Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,4,Mod(1,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2025.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(119.478867762\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 91 x^{14} + 3268 x^{12} - 59128 x^{10} + 571975 x^{8} - 2881141 x^{6} + 6555196 x^{4} + \cdots + 614656 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{12}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(2.46385\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.46385 | 0.871102 | 0.435551 | − | 0.900164i | \(-0.356553\pi\) | ||||
0.435551 | + | 0.900164i | \(0.356553\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.92944 | −0.241181 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −19.2401 | −1.03887 | −0.519435 | − | 0.854510i | \(-0.673858\pi\) | ||||
−0.519435 | + | 0.854510i | \(0.673858\pi\) | |||||||
\(8\) | −24.4647 | −1.08120 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.8548 | −1.09243 | −0.546213 | − | 0.837646i | \(-0.683931\pi\) | ||||
−0.546213 | + | 0.837646i | \(0.683931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00910 | 0.0215287 | 0.0107643 | − | 0.999942i | \(-0.496574\pi\) | ||||
0.0107643 | + | 0.999942i | \(0.496574\pi\) | |||||||
\(14\) | −47.4048 | −0.904962 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −44.8417 | −0.700651 | ||||||||
\(17\) | −52.6170 | −0.750676 | −0.375338 | − | 0.926888i | \(-0.622473\pi\) | ||||
−0.375338 | + | 0.926888i | \(0.622473\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −49.5371 | −0.598136 | −0.299068 | − | 0.954232i | \(-0.596676\pi\) | ||||
−0.299068 | + | 0.954232i | \(0.596676\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −98.1964 | −0.951615 | ||||||||
\(23\) | −27.4019 | −0.248421 | −0.124210 | − | 0.992256i | \(-0.539640\pi\) | ||||
−0.124210 | + | 0.992256i | \(0.539640\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.48626 | 0.0187537 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 37.1228 | 0.250555 | ||||||||
\(29\) | 254.953 | 1.63254 | 0.816269 | − | 0.577672i | \(-0.196039\pi\) | ||||
0.816269 | + | 0.577672i | \(0.196039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −168.656 | −0.977147 | −0.488574 | − | 0.872523i | \(-0.662483\pi\) | ||||
−0.488574 | + | 0.872523i | \(0.662483\pi\) | |||||||
\(32\) | 85.2341 | 0.470856 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −129.640 | −0.653916 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −419.938 | −1.86588 | −0.932938 | − | 0.360038i | \(-0.882764\pi\) | ||||
−0.932938 | + | 0.360038i | \(0.882764\pi\) | |||||||
\(38\) | −122.052 | −0.521038 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −398.570 | −1.51820 | −0.759100 | − | 0.650974i | \(-0.774361\pi\) | ||||
−0.759100 | + | 0.650974i | \(0.774361\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 358.828 | 1.27258 | 0.636288 | − | 0.771452i | \(-0.280469\pi\) | ||||
0.636288 | + | 0.771452i | \(0.280469\pi\) | |||||||
\(44\) | 76.8977 | 0.263472 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −67.5141 | −0.216400 | ||||||||
\(47\) | −141.302 | −0.438532 | −0.219266 | − | 0.975665i | \(-0.570366\pi\) | ||||
−0.219266 | + | 0.975665i | \(0.570366\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 27.1829 | 0.0792505 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.94699 | −0.00519230 | ||||||||
\(53\) | −290.878 | −0.753872 | −0.376936 | − | 0.926239i | \(-0.623022\pi\) | ||||
−0.376936 | + | 0.926239i | \(0.623022\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 470.703 | 1.12322 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 628.166 | 1.42211 | ||||||||
\(59\) | −28.7319 | −0.0633995 | −0.0316998 | − | 0.999497i | \(-0.510092\pi\) | ||||
−0.0316998 | + | 0.999497i | \(0.510092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 732.727 | 1.53797 | 0.768985 | − | 0.639267i | \(-0.220762\pi\) | ||||
0.768985 | + | 0.639267i | \(0.220762\pi\) | |||||||
\(62\) | −415.544 | −0.851195 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 568.737 | 1.11082 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −176.546 | −0.321918 | −0.160959 | − | 0.986961i | \(-0.551459\pi\) | ||||
−0.160959 | + | 0.986961i | \(0.551459\pi\) | |||||||
\(68\) | 101.522 | 0.181049 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 802.814 | 1.34192 | 0.670961 | − | 0.741493i | \(-0.265882\pi\) | ||||
0.670961 | + | 0.741493i | \(0.265882\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 512.820 | 0.822205 | 0.411103 | − | 0.911589i | \(-0.365144\pi\) | ||||
0.411103 | + | 0.911589i | \(0.365144\pi\) | |||||||
\(74\) | −1034.66 | −1.62537 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 95.5791 | 0.144259 | ||||||||
\(77\) | 766.813 | 1.13489 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 612.348 | 0.872082 | 0.436041 | − | 0.899927i | \(-0.356380\pi\) | ||||
0.436041 | + | 0.899927i | \(0.356380\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −982.017 | −1.32251 | ||||||||
\(83\) | −80.8162 | −0.106876 | −0.0534382 | − | 0.998571i | \(-0.517018\pi\) | ||||
−0.0534382 | + | 0.998571i | \(0.517018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 884.098 | 1.10854 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 975.035 | 1.18113 | ||||||||
\(89\) | −24.0097 | −0.0285957 | −0.0142979 | − | 0.999898i | \(-0.504551\pi\) | ||||
−0.0142979 | + | 0.999898i | \(0.504551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.4151 | −0.0223655 | ||||||||
\(92\) | 52.8704 | 0.0599143 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −348.147 | −0.382006 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1367.92 | 1.43187 | 0.715934 | − | 0.698168i | \(-0.246001\pi\) | ||||
0.715934 | + | 0.698168i | \(0.246001\pi\) | |||||||
\(98\) | 66.9747 | 0.0690353 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −568.413 | −0.559992 | −0.279996 | − | 0.960001i | \(-0.590333\pi\) | ||||
−0.279996 | + | 0.960001i | \(0.590333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 475.159 | 0.454551 | 0.227276 | − | 0.973830i | \(-0.427018\pi\) | ||||
0.227276 | + | 0.973830i | \(0.427018\pi\) | |||||||
\(104\) | −24.6872 | −0.0232767 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −716.680 | −0.656700 | ||||||||
