 | ||||||||
\(817\) | 582.000 | 0.0249224 | ||||||||
\(818\) | − | 3762.00i | − | 0.160801i | ||||||
\(819\) | −15210.0 | + | 10140.0i | −0.648938 | + | 0.432625i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1095.00i | − | 0.0465478i | −0.999729 | − | 0.0232739i | \(-0.992591\pi\) | ||
0.999729 | − | 0.0232739i | \(-0.00740899\pi\) | |||||||
\(822\) | − | 1242.00i | − | 0.0527004i | ||||||
\(823\) | − | 2554.00i | − | 0.108174i | −0.998536 | − | 0.0540868i | \(-0.982775\pi\) | ||
0.998536 | − | 0.0540868i | \(-0.0172248\pi\) | |||||||
\(824\) | 3822.00i | 0.161585i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23490.0i | 0.989494i | ||||||||
\(827\) | 21522.0 | 0.904950 | 0.452475 | − | 0.891777i | \(-0.350541\pi\) | ||||
0.452475 | + | 0.891777i | \(0.350541\pi\) | |||||||
\(828\) | 4212.00i | 0.176784i | ||||||||
\(829\) | 13124.0 | 0.549838 | 0.274919 | − | 0.961467i | \(-0.411349\pi\) | ||||
0.274919 | + | 0.961467i | \(0.411349\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1384.00 | 0.0577743 | ||||||||
\(832\) | −16887.0 | + | 11258.0i | −0.703668 | + | 0.469112i | ||||
\(833\) | − | 5310.00i | − | 0.220865i | ||||||
\(834\) | 7257.00i | 0.301306i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 288.000 | 0.0119147 | ||||||||
\(837\) | −13992.0 | −0.577819 | ||||||||
\(838\) | 17469.0 | 0.720115 | ||||||||
\(839\) | 23424.0i | 0.963869i | 0.876207 | + | 0.481935i | \(0.160066\pi\) | ||||
−0.876207 | + | 0.481935i | \(0.839934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3653.00 | −0.149781 | ||||||||
\(842\) | − | 22023.0i | − | 0.901381i | ||||||
\(843\) | −4062.00 | −0.165958 | ||||||||
\(844\) | 2833.00 | 0.115540 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8658.00 | −0.351854 | ||||||||
\(847\) | −14595.0 | −0.592078 | ||||||||
\(848\) | 29394.0i | 1.19032i | ||||||||
\(849\) | −3764.00 | −0.152156 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49086.0i | 1.97726i | ||||||||
\(852\) | −357.000 | −0.0143552 | ||||||||
\(853\) | −31077.0 | −1.24743 | −0.623714 | − | 0.781653i | \(-0.714377\pi\) | ||||
−0.623714 | + | 0.781653i | \(0.714377\pi\) | |||||||
\(854\) | −16920.0 | −0.677975 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12852.0i | 0.513169i | ||||||||
\(857\) | 19422.0i | 0.774146i | 0.922049 | + | 0.387073i | \(0.126514\pi\) | ||||
−0.922049 | + | 0.387073i | \(0.873486\pi\) | |||||||
\(858\) | −5616.00 | + | 3744.00i | −0.223458 | + | 0.148972i | ||||
\(859\) | −1744.00 | −0.0692718 | −0.0346359 | − | 0.999400i | \(-0.511027\pi\) | ||||
−0.0346359 | + | 0.999400i | \(0.511027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2880.00 | 0.113996 | ||||||||
\(862\) | − | 22455.0i | − | 0.887263i | ||||||
\(863\) | 19179.0 | 0.756501 | 0.378251 | − | 0.925703i | \(-0.376526\pi\) | ||||
0.378251 | + | 0.925703i | \(0.376526\pi\) | |||||||
\(864\) | − | 2385.00i | − | 0.0939113i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 45609.0i | 1.78967i | ||||||||
\(867\) | − | 2888.00i | − | 0.113128i | ||||||
\(868\) | − | 3960.00i | − | 0.154852i | ||||||
\(869\) | − | 39840.0i | − | 1.55521i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1404.00 | + | 936.000i | −0.0546185 | + | 0.0364123i | ||||
