Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("825.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(48.6765757547\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 15x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.76300\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.76300 | −1.33042 | −0.665211 | − | 0.746655i | \(-0.731659\pi\) | ||||
−0.665211 | + | 0.746655i | \(0.731659\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 6.16019 | 0.770024 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 11.2890 | 0.768120 | ||||||||
\(7\) | 23.6321 | 1.27601 | 0.638007 | − | 0.770031i | \(-0.279759\pi\) | ||||
0.638007 | + | 0.770031i | \(0.279759\pi\) | |||||||
\(8\) | 6.92320 | 0.305965 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −18.4806 | −0.444574 | ||||||||
\(13\) | −7.39511 | −0.157772 | −0.0788860 | − | 0.996884i | \(-0.525136\pi\) | ||||
−0.0788860 | + | 0.996884i | \(0.525136\pi\) | |||||||
\(14\) | −88.9277 | −1.69764 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −75.3336 | −1.17709 | ||||||||
\(17\) | −8.68828 | −0.123954 | −0.0619770 | − | 0.998078i | \(-0.519741\pi\) | ||||
−0.0619770 | + | 0.998078i | \(0.519741\pi\) | |||||||
\(18\) | −33.8670 | −0.443474 | ||||||||
\(19\) | −69.7002 | −0.841597 | −0.420798 | − | 0.907154i | \(-0.638250\pi\) | ||||
−0.420798 | + | 0.907154i | \(0.638250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −70.8963 | −0.736707 | ||||||||
\(22\) | −41.3930 | −0.401137 | ||||||||
\(23\) | 10.1643 | 0.0921484 | 0.0460742 | − | 0.998938i | \(-0.485329\pi\) | ||||
0.0460742 | + | 0.998938i | \(0.485329\pi\) | |||||||
\(24\) | −20.7696 | −0.176649 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 27.8278 | 0.209903 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 145.578 | 0.982562 | ||||||||
\(29\) | −73.2803 | −0.469235 | −0.234617 | − | 0.972088i | \(-0.575384\pi\) | ||||
−0.234617 | + | 0.972088i | \(0.575384\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −290.970 | −1.68580 | −0.842898 | − | 0.538073i | \(-0.819153\pi\) | ||||
−0.842898 | + | 0.538073i | \(0.819153\pi\) | |||||||
\(32\) | 228.095 | 1.26006 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | 32.6940 | 0.164911 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 55.4417 | 0.256675 | ||||||||
\(37\) | 105.618 | 0.469284 | 0.234642 | − | 0.972082i | \(-0.424608\pi\) | ||||
0.234642 | + | 0.972082i | \(0.424608\pi\) | |||||||
\(38\) | 262.282 | 1.11968 | ||||||||
\(39\) | 22.1853 | 0.0910897 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.5108 | 0.154310 | 0.0771551 | − | 0.997019i | \(-0.475416\pi\) | ||||
0.0771551 | + | 0.997019i | \(0.475416\pi\) | |||||||
\(42\) | 266.783 | 0.980132 | ||||||||
\(43\) | 77.3133 | 0.274190 | 0.137095 | − | 0.990558i | \(-0.456223\pi\) | ||||
0.137095 | + | 0.990558i | \(0.456223\pi\) | |||||||
\(44\) | 67.7621 | 0.232171 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −38.2485 | −0.122596 | ||||||||
\(47\) | 472.981 | 1.46790 | 0.733951 | − | 0.679202i | \(-0.237674\pi\) | ||||
0.733951 | + | 0.679202i | \(0.237674\pi\) | |||||||
\(48\) | 226.001 | 0.679591 | ||||||||
\(49\) | 215.477 | 0.628212 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 26.0648 | 0.0715648 | ||||||||
\(52\) | −45.5553 | −0.121488 | ||||||||
\(53\) | −205.479 | −0.532541 | −0.266271 | − | 0.963898i | \(-0.585792\pi\) | ||||
−0.266271 | + | 0.963898i | \(0.585792\pi\) | |||||||
\(54\) | 101.601 | 0.256040 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 163.610 | 0.390416 | ||||||||
\(57\) | 209.101 | 0.485896 | ||||||||
\(58\) | 275.754 | 0.624281 | ||||||||
\(59\) | 330.261 | 0.728751 | 0.364376 | − | 0.931252i | \(-0.381282\pi\) | ||||
0.364376 | + | 0.931252i | \(0.381282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −931.991 | −1.95622 | −0.978109 | − | 0.208094i | \(-0.933274\pi\) | ||||
−0.978109 | + | 0.208094i | \(0.933274\pi\) | |||||||
\(62\) | 1094.92 | 2.24282 | ||||||||
\(63\) | 212.689 | 0.425338 | ||||||||
\(64\) | −255.653 | −0.499323 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 124.179 | 0.231597 | ||||||||
\(67\) | 418.252 | 0.762652 | 0.381326 | − | 0.924441i | \(-0.375468\pi\) | ||||