\(107\) | −1452.60 | −1.31242 | −0.656208 | − | 0.754580i | \(-0.727841\pi\) | ||||
−0.656208 | + | 0.754580i | \(0.727841\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1962.92 | −1.72490 | −0.862448 | − | 0.506146i | \(-0.831070\pi\) | ||||
−0.862448 | + | 0.506146i | \(0.831070\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 862.760 | 0.727886 | ||||||||
\(113\) | 978.286 | 0.814419 | 0.407210 | − | 0.913335i | \(-0.366502\pi\) | ||||
0.407210 | + | 0.913335i | \(0.366502\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −491.918 | −0.393736 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −70.7910 | −0.0552275 | ||||||||
\(119\) | 1012.36 | 0.779855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 257.409 | 0.193395 | ||||||||
\(122\) | 1805.33 | 1.33973 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 325.413 | 0.235669 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 865.941 | 0.605038 | 0.302519 | − | 0.953143i | \(-0.402172\pi\) | ||||
0.302519 | + | 0.953143i | \(0.402172\pi\) | |||||||
\(128\) | 719.411 | 0.496778 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1468.96 | 0.979720 | 0.489860 | − | 0.871801i | \(-0.337048\pi\) | ||||
0.489860 | + | 0.871801i | \(0.337048\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 953.101 | 0.621386 | ||||||||
\(134\) | −434.983 | −0.280424 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1287.26 | 0.811628 | ||||||||
\(137\) | 71.5353 | 0.0446108 | 0.0223054 | − | 0.999751i | \(-0.492899\pi\) | ||||
0.0223054 | + | 0.999751i | \(0.492899\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 229.065 | 0.139777 | 0.0698886 | − | 0.997555i | \(-0.477736\pi\) | ||||
0.0698886 | + | 0.997555i | \(0.477736\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1978.01 | 1.16895 | ||||||||
\(143\) | −40.2174 | −0.0235185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1263.51 | 0.716225 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 810.247 | 0.450013 | ||||||||
\(149\) | 835.144 | 0.459179 | 0.229589 | − | 0.973288i | \(-0.426262\pi\) | ||||
0.229589 | + | 0.973288i | \(0.426262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1866.58 | −1.00596 | −0.502982 | − | 0.864297i | \(-0.667764\pi\) | ||||
−0.502982 | + | 0.864297i | \(0.667764\pi\) | |||||||
\(152\) | 1211.91 | 0.646702 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1889.31 | 0.988604 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2299.91 | 1.16913 | 0.584563 | − | 0.811348i | \(-0.301266\pi\) | ||||
0.584563 | + | 0.811348i | \(0.301266\pi\) | |||||||
\(158\) | 1508.73 | 0.759673 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 527.215 | 0.258077 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −44.9023 | −0.0215768 | −0.0107884 | − | 0.999942i | \(-0.503434\pi\) | ||||
−0.0107884 | + | 0.999942i | \(0.503434\pi\) | |||||||
\(164\) | 769.019 | 0.366160 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −199.119 | −0.0931002 | ||||||||
\(167\) | −1176.56 | −0.545180 | −0.272590 | − | 0.962130i | \(-0.587880\pi\) | ||||
−0.272590 | + | 0.962130i | \(0.587880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2195.98 | −0.999537 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −692.339 | −0.306921 | ||||||||
\(173\) | 1068.09 | 0.469396 | 0.234698 | − | 0.972068i | \(-0.424590\pi\) | ||||
0.234698 | + | 0.972068i | \(0.424590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1787.16 | 0.765410 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −59.1562 | −0.0249098 | ||||||||
\(179\) | 2779.66 | 1.16068 | 0.580339 | − | 0.814375i | \(-0.302920\pi\) | ||||
0.580339 | + | 0.814375i | \(0.302920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3568.66 | −1.46550 | −0.732752 | − | 0.680496i | \(-0.761764\pi\) | ||||
−0.732752 | + | 0.680496i | \(0.761764\pi\) | |||||||
\(182\) | −47.8360 | −0.0194826 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 670.377 | 0.268592 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2097.04 | 0.820059 | ||||||||
\(188\) | 272.634 | 0.105765 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3338.62 | 1.26478 | 0.632392 | − | 0.774648i | \(-0.282073\pi\) | ||||
0.632392 | + | 0.774648i | \(0.282073\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1940.87 | −0.723868 | −0.361934 | − | 0.932204i | \(-0.617883\pi\) | ||||
−0.361934 | + | 0.932204i | \(0.617883\pi\) | |||||||
\(194\) | 3370.35 | 1.24730 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −52.4480 | −0.0191137 | ||||||||
\(197\) | −1035.75 | −0.374588 | −0.187294 | − | 0.982304i | \(-0.559972\pi\) | ||||
−0.187294 | + | 0.982304i | \(0.559972\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1565.53 | 0.557675 | 0.278838 | − | 0.960338i | \(-0.410051\pi\) | ||||
0.278838 | + | 0.960338i | \(0.410051\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1400.48 | −0.487810 | ||||||||
\(203\) | −4905.33 | −1.69599 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1170.72 | 0.395961 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −45.2496 | −0.0150841 | ||||||||
\(209\) | 1974.29 | 0.653420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3385.27 | 1.10451 | 0.552255 | − | 0.833675i | \(-0.313767\pi\) | ||||
0.552255 | + | 0.833675i | \(0.313767\pi\) | |||||||
\(212\) | 561.234 | 0.181819 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3579.00 | −1.14325 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3244.97 | 1.01513 | ||||||||
\(218\) | −4836.34 | −1.50256 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −53.0956 | −0.0161611 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2365.54 | −0.710352 | −0.355176 | − | 0.934799i | \(-0.615579\pi\) | ||||
−0.355176 | + | 0.934799i | \(0.615579\pi\) | |||||||
\(224\) | −1639.92 | −0.489158 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2410.35 | 0.709443 | ||||||||
\(227\) | −976.230 | −0.285439 | −0.142720 | − | 0.989763i | \(-0.545585\pi\) | ||||
−0.142720 | + | 0.989763i | \(0.545585\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1595.28 | 0.460345 | 0.230173 | − | 0.973150i | \(-0.426071\pi\) | ||||
0.230173 | + | 0.973150i | \(0.426071\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6237.34 | −1.76509 | ||||||||
\(233\) | −943.571 | −0.265302 | −0.132651 | − | 0.991163i | \(-0.542349\pi\) | ||||
