Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, 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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 100 x^{16} + 4066 x^{14} - 86197 x^{12} + 1016064 x^{10} - 6594119 x^{8} + 22251817 x^{6} + \cdots - 6889792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7\cdot 13^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.32218\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32218 | −0.467462 | −0.233731 | − | 0.972301i | \(-0.575093\pi\) | ||||
−0.233731 | + | 0.972301i | \(0.575093\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.25184 | −0.781480 | ||||||||
\(5\) | 12.9610 | 1.15926 | 0.579631 | − | 0.814879i | \(-0.303197\pi\) | ||||
0.579631 | + | 0.814879i | \(0.303197\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.54391 | 0.299343 | 0.149672 | − | 0.988736i | \(-0.452178\pi\) | ||||
0.149672 | + | 0.988736i | \(0.452178\pi\) | |||||||
\(8\) | 18.8435 | 0.832773 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −17.1367 | −0.541911 | ||||||||
\(11\) | −0.841909 | −0.0230768 | −0.0115384 | − | 0.999933i | \(-0.503673\pi\) | ||||
−0.0115384 | + | 0.999933i | \(0.503673\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −7.33006 | −0.139931 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 25.1002 | 0.392190 | ||||||||
\(17\) | 10.1858 | 0.145318 | 0.0726591 | − | 0.997357i | \(-0.476851\pi\) | ||||
0.0726591 | + | 0.997357i | \(0.476851\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −73.0894 | −0.882519 | −0.441260 | − | 0.897380i | \(-0.645468\pi\) | ||||
−0.441260 | + | 0.897380i | \(0.645468\pi\) | |||||||
\(20\) | −81.0298 | −0.905940 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.11316 | 0.0107875 | ||||||||
\(23\) | 139.073 | 1.26081 | 0.630407 | − | 0.776265i | \(-0.282888\pi\) | ||||
0.630407 | + | 0.776265i | \(0.282888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 42.9863 | 0.343890 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −34.6596 | −0.233931 | ||||||||
\(29\) | 250.377 | 1.60323 | 0.801617 | − | 0.597838i | \(-0.203973\pi\) | ||||
0.801617 | + | 0.597838i | \(0.203973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −161.445 | −0.935366 | −0.467683 | − | 0.883896i | \(-0.654911\pi\) | ||||
−0.467683 | + | 0.883896i | \(0.654911\pi\) | |||||||
\(32\) | −183.935 | −1.01611 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.4674 | −0.0679307 | ||||||||
\(35\) | 71.8544 | 0.347017 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 195.826 | 0.870099 | 0.435049 | − | 0.900407i | \(-0.356731\pi\) | ||||
0.435049 | + | 0.900407i | \(0.356731\pi\) | |||||||
\(38\) | 96.6374 | 0.412544 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 244.230 | 0.965403 | ||||||||
\(41\) | 183.760 | 0.699962 | 0.349981 | − | 0.936757i | \(-0.386188\pi\) | ||||
0.349981 | + | 0.936757i | \(0.386188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 115.071 | 0.408097 | 0.204049 | − | 0.978961i | \(-0.434590\pi\) | ||||
0.204049 | + | 0.978961i | \(0.434590\pi\) | |||||||
\(44\) | 5.26348 | 0.0180341 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −183.880 | −0.589382 | ||||||||
\(47\) | 551.780 | 1.71245 | 0.856227 | − | 0.516600i | \(-0.172802\pi\) | ||||
0.856227 | + | 0.516600i | \(0.172802\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −312.265 | −0.910394 | ||||||||
\(50\) | −56.8357 | −0.160755 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −324.717 | −0.841572 | −0.420786 | − | 0.907160i | \(-0.638246\pi\) | ||||
−0.420786 | + | 0.907160i | \(0.638246\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.9119 | −0.0267521 | ||||||||
\(56\) | 104.467 | 0.249285 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −331.043 | −0.749450 | ||||||||
\(59\) | −521.559 | −1.15087 | −0.575434 | − | 0.817848i | \(-0.695167\pi\) | ||||
−0.575434 | + | 0.817848i | \(0.695167\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −444.586 | −0.933170 | −0.466585 | − | 0.884476i | \(-0.654516\pi\) | ||||
−0.466585 | + | 0.884476i | \(0.654516\pi\) | |||||||
\(62\) | 213.459 | 0.437248 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 42.3942 | 0.0828011 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 55.0046 | 0.100297 | 0.0501484 | − | 0.998742i | \(-0.484031\pi\) | ||||
0.0501484 | + | 0.998742i | \(0.484031\pi\) | |||||||
\(68\) | −63.6797 | −0.113563 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −95.0045 | −0.162217 | ||||||||
\(71\) | 279.871 | 0.467811 | 0.233906 | − | 0.972259i | \(-0.424849\pi\) | ||||
0.233906 | + | 0.972259i | \(0.424849\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 908.097 | 1.45596 | 0.727978 | − | 0.685601i | \(-0.240460\pi\) | ||||
0.727978 | + | 0.685601i | \(0.240460\pi\) | |||||||
\(74\) | −258.918 | −0.406738 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 456.943 | 0.689671 | ||||||||
\(77\) | −4.66747 | −0.00690789 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 941.507 | 1.34086 | 0.670429 | − | 0.741974i | \(-0.266110\pi\) | ||||
0.670429 | + | 0.741974i | \(0.266110\pi\) | |||||||
\(80\) | 325.322 | 0.454651 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −242.964 | −0.327206 | ||||||||
\(83\) | −946.563 | −1.25179 | −0.625896 | − | 0.779906i | \(-0.715267\pi\) | ||||
−0.625896 | + | 0.779906i | \(0.715267\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 132.017 | 0.168462 | ||||||||
\(86\) | −152.145 | −0.190770 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.8645 | −0.0192178 | ||||||||
\(89\) | −32.9886 | −0.0392897 | −0.0196448 | − | 0.999807i | \(-0.506254\pi\) | ||||
−0.0196448 | + | 0.999807i | \(0.506254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −869.461 | −0.985300 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −729.553 | −0.800507 | ||||||||
\(95\) | −947.308 | −1.02307 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −68.2675 | −0.0714589 | −0.0357294 | − | 0.999361i | \(-0.511375\pi\) | ||||
−0.0357294 | + | 0.999361i | \(0.511375\pi\) | |||||||
\(98\) | 412.871 | 0.425574 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −268.743 | −0.268743 | ||||||||
\(101\) | −1643.68 | −1.61933 | −0.809667 | − | 0.586890i | \(-0.800352\pi\) | ||||
−0.809667 | + | 0.586890i | \(0.800352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −166.289 | −0.159078 | −0.0795388 | − | 0.996832i | \(-0.525345\pi\) | ||||
−0.0795388 | + | 0.996832i | \(0.525345\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 429.335 | 0.393403 | ||||||||