0.381326 | + | 0.924441i | \(0.375468\pi\) | |||||||
\(68\) | −53.5215 | −0.0954475 | ||||||||
\(69\) | −30.4930 | −0.0532019 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −506.329 | −0.846340 | −0.423170 | − | 0.906050i | \(-0.639083\pi\) | ||||
−0.423170 | + | 0.906050i | \(0.639083\pi\) | |||||||
\(72\) | 62.3088 | 0.101988 | ||||||||
\(73\) | −612.497 | −0.982018 | −0.491009 | − | 0.871154i | \(-0.663372\pi\) | ||||
−0.491009 | + | 0.871154i | \(0.663372\pi\) | |||||||
\(74\) | −397.441 | −0.624346 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −429.367 | −0.648050 | ||||||||
\(77\) | 259.953 | 0.384733 | ||||||||
\(78\) | −83.4835 | −0.121188 | ||||||||
\(79\) | 54.6657 | 0.0778528 | 0.0389264 | − | 0.999242i | \(-0.487606\pi\) | ||||
0.0389264 | + | 0.999242i | \(0.487606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −152.442 | −0.205298 | ||||||||
\(83\) | −538.964 | −0.712759 | −0.356379 | − | 0.934341i | \(-0.615989\pi\) | ||||
−0.356379 | + | 0.934341i | \(0.615989\pi\) | |||||||
\(84\) | −436.735 | −0.567282 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −290.930 | −0.364788 | ||||||||
\(87\) | 219.841 | 0.270913 | ||||||||
\(88\) | 76.1552 | 0.0922519 | ||||||||
\(89\) | 781.086 | 0.930280 | 0.465140 | − | 0.885237i | \(-0.346004\pi\) | ||||
0.465140 | + | 0.885237i | \(0.346004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −174.762 | −0.201319 | ||||||||
\(92\) | 62.6144 | 0.0709565 | ||||||||
\(93\) | 872.909 | 0.973295 | ||||||||
\(94\) | −1779.83 | −1.95293 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −684.285 | −0.727495 | ||||||||
\(97\) | 531.762 | 0.556621 | 0.278311 | − | 0.960491i | \(-0.410226\pi\) | ||||
0.278311 | + | 0.960491i | \(0.410226\pi\) | |||||||
\(98\) | −810.839 | −0.835787 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1898.16 | 1.87004 | 0.935022 | − | 0.354591i | \(-0.115380\pi\) | ||||
0.935022 | + | 0.354591i | \(0.115380\pi\) | |||||||
\(102\) | −98.0820 | −0.0952115 | ||||||||
\(103\) | −1308.66 | −1.25190 | −0.625952 | − | 0.779861i | \(-0.715290\pi\) | ||||
−0.625952 | + | 0.779861i | \(0.715290\pi\) | |||||||
\(104\) | −51.1978 | −0.0482727 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 773.218 | 0.708505 | ||||||||
\(107\) | −206.655 | −0.186711 | −0.0933554 | − | 0.995633i | \(-0.529759\pi\) | ||||
−0.0933554 | + | 0.995633i | \(0.529759\pi\) | |||||||
\(108\) | −166.325 | −0.148191 | ||||||||
\(109\) | 595.701 | 0.523466 | 0.261733 | − | 0.965140i | \(-0.415706\pi\) | ||||
0.261733 | + | 0.965140i | \(0.415706\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −316.854 | −0.270941 | ||||||||
\(112\) | −1780.29 | −1.50198 | ||||||||
\(113\) | −1513.00 | −1.25957 | −0.629785 | − | 0.776769i | \(-0.716857\pi\) | ||||
−0.629785 | + | 0.776769i | \(0.716857\pi\) | |||||||
\(114\) | −786.847 | −0.646447 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −451.421 | −0.361322 | ||||||||
\(117\) | −66.5560 | −0.0525907 | ||||||||
\(118\) | −1242.77 | −0.969547 | ||||||||
\(119\) | −205.322 | −0.158167 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 3507.09 | 2.60260 | ||||||||
\(123\) | −121.532 | −0.0890911 | ||||||||
\(124\) | −1792.43 | −1.29810 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −800.349 | −0.565879 | ||||||||
\(127\) | −77.9297 | −0.0544499 | −0.0272250 | − | 0.999629i | \(-0.508667\pi\) | ||||
−0.0272250 | + | 0.999629i | \(0.508667\pi\) | |||||||
\(128\) | −862.735 | −0.595748 | ||||||||
\(129\) | −231.940 | −0.158304 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.60213 | −0.00573719 | −0.00286859 | − | 0.999996i | \(-0.500913\pi\) | ||||
−0.00286859 | + | 0.999996i | \(0.500913\pi\) | |||||||
\(132\) | −203.286 | −0.134044 | ||||||||
\(133\) | −1647.16 | −1.07389 | ||||||||
\(134\) | −1573.89 | −1.01465 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −60.1507 | −0.0379256 | ||||||||
\(137\) | 665.161 | 0.414807 | 0.207403 | − | 0.978255i | \(-0.433499\pi\) | ||||
0.207403 | + | 0.978255i | \(0.433499\pi\) | |||||||
\(138\) | 114.745 | 0.0707810 | ||||||||
\(139\) | 745.658 | 0.455006 | 0.227503 | − | 0.973777i | \(-0.426944\pi\) | ||||