−0.132651 | + | 0.991163i | \(0.542349\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 55.4366 | 0.0152907 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2494.30 | 0.679334 | ||||||||
\(239\) | −2731.50 | −0.739271 | −0.369635 | − | 0.929177i | \(-0.620517\pi\) | ||||
−0.369635 | + | 0.929177i | \(0.620517\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3417.23 | 0.913375 | 0.456687 | − | 0.889627i | \(-0.349036\pi\) | ||||
0.456687 | + | 0.889627i | \(0.349036\pi\) | |||||||
\(242\) | 634.217 | 0.168467 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1413.76 | −0.370928 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −49.9877 | −0.0128771 | ||||||||
\(248\) | 4126.12 | 1.05649 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3164.50 | 0.795782 | 0.397891 | − | 0.917433i | \(-0.369742\pi\) | ||||
0.397891 | + | 0.917433i | \(0.369742\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1092.10 | 0.271382 | ||||||||
\(254\) | 2133.55 | 0.527050 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2777.38 | −0.678071 | ||||||||
\(257\) | −5549.43 | −1.34694 | −0.673471 | − | 0.739214i | \(-0.735197\pi\) | ||||
−0.673471 | + | 0.739214i | \(0.735197\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8079.67 | 1.93840 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3619.29 | 0.853436 | ||||||||
\(263\) | 4137.64 | 0.970106 | 0.485053 | − | 0.874485i | \(-0.338800\pi\) | ||||
0.485053 | + | 0.874485i | \(0.338800\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2348.30 | 0.541291 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 340.636 | 0.0776404 | ||||||||
\(269\) | 1026.74 | 0.232719 | 0.116359 | − | 0.993207i | \(-0.462878\pi\) | ||||
0.116359 | + | 0.993207i | \(0.462878\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3400.66 | 0.762270 | 0.381135 | − | 0.924519i | \(-0.375533\pi\) | ||||
0.381135 | + | 0.924519i | \(0.375533\pi\) | |||||||
\(272\) | 2359.44 | 0.525962 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 176.252 | 0.0388605 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3568.81 | −0.774112 | −0.387056 | − | 0.922056i | \(-0.626508\pi\) | ||||
−0.387056 | + | 0.922056i | \(0.626508\pi\) | |||||||
\(278\) | 564.381 | 0.121760 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6018.68 | 1.27774 | 0.638869 | − | 0.769316i | \(-0.279403\pi\) | ||||
0.638869 | + | 0.769316i | \(0.279403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4578.17 | −0.961638 | −0.480819 | − | 0.876820i | \(-0.659661\pi\) | ||||
−0.480819 | + | 0.876820i | \(0.659661\pi\) | |||||||
\(284\) | −1548.98 | −0.323646 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −99.0895 | −0.0204870 | ||||||||
\(287\) | 7668.55 | 1.57721 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2144.45 | −0.436485 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −989.457 | −0.198300 | ||||||||
\(293\) | −6479.73 | −1.29198 | −0.645990 | − | 0.763346i | \(-0.723555\pi\) | ||||
−0.645990 | + | 0.763346i | \(0.723555\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10273.6 | 2.01738 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2057.67 | 0.399992 | ||||||||
\(299\) | −27.6511 | −0.00534818 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6903.90 | −1.32204 | ||||||||
\(302\) | −4598.98 | −0.876297 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2221.33 | 0.419085 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 708.452 | 0.131705 | 0.0658526 | − | 0.997829i | \(-0.479023\pi\) | ||||
0.0658526 | + | 0.997829i | \(0.479023\pi\) | |||||||
\(308\) | −1479.52 | −0.273713 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6234.64 | 1.13676 | 0.568382 | − | 0.822765i | \(-0.307570\pi\) | ||||
0.568382 | + | 0.822765i | \(0.307570\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2631.41 | −0.475196 | −0.237598 | − | 0.971364i | \(-0.576360\pi\) | ||||
−0.237598 | + | 0.971364i | \(0.576360\pi\) | |||||||
\(314\) | 5666.63 | 1.01843 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1181.49 | −0.210329 | ||||||||
\(317\) | 502.534 | 0.0890383 | 0.0445191 | − | 0.999009i | \(-0.485824\pi\) | ||||
0.0445191 | + | 0.999009i | \(0.485824\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10161.1 | −1.78343 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1298.98 | 0.224812 | ||||||||
\(323\) | 2606.49 | 0.449007 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −110.632 | −0.0187956 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9750.89 | 1.64147 | ||||||||
\(329\) | 2718.67 | 0.455578 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3087.14 | 0.512642 | 0.256321 | − | 0.966592i | \(-0.417490\pi\) | ||||
0.256321 | + | 0.966592i | \(0.417490\pi\) | |||||||
\(332\) | 155.930 | 0.0257765 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2898.87 | −0.474908 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5985.80 | −0.967559 | −0.483780 | − | 0.875190i | \(-0.660736\pi\) | ||||
−0.483780 | + | 0.875190i | \(0.660736\pi\) | |||||||
\(338\) | −5410.57 | −0.870699 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6721.77 | 1.06746 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6076.36 | 0.956539 | ||||||||
\(344\) | −8778.60 | −1.37590 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2631.61 | 0.408892 | ||||||||
\(347\) | −1006.65 | −0.155734 | −0.0778671 | − | 0.996964i | \(-0.524811\pi\) | ||||
−0.0778671 | + | 0.996964i | \(0.524811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1949.36 | −0.298987 | −0.149494 | − | 0.988763i | \(-0.547764\pi\) | ||||
−0.149494 | + | 0.988763i | \(0.547764\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3396.99 | −0.514376 | ||||||||
\(353\) | −2591.73 | −0.390776 | −0.195388 | − | 0.980726i | \(-0.562597\pi\) | ||||
−0.195388 | + | 0.980726i | \(0.562597\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 46.3253 | 0.00689674 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6848.65 | 1.01107 | ||||||||
\(359\) | 605.954 | 0.0890837 | 0.0445418 | − | 0.999008i | \(-0.485817\pi\) | ||||
0.0445418 | + | 0.999008i | \(0.485817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4405.08 | −0.642233 | ||||||||
\(362\) | −8792.63 | −1.27660 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 37.4604 | 0.00539412 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9760.26 | −1.38823 | −0.694117 | − | 0.719863i | \(-0.744205\pi\) | ||||