\(107\) | −445.544 | −0.402546 | −0.201273 | − | 0.979535i | \(-0.564508\pi\) | ||||
−0.201273 | + | 0.979535i | \(0.564508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −884.955 | −0.777645 | −0.388822 | − | 0.921313i | \(-0.627118\pi\) | ||||
−0.388822 | + | 0.921313i | \(0.627118\pi\) | |||||||
\(110\) | 14.4276 | 0.0125056 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 139.153 | 0.117399 | ||||||||
\(113\) | 1513.58 | 1.26005 | 0.630023 | − | 0.776576i | \(-0.283045\pi\) | ||||
0.630023 | + | 0.776576i | \(0.283045\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1802.52 | 1.46161 | ||||||||
\(116\) | −1565.31 | −1.25289 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 689.596 | 0.537987 | ||||||||
\(119\) | 56.4690 | 0.0435000 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.29 | −0.999467 | ||||||||
\(122\) | 587.823 | 0.436221 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1009.33 | 0.730970 | ||||||||
\(125\) | −1062.98 | −0.760604 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2584.41 | 1.80574 | 0.902871 | − | 0.429912i | \(-0.141455\pi\) | ||||
0.902871 | + | 0.429912i | \(0.141455\pi\) | |||||||
\(128\) | 1415.43 | 0.977401 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1486.33 | 0.991311 | 0.495655 | − | 0.868519i | \(-0.334928\pi\) | ||||
0.495655 | + | 0.868519i | \(0.334928\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −405.201 | −0.264176 | ||||||||
\(134\) | −72.7261 | −0.0468849 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 191.935 | 0.121017 | ||||||||
\(137\) | −1481.51 | −0.923895 | −0.461947 | − | 0.886907i | \(-0.652849\pi\) | ||||
−0.461947 | + | 0.886907i | \(0.652849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −917.381 | −0.559793 | −0.279897 | − | 0.960030i | \(-0.590300\pi\) | ||||
−0.279897 | + | 0.960030i | \(0.590300\pi\) | |||||||
\(140\) | −449.222 | −0.271187 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −370.040 | −0.218684 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3245.12 | 1.85857 | ||||||||
\(146\) | −1200.67 | −0.680603 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1224.27 | −0.679965 | ||||||||
\(149\) | 2278.14 | 1.25257 | 0.626283 | − | 0.779596i | \(-0.284576\pi\) | ||||
0.626283 | + | 0.779596i | \(0.284576\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2196.92 | 1.18399 | 0.591996 | − | 0.805941i | \(-0.298340\pi\) | ||||
0.591996 | + | 0.805941i | \(0.298340\pi\) | |||||||
\(152\) | −1377.26 | −0.734938 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.17124 | 0.00322917 | ||||||||
\(155\) | −2092.48 | −1.08434 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3197.69 | 1.62550 | 0.812750 | − | 0.582612i | \(-0.197969\pi\) | ||||
0.812750 | + | 0.582612i | \(0.197969\pi\) | |||||||
\(158\) | −1244.84 | −0.626800 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2383.97 | −1.17794 | ||||||||
\(161\) | 771.008 | 0.377416 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3083.17 | 1.48155 | 0.740774 | − | 0.671754i | \(-0.234459\pi\) | ||||
0.740774 | + | 0.671754i | \(0.234459\pi\) | |||||||
\(164\) | −1148.84 | −0.547006 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1251.53 | 0.585165 | ||||||||
\(167\) | 524.082 | 0.242842 | 0.121421 | − | 0.992601i | \(-0.461255\pi\) | ||||
0.121421 | + | 0.992601i | \(0.461255\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −174.551 | −0.0787495 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −719.405 | −0.318919 | ||||||||
\(173\) | −2981.68 | −1.31036 | −0.655182 | − | 0.755471i | \(-0.727408\pi\) | ||||
−0.655182 | + | 0.755471i | \(0.727408\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 238.312 | 0.102941 | ||||||||
\(176\) | −21.1321 | −0.00905050 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 43.6168 | 0.0183664 | ||||||||
\(179\) | 332.862 | 0.138990 | 0.0694952 | − | 0.997582i | \(-0.477861\pi\) | ||||
0.0694952 | + | 0.997582i | \(0.477861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2546.13 | −1.04559 | −0.522796 | − | 0.852458i | \(-0.675111\pi\) | ||||
−0.522796 | + | 0.852458i | \(0.675111\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2620.62 | 1.04997 | ||||||||
\(185\) | 2538.10 | 1.00867 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.57548 | −0.00335348 | ||||||||
\(188\) | −3449.64 | −1.33825 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1252.51 | 0.478247 | ||||||||
\(191\) | 3424.25 | 1.29723 | 0.648613 | − | 0.761118i | \(-0.275349\pi\) | ||||
0.648613 | + | 0.761118i | \(0.275349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2912.13 | 1.08611 | 0.543055 | − | 0.839697i | \(-0.317267\pi\) | ||||
0.543055 | + | 0.839697i | \(0.317267\pi\) | |||||||
\(194\) | 90.2620 | 0.0334043 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1952.23 | 0.711454 | ||||||||
\(197\) | 80.9189 | 0.0292651 | 0.0146326 | − | 0.999893i | \(-0.495342\pi\) | ||||
0.0146326 | + | 0.999893i | \(0.495342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −875.929 | −0.312025 | −0.156013 | − | 0.987755i | \(-0.549864\pi\) | ||||
−0.156013 | + | 0.987755i | \(0.549864\pi\) | |||||||
\(200\) | 810.012 | 0.286383 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2173.25 | 0.756977 | ||||||||
\(203\) | 1388.07 | 0.479917 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2381.70 | 0.811440 | ||||||||
\(206\) | 219.865 | 0.0743626 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 61.5347 | 0.0203657 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3862.86 | −1.26033 | −0.630167 | − | 0.776460i | \(-0.717014\pi\) | ||||
−0.630167 | + | 0.776460i | \(0.717014\pi\) | |||||||
\(212\) | 2030.08 | 0.657672 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 589.090 | 0.188175 | ||||||||
\(215\) | 1491.43 | 0.473092 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −895.036 | −0.279996 | ||||||||
\(218\) | 1170.07 | 0.363519 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 68.2197 | 0.0209062 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6391.24 | 1.91923 | 0.959617 | − | 0.281311i | \(-0.0907693\pi\) | ||||
0.959617 | + | 0.281311i | \(0.0907693\pi\) | |||||||
\(224\) | −1019.72 | −0.304165 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2001.22 | −0.589023 | ||||||||
\(227\) | 1271.34 | 0.371727 | 0.185864 | − | 0.982576i | \(-0.440492\pi\) | ||||
0.185864 | + | 0.982576i | \(0.440492\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5964.71 | 1.72122 | 0.860610 | − | 0.509265i | \(-0.170083\pi\) | ||||
0.860610 | + | 0.509265i | \(0.170083\pi\) | |||||||