0.227503 | + | 0.973777i | \(0.426944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1418.94 | −0.847494 | ||||||||
\(142\) | 1905.32 | 1.12599 | ||||||||
\(143\) | −81.3462 | −0.0475700 | ||||||||
\(144\) | −678.002 | −0.392362 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2304.83 | 1.30650 | ||||||||
\(147\) | −646.430 | −0.362698 | ||||||||
\(148\) | 650.628 | 0.361360 | ||||||||
\(149\) | −2398.49 | −1.31874 | −0.659370 | − | 0.751819i | \(-0.729177\pi\) | ||||
−0.659370 | + | 0.751819i | \(0.729177\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3254.28 | −1.75384 | −0.876920 | − | 0.480637i | \(-0.840405\pi\) | ||||
−0.876920 | + | 0.480637i | \(0.840405\pi\) | |||||||
\(152\) | −482.549 | −0.257499 | ||||||||
\(153\) | −78.1945 | −0.0413180 | ||||||||
\(154\) | −978.205 | −0.511857 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 136.666 | 0.0701413 | ||||||||
\(157\) | −2492.15 | −1.26685 | −0.633424 | − | 0.773805i | \(-0.718351\pi\) | ||||
−0.633424 | + | 0.773805i | \(0.718351\pi\) | |||||||
\(158\) | −205.707 | −0.103577 | ||||||||
\(159\) | 616.437 | 0.307463 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 240.205 | 0.117583 | ||||||||
\(162\) | −304.803 | −0.147825 | ||||||||
\(163\) | 807.550 | 0.388050 | 0.194025 | − | 0.980997i | \(-0.437846\pi\) | ||||
0.194025 | + | 0.980997i | \(0.437846\pi\) | |||||||
\(164\) | 249.554 | 0.118823 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2028.12 | 0.948270 | ||||||||
\(167\) | −1833.28 | −0.849484 | −0.424742 | − | 0.905314i | \(-0.639635\pi\) | ||||
−0.424742 | + | 0.905314i | \(0.639635\pi\) | |||||||
\(168\) | −490.829 | −0.225407 | ||||||||
\(169\) | −2142.31 | −0.975108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −627.302 | −0.280532 | ||||||||
\(172\) | 476.265 | 0.211133 | ||||||||
\(173\) | 1046.74 | 0.460011 | 0.230005 | − | 0.973189i | \(-0.426126\pi\) | ||||
0.230005 | + | 0.973189i | \(0.426126\pi\) | |||||||
\(174\) | −827.262 | −0.360429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −828.669 | −0.354905 | ||||||||
\(177\) | −990.783 | −0.420745 | ||||||||
\(178\) | −2939.23 | −1.23767 | ||||||||
\(179\) | 1880.80 | 0.785348 | 0.392674 | − | 0.919678i | \(-0.371550\pi\) | ||||
0.392674 | + | 0.919678i | \(0.371550\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1921.82 | −0.789216 | −0.394608 | − | 0.918850i | \(-0.629120\pi\) | ||||
−0.394608 | + | 0.918850i | \(0.629120\pi\) | |||||||
\(182\) | 657.630 | 0.267840 | ||||||||
\(183\) | 2795.97 | 1.12942 | ||||||||
\(184\) | 70.3698 | 0.0281942 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3284.76 | −1.29489 | ||||||||
\(187\) | −95.5711 | −0.0373735 | ||||||||
\(188\) | 2913.66 | 1.13032 | ||||||||
\(189\) | −638.067 | −0.245569 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 203.716 | 0.0771747 | 0.0385874 | − | 0.999255i | \(-0.487714\pi\) | ||||
0.0385874 | + | 0.999255i | \(0.487714\pi\) | |||||||
\(192\) | 766.960 | 0.288284 | ||||||||
\(193\) | −2858.36 | −1.06606 | −0.533030 | − | 0.846096i | \(-0.678947\pi\) | ||||
−0.533030 | + | 0.846096i | \(0.678947\pi\) | |||||||
\(194\) | −2001.02 | −0.740542 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1327.38 | 0.483738 | ||||||||
\(197\) | 1140.57 | 0.412499 | 0.206250 | − | 0.978499i | \(-0.433874\pi\) | ||||
0.206250 | + | 0.978499i | \(0.433874\pi\) | |||||||
\(198\) | −372.537 | −0.133712 | ||||||||
\(199\) | −3223.56 | −1.14830 | −0.574151 | − | 0.818749i | \(-0.694668\pi\) | ||||
−0.574151 | + | 0.818749i | \(0.694668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1254.76 | −0.440317 | ||||||||
\(202\) | −7142.80 | −2.48795 | ||||||||
\(203\) | −1731.77 | −0.598750 | ||||||||
\(204\) | 160.564 | 0.0551067 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4924.50 | 1.66556 | ||||||||
\(207\) | 91.4791 | 0.0307161 | ||||||||
\(208\) | 557.100 | 0.185711 | ||||||||
\(209\) | −766.703 | −0.253751 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1679.38 | 0.547930 | 0.273965 | − | 0.961740i | \(-0.411665\pi\) | ||||
0.273965 | + | 0.961740i | \(0.411665\pi\) | |||||||
\(212\) | −1265.79 | −0.410070 | ||||||||