−0.694117 | + | 0.719863i | \(0.744205\pi\) | |||||||
\(368\) | 1228.75 | 0.174056 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5596.54 | 0.783175 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7823.62 | −1.08604 | −0.543018 | − | 0.839721i | \(-0.682719\pi\) | ||||
−0.543018 | + | 0.839721i | \(0.682719\pi\) | |||||||
\(374\) | 5166.80 | 0.714355 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3456.90 | 0.474139 | ||||||||
\(377\) | 257.272 | 0.0351464 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2731.46 | 0.370200 | 0.185100 | − | 0.982720i | \(-0.440739\pi\) | ||||
0.185100 | + | 0.982720i | \(0.440739\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8225.85 | 1.10176 | ||||||||
\(383\) | 12599.9 | 1.68100 | 0.840500 | − | 0.541812i | \(-0.182262\pi\) | ||||
0.840500 | + | 0.541812i | \(0.182262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4782.00 | −0.630563 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2639.33 | −0.345339 | ||||||||
\(389\) | 4943.46 | 0.644327 | 0.322163 | − | 0.946684i | \(-0.395590\pi\) | ||||
0.322163 | + | 0.946684i | \(0.395590\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1441.80 | 0.186484 | ||||||||
\(392\) | −665.021 | −0.0856853 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2551.92 | −0.326305 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7067.06 | 0.893415 | 0.446707 | − | 0.894680i | \(-0.352597\pi\) | ||||
0.446707 | + | 0.894680i | \(0.352597\pi\) | |||||||
\(398\) | 3857.23 | 0.485792 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 917.584 | 0.114269 | 0.0571346 | − | 0.998366i | \(-0.481804\pi\) | ||||
0.0571346 | + | 0.998366i | \(0.481804\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −170.190 | −0.0210367 | ||||||||
\(404\) | 1096.72 | 0.135059 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12086.0 | −1.47738 | ||||||||
\(407\) | 16736.6 | 2.03833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14735.5 | 1.78148 | 0.890739 | − | 0.454515i | \(-0.150187\pi\) | ||||
0.890739 | + | 0.454515i | \(0.150187\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −916.792 | −0.109629 | ||||||||
\(413\) | 552.805 | 0.0658638 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 86.0094 | 0.0101369 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4864.36 | 0.569196 | ||||||||
\(419\) | 9254.92 | 1.07907 | 0.539537 | − | 0.841962i | \(-0.318599\pi\) | ||||
0.539537 | + | 0.841962i | \(0.318599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10202.0 | −1.18103 | −0.590514 | − | 0.807027i | \(-0.701075\pi\) | ||||
−0.590514 | + | 0.807027i | \(0.701075\pi\) | |||||||
\(422\) | 8340.80 | 0.962142 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7116.24 | 0.815083 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14097.8 | −1.59775 | ||||||||
\(428\) | 2802.72 | 0.316529 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8057.20 | −0.900468 | −0.450234 | − | 0.892911i | \(-0.648659\pi\) | ||||
−0.450234 | + | 0.892911i | \(0.648659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4306.26 | −0.477935 | −0.238967 | − | 0.971028i | \(-0.576809\pi\) | ||||
−0.238967 | + | 0.971028i | \(0.576809\pi\) | |||||||
\(434\) | 7995.12 | 0.884281 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3787.34 | 0.416011 | ||||||||
\(437\) | 1357.41 | 0.148590 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4721.79 | −0.513346 | −0.256673 | − | 0.966498i | \(-0.582626\pi\) | ||||
−0.256673 | + | 0.966498i | \(0.582626\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −130.820 | −0.0140779 | ||||||||
\(443\) | 15354.4 | 1.64675 | 0.823373 | − | 0.567501i | \(-0.192090\pi\) | ||||
0.823373 | + | 0.567501i | \(0.192090\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5828.35 | −0.618790 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10942.6 | −1.15399 | ||||||||
\(449\) | −5448.64 | −0.572688 | −0.286344 | − | 0.958127i | \(-0.592440\pi\) | ||||
−0.286344 | + | 0.958127i | \(0.592440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15885.0 | 1.65852 | ||||||||
\(452\) | −1887.55 | −0.196422 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2405.28 | −0.248647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 52.7307 | 0.00539746 | 0.00269873 | − | 0.999996i | \(-0.499141\pi\) | ||||
0.00269873 | + | 0.999996i | \(0.499141\pi\) | |||||||
\(458\) | 3930.53 | 0.401008 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3167.02 | 0.319963 | 0.159982 | − | 0.987120i | \(-0.448857\pi\) | ||||
0.159982 | + | 0.987120i | \(0.448857\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13092.4 | −1.31416 | −0.657081 | − | 0.753820i | \(-0.728209\pi\) | ||||
−0.657081 | + | 0.753820i | \(0.728209\pi\) | |||||||
\(464\) | −11432.5 | −1.14384 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2324.82 | −0.231105 | ||||||||
\(467\) | −13225.4 | −1.31049 | −0.655246 | − | 0.755416i | \(-0.727435\pi\) | ||||
−0.655246 | + | 0.755416i | \(0.727435\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3396.77 | 0.334431 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 702.915 | 0.0685473 | ||||||||
\(473\) | −14301.0 | −1.39020 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1953.29 | −0.188086 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6729.99 | −0.643981 | ||||||||
\(479\) | 8558.59 | 0.816393 | 0.408196 | − | 0.912894i | \(-0.366158\pi\) | ||||
0.408196 | + | 0.912894i | \(0.366158\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −423.758 | −0.0401698 | ||||||||
\(482\) | 8419.55 | 0.795643 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −496.656 | −0.0466432 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19531.3 | −1.81735 | −0.908674 | − | 0.417506i | \(-0.862904\pi\) | ||||
−0.908674 | + | 0.417506i | \(0.862904\pi\) | |||||||
\(488\) | −17925.9 | −1.66285 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19488.2 | 1.79122 | 0.895612 | − | 0.444835i | \(-0.146738\pi\) | ||||
0.895612 | + | 0.444835i | \(0.146738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13414.9 | −1.22551 | ||||||||
\(494\) | −123.162 | −0.0112173 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7562.83 | 0.684640 | ||||||||