\(230\) | −2383.25 | −0.683249 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4717.98 | 1.33513 | ||||||||
\(233\) | 5160.98 | 1.45110 | 0.725551 | − | 0.688168i | \(-0.241585\pi\) | ||||
0.725551 | + | 0.688168i | \(0.241585\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7151.59 | 1.98518 | ||||||||
\(236\) | 3260.70 | 0.899380 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −74.6622 | −0.0203346 | ||||||||
\(239\) | −3799.33 | −1.02828 | −0.514139 | − | 0.857707i | \(-0.671888\pi\) | ||||
−0.514139 | + | 0.857707i | \(0.671888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −120.502 | −0.0322083 | −0.0161042 | − | 0.999870i | \(-0.505126\pi\) | ||||
−0.0161042 | + | 0.999870i | \(0.505126\pi\) | |||||||
\(242\) | 1758.89 | 0.467213 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2779.48 | 0.729253 | ||||||||
\(245\) | −4047.25 | −1.05539 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3042.19 | −0.778948 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1405.45 | 0.355553 | ||||||||
\(251\) | 6961.35 | 1.75058 | 0.875292 | − | 0.483595i | \(-0.160669\pi\) | ||||
0.875292 | + | 0.483595i | \(0.160669\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −117.087 | −0.0290956 | ||||||||
\(254\) | −3417.06 | −0.844115 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2210.60 | −0.539698 | ||||||||
\(257\) | 1154.03 | 0.280103 | 0.140052 | − | 0.990144i | \(-0.455273\pi\) | ||||
0.140052 | + | 0.990144i | \(0.455273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1085.64 | 0.260458 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1965.20 | −0.463400 | ||||||||
\(263\) | 2627.40 | 0.616018 | 0.308009 | − | 0.951383i | \(-0.400337\pi\) | ||||
0.308009 | + | 0.951383i | \(0.400337\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4208.64 | −0.975604 | ||||||||
\(266\) | 535.750 | 0.123492 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −343.880 | −0.0783799 | ||||||||
\(269\) | −5162.02 | −1.17001 | −0.585007 | − | 0.811028i | \(-0.698908\pi\) | ||||
−0.585007 | + | 0.811028i | \(0.698908\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3053.24 | 0.684394 | 0.342197 | − | 0.939628i | \(-0.388829\pi\) | ||||
0.342197 | + | 0.939628i | \(0.388829\pi\) | |||||||
\(272\) | 255.664 | 0.0569924 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1958.82 | 0.431885 | ||||||||
\(275\) | −36.1905 | −0.00793590 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3425.81 | −0.743094 | −0.371547 | − | 0.928414i | \(-0.621173\pi\) | ||||
−0.371547 | + | 0.928414i | \(0.621173\pi\) | |||||||
\(278\) | 1212.94 | 0.261682 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1353.99 | 0.288987 | ||||||||
\(281\) | 5619.38 | 1.19297 | 0.596484 | − | 0.802625i | \(-0.296564\pi\) | ||||
0.596484 | + | 0.802625i | \(0.296564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2181.00 | −0.458116 | −0.229058 | − | 0.973413i | \(-0.573565\pi\) | ||||
−0.229058 | + | 0.973413i | \(0.573565\pi\) | |||||||
\(284\) | −1749.71 | −0.365585 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1018.75 | 0.209529 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4809.25 | −0.978883 | ||||||||
\(290\) | −4290.64 | −0.868810 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5677.28 | −1.13780 | ||||||||
\(293\) | 4610.74 | 0.919325 | 0.459662 | − | 0.888094i | \(-0.347970\pi\) | ||||
0.459662 | + | 0.888094i | \(0.347970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6759.91 | −1.33416 | ||||||||
\(296\) | 3690.06 | 0.724595 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3012.11 | −0.585526 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 637.944 | 0.122161 | ||||||||
\(302\) | −2904.73 | −0.553471 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1834.56 | −0.346115 | ||||||||
\(305\) | −5762.25 | −1.08179 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4432.85 | 0.824091 | 0.412045 | − | 0.911163i | \(-0.364814\pi\) | ||||
0.412045 | + | 0.911163i | \(0.364814\pi\) | |||||||
\(308\) | 29.1803 | 0.00539838 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2766.64 | 0.506885 | ||||||||
\(311\) | 8942.00 | 1.63040 | 0.815200 | − | 0.579180i | \(-0.196627\pi\) | ||||
0.815200 | + | 0.579180i | \(0.196627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7883.46 | 1.42364 | 0.711820 | − | 0.702362i | \(-0.247871\pi\) | ||||
0.711820 | + | 0.702362i | \(0.247871\pi\) | |||||||
\(314\) | −4227.93 | −0.759859 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5886.15 | −1.04785 | ||||||||
\(317\) | −670.707 | −0.118835 | −0.0594174 | − | 0.998233i | \(-0.518924\pi\) | ||||
−0.0594174 | + | 0.998233i | \(0.518924\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −210.794 | −0.0369976 | ||||||||
\(320\) | 549.469 | 0.0959882 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1019.41 | −0.176427 | ||||||||
\(323\) | −744.471 | −0.128246 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4076.51 | −0.692567 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3462.68 | 0.582910 | ||||||||
\(329\) | 3059.02 | 0.512611 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2842.70 | −0.472051 | −0.236026 | − | 0.971747i | \(-0.575845\pi\) | ||||
−0.236026 | + | 0.971747i | \(0.575845\pi\) | |||||||
\(332\) | 5917.76 | 0.978251 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −692.931 | −0.113520 | ||||||||
\(335\) | 712.912 | 0.116270 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1886.14 | 0.304880 | 0.152440 | − | 0.988313i | \(-0.451287\pi\) | ||||
0.152440 | + | 0.988313i | \(0.451287\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −825.350 | −0.131650 | ||||||||
\(341\) | 135.922 | 0.0215853 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3632.73 | −0.571863 | ||||||||
\(344\) | 2168.34 | 0.339852 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3942.32 | 0.612545 | ||||||||
\(347\) | 4059.65 | 0.628050 | 0.314025 | − | 0.949415i | \(-0.398322\pi\) | ||||
0.314025 | + | 0.949415i | \(0.398322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7316.53 | 1.12219 | 0.561096 | − | 0.827751i | \(-0.310380\pi\) | ||||
0.561096 | + | 0.827751i | \(0.310380\pi\) | |||||||
\(350\) | −315.092 | −0.0481211 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 154.857 | 0.0234485 | ||||||||
\(353\) | 3390.13 | 0.511157 | 0.255579 | − | 0.966788i | \(-0.417734\pi\) | ||||
0.255579 | + | 0.966788i | \(0.417734\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3627.40 | 0.542316 | ||||||||