\(213\) | 1518.99 | 0.488635 | ||||||||
\(214\) | 777.642 | 0.248404 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −186.926 | −0.0588830 | ||||||||
\(217\) | −6876.23 | −2.15110 | ||||||||
\(218\) | −2241.62 | −0.696431 | ||||||||
\(219\) | 1837.49 | 0.566969 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 64.2508 | 0.0195565 | ||||||||
\(222\) | 1192.32 | 0.360466 | ||||||||
\(223\) | 6121.75 | 1.83831 | 0.919154 | − | 0.393898i | \(-0.128874\pi\) | ||||
0.919154 | + | 0.393898i | \(0.128874\pi\) | |||||||
\(224\) | 5390.36 | 1.60785 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5693.44 | 1.67576 | ||||||||
\(227\) | 1760.23 | 0.514671 | 0.257335 | − | 0.966322i | \(-0.417155\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417155\pi\) | |||||||
\(228\) | 1288.10 | 0.374152 | ||||||||
\(229\) | −5780.58 | −1.66808 | −0.834042 | − | 0.551700i | \(-0.813979\pi\) | ||||
−0.834042 | + | 0.551700i | \(0.813979\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −779.860 | −0.222126 | ||||||||
\(232\) | −507.334 | −0.143569 | ||||||||
\(233\) | −5433.94 | −1.52785 | −0.763925 | − | 0.645305i | \(-0.776730\pi\) | ||||
−0.763925 | + | 0.645305i | \(0.776730\pi\) | |||||||
\(234\) | 250.451 | 0.0699678 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2034.47 | 0.561156 | ||||||||
\(237\) | −163.997 | −0.0449484 | ||||||||
\(238\) | 772.629 | 0.210429 | ||||||||
\(239\) | 583.827 | 0.158011 | 0.0790055 | − | 0.996874i | \(-0.474826\pi\) | ||||
0.0790055 | + | 0.996874i | \(0.474826\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4217.86 | 1.12737 | 0.563686 | − | 0.825989i | \(-0.309383\pi\) | ||||
0.563686 | + | 0.825989i | \(0.309383\pi\) | |||||||
\(242\) | −455.323 | −0.120948 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −5741.25 | −1.50633 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 457.327 | 0.118529 | ||||||||
\(247\) | 515.441 | 0.132780 | ||||||||
\(248\) | −2014.44 | −0.515795 | ||||||||
\(249\) | 1616.89 | 0.411511 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4836.75 | −1.21631 | −0.608153 | − | 0.793820i | \(-0.708089\pi\) | ||||
−0.608153 | + | 0.793820i | \(0.708089\pi\) | |||||||
\(252\) | 1310.21 | 0.327521 | ||||||||
\(253\) | 111.808 | 0.0277838 | ||||||||
\(254\) | 293.250 | 0.0724414 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5291.70 | 1.29192 | ||||||||
\(257\) | 4654.14 | 1.12964 | 0.564819 | − | 0.825215i | \(-0.308946\pi\) | ||||
0.564819 | + | 0.825215i | \(0.308946\pi\) | |||||||
\(258\) | 872.790 | 0.210611 | ||||||||
\(259\) | 2495.98 | 0.598813 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −659.523 | −0.156412 | ||||||||
\(262\) | 32.3698 | 0.00763288 | ||||||||
\(263\) | −5102.11 | −1.19624 | −0.598118 | − | 0.801408i | \(-0.704084\pi\) | ||||
−0.598118 | + | 0.801408i | \(0.704084\pi\) | |||||||
\(264\) | −228.466 | −0.0532617 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6198.28 | 1.42873 | ||||||||
\(267\) | −2343.26 | −0.537097 | ||||||||
\(268\) | 2576.52 | 0.587260 | ||||||||
\(269\) | 4475.15 | 1.01433 | 0.507165 | − | 0.861849i | \(-0.330694\pi\) | ||||
0.507165 | + | 0.861849i | \(0.330694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7829.40 | −1.75499 | −0.877495 | − | 0.479586i | \(-0.840787\pi\) | ||||
−0.877495 | + | 0.479586i | \(0.840787\pi\) | |||||||
\(272\) | 654.519 | 0.145905 | ||||||||
\(273\) | 524.286 | 0.116232 | ||||||||
\(274\) | −2503.00 | −0.551868 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −187.843 | −0.0409668 | ||||||||
\(277\) | −3692.51 | −0.800943 | −0.400472 | − | 0.916309i | \(-0.631154\pi\) | ||||
−0.400472 | + | 0.916309i | \(0.631154\pi\) | |||||||
\(278\) | −2805.91 | −0.605351 | ||||||||
\(279\) | −2618.73 | −0.561932 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1296.21 | −0.275179 | −0.137589 | − | 0.990489i | \(-0.543935\pi\) | ||||
−0.137589 | + | 0.990489i | \(0.543935\pi\) | |||||||
\(282\) | 5339.49 | 1.12752 | ||||||||
\(283\) | −1168.50 | −0.245442 | −0.122721 | − | 0.992441i | \(-0.539162\pi\) | ||||
−0.122721 | + | 0.992441i | \(0.539162\pi\) | |||||||
\(284\) | −3119.08 | −0.651703 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 306.106 | 0.0632882 | ||||||||