\(497\) | −15446.2 | −1.39408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −339.530 | −0.0304598 | −0.0152299 | − | 0.999884i | \(-0.504848\pi\) | ||||
−0.0152299 | + | 0.999884i | \(0.504848\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7796.84 | 0.693208 | ||||||||
\(503\) | −5550.25 | −0.491995 | −0.245998 | − | 0.969270i | \(-0.579116\pi\) | ||||
−0.245998 | + | 0.969270i | \(0.579116\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2690.76 | 0.236401 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1670.79 | −0.145923 | ||||||||
\(509\) | −5648.99 | −0.491920 | −0.245960 | − | 0.969280i | \(-0.579103\pi\) | ||||
−0.245960 | + | 0.969280i | \(0.579103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9866.72 | −0.854164 | ||||||||
\(512\) | −12598.3 | −1.08745 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13673.0 | −1.17332 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5631.57 | 0.479064 | ||||||||
\(518\) | 19907.1 | 1.68855 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11159.0 | 0.938359 | 0.469180 | − | 0.883103i | \(-0.344550\pi\) | ||||
0.469180 | + | 0.883103i | \(0.344550\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9476.61 | −0.792320 | −0.396160 | − | 0.918182i | \(-0.629657\pi\) | ||||
−0.396160 | + | 0.918182i | \(0.629657\pi\) | |||||||
\(524\) | −2834.27 | −0.236289 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10194.5 | 0.845062 | ||||||||
\(527\) | 8874.19 | 0.733521 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11416.1 | −0.938287 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1838.95 | −0.149866 | ||||||||
\(533\) | −402.196 | −0.0326849 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4319.14 | 0.348057 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2529.73 | 0.202722 | ||||||||
\(539\) | −1083.37 | −0.0865754 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8285.40 | 0.658442 | 0.329221 | − | 0.944253i | \(-0.393214\pi\) | ||||
0.329221 | + | 0.944253i | \(0.393214\pi\) | |||||||
\(542\) | 8378.71 | 0.664015 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4484.76 | −0.353461 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6918.30 | 0.540777 | 0.270389 | − | 0.962751i | \(-0.412848\pi\) | ||||
0.270389 | + | 0.962751i | \(0.412848\pi\) | |||||||
\(548\) | −138.023 | −0.0107593 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12629.6 | −0.976480 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11781.7 | −0.905980 | ||||||||
\(554\) | −8793.01 | −0.674331 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −441.968 | −0.0337115 | ||||||||
\(557\) | 15622.7 | 1.18843 | 0.594216 | − | 0.804305i | \(-0.297462\pi\) | ||||
0.594216 | + | 0.804305i | \(0.297462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 362.092 | 0.0273969 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14829.1 | 1.11304 | ||||||||
\(563\) | −8129.30 | −0.608542 | −0.304271 | − | 0.952585i | \(-0.598413\pi\) | ||||
−0.304271 | + | 0.952585i | \(0.598413\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11279.9 | −0.837686 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19640.6 | −1.45088 | ||||||||
\(569\) | −8175.67 | −0.602359 | −0.301179 | − | 0.953568i | \(-0.597380\pi\) | ||||
−0.301179 | + | 0.953568i | \(0.597380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7878.84 | 0.577442 | 0.288721 | − | 0.957413i | \(-0.406770\pi\) | ||||
0.288721 | + | 0.957413i | \(0.406770\pi\) | |||||||
\(572\) | 77.5972 | 0.00567220 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18894.1 | 1.37391 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16673.4 | −1.20299 | −0.601493 | − | 0.798878i | \(-0.705427\pi\) | ||||
−0.601493 | + | 0.798878i | \(0.705427\pi\) | |||||||
\(578\) | −5283.60 | −0.380223 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1554.92 | 0.111031 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11592.9 | 0.823549 | ||||||||
\(584\) | −12546.0 | −0.888965 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15965.1 | −1.12545 | ||||||||
\(587\) | −3012.18 | −0.211799 | −0.105900 | − | 0.994377i | \(-0.533772\pi\) | ||||
−0.105900 | + | 0.994377i | \(0.533772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8354.74 | 0.584467 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18830.7 | 1.30733 | ||||||||
\(593\) | −7922.71 | −0.548645 | −0.274323 | − | 0.961638i | \(-0.588454\pi\) | ||||
−0.274323 | + | 0.961638i | \(0.588454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1611.36 | −0.110745 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −68.1282 | −0.00465881 | ||||||||
\(599\) | 22578.5 | 1.54012 | 0.770061 | − | 0.637970i | \(-0.220226\pi\) | ||||
0.770061 | + | 0.637970i | \(0.220226\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10618.7 | 0.720709 | 0.360354 | − | 0.932815i | \(-0.382656\pi\) | ||||
0.360354 | + | 0.932815i | \(0.382656\pi\) | |||||||
\(602\) | −17010.2 | −1.15163 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3601.47 | 0.242619 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13590.6 | −0.908771 | −0.454385 | − | 0.890805i | \(-0.650141\pi\) | ||||
−0.454385 | + | 0.890805i | \(0.650141\pi\) | |||||||
\(608\) | −4222.25 | −0.281636 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −142.587 | −0.00944102 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5457.57 | −0.359591 | −0.179796 | − | 0.983704i | \(-0.557544\pi\) | ||||
−0.179796 | + | 0.983704i | \(0.557544\pi\) | |||||||
\(614\) | 1745.52 | 0.114729 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18759.8 | −1.22704 | ||||||||
\(617\) | 5972.10 | 0.389672 | 0.194836 | − | 0.980836i | \(-0.437583\pi\) | ||||
0.194836 | + | 0.980836i | \(0.437583\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −839.633 | −0.0545197 | −0.0272598 | − | 0.999628i | \(-0.508678\pi\) | ||||
−0.0272598 | + | 0.999628i | \(0.508678\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15361.2 | 0.990238 | ||||||||
\(623\) | 461.949 | 0.0297072 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6483.41 | −0.413944 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4437.55 | −0.281970 | ||||||||
\(629\) | 22095.9 | 1.40067 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13699.4 | −0.864284 | −0.432142 | − | 0.901806i | \(-0.642242\pi\) | ||||