\(356\) | 206.239 | 0.0307041 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −440.104 | −0.0649727 | ||||||||
\(359\) | −12580.6 | −1.84952 | −0.924759 | − | 0.380552i | \(-0.875734\pi\) | ||||
−0.924759 | + | 0.380552i | \(0.875734\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1516.94 | −0.221160 | ||||||||
\(362\) | 3366.44 | 0.488774 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11769.8 | 1.68783 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1833.08 | −0.260725 | −0.130362 | − | 0.991466i | \(-0.541614\pi\) | ||||
−0.130362 | + | 0.991466i | \(0.541614\pi\) | |||||||
\(368\) | 3490.75 | 0.494478 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3355.82 | −0.471516 | ||||||||
\(371\) | −1800.20 | −0.251919 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1383.58 | 0.192062 | 0.0960312 | − | 0.995378i | \(-0.469385\pi\) | ||||
0.0960312 | + | 0.995378i | \(0.469385\pi\) | |||||||
\(374\) | 11.3383 | 0.00156763 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10397.5 | 1.42609 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1495.54 | −0.202693 | −0.101346 | − | 0.994851i | \(-0.532315\pi\) | ||||
−0.101346 | + | 0.994851i | \(0.532315\pi\) | |||||||
\(380\) | 5922.42 | 0.799510 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4527.48 | −0.606404 | ||||||||
\(383\) | 1454.92 | 0.194107 | 0.0970537 | − | 0.995279i | \(-0.469058\pi\) | ||||
0.0970537 | + | 0.995279i | \(0.469058\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −60.4949 | −0.00800806 | ||||||||
\(386\) | −3850.36 | −0.507715 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 426.797 | 0.0558437 | ||||||||
\(389\) | −14163.0 | −1.84600 | −0.922999 | − | 0.384801i | \(-0.874270\pi\) | ||||
−0.922999 | + | 0.384801i | \(0.874270\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1416.56 | 0.183219 | ||||||||
\(392\) | −5884.17 | −0.758152 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −106.989 | −0.0136803 | ||||||||
\(395\) | 12202.8 | 1.55441 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4877.38 | −0.616596 | −0.308298 | − | 0.951290i | \(-0.599759\pi\) | ||||
−0.308298 | + | 0.951290i | \(0.599759\pi\) | |||||||
\(398\) | 1158.14 | 0.145860 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1078.96 | 0.134870 | ||||||||
\(401\) | −1233.69 | −0.153635 | −0.0768176 | − | 0.997045i | \(-0.524476\pi\) | ||||
−0.0768176 | + | 0.997045i | \(0.524476\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10276.0 | 1.26548 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1835.28 | −0.224343 | ||||||||
\(407\) | −164.868 | −0.0200791 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5113.24 | 0.618174 | 0.309087 | − | 0.951034i | \(-0.399977\pi\) | ||||
0.309087 | + | 0.951034i | \(0.399977\pi\) | |||||||
\(410\) | −3149.04 | −0.379317 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1039.61 | 0.124316 | ||||||||
\(413\) | −2891.48 | −0.344505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12268.4 | −1.45116 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −81.3600 | −0.00952021 | ||||||||
\(419\) | −8630.26 | −1.00624 | −0.503121 | − | 0.864216i | \(-0.667815\pi\) | ||||
−0.503121 | + | 0.864216i | \(0.667815\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13265.8 | 1.53571 | 0.767854 | − | 0.640624i | \(-0.221324\pi\) | ||||
0.767854 | + | 0.640624i | \(0.221324\pi\) | |||||||
\(422\) | 5107.40 | 0.589158 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6118.81 | −0.700839 | ||||||||
\(425\) | 437.848 | 0.0499735 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2464.74 | −0.279338 | ||||||||
\(428\) | 2785.47 | 0.314581 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1971.94 | −0.221152 | ||||||||
\(431\) | −4617.20 | −0.516015 | −0.258008 | − | 0.966143i | \(-0.583066\pi\) | ||||
−0.258008 | + | 0.966143i | \(0.583066\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12484.6 | 1.38561 | 0.692805 | − | 0.721125i | \(-0.256374\pi\) | ||||
0.692805 | + | 0.721125i | \(0.256374\pi\) | |||||||
\(434\) | 1183.40 | 0.130887 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5532.59 | 0.607714 | ||||||||
\(437\) | −10164.8 | −1.11269 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5668.93 | −0.616317 | −0.308159 | − | 0.951335i | \(-0.599713\pi\) | ||||
−0.308159 | + | 0.951335i | \(0.599713\pi\) | |||||||
\(440\) | −205.619 | −0.0222785 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4801.47 | −0.514954 | −0.257477 | − | 0.966284i | \(-0.582891\pi\) | ||||
−0.257477 | + | 0.966284i | \(0.582891\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −427.563 | −0.0455470 | ||||||||
\(446\) | −8450.38 | −0.897168 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 235.029 | 0.0247859 | ||||||||
\(449\) | 16254.1 | 1.70841 | 0.854207 | − | 0.519934i | \(-0.174043\pi\) | ||||
0.854207 | + | 0.519934i | \(0.174043\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −154.709 | −0.0161529 | ||||||||
\(452\) | −9462.63 | −0.984700 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1680.95 | −0.173768 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7646.07 | 0.782643 | 0.391322 | − | 0.920254i | \(-0.372018\pi\) | ||||
0.391322 | + | 0.920254i | \(0.372018\pi\) | |||||||
\(458\) | −7886.43 | −0.804604 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11269.0 | −1.14222 | ||||||||
\(461\) | −5645.67 | −0.570380 | −0.285190 | − | 0.958471i | \(-0.592057\pi\) | ||||
−0.285190 | + | 0.958471i | \(0.592057\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3141.05 | 0.315285 | 0.157642 | − | 0.987496i | \(-0.449611\pi\) | ||||
0.157642 | + | 0.987496i | \(0.449611\pi\) | |||||||
\(464\) | 6284.49 | 0.628772 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6823.75 | −0.678335 | ||||||||
\(467\) | 1234.77 | 0.122352 | 0.0611759 | − | 0.998127i | \(-0.480515\pi\) | ||||
0.0611759 | + | 0.998127i | \(0.480515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 304.941 | 0.0300231 | ||||||||
\(470\) | −9455.70 | −0.927998 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9828.01 | −0.958413 | ||||||||
\(473\) | −96.8794 | −0.00941759 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3141.84 | −0.303490 | ||||||||
\(476\) | −353.035 | −0.0339944 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5023.41 | 0.480680 | ||||||||
\(479\) | 11758.1 | 1.12159 | 0.560795 | − | 0.827955i | \(-0.310495\pi\) | ||||
0.560795 | + | 0.827955i | \(0.310495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 159.325 | 0.0150562 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8316.76 | 0.781063 | ||||||||