\(287\) | 957.355 | 0.196902 | ||||||||
\(288\) | 2052.85 | 0.420019 | ||||||||
\(289\) | −4837.51 | −0.984635 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1595.29 | −0.321365 | ||||||||
\(292\) | −3773.10 | −0.756178 | ||||||||
\(293\) | 8879.43 | 1.77045 | 0.885224 | − | 0.465164i | \(-0.154005\pi\) | ||||
0.885224 | + | 0.465164i | \(0.154005\pi\) | |||||||
\(294\) | 2432.52 | 0.482542 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 731.215 | 0.143584 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | 9025.54 | 1.75448 | ||||||||
\(299\) | −75.1665 | −0.0145384 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1827.08 | 0.349870 | ||||||||
\(302\) | 12245.9 | 2.33335 | ||||||||
\(303\) | −5694.49 | −1.07967 | ||||||||
\(304\) | 5250.77 | 0.990632 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 294.246 | 0.0549704 | ||||||||
\(307\) | 4724.14 | 0.878244 | 0.439122 | − | 0.898427i | \(-0.355290\pi\) | ||||
0.439122 | + | 0.898427i | \(0.355290\pi\) | |||||||
\(308\) | 1601.36 | 0.296253 | ||||||||
\(309\) | 3925.98 | 0.722788 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 53.7156 | 0.00979399 | 0.00489700 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489700 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(312\) | 153.593 | 0.0278703 | ||||||||
\(313\) | 4663.77 | 0.842210 | 0.421105 | − | 0.907012i | \(-0.361642\pi\) | ||||
0.421105 | + | 0.907012i | \(0.361642\pi\) | |||||||
\(314\) | 9377.96 | 1.68544 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 336.751 | 0.0599486 | ||||||||
\(317\) | −8664.97 | −1.53525 | −0.767624 | − | 0.640901i | \(-0.778561\pi\) | ||||
−0.767624 | + | 0.640901i | \(0.778561\pi\) | |||||||
\(318\) | −2319.65 | −0.409056 | ||||||||
\(319\) | −806.084 | −0.141480 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 619.964 | 0.107798 | ||||||||
\(322\) | −903.892 | −0.156435 | ||||||||
\(323\) | 605.575 | 0.104319 | ||||||||
\(324\) | 498.976 | 0.0855582 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3038.81 | −0.516271 | ||||||||
\(327\) | −1787.10 | −0.302223 | ||||||||
\(328\) | 280.464 | 0.0472135 | ||||||||
\(329\) | 11177.5 | 1.87306 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3422.54 | −0.568337 | −0.284169 | − | 0.958774i | \(-0.591718\pi\) | ||||
−0.284169 | + | 0.958774i | \(0.591718\pi\) | |||||||
\(332\) | −3320.12 | −0.548841 | ||||||||
\(333\) | 950.563 | 0.156428 | ||||||||
\(334\) | 6898.66 | 1.13017 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5340.87 | 0.867168 | ||||||||
\(337\) | −118.863 | −0.0192134 | −0.00960668 | − | 0.999954i | \(-0.503058\pi\) | ||||
−0.00960668 | + | 0.999954i | \(0.503058\pi\) | |||||||
\(338\) | 8061.53 | 1.29731 | ||||||||
\(339\) | 4539.01 | 0.727213 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3200.67 | −0.508287 | ||||||||
\(342\) | 2360.54 | 0.373226 | ||||||||
\(343\) | −3013.65 | −0.474407 | ||||||||
\(344\) | 535.255 | 0.0838925 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3938.87 | −0.612009 | ||||||||
\(347\) | 10434.7 | 1.61431 | 0.807154 | − | 0.590341i | \(-0.201007\pi\) | ||||
0.807154 | + | 0.590341i | \(0.201007\pi\) | |||||||
\(348\) | 1354.26 | 0.208610 | ||||||||
\(349\) | 7528.91 | 1.15477 | 0.577383 | − | 0.816473i | \(-0.304074\pi\) | ||||
0.577383 | + | 0.816473i | \(0.304074\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 199.668 | 0.0303632 | ||||||||
\(352\) | 2509.04 | 0.379922 | ||||||||
\(353\) | 215.454 | 0.0324857 | 0.0162428 | − | 0.999868i | \(-0.494830\pi\) | ||||
0.0162428 | + | 0.999868i | \(0.494830\pi\) | |||||||
\(354\) | 3728.32 | 0.559768 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4811.64 | 0.716338 | ||||||||
\(357\) | 615.967 | 0.0913177 | ||||||||
\(358\) | −7077.45 | −1.04485 | ||||||||
\(359\) | 9105.02 | 1.33856 | 0.669282 | − | 0.743008i | \(-0.266602\pi\) | ||||
0.669282 | + | 0.743008i | \(0.266602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2000.88 | −0.291715 | ||||||||
\(362\) | 7231.83 | 1.04999 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | −1076.57 | −0.155021 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10521.3 | −1.50261 | ||||||||