−0.432142 | + | 0.901806i | \(0.642242\pi\) | |||||||
\(632\) | −14980.9 | −0.942892 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1238.17 | 0.0775615 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.4302 | 0.00170616 | ||||||||
\(638\) | −25035.5 | −1.55355 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7939.36 | 0.489214 | 0.244607 | − | 0.969622i | \(-0.421341\pi\) | ||||
0.244607 | + | 0.969622i | \(0.421341\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7635.95 | 0.468324 | 0.234162 | − | 0.972198i | \(-0.424765\pi\) | ||||
0.234162 | + | 0.972198i | \(0.424765\pi\) | |||||||
\(644\) | −1017.23 | −0.0622432 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6422.01 | 0.391131 | ||||||||
\(647\) | −22084.3 | −1.34192 | −0.670962 | − | 0.741491i | \(-0.734119\pi\) | ||||
−0.670962 | + | 0.741491i | \(0.734119\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1145.10 | 0.0692593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 86.6364 | 0.00520390 | ||||||||
\(653\) | 6637.97 | 0.397801 | 0.198900 | − | 0.980020i | \(-0.436263\pi\) | ||||
0.198900 | + | 0.980020i | \(0.436263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17872.6 | 1.06373 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6698.39 | 0.396855 | ||||||||
\(659\) | −23812.3 | −1.40758 | −0.703789 | − | 0.710409i | \(-0.748510\pi\) | ||||
−0.703789 | + | 0.710409i | \(0.748510\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −999.824 | −0.0588330 | −0.0294165 | − | 0.999567i | \(-0.509365\pi\) | ||||
−0.0294165 | + | 0.999567i | \(0.509365\pi\) | |||||||
\(662\) | 7606.24 | 0.446563 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1977.14 | 0.115554 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6986.19 | −0.405557 | ||||||||
\(668\) | 2270.11 | 0.131487 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29202.7 | −1.68012 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10622.1 | −0.608396 | −0.304198 | − | 0.952609i | \(-0.598388\pi\) | ||||
−0.304198 | + | 0.952609i | \(0.598388\pi\) | |||||||
\(674\) | −14748.1 | −0.842843 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4237.02 | 0.241069 | ||||||||
\(677\) | 24907.8 | 1.41401 | 0.707005 | − | 0.707209i | \(-0.250046\pi\) | ||||
0.707005 | + | 0.707209i | \(0.250046\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26319.0 | −1.48753 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16561.4 | 0.929868 | ||||||||
\(683\) | 17115.6 | 0.958874 | 0.479437 | − | 0.877576i | \(-0.340841\pi\) | ||||
0.479437 | + | 0.877576i | \(0.340841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14971.2 | 0.833243 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16090.5 | −0.891632 | ||||||||
\(689\) | −293.524 | −0.0162299 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28899.8 | 1.59103 | 0.795514 | − | 0.605935i | \(-0.207201\pi\) | ||||
0.795514 | + | 0.605935i | \(0.207201\pi\) | |||||||
\(692\) | −2060.82 | −0.113209 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2480.23 | −0.135660 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20971.6 | 1.13968 | ||||||||
\(698\) | −4802.92 | −0.260449 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −576.680 | −0.0310712 | −0.0155356 | − | 0.999879i | \(-0.504945\pi\) | ||||
−0.0155356 | + | 0.999879i | \(0.504945\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20802.5 | 1.11605 | ||||||||
\(704\) | −22666.9 | −1.21348 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6385.63 | −0.340406 | ||||||||
\(707\) | 10936.3 | 0.581759 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5717.55 | 0.302859 | 0.151430 | − | 0.988468i | \(-0.451612\pi\) | ||||
0.151430 | + | 0.988468i | \(0.451612\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 587.389 | 0.0309176 | ||||||||
\(713\) | 4621.50 | 0.242744 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5363.19 | −0.279933 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1492.98 | 0.0776010 | ||||||||
\(719\) | 14799.9 | 0.767655 | 0.383827 | − | 0.923405i | \(-0.374606\pi\) | ||||
0.383827 | + | 0.923405i | \(0.374606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9142.12 | −0.472219 | ||||||||
\(722\) | −10853.4 | −0.559451 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6885.52 | 0.353451 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6410.40 | −0.327027 | −0.163513 | − | 0.986541i | \(-0.552283\pi\) | ||||
−0.163513 | + | 0.986541i | \(0.552283\pi\) | |||||||
\(728\) | 474.985 | 0.0241815 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18880.5 | −0.955292 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17869.2 | 0.900431 | 0.450215 | − | 0.892920i | \(-0.351347\pi\) | ||||
0.450215 | + | 0.892920i | \(0.351347\pi\) | |||||||
\(734\) | −24047.8 | −1.20929 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2335.57 | −0.116971 | ||||||||
\(737\) | 7036.21 | 0.351672 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11099.7 | 0.552516 | 0.276258 | − | 0.961084i | \(-0.410906\pi\) | ||||
0.276258 | + | 0.961084i | \(0.410906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13789.0 | 0.682225 | ||||||||
\(743\) | 10857.6 | 0.536107 | 0.268053 | − | 0.963404i | \(-0.413620\pi\) | ||||
0.268053 | + | 0.963404i | \(0.413620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −19276.2 | −0.946049 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4046.13 | −0.197782 | ||||||||
\(749\) | 27948.3 | 1.36343 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32233.9 | −1.56622 | −0.783111 | − | 0.621882i | \(-0.786368\pi\) | ||||
−0.783111 | + | 0.621882i | \(0.786368\pi\) | |||||||
\(752\) | 6336.22 | 0.307258 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 633.880 | 0.0306161 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9410.28 | 0.451813 | 0.225906 | − | 0.974149i | \(-0.427466\pi\) | ||||
0.225906 | + | 0.974149i | \(0.427466\pi\) | |||||||
\(758\) | 6729.91 | 0.322482 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34767.1 | −1.65612 | −0.828060 | − | 0.560640i | \(-0.810555\pi\) | ||||
−0.828060 | + | 0.560640i | \(0.810555\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37766.8 | 1.79194 | ||||||||
\(764\) | −6441.68 | −0.305042 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31044.2 | 1.46432 | ||||||||