\(872\) | 22743.0i | 0.883228i | ||||||||
\(873\) | 22152.0 | 0.858799 | ||||||||
\(874\) | 2916.00 | 0.112855 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 1098.00i | − | 0.0423493i | ||||||
\(877\) | −29217.0 | −1.12496 | −0.562479 | − | 0.826812i | \(-0.690152\pi\) | ||||
−0.562479 | + | 0.826812i | \(0.690152\pi\) | |||||||
\(878\) | −5286.00 | −0.203182 | ||||||||
\(879\) | 4227.00i | 0.162199i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15633.0 | −0.597831 | −0.298916 | − | 0.954280i | \(-0.596625\pi\) | ||||
−0.298916 | + | 0.954280i | \(0.596625\pi\) | |||||||
\(882\) | 9204.00 | 0.351377 | ||||||||
\(883\) | 30589.0i | 1.16580i | 0.812544 | + | 0.582900i | \(0.198082\pi\) | ||||
−0.812544 | + | 0.582900i | \(0.801918\pi\) | |||||||
\(884\) | −1170.00 | − | 1755.00i | −0.0445151 | − | 0.0667727i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21951.0i | 0.832346i | ||||||||
\(887\) | 25884.0i | 0.979819i | 0.871773 | + | 0.489910i | \(0.162970\pi\) | ||||
−0.871773 | + | 0.489910i | \(0.837030\pi\) | |||||||
\(888\) | − | 6363.00i | − | 0.240460i | ||||||
\(889\) | − | 31290.0i | − | 1.18046i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 31152.0i | − | 1.17130i | ||||||
\(892\) | −3507.00 | −0.131640 | ||||||||
\(893\) | 666.000i | 0.0249573i | ||||||||
\(894\) | 2790.00 | 0.104375 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −24885.0 | −0.927845 | ||||||||
\(897\) | −6318.00 | + | 4212.00i | −0.235175 | + | 0.156783i | ||||
\(898\) | − | 15048.0i | − | 0.559196i | ||||||
\(899\) | − | 38016.0i | − | 1.41035i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18630.0 | 0.688852 | ||||||||
\(902\) | −27648.0 | −1.02060 | ||||||||
\(903\) | −1455.00 | −0.0536206 | ||||||||
\(904\) | 1890.00i | 0.0695359i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5049.00 | 0.185145 | ||||||||
\(907\) | 12305.0i | 0.450475i | 0.974304 | + | 0.225237i | \(0.0723158\pi\) | ||||
−0.974304 | + | 0.225237i | \(0.927684\pi\) | |||||||
\(908\) | 228.000 | 0.00833309 | ||||||||
\(909\) | 10296.0 | 0.375684 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29772.0 | 1.08276 | 0.541378 | − | 0.840779i | \(-0.317903\pi\) | ||||
0.541378 | + | 0.840779i | \(0.317903\pi\) | |||||||
\(912\) | −426.000 | −0.0154674 | ||||||||
\(913\) | 21024.0i | 0.762095i | ||||||||
\(914\) | 29610.0 | 1.07157 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 5493.00i | − | 0.198137i | ||||||
\(917\) | −22005.0 | −0.792442 | ||||||||
\(918\) | −7155.00 | −0.257244 | ||||||||
\(919\) | −47644.0 | −1.71015 | −0.855076 | − | 0.518502i | \(-0.826490\pi\) | ||||
−0.855076 | + | 0.518502i | \(0.826490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 306.000i | − | 0.0109479i | ||||||
\(922\) | − | 43623.0i | − | 1.55819i | ||||||
\(923\) | 9282.00 | + | 13923.0i | 0.331008 | + | 0.496513i | ||||
\(924\) | −720.000 | −0.0256345 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6336.00 | −0.224853 | ||||||||
\(927\) | 4732.00i | 0.167658i | ||||||||
\(928\) | 6480.00 | 0.229220 | ||||||||
\(929\) | 21924.0i | 0.774277i | 0.922022 | + | 0.387138i | \(0.126536\pi\) | ||||
−0.922022 | + | 0.387138i | \(0.873464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 708.000i | − | 0.0249235i | ||||||