\(485\) | −884.811 | −0.0828396 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8650.25 | 0.804888 | 0.402444 | − | 0.915445i | \(-0.368161\pi\) | ||||
0.402444 | + | 0.915445i | \(0.368161\pi\) | |||||||
\(488\) | −8377.56 | −0.777119 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5351.20 | 0.493352 | ||||||||
\(491\) | 3819.18 | 0.351033 | 0.175516 | − | 0.984476i | \(-0.443840\pi\) | ||||
0.175516 | + | 0.984476i | \(0.443840\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2550.28 | 0.232979 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4052.29 | −0.366841 | ||||||||
\(497\) | 1551.58 | 0.140036 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17077.9 | 1.53208 | 0.766042 | − | 0.642791i | \(-0.222224\pi\) | ||||
0.766042 | + | 0.642791i | \(0.222224\pi\) | |||||||
\(500\) | 6645.55 | 0.594396 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9204.17 | −0.818331 | ||||||||
\(503\) | −2996.47 | −0.265618 | −0.132809 | − | 0.991142i | \(-0.542400\pi\) | ||||
−0.132809 | + | 0.991142i | \(0.542400\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21303.7 | −1.87723 | ||||||||
\(506\) | 154.810 | 0.0136011 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16157.3 | −1.41115 | ||||||||
\(509\) | 8256.37 | 0.718973 | 0.359486 | − | 0.933150i | \(-0.382952\pi\) | ||||
0.359486 | + | 0.933150i | \(0.382952\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5034.41 | 0.435830 | ||||||||
\(512\) | −8400.60 | −0.725113 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1525.84 | −0.130938 | ||||||||
\(515\) | −2155.27 | −0.184413 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −464.548 | −0.0395180 | ||||||||
\(518\) | −1435.42 | −0.121754 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6348.47 | −0.533842 | −0.266921 | − | 0.963718i | \(-0.586006\pi\) | ||||
−0.266921 | + | 0.963718i | \(0.586006\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7444.93 | 0.622455 | 0.311228 | − | 0.950335i | \(-0.399260\pi\) | ||||
0.311228 | + | 0.950335i | \(0.399260\pi\) | |||||||
\(524\) | −9292.32 | −0.774689 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3473.91 | −0.287965 | ||||||||
\(527\) | −1644.44 | −0.135926 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7174.28 | 0.589651 | ||||||||
\(530\) | 5564.59 | 0.456057 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2533.25 | 0.206448 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5774.68 | −0.466656 | ||||||||
\(536\) | 1036.48 | 0.0835245 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6825.12 | 0.546937 | ||||||||
\(539\) | 262.899 | 0.0210090 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6247.50 | −0.496490 | −0.248245 | − | 0.968697i | \(-0.579854\pi\) | ||||
−0.248245 | + | 0.968697i | \(0.579854\pi\) | |||||||
\(542\) | −4036.93 | −0.319928 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1873.52 | −0.147659 | ||||||||
\(545\) | −11469.9 | −0.901495 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23338.4 | −1.82427 | −0.912137 | − | 0.409884i | \(-0.865569\pi\) | ||||
−0.912137 | + | 0.409884i | \(0.865569\pi\) | |||||||
\(548\) | 9262.13 | 0.722005 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 47.8505 | 0.00370973 | ||||||||
\(551\) | −18299.9 | −1.41488 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5219.63 | 0.401377 | ||||||||
\(554\) | 4529.54 | 0.347368 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5735.32 | 0.437467 | ||||||||
\(557\) | −14975.3 | −1.13918 | −0.569592 | − | 0.821927i | \(-0.692899\pi\) | ||||
−0.569592 | + | 0.821927i | \(0.692899\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1803.56 | 0.136097 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7429.84 | −0.557667 | ||||||||
\(563\) | 23463.5 | 1.75642 | 0.878212 | − | 0.478271i | \(-0.158736\pi\) | ||||
0.878212 | + | 0.478271i | \(0.158736\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19617.4 | 1.46072 | ||||||||
\(566\) | 2883.67 | 0.214152 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5273.75 | 0.389581 | ||||||||
\(569\) | −22359.6 | −1.64739 | −0.823694 | − | 0.567035i | \(-0.808091\pi\) | ||||
−0.823694 | + | 0.567035i | \(0.808091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2998.13 | −0.219733 | −0.109867 | − | 0.993946i | \(-0.535042\pi\) | ||||
−0.109867 | + | 0.993946i | \(0.535042\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1346.97 | −0.0979467 | ||||||||
\(575\) | 5978.23 | 0.433581 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3370.06 | 0.243150 | 0.121575 | − | 0.992582i | \(-0.461205\pi\) | ||||
0.121575 | + | 0.992582i | \(0.461205\pi\) | |||||||
\(578\) | 6358.70 | 0.457590 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20288.0 | −1.45243 | ||||||||
\(581\) | −5247.66 | −0.374716 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 273.382 | 0.0194208 | ||||||||
\(584\) | 17111.7 | 1.21248 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6096.23 | −0.429749 | ||||||||
\(587\) | 21645.2 | 1.52197 | 0.760983 | − | 0.648772i | \(-0.224717\pi\) | ||||
0.760983 | + | 0.648772i | \(0.224717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11799.9 | 0.825479 | ||||||||
\(590\) | 8937.82 | 0.623668 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4915.27 | 0.341244 | ||||||||
\(593\) | 22232.6 | 1.53960 | 0.769801 | − | 0.638284i | \(-0.220355\pi\) | ||||
0.769801 | + | 0.638284i | \(0.220355\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 731.891 | 0.0504279 | ||||||||
\(596\) | −14242.5 | −0.978854 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21337.0 | −1.45544 | −0.727718 | − | 0.685877i | \(-0.759419\pi\) | ||||
−0.727718 | + | 0.685877i | \(0.759419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1592.47 | −0.108084 | −0.0540419 | − | 0.998539i | \(-0.517210\pi\) | ||||
−0.0540419 | + | 0.998539i | \(0.517210\pi\) | |||||||
\(602\) | −843.477 | −0.0571056 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13734.8 | −0.925266 | ||||||||
\(605\) | −17241.8 | −1.15865 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18462.3 | 1.23454 | 0.617268 | − | 0.786753i | \(-0.288239\pi\) | ||||
0.617268 | + | 0.786753i | \(0.288239\pi\) | |||||||
\(608\) | 13443.7 | 0.896734 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7618.74 | 0.505695 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20041.2 | −1.32048 | −0.660241 | − | 0.751054i | \(-0.729546\pi\) | ||||
−0.660241 | + | 0.751054i | \(0.729546\pi\) | |||||||
\(614\) | −5861.03 | −0.385231 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −87.9515 | −0.00575271 | ||||||||
\(617\) | −18752.7 | −1.22359 | −0.611796 | − | 0.791016i | \(-0.709553\pi\) | ||||
−0.611796 | + | 0.791016i | \(0.709553\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7276.59 | −0.472489 | −0.236245 | − | 0.971694i | \(-0.575917\pi\) | ||||
−0.236245 | + | 0.971694i | \(0.575917\pi\) | |||||||
\(620\) | 13081.8 | 0.847386 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11822.9 | −0.762149 | ||||||||
\(623\) | −182.886 | −0.0117611 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19150.5 | −1.22563 | ||||||||
\(626\) | −10423.4 | −0.665497 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19991.5 | −1.27030 | ||||||||
\(629\) | 1994.64 | 0.126441 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22411.5 | −1.41393 | −0.706963 | − | 0.707251i | \(-0.749935\pi\) | ||||
−0.706963 | + | 0.707251i | \(0.749935\pi\) | |||||||
\(632\) | 17741.3 | 1.11663 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 886.796 | 0.0555507 | ||||||||
\(635\) | 33496.4 | 2.09333 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 278.708 | 0.0172949 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18345.3 | 1.13306 | ||||||||
\(641\) | −18756.0 | −1.15572 | −0.577861 | − | 0.816135i | \(-0.696113\pi\) | ||||
−0.577861 | + | 0.816135i | \(0.696113\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14712.9 | 0.902366 | 0.451183 | − | 0.892431i | \(-0.351002\pi\) | ||||
0.451183 | + | 0.892431i | \(0.351002\pi\) | |||||||
\(644\) | −4820.22 | −0.294943 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 984.326 | 0.0599501 | ||||||||
\(647\) | 17409.3 | 1.05785 | 0.528925 | − | 0.848668i | \(-0.322595\pi\) | ||||
0.528925 | + | 0.848668i | \(0.322595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 439.106 | 0.0265584 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19275.5 | −1.15780 | ||||||||
\(653\) | 17232.4 | 1.03270 | 0.516351 | − | 0.856377i | \(-0.327290\pi\) | ||||
0.516351 | + | 0.856377i | \(0.327290\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19264.3 | 1.14919 | ||||||||
\(656\) | 4612.40 | 0.274518 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4044.58 | −0.239626 | ||||||||
\(659\) | 7718.22 | 0.456236 | 0.228118 | − | 0.973634i | \(-0.426743\pi\) | ||||
0.228118 | + | 0.973634i | \(0.426743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31375.2 | −1.84623 | −0.923113 | − | 0.384530i | \(-0.874364\pi\) | ||||
−0.923113 | + | 0.384530i | \(0.874364\pi\) | |||||||
\(662\) | 3758.57 | 0.220666 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17836.6 | −1.04246 | ||||||||
\(665\) | −5251.79 | −0.306249 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34820.6 | 2.02138 | ||||||||
\(668\) | −3276.48 | −0.189776 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −942.599 | −0.0543519 | ||||||||
\(671\) | 374.301 | 0.0215346 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24768.7 | −1.41867 | −0.709333 | − | 0.704873i | \(-0.751004\pi\) | ||||
−0.709333 | + | 0.704873i | \(0.751004\pi\) | |||||||
\(674\) | −2493.82 | −0.142520 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17050.3 | −0.967944 | −0.483972 | − | 0.875084i | \(-0.660806\pi\) | ||||
−0.483972 | + | 0.875084i | \(0.660806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −378.469 | −0.0213907 | ||||||||
\(680\) | 2487.67 | 0.140291 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −179.713 | −0.0100903 | ||||||||
\(683\) | −23209.9 | −1.30029 | −0.650147 | − | 0.759808i | \(-0.725293\pi\) | ||||
−0.650147 | + | 0.759808i | \(0.725293\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19201.7 | −1.07104 | ||||||||
\(686\) | 4803.13 | 0.267324 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2888.30 | 0.160052 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1501.07 | 0.0826389 | 0.0413195 | − | 0.999146i | \(-0.486844\pi\) | ||||
0.0413195 | + | 0.999146i | \(0.486844\pi\) | |||||||
\(692\) | 18641.0 | 1.02402 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5367.59 | −0.293589 | ||||||||
\(695\) | −11890.1 | −0.648948 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1871.73 | 0.101717 | ||||||||
\(698\) | −9673.78 | −0.524581 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1489.89 | −0.0804464 | ||||||||
\(701\) | −3944.82 | −0.212544 | −0.106272 | − | 0.994337i | \(-0.533891\pi\) | ||||
−0.106272 | + | 0.994337i | \(0.533891\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14312.8 | −0.767879 | ||||||||
\(704\) | −35.6920 | −0.00191079 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4482.37 | −0.238946 | ||||||||
\(707\) | −9112.44 | −0.484736 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24251.8 | −1.28462 | −0.642311 | − | 0.766444i | \(-0.722024\pi\) | ||||
−0.642311 | + | 0.766444i | \(0.722024\pi\) | |||||||
\(710\) | −4796.07 | −0.253512 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −621.620 | −0.0327194 | ||||||||
\(713\) | −22452.6 | −1.17932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2081.00 | −0.108618 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16633.8 | 0.864579 | ||||||||
\(719\) | −6941.00 | −0.360022 | −0.180011 | − | 0.983665i | \(-0.557613\pi\) | ||||
−0.180011 | + | 0.983665i | \(0.557613\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −921.894 | −0.0476188 | ||||||||
\(722\) | 2005.67 | 0.103384 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15918.0 | 0.817108 | ||||||||
\(725\) | 10762.8 | 0.551336 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3587.40 | 0.183011 | 0.0915056 | − | 0.995805i | \(-0.470832\pi\) | ||||
0.0915056 | + | 0.995805i | \(0.470832\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15561.8 | −0.788998 | ||||||||
\(731\) | 1172.09 | 0.0593039 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32867.4 | 1.65619 | 0.828093 | − | 0.560591i | \(-0.189426\pi\) | ||||
0.828093 | + | 0.560591i | \(0.189426\pi\) | |||||||
\(734\) | 2423.66 | 0.121879 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25580.4 | −1.28112 | ||||||||
\(737\) | −46.3089 | −0.00231453 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19818.9 | −0.986534 | −0.493267 | − | 0.869878i | \(-0.664197\pi\) | ||||
−0.493267 | + | 0.869878i | \(0.664197\pi\) | |||||||
\(740\) | −15867.8 | −0.788258 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2380.20 | 0.117762 | ||||||||
\(743\) | 13341.0 | 0.658727 | 0.329364 | − | 0.944203i | \(-0.393166\pi\) | ||||
0.329364 | + | 0.944203i | \(0.393166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29526.8 | 1.45205 | ||||||||
\(746\) | −1829.35 | −0.0897818 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 53.6125 | 0.00262068 | ||||||||
\(749\) | −2470.06 | −0.120499 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32392.8 | −1.57394 | −0.786971 | − | 0.616990i | \(-0.788352\pi\) | ||||
−0.786971 | + | 0.616990i | \(0.788352\pi\) | |||||||
\(752\) | 13849.8 | 0.671607 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28474.2 | 1.37256 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6177.77 | −0.296612 | −0.148306 | − | 0.988942i | \(-0.547382\pi\) | ||||
−0.148306 | + | 0.988942i | \(0.547382\pi\) | |||||||
\(758\) | 1977.37 | 0.0947512 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17850.6 | −0.851987 | ||||||||
\(761\) | −4215.28 | −0.200793 | −0.100397 | − | 0.994947i | \(-0.532011\pi\) | ||||
−0.100397 | + | 0.994947i | \(0.532011\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4906.11 | −0.232783 | ||||||||
\(764\) | −21407.9 | −1.01376 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1923.67 | −0.0907378 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6536.90 | −0.306536 | −0.153268 | − | 0.988185i | \(-0.548980\pi\) | ||||
−0.153268 | + | 0.988185i | \(0.548980\pi\) | |||||||
\(770\) | 79.9852 | 0.00374346 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18206.1 | −0.848773 | ||||||||
\(773\) | 9953.50 | 0.463134 | 0.231567 | − | 0.972819i | \(-0.425615\pi\) | ||||
0.231567 | + | 0.972819i | \(0.425615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6939.92 | −0.321663 | ||||||||
\(776\) | −1286.40 | −0.0595091 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18726.1 | 0.862934 | ||||||||
\(779\) | −13430.9 | −0.617730 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −235.626 | −0.0107956 | ||||||||
\(782\) | −1872.95 | −0.0856479 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7837.90 | −0.357047 | ||||||||
\(785\) | 41445.1 | 1.88438 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17827.4 | −0.807467 | −0.403733 | − | 0.914877i | \(-0.632288\pi\) | ||||
−0.403733 | + | 0.914877i | \(0.632288\pi\) | |||||||
\(788\) | −505.892 | −0.0228701 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16134.3 | −0.726626 | ||||||||
\(791\) | 8391.13 | 0.377186 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 6448.78 | 0.288235 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5476.17 | 0.243841 | ||||||||
\(797\) | 249.882 | 0.0111057 | 0.00555287 | − | 0.999985i | \(-0.498232\pi\) | ||||
0.00555287 | + | 0.999985i | \(0.498232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5620.30 | 0.248851 | ||||||||
\(800\) | −7906.68 | −0.349429 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1631.17 | 0.0718185 | ||||||||
\(803\) | −764.535 | −0.0335988 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9993.00 | 0.437524 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −30972.8 | −1.34854 | ||||||||
\(809\) | −13019.9 | −0.565829 | −0.282914 | − | 0.959145i | \(-0.591301\pi\) | ||||
−0.282914 | + | 0.959145i | \(0.591301\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −956.251 | −0.0414038 | −0.0207019 | − | 0.999786i | \(-0.506590\pi\) | ||||
−0.0207019 | + | 0.999786i | \(0.506590\pi\) | |||||||
\(812\) | −8677.96 | −0.375045 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 217.985 | 0.00938622 | ||||||||
\(815\) | 39960.8 | 1.71750 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8410.48 | −0.360153 | ||||||||
\(818\) | −6760.62 | −0.288973 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14890.0 | −0.634124 | ||||||||
\(821\) | 7853.26 | 0.333837 | 0.166919 | − | 0.985971i | \(-0.446618\pi\) | ||||
0.166919 | + | 0.985971i | \(0.446618\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33820.9 | 1.43247 | 0.716236 | − | 0.697858i | \(-0.245863\pi\) | ||||
0.716236 | + | 0.697858i | \(0.245863\pi\) | |||||||
\(824\) | −3133.48 | −0.132476 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3823.06 | 0.161043 | ||||||||
\(827\) | −7297.39 | −0.306838 | −0.153419 | − | 0.988161i | \(-0.549028\pi\) | ||||
−0.153419 | + | 0.988161i | \(0.549028\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8454.13 | −0.354191 | −0.177095 | − | 0.984194i | \(-0.556670\pi\) | ||||
−0.177095 | + | 0.984194i | \(0.556670\pi\) | |||||||
\(830\) | 16221.0 | 0.678360 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3180.66 | −0.132297 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6792.60 | 0.281518 | ||||||||
\(836\) | −384.705 | −0.0159154 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11410.8 | 0.470380 | ||||||||
\(839\) | 32007.9 | 1.31709 | 0.658543 | − | 0.752543i | \(-0.271173\pi\) | ||||
0.658543 | + | 0.752543i | \(0.271173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38299.5 | 1.57036 | ||||||||
\(842\) | −17539.7 | −0.717885 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24150.0 | 0.984925 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7375.02 | −0.299184 | ||||||||
\(848\) | −8150.45 | −0.330056 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −578.914 | −0.0233607 | ||||||||
\(851\) | 27234.1 | 1.09703 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9986.02 | 0.400838 | 0.200419 | − | 0.979710i | \(-0.435770\pi\) | ||||
0.200419 | + | 0.979710i | \(0.435770\pi\) | |||||||
\(854\) | 3258.84 | 0.130580 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8395.62 | −0.335229 | ||||||||
\(857\) | −289.524 | −0.0115402 | −0.00577010 | − | 0.999983i | \(-0.501837\pi\) | ||||
−0.00577010 | + | 0.999983i | \(0.501837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7833.85 | −0.311161 | −0.155581 | − | 0.987823i | \(-0.549725\pi\) | ||||
−0.155581 | + | 0.987823i | \(0.549725\pi\) | |||||||
\(860\) | −9324.18 | −0.369712 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6104.77 | 0.241217 | ||||||||
\(863\) | −33370.8 | −1.31629 | −0.658143 | − | 0.752893i | \(-0.728658\pi\) | ||||
−0.658143 | + | 0.752893i | \(0.728658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38645.4 | −1.51906 | ||||||||
\(866\) | −16506.8 | −0.647720 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5595.62 | 0.218811 | ||||||||
\(869\) | −792.663 | −0.0309428 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −16675.7 | −0.647602 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13439.7 | 0.520141 | ||||||||
\(875\) | −5893.04 | −0.227681 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25422.4 | −0.978852 | −0.489426 | − | 0.872045i | \(-0.662794\pi\) | ||||
−0.489426 | + | 0.872045i | \(0.662794\pi\) | |||||||
\(878\) | 7495.35 | 0.288105 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −273.892 | −0.0104919 | ||||||||
\(881\) | −40373.6 | −1.54395 | −0.771976 | − | 0.635652i | \(-0.780731\pi\) | ||||
−0.771976 | + | 0.635652i | \(0.780731\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16898.9 | −0.644045 | −0.322023 | − | 0.946732i | \(-0.604363\pi\) | ||||
−0.322023 | + | 0.946732i | \(0.604363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6348.41 | 0.240721 | ||||||||
\(887\) | −49889.1 | −1.88851 | −0.944257 | − | 0.329210i | \(-0.893218\pi\) | ||||
−0.944257 | + | 0.329210i | \(0.893218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14327.7 | 0.540536 | ||||||||
\(890\) | 565.316 | 0.0212915 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −39957.0 | −1.49984 | ||||||||
\(893\) | −40329.3 | −1.51127 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4314.21 | 0.161126 | ||||||||
\(896\) | 7847.01 | 0.292578 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21490.8 | −0.798618 | ||||||||
\(899\) | −40422.0 | −1.49961 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3307.49 | −0.122296 | ||||||||
\(902\) | 204.553 | 0.00755087 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28521.1 | 1.04933 | ||||||||
\(905\) | −33000.2 | −1.21212 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3061.06 | −0.112063 | −0.0560313 | − | 0.998429i | \(-0.517845\pi\) | ||||
−0.0560313 | + | 0.998429i | \(0.517845\pi\) | |||||||
\(908\) | −7948.24 | −0.290497 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15247.2 | 0.554514 | 0.277257 | − | 0.960796i | \(-0.410575\pi\) | ||||
0.277257 | + | 0.960796i | \(0.410575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 796.920 | 0.0288874 | ||||||||
\(914\) | −10109.5 | −0.365856 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −37290.4 | −1.34510 | ||||||||
\(917\) | 8240.11 | 0.296742 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29419.2 | −1.05599 | −0.527993 | − | 0.849249i | \(-0.677055\pi\) | ||||
−0.527993 | + | 0.849249i | \(0.677055\pi\) | |||||||
\(920\) | 33965.8 | 1.21719 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7464.60 | 0.266631 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8417.85 | 0.299219 | ||||||||
\(926\) | −4153.03 | −0.147383 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −46053.0 | −1.62906 | ||||||||
\(929\) | 16910.0 | 0.597200 | 0.298600 | − | 0.954378i | \(-0.403480\pi\) | ||||
0.298600 | + | 0.954378i | \(0.403480\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22823.3 | 0.803440 | ||||||||
\(932\) | −32265.6 | −1.13401 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1632.59 | −0.0571948 | ||||||||
\(935\) | −111.146 | −0.00388757 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32828.7 | 1.14457 | 0.572287 | − | 0.820053i | \(-0.306056\pi\) | ||||
0.572287 | + | 0.820053i | \(0.306056\pi\) | |||||||
\(938\) | −403.187 | −0.0140347 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −44710.6 | −1.55138 | ||||||||
\(941\) | −22244.7 | −0.770623 | −0.385311 | − | 0.922787i | \(-0.625906\pi\) | ||||
−0.385311 | + | 0.922787i | \(0.625906\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25556.0 | 0.882522 | ||||||||
\(944\) | −13091.2 | −0.451359 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 128.092 | 0.00440236 | ||||||||
\(947\) | −17502.1 | −0.600573 | −0.300287 | − | 0.953849i | \(-0.597082\pi\) | ||||
−0.300287 | + | 0.953849i | \(0.597082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4154.08 | 0.141870 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1064.07 | 0.0362256 | ||||||||
\(953\) | −31522.6 | −1.07148 | −0.535739 | − | 0.844384i | \(-0.679967\pi\) | ||||
−0.535739 | + | 0.844384i | \(0.679967\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44381.6 | 1.50383 | ||||||||
\(956\) | 23752.8 | 0.803578 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15546.4 | −0.524301 | ||||||||
\(959\) | −8213.34 | −0.276562 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3726.54 | −0.125090 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 753.358 | 0.0251701 | ||||||||
\(965\) | 37743.9 | 1.25909 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35433.0 | 1.17833 | 0.589167 | − | 0.808011i | \(-0.299456\pi\) | ||||
0.589167 | + | 0.808011i | \(0.299456\pi\) | |||||||
\(968\) | −25067.4 | −0.832330 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1169.88 | 0.0387243 | ||||||||
\(971\) | 5907.77 | 0.195252 | 0.0976258 | − | 0.995223i | \(-0.468875\pi\) | ||||
0.0976258 | + | 0.995223i | \(0.468875\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5085.88 | −0.167570 | ||||||||
\(974\) | −11437.2 | −0.376254 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11159.2 | −0.365980 | ||||||||
\(977\) | 231.490 | 0.00758035 | 0.00379018 | − | 0.999993i | \(-0.498794\pi\) | ||||
0.00379018 | + | 0.999993i | \(0.498794\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.7734 | 0.000906681 0 | ||||||||
\(980\) | 25302.8 | 0.824762 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5049.65 | −0.164094 | ||||||||
\(983\) | 7577.90 | 0.245877 | 0.122939 | − | 0.992414i | \(-0.460768\pi\) | ||||
0.122939 | + | 0.992414i | \(0.460768\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1048.79 | 0.0339260 | ||||||||
\(986\) | −3371.93 | −0.108909 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16003.3 | 0.514534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6578.71 | −0.210878 | −0.105439 | − | 0.994426i | \(-0.533625\pi\) | ||||
−0.105439 | + | 0.994426i | \(0.533625\pi\) | |||||||
\(992\) | 29695.4 | 0.950433 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2051.47 | −0.0654615 | ||||||||
\(995\) | −11352.9 | −0.361719 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14907.8 | 0.473556 | 0.236778 | − | 0.971564i | \(-0.423909\pi\) | ||||
0.236778 | + | 0.971564i | \(0.423909\pi\) | |||||||
\(998\) | −22580.0 | −0.716190 | ||||||||
\(999\) | 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 | 1521.4.a.bn.1.7 | yes | 18 | |
3.2 | odd | 2 | inner | 1521.4.a.bn.1.12 | yes | 18 | |
13.12 | even | 2 | 1521.4.a.bm.1.12 | yes | 18 | ||
39.38 | odd | 2 | 1521.4.a.bm.1.7 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1521.4.a.bm.1.7 | ✓ | 18 | 39.38 | odd | 2 | ||
1521.4.a.bm.1.12 | yes | 18 | 13.12 | even | 2 | ||
1521.4.a.bn.1.7 | yes | 18 | 1.1 | even | 1 | trivial | |
1521.4.a.bn.1.12 | yes | 18 | 3.2 | odd | 2 | inner |