\(767\) | −28.9932 | −0.00136491 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29086.5 | −1.36396 | −0.681980 | − | 0.731371i | \(-0.738881\pi\) | ||||
−0.681980 | + | 0.731371i | \(0.738881\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3744.79 | 0.174583 | ||||||||
\(773\) | −2942.77 | −0.136927 | −0.0684633 | − | 0.997654i | \(-0.521810\pi\) | ||||
−0.0684633 | + | 0.997654i | \(0.521810\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −33465.7 | −1.54813 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12179.9 | 0.561275 | ||||||||
\(779\) | 19744.0 | 0.908091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31996.0 | −1.46595 | ||||||||
\(782\) | 3552.39 | 0.162446 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1218.93 | −0.0555270 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33829.1 | −1.53225 | −0.766124 | − | 0.642693i | \(-0.777817\pi\) | ||||
−0.766124 | + | 0.642693i | \(0.777817\pi\) | |||||||
\(788\) | 1998.41 | 0.0903434 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18822.4 | −0.846076 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 739.392 | 0.0331105 | ||||||||
\(794\) | 17412.2 | 0.778256 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3020.60 | −0.134500 | ||||||||
\(797\) | −22904.7 | −1.01797 | −0.508987 | − | 0.860774i | \(-0.669980\pi\) | ||||
−0.508987 | + | 0.860774i | \(0.669980\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7434.89 | 0.329196 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2260.79 | 0.0995402 | ||||||||
\(803\) | −20438.3 | −0.898199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −419.324 | −0.0183251 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13906.0 | 0.605461 | ||||||||
\(809\) | 30665.7 | 1.33269 | 0.666347 | − | 0.745642i | \(-0.267857\pi\) | ||||
0.666347 | + | 0.745642i | \(0.267857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35135.2 | −1.52129 | −0.760644 | − | 0.649169i | \(-0.775117\pi\) | ||||
−0.760644 | + | 0.649169i | \(0.775117\pi\) | |||||||
\(812\) | 9464.57 | 0.409041 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 41236.4 | 1.77560 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17775.3 | −0.761174 | ||||||||
\(818\) | 36306.1 | 1.55185 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34437.0 | −1.46390 | −0.731948 | − | 0.681361i | \(-0.761389\pi\) | ||||
−0.731948 | + | 0.681361i | \(0.761389\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42801.8 | 1.81285 | 0.906426 | − | 0.422365i | \(-0.138800\pi\) | ||||
0.906426 | + | 0.422365i | \(0.138800\pi\) | |||||||
\(824\) | −11624.6 | −0.491459 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1362.03 | 0.0573742 | ||||||||
\(827\) | 23589.1 | 0.991868 | 0.495934 | − | 0.868360i | \(-0.334826\pi\) | ||||
0.495934 | + | 0.868360i | \(0.334826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26766.2 | −1.12139 | −0.560693 | − | 0.828024i | \(-0.689465\pi\) | ||||
−0.560693 | + | 0.828024i | \(0.689465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 573.911 | 0.0239144 | ||||||||
\(833\) | −1430.28 | −0.0594915 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3809.29 | −0.157592 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22802.7 | 0.939985 | ||||||||
\(839\) | 30334.3 | 1.24822 | 0.624110 | − | 0.781336i | \(-0.285462\pi\) | ||||
0.624110 | + | 0.781336i | \(0.285462\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40612.1 | 1.66518 | ||||||||
\(842\) | −25136.1 | −1.02880 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6531.69 | −0.266386 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4952.58 | −0.200912 | ||||||||
\(848\) | 13043.5 | 0.528201 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11507.1 | 0.463523 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6533.77 | 0.262265 | 0.131133 | − | 0.991365i | \(-0.458139\pi\) | ||||
0.131133 | + | 0.991365i | \(0.458139\pi\) | |||||||
\(854\) | −34734.8 | −1.39180 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35537.5 | 1.41898 | ||||||||
\(857\) | −37553.0 | −1.49683 | −0.748417 | − | 0.663228i | \(-0.769186\pi\) | ||||
−0.748417 | + | 0.663228i | \(0.769186\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36637.9 | 1.45526 | 0.727631 | − | 0.685969i | \(-0.240621\pi\) | ||||
0.727631 | + | 0.685969i | \(0.240621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19851.7 | −0.784400 | ||||||||
\(863\) | −14614.7 | −0.576467 | −0.288233 | − | 0.957560i | \(-0.593068\pi\) | ||||
−0.288233 | + | 0.957560i | \(0.593068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10610.0 | −0.416330 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6260.99 | −0.244829 | ||||||||
\(869\) | −24405.0 | −0.952686 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −178.152 | −0.00693047 | ||||||||
\(872\) | 48022.2 | 1.86495 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3344.45 | 0.129437 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1388.56 | 0.0534646 | 0.0267323 | − | 0.999643i | \(-0.491490\pi\) | ||||
0.0267323 | + | 0.999643i | \(0.491490\pi\) | |||||||
\(878\) | −11633.8 | −0.447177 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23664.2 | −0.904957 | −0.452478 | − | 0.891775i | \(-0.649460\pi\) | ||||
−0.452478 | + | 0.891775i | \(0.649460\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49607.6 | 1.89063 | 0.945317 | − | 0.326152i | \(-0.105752\pi\) | ||||
0.945317 | + | 0.326152i | \(0.105752\pi\) | |||||||
\(884\) | 102.445 | 0.00389774 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 37830.9 | 1.43448 | ||||||||
\(887\) | −11477.0 | −0.434454 | −0.217227 | − | 0.976121i | \(-0.569701\pi\) | ||||
−0.217227 | + | 0.976121i | \(0.569701\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16660.8 | −0.628556 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4564.19 | 0.171323 | ||||||||
\(893\) | 6999.69 | 0.262302 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13841.6 | −0.516087 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13424.6 | −0.498870 | ||||||||
\(899\) | −42999.4 | −1.59523 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15305.1 | 0.565914 | ||||||||