\(932\) | 3627.00i | 0.127475i | ||||||||
\(933\) | 2106.00i | 0.0738985i | ||||||||
\(934\) | 9828.00i | 0.344306i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −21294.0 | + | 14196.0i | −0.743607 | + | 0.495738i | ||||
\(937\) | − | 32398.0i | − | 1.12956i | −0.825242 | − | 0.564779i | \(-0.808961\pi\) | ||
0.825242 | − | 0.564779i | \(-0.191039\pi\) | |||||||
\(938\) | −1620.00 | −0.0563911 | ||||||||
\(939\) | 10051.0 | 0.349310 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2097.00i | − | 0.0726464i | −0.999340 | − | 0.0363232i | \(-0.988435\pi\) | ||
0.999340 | − | 0.0363232i | \(-0.0115646\pi\) | |||||||
\(942\) | 5622.00 | 0.194453 | ||||||||
\(943\) | −31104.0 | −1.07411 | ||||||||
\(944\) | 37062.0i | 1.27782i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13968.0 | 0.480062 | ||||||||
\(947\) | −20016.0 | −0.686835 | −0.343417 | − | 0.939183i | \(-0.611585\pi\) | ||||
−0.343417 | + | 0.939183i | \(0.611585\pi\) | |||||||
\(948\) | − | 830.000i | − | 0.0284358i | ||||||
\(949\) | −42822.0 | + | 28548.0i | −1.46476 | + | 0.976509i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2154.00i | − | 0.0734471i | ||||||
\(952\) | 14175.0i | 0.482578i | ||||||||
\(953\) | 24993.0i | 0.849531i | 0.905304 | + | 0.424765i | \(0.139643\pi\) | ||||
−0.905304 | + | 0.424765i | \(0.860357\pi\) | |||||||
\(954\) | 32292.0i | 1.09590i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6075.00i | 0.205523i | ||||||||
\(957\) | −6912.00 | −0.233473 | ||||||||
\(958\) | − | 46359.0i | − | 1.56346i | ||||||
\(959\) | −6210.00 | −0.209105 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39905.0 | −1.33950 | ||||||||
\(962\) | 35451.0 | − | 23634.0i | 1.18814 | − | 0.792090i | ||||
\(963\) | 15912.0i | 0.532458i | ||||||||
\(964\) | 210.000i | 0.00701623i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7290.00 | −0.242807 | ||||||||
\(967\) | 40959.0 | 1.36210 | 0.681051 | − | 0.732236i | \(-0.261523\pi\) | ||||
0.681051 | + | 0.732236i | \(0.261523\pi\) | |||||||
\(968\) | −20433.0 | −0.678452 | ||||||||
\(969\) | 270.000i | 0.00895113i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48933.0 | −1.61723 | −0.808617 | − | 0.588335i | \(-0.799784\pi\) | ||||
−0.808617 | + | 0.588335i | \(0.799784\pi\) | |||||||
\(972\) | − | 2080.00i | − | 0.0686379i | ||||||
\(973\) | 36285.0 | 1.19552 | ||||||||
\(974\) | −10980.0 | −0.361213 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26696.0 | −0.875531 | ||||||||
\(977\) | −47388.0 | −1.55177 | −0.775884 | − | 0.630876i | \(-0.782696\pi\) | ||||
−0.775884 | + | 0.630876i | \(0.782696\pi\) | |||||||
\(978\) | 3582.00i | 0.117116i | ||||||||
\(979\) | 21024.0 | 0.686343 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28158.0i | 0.916428i | ||||||||
\(982\) | −2241.00 | −0.0728240 | ||||||||
\(983\) | −16803.0 | −0.545201 | −0.272600 | − | 0.962127i | \(-0.587884\pi\) | ||||
−0.272600 | + | 0.962127i | \(0.587884\pi\) | |||||||
\(984\) | 4032.00 | 0.130625 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 19440.0i | − | 0.627886i | ||||||
\(987\) | − | 1665.00i | − | 0.0536956i | ||||||
\(988\) | −156.000 | − | 234.000i | −0.00502330 | − | 0.00753495i | ||||