\(367\) | −3763.06 | −0.535232 | −0.267616 | − | 0.963526i | \(-0.586236\pi\) | ||||
−0.267616 | + | 0.963526i | \(0.586236\pi\) | |||||||
\(368\) | −765.717 | −0.108467 | ||||||||
\(369\) | 364.597 | 0.0514368 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4855.90 | −0.679530 | ||||||||
\(372\) | 5377.29 | 0.749461 | ||||||||
\(373\) | −375.989 | −0.0521929 | −0.0260965 | − | 0.999659i | \(-0.508308\pi\) | ||||
−0.0260965 | + | 0.999659i | \(0.508308\pi\) | |||||||
\(374\) | 359.634 | 0.0497226 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3274.54 | 0.449127 | ||||||||
\(377\) | 541.916 | 0.0740321 | ||||||||
\(378\) | 2401.05 | 0.326711 | ||||||||
\(379\) | 2967.48 | 0.402187 | 0.201094 | − | 0.979572i | \(-0.435550\pi\) | ||||
0.201094 | + | 0.979572i | \(0.435550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 233.789 | 0.0314367 | ||||||||
\(382\) | −766.584 | −0.102675 | ||||||||
\(383\) | 1550.93 | 0.206916 | 0.103458 | − | 0.994634i | \(-0.467009\pi\) | ||||
0.103458 | + | 0.994634i | \(0.467009\pi\) | |||||||
\(384\) | 2588.20 | 0.343955 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10756.0 | 1.41831 | ||||||||
\(387\) | 695.820 | 0.0913966 | ||||||||
\(388\) | 3275.76 | 0.428612 | ||||||||
\(389\) | −7511.63 | −0.979061 | −0.489530 | − | 0.871986i | \(-0.662832\pi\) | ||||
−0.489530 | + | 0.871986i | \(0.662832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −88.3107 | −0.0114222 | ||||||||
\(392\) | 1491.79 | 0.192211 | ||||||||
\(393\) | 25.8064 | 0.00331237 | ||||||||
\(394\) | −4291.97 | −0.548798 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 609.859 | 0.0773903 | ||||||||
\(397\) | −11125.1 | −1.40643 | −0.703217 | − | 0.710975i | \(-0.748254\pi\) | ||||
−0.703217 | + | 0.710975i | \(0.748254\pi\) | |||||||
\(398\) | 12130.3 | 1.52773 | ||||||||
\(399\) | 4941.49 | 0.620010 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13478.0 | −1.67845 | −0.839225 | − | 0.543784i | \(-0.816991\pi\) | ||||
−0.839225 | + | 0.543784i | \(0.816991\pi\) | |||||||
\(402\) | 4721.66 | 0.585808 | ||||||||
\(403\) | 2151.75 | 0.265971 | ||||||||
\(404\) | 11693.1 | 1.43998 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6516.65 | 0.796591 | ||||||||
\(407\) | 1161.80 | 0.141494 | ||||||||
\(408\) | 180.452 | 0.0218963 | ||||||||
\(409\) | 12911.4 | 1.56095 | 0.780474 | − | 0.625188i | \(-0.214978\pi\) | ||||
0.780474 | + | 0.625188i | \(0.214978\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1995.48 | −0.239489 | ||||||||
\(412\) | −8061.61 | −0.963997 | ||||||||
\(413\) | 7804.76 | 0.929897 | ||||||||
\(414\) | −344.236 | −0.0408654 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1686.79 | −0.198802 | ||||||||
\(417\) | −2236.97 | −0.262698 | ||||||||
\(418\) | 2885.10 | 0.337596 | ||||||||
\(419\) | −8906.41 | −1.03844 | −0.519220 | − | 0.854640i | \(-0.673778\pi\) | ||||
−0.519220 | + | 0.854640i | \(0.673778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1852.36 | 0.214439 | 0.107219 | − | 0.994235i | \(-0.465805\pi\) | ||||
0.107219 | + | 0.994235i | \(0.465805\pi\) | |||||||
\(422\) | −6319.51 | −0.728978 | ||||||||
\(423\) | 4256.83 | 0.489301 | ||||||||
\(424\) | −1422.57 | −0.162939 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5715.95 | −0.650091 | ||||||||
\(427\) | −22024.9 | −2.49616 | ||||||||
\(428\) | −1273.03 | −0.143772 | ||||||||
\(429\) | 244.039 | 0.0274646 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4090.74 | −0.457178 | −0.228589 | − | 0.973523i | \(-0.573411\pi\) | ||||
−0.228589 | + | 0.973523i | \(0.573411\pi\) | |||||||
\(432\) | 2034.01 | 0.226530 | ||||||||
\(433\) | −8253.94 | −0.916071 | −0.458036 | − | 0.888934i | \(-0.651447\pi\) | ||||
−0.458036 | + | 0.888934i | \(0.651447\pi\) | |||||||
\(434\) | 25875.3 | 2.86187 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3669.63 | 0.403082 | ||||||||
\(437\) | −708.458 | −0.0775518 | ||||||||
\(438\) | −6914.48 | −0.754308 | ||||||||
\(439\) | 979.240 | 0.106461 | 0.0532307 | − | 0.998582i | \(-0.483048\pi\) | ||||
0.0532307 | + | 0.998582i | \(0.483048\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1939.29 | 0.209404 | ||||||||
\(442\) | −241.776 | −0.0260183 | ||||||||
\(443\) | −89.5194 | −0.00960089 | −0.00480045 | − | 0.999988i | \(-0.501528\pi\) | ||||
−0.00480045 | + | 0.999988i | \(0.501528\pi\) | |||||||
\(444\) | −1951.88 | −0.208631 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23036.2 | −2.44573 | ||||||||
\(447\) | 7195.48 | 0.761375 | ||||||||
\(448\) | −6041.63 | −0.637143 | ||||||||
\(449\) | −17119.1 | −1.79933 | −0.899666 | − | 0.436579i | \(-0.856190\pi\) | ||||
−0.899666 | + | 0.436579i | \(0.856190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 445.619 | 0.0465263 | ||||||||
\(452\) | −9320.40 | −0.969899 | ||||||||
\(453\) | 9762.85 | 1.01258 | ||||||||
\(454\) | −6623.74 | −0.684730 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1447.65 | 0.148667 | ||||||||
\(457\) | 1780.97 | 0.182298 | 0.0911492 | − | 0.995837i | \(-0.470946\pi\) | ||||
0.0911492 | + | 0.995837i | \(0.470946\pi\) | |||||||
\(458\) | 21752.3 | 2.21926 | ||||||||
\(459\) | 234.583 | 0.0238549 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7216.14 | −0.729043 | −0.364522 | − | 0.931195i | \(-0.618767\pi\) | ||||
−0.364522 | + | 0.931195i | \(0.618767\pi\) | |||||||
\(462\) | 2934.61 | 0.295521 | ||||||||
\(463\) | −9451.28 | −0.948679 | −0.474339 | − | 0.880342i | \(-0.657313\pi\) | ||||
−0.474339 | + | 0.880342i | \(0.657313\pi\) | |||||||
\(464\) | 5520.47 | 0.552330 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20447.9 | 2.03269 | ||||||||
\(467\) | −7188.38 | −0.712289 | −0.356144 | − | 0.934431i | \(-0.615909\pi\) | ||||
−0.356144 | + | 0.934431i | \(0.615909\pi\) | |||||||
\(468\) | −409.998 | −0.0404961 | ||||||||
\(469\) | 9884.19 | 0.973154 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7476.44 | 0.731415 | ||||||||
\(472\) | 2286.46 | 0.222972 | ||||||||
\(473\) | 850.446 | 0.0826714 | ||||||||
\(474\) | 617.122 | 0.0598003 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1264.83 | −0.121792 | ||||||||
\(477\) | −1849.31 | −0.177514 | ||||||||
\(478\) | −2196.94 | −0.210221 | ||||||||
\(479\) | −8224.85 | −0.784558 | −0.392279 | − | 0.919846i | \(-0.628313\pi\) | ||||
−0.392279 | + | 0.919846i | \(0.628313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −781.058 | −0.0740399 | ||||||||
\(482\) | −15871.8 | −1.49988 | ||||||||
\(483\) | −720.615 | −0.0678864 | ||||||||
\(484\) | 745.383 | 0.0700022 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 914.410 | 0.0853466 | ||||||||
\(487\) | 4817.49 | 0.448257 | 0.224129 | − | 0.974560i | \(-0.428046\pi\) | ||||
0.224129 | + | 0.974560i | \(0.428046\pi\) | |||||||
\(488\) | −6452.36 | −0.598534 | ||||||||
\(489\) | −2422.65 | −0.224041 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4944.04 | −0.454422 | −0.227211 | − | 0.973846i | \(-0.572961\pi\) | ||||
−0.227211 | + | 0.973846i | \(0.572961\pi\) | |||||||
\(492\) | −748.663 | −0.0686023 | ||||||||
\(493\) | 636.680 | 0.0581635 | ||||||||
\(494\) | −1939.61 | −0.176654 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21919.8 | 1.98433 | ||||||||
\(497\) | −11965.6 | −1.07994 | ||||||||
\(498\) | −6084.37 | −0.547484 | ||||||||
\(499\) | −3616.97 | −0.324485 | −0.162242 | − | 0.986751i | \(-0.551873\pi\) | ||||
−0.162242 | + | 0.986751i | \(0.551873\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5499.85 | 0.490450 | ||||||||
\(502\) | 18200.7 | 1.61820 | ||||||||
\(503\) | 1176.71 | 0.104308 | 0.0521540 | − | 0.998639i | \(-0.483391\pi\) | ||||
0.0521540 | + | 0.998639i | \(0.483391\pi\) | |||||||
\(504\) | 1472.49 | 0.130139 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −420.733 | −0.0369642 | ||||||||
\(507\) | 6426.94 | 0.562979 | ||||||||
\(508\) | −480.062 | −0.0419278 | ||||||||
\(509\) | −14606.6 | −1.27196 | −0.635981 | − | 0.771705i | \(-0.719404\pi\) | ||||
−0.635981 | + | 0.771705i | \(0.719404\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14474.6 | −1.25307 | ||||||||
\(512\) | −13010.8 | −1.12305 | ||||||||
\(513\) | 1881.91 | 0.161965 | ||||||||
\(514\) | −17513.5 | −1.50290 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1428.79 | −0.121898 | ||||||||
\(517\) | 5202.79 | 0.442589 | ||||||||
\(518\) | −9392.38 | −0.796674 | ||||||||
\(519\) | −3140.21 | −0.265587 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4175.52 | 0.351119 | 0.175559 | − | 0.984469i | \(-0.443827\pi\) | ||||
0.175559 | + | 0.984469i | \(0.443827\pi\) | |||||||
\(522\) | 2481.79 | 0.208094 | ||||||||
\(523\) | −7136.72 | −0.596686 | −0.298343 | − | 0.954459i | \(-0.596434\pi\) | ||||
−0.298343 | + | 0.954459i | \(0.596434\pi\) | |||||||
\(524\) | −52.9908 | −0.00441777 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19199.3 | 1.59150 | ||||||||
\(527\) | 2528.03 | 0.208961 | ||||||||
\(528\) | 2486.01 | 0.204905 | ||||||||
\(529\) | −12063.7 | −0.991509 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2972.35 | 0.242917 | ||||||||
\(532\) | −10146.8 | −0.826920 | ||||||||
\(533\) | −299.582 | −0.0243458 | ||||||||
\(534\) | 8817.68 | 0.714566 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2895.64 | 0.233345 | ||||||||
\(537\) | −5642.39 | −0.453421 | ||||||||
\(538\) | −16840.0 | −1.34949 | ||||||||
\(539\) | 2370.24 | 0.189413 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18984.0 | 1.50866 | 0.754329 | − | 0.656496i | \(-0.227962\pi\) | ||||
0.754329 | + | 0.656496i | \(0.227962\pi\) | |||||||
\(542\) | 29462.1 | 2.33488 | ||||||||
\(543\) | 5765.47 | 0.455654 | ||||||||
\(544\) | −1981.75 | −0.156189 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1972.89 | −0.154637 | ||||||||
\(547\) | −13084.1 | −1.02273 | −0.511366 | − | 0.859363i | \(-0.670860\pi\) | ||||
−0.511366 | + | 0.859363i | \(0.670860\pi\) | |||||||
\(548\) | 4097.52 | 0.319411 | ||||||||
\(549\) | −8387.92 | −0.652073 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5107.66 | 0.394907 | ||||||||
\(552\) | −211.109 | −0.0162779 | ||||||||
\(553\) | 1291.87 | 0.0993413 | ||||||||
\(554\) | 13894.9 | 1.06559 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4593.40 | 0.350366 | ||||||||
\(557\) | 11677.1 | 0.888284 | 0.444142 | − | 0.895956i | \(-0.353509\pi\) | ||||
0.444142 | + | 0.895956i | \(0.353509\pi\) | |||||||
\(558\) | 9854.28 | 0.747607 | ||||||||
\(559\) | −571.740 | −0.0432595 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 286.713 | 0.0215776 | ||||||||
\(562\) | 4877.63 | 0.366104 | ||||||||
\(563\) | −13214.1 | −0.989180 | −0.494590 | − | 0.869127i | \(-0.664682\pi\) | ||||
−0.494590 | + | 0.869127i | \(0.664682\pi\) | |||||||
\(564\) | −8740.97 | −0.652591 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4397.06 | 0.326541 | ||||||||
\(567\) | 1914.20 | 0.141779 | ||||||||
\(568\) | −3505.41 | −0.258951 | ||||||||
\(569\) | −22207.0 | −1.63614 | −0.818070 | − | 0.575118i | \(-0.804956\pi\) | ||||
−0.818070 | + | 0.575118i | \(0.804956\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7251.49 | −0.531463 | −0.265731 | − | 0.964047i | \(-0.585613\pi\) | ||||
−0.265731 | + | 0.964047i | \(0.585613\pi\) | |||||||
\(572\) | −501.109 | −0.0366301 | ||||||||
\(573\) | −611.148 | −0.0445569 | ||||||||
\(574\) | −3602.53 | −0.261963 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2300.88 | −0.166441 | ||||||||
\(577\) | 8190.57 | 0.590949 | 0.295475 | − | 0.955351i | \(-0.404522\pi\) | ||||
0.295475 | + | 0.955351i | \(0.404522\pi\) | |||||||
\(578\) | 18203.6 | 1.30998 | ||||||||
\(579\) | 8575.09 | 0.615490 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12736.9 | −0.909490 | ||||||||
\(582\) | 6003.07 | 0.427552 | ||||||||
\(583\) | −2260.27 | −0.160567 | ||||||||
\(584\) | −4240.44 | −0.300463 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −33413.3 | −2.35545 | ||||||||
\(587\) | −9678.56 | −0.680540 | −0.340270 | − | 0.940328i | \(-0.610518\pi\) | ||||
−0.340270 | + | 0.940328i | \(0.610518\pi\) | |||||||
\(588\) | −3982.13 | −0.279286 | ||||||||
\(589\) | 20280.7 | 1.41876 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3421.71 | −0.238156 | ||||||||
\(592\) | −7956.59 | −0.552388 | ||||||||
\(593\) | 12938.6 | 0.895994 | 0.447997 | − | 0.894035i | \(-0.352137\pi\) | ||||
0.447997 | + | 0.894035i | \(0.352137\pi\) | |||||||
\(594\) | 1117.61 | 0.0771989 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14775.2 | −1.01546 | ||||