\(902\) | 39138.1 | 1.44474 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23933.4 | −0.880547 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11733.8 | −0.429563 | −0.214782 | − | 0.976662i | \(-0.568904\pi\) | ||||
−0.214782 | + | 0.976662i | \(0.568904\pi\) | |||||||
\(908\) | 1883.58 | 0.0688424 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35013.4 | 1.27338 | 0.636688 | − | 0.771122i | \(-0.280304\pi\) | ||||
0.636688 | + | 0.771122i | \(0.280304\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3220.92 | 0.116755 | ||||||||
\(914\) | 129.920 | 0.00470174 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3078.00 | −0.111026 | ||||||||
\(917\) | −28262.9 | −1.01780 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16026.6 | 0.575264 | 0.287632 | − | 0.957741i | \(-0.407132\pi\) | ||||
0.287632 | + | 0.957741i | \(0.407132\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7803.07 | 0.278721 | ||||||||
\(923\) | 810.116 | 0.0288898 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −32257.8 | −1.14477 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 21730.7 | 0.768691 | ||||||||
\(929\) | −25886.8 | −0.914229 | −0.457114 | − | 0.889408i | \(-0.651117\pi\) | ||||
−0.457114 | + | 0.889408i | \(0.651117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1346.56 | −0.0474026 | ||||||||
\(932\) | 1820.57 | 0.0639857 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32585.5 | −1.14157 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6331.15 | 0.220736 | 0.110368 | − | 0.993891i | \(-0.464797\pi\) | ||||
0.110368 | + | 0.993891i | \(0.464797\pi\) | |||||||
\(938\) | 8369.13 | 0.291324 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28754.7 | 0.996149 | 0.498075 | − | 0.867134i | \(-0.334041\pi\) | ||||
0.498075 | + | 0.867134i | \(0.334041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10921.6 | 0.377153 | ||||||||
\(944\) | 1288.39 | 0.0444210 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35235.6 | −1.21100 | ||||||||
\(947\) | 29240.7 | 1.00337 | 0.501687 | − | 0.865049i | \(-0.332713\pi\) | ||||
0.501687 | + | 0.865049i | \(0.332713\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 517.484 | 0.0177010 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −24767.0 | −0.843176 | ||||||||
\(953\) | 28758.3 | 0.977517 | 0.488758 | − | 0.872419i | \(-0.337450\pi\) | ||||
0.488758 | + | 0.872419i | \(0.337450\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5270.27 | 0.178298 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21087.1 | 0.711161 | ||||||||
\(959\) | −1376.35 | −0.0463448 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1346.05 | −0.0451831 | ||||||||
\(962\) | −1044.08 | −0.0349920 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6593.36 | −0.220288 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44695.1 | −1.48635 | −0.743174 | − | 0.669099i | \(-0.766680\pi\) | ||||
−0.743174 | + | 0.669099i | \(0.766680\pi\) | |||||||
\(968\) | −6297.42 | −0.209098 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30462.4 | 1.00678 | 0.503391 | − | 0.864059i | \(-0.332086\pi\) | ||||
0.503391 | + | 0.864059i | \(0.332086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4407.24 | −0.145210 | ||||||||
\(974\) | −48122.2 | −1.58310 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −32856.7 | −1.07758 | ||||||||
\(977\) | 11808.0 | 0.386665 | 0.193332 | − | 0.981133i | \(-0.438070\pi\) | ||||
0.193332 | + | 0.981133i | \(0.438070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 956.902 | 0.0312387 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 48016.1 | 1.56034 | ||||||||
\(983\) | 24702.9 | 0.801526 | 0.400763 | − | 0.916182i | \(-0.368745\pi\) | ||||
0.400763 | + | 0.916182i | \(0.368745\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −33052.2 | −1.06754 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 96.4485 | 0.00310570 | ||||||||
\(989\) | −9832.55 | −0.316134 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14443.0 | 0.462965 | 0.231482 | − | 0.972839i | \(-0.425642\pi\) | ||||
0.231482 | + | 0.972839i | \(0.425642\pi\) | |||||||
\(992\) | −14375.3 | −0.460096 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −38057.2 | −1.21439 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47669.3 | −1.51425 | −0.757123 | − | 0.653273i | \(-0.773396\pi\) | ||||
−0.757123 | + | 0.653273i | \(0.773396\pi\) | |||||||
\(998\) | −836.551 | −0.0265336 | ||||||||
\(999\) | 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 | 2025.4.a.bl.1.11 | 16 | ||
3.2 | odd | 2 | 2025.4.a.bk.1.6 | 16 | |||
5.2 | odd | 4 | 405.4.b.f.244.11 | 16 | |||
5.3 | odd | 4 | 405.4.b.f.244.6 | 16 | |||
5.4 | even | 2 | inner | 2025.4.a.bl.1.6 | 16 | ||
9.2 | odd | 6 | 225.4.e.g.76.11 | 32 | |||
9.5 | odd | 6 | 225.4.e.g.151.11 | 32 | |||
15.2 | even | 4 | 405.4.b.e.244.6 | 16 | |||
15.8 | even | 4 | 405.4.b.e.244.11 | 16 | |||
15.14 | odd | 2 | 2025.4.a.bk.1.11 | 16 | |||
45.2 | even | 12 | 45.4.j.a.4.6 | ✓ | 32 | ||
45.7 | odd | 12 | 135.4.j.a.64.11 | 32 | |||
45.13 | odd | 12 | 135.4.j.a.19.11 | 32 | |||
45.14 | odd | 6 | 225.4.e.g.151.6 | 32 | |||
45.22 | odd | 12 | 135.4.j.a.19.6 | 32 | |||
45.23 | even | 12 | 45.4.j.a.34.6 | yes | 32 | ||
45.29 | odd | 6 | 225.4.e.g.76.6 | 32 | |||
45.32 | even | 12 | 45.4.j.a.34.11 | yes | 32 | ||
45.38 | even | 12 | 45.4.j.a.4.11 | yes | 32 | ||
45.43 | odd | 12 | 135.4.j.a.64.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.j.a.4.6 | ✓ | 32 | 45.2 | even | 12 | ||
45.4.j.a.4.11 | yes | 32 | 45.38 | even | 12 | ||
45.4.j.a.34.6 | yes | 32 | 45.23 | even | 12 | ||
45.4.j.a.34.11 | yes | 32 | 45.32 | even | 12 | ||
135.4.j.a.19.6 | 32 | 45.22 | odd | 12 | |||
135.4.j.a.19.11 | 32 | 45.13 | odd | 12 | |||
135.4.j.a.64.6 | 32 | 45.43 | odd | 12 | |||
135.4.j.a.64.11 | 32 | 45.7 | odd | 12 | |||
225.4.e.g.76.6 | 32 | 45.29 | odd | 6 | |||
225.4.e.g.76.11 | 32 | 9.2 | odd | 6 | |||
225.4.e.g.151.6 | 32 | 45.14 | odd | 6 | |||
225.4.e.g.151.11 | 32 | 9.5 | odd | 6 | |||
405.4.b.e.244.6 | 16 | 15.2 | even | 4 | |||
405.4.b.e.244.11 | 16 | 15.8 | even | 4 | |||
405.4.b.f.244.6 | 16 | 5.3 | odd | 4 | |||
405.4.b.f.244.11 | 16 | 5.2 | odd | 4 | |||
2025.4.a.bk.1.6 | 16 | 3.2 | odd | 2 | |||
2025.4.a.bk.1.11 | 16 | 15.14 | odd | 2 | |||
2025.4.a.bl.1.6 | 16 | 5.4 | even | 2 | inner | ||
2025.4.a.bl.1.11 | 16 | 1.1 | even | 1 | trivial |