\(989\) | 15714.0 | 0.505234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57526.0 | −1.84397 | −0.921985 | − | 0.387226i | \(-0.873433\pi\) | ||||
−0.921985 | + | 0.387226i | \(0.873433\pi\) | |||||||
\(992\) | − | 11880.0i | − | 0.380232i | ||||||
\(993\) | −10770.0 | −0.344185 | ||||||||
\(994\) | 16065.0i | 0.512627i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 438.000i | 0.0139343i | ||||||||
\(997\) | 25000.0i | 0.794140i | 0.917788 | + | 0.397070i | \(0.129973\pi\) | ||||
−0.917788 | + | 0.397070i | \(0.870027\pi\) | |||||||
\(998\) | 47412.0i | 1.50381i | ||||||||
\(999\) | − | 16059.0i | − | 0.508593i |
(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 | 325.4.d.a.324.1 | 2 | ||
5.2 | odd | 4 | 13.4.b.a.12.1 | ✓ | 2 | ||
5.3 | odd | 4 | 325.4.c.b.51.2 | 2 | |||
5.4 | even | 2 | 325.4.d.b.324.2 | 2 | |||
13.12 | even | 2 | 325.4.d.b.324.1 | 2 | |||
15.2 | even | 4 | 117.4.b.a.64.2 | 2 | |||
20.7 | even | 4 | 208.4.f.b.129.2 | 2 | |||
40.27 | even | 4 | 832.4.f.c.129.1 | 2 | |||
40.37 | odd | 4 | 832.4.f.e.129.1 | 2 | |||
65.2 | even | 12 | 169.4.c.c.22.1 | 2 | |||
65.7 | even | 12 | 169.4.c.b.146.1 | 2 | |||
65.12 | odd | 4 | 13.4.b.a.12.2 | yes | 2 | ||
65.17 | odd | 12 | 169.4.e.d.23.2 | 4 | |||
65.22 | odd | 12 | 169.4.e.d.23.1 | 4 | |||
65.32 | even | 12 | 169.4.c.c.146.1 | 2 | |||
65.37 | even | 12 | 169.4.c.b.22.1 | 2 | |||
65.38 | odd | 4 | 325.4.c.b.51.1 | 2 | |||
65.42 | odd | 12 | 169.4.e.d.147.2 | 4 | |||
65.47 | even | 4 | 169.4.a.c.1.1 | 1 | |||
65.57 | even | 4 | 169.4.a.b.1.1 | 1 | |||
65.62 | odd | 12 | 169.4.e.d.147.1 | 4 | |||
65.64 | even | 2 | inner | 325.4.d.a.324.2 | 2 | ||
195.47 | odd | 4 | 1521.4.a.d.1.1 | 1 | |||
195.77 | even | 4 | 117.4.b.a.64.1 | 2 | |||
195.122 | odd | 4 | 1521.4.a.i.1.1 | 1 | |||
260.207 | even | 4 | 208.4.f.b.129.1 | 2 | |||
520.77 | odd | 4 | 832.4.f.e.129.2 | 2 | |||
520.467 | even | 4 | 832.4.f.c.129.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.b.a.12.1 | ✓ | 2 | 5.2 | odd | 4 | ||
13.4.b.a.12.2 | yes | 2 | 65.12 | odd | 4 | ||
117.4.b.a.64.1 | 2 | 195.77 | even | 4 | |||
117.4.b.a.64.2 | 2 | 15.2 | even | 4 | |||
169.4.a.b.1.1 | 1 | 65.57 | even | 4 | |||
169.4.a.c.1.1 | 1 | 65.47 | even | 4 | |||
169.4.c.b.22.1 | 2 | 65.37 | even | 12 | |||
169.4.c.b.146.1 | 2 | 65.7 | even | 12 | |||
169.4.c.c.22.1 | 2 | 65.2 | even | 12 | |||
169.4.c.c.146.1 | 2 | 65.32 | even | 12 | |||
169.4.e.d.23.1 | 4 | 65.22 | odd | 12 | |||
169.4.e.d.23.2 | 4 | 65.17 | odd | 12 | |||
169.4.e.d.147.1 | 4 | 65.62 | odd | 12 | |||
169.4.e.d.147.2 | 4 | 65.42 | odd | 12 | |||
208.4.f.b.129.1 | 2 | 260.207 | even | 4 | |||
208.4.f.b.129.2 | 2 | 20.7 | even | 4 | |||
325.4.c.b.51.1 | 2 | 65.38 | odd | 4 | |||
325.4.c.b.51.2 | 2 | 5.3 | odd | 4 | |||
325.4.d.a.324.1 | 2 | 1.1 | even | 1 | trivial | ||
325.4.d.a.324.2 | 2 | 65.64 | even | 2 | inner | ||
325.4.d.b.324.1 | 2 | 13.12 | even | 2 | |||
325.4.d.b.324.2 | 2 | 5.4 | even | 2 | |||
832.4.f.c.129.1 | 2 | 40.27 | even | 4 | |||
832.4.f.c.129.2 | 2 | 520.467 | even | 4 | |||
832.4.f.e.129.1 | 2 | 40.37 | odd | 4 | |||
832.4.f.e.129.2 | 2 | 520.77 | odd | 4 | |||
1521.4.a.d.1.1 | 1 | 195.47 | odd | 4 | |||
1521.4.a.i.1.1 | 1 | 195.122 | odd | 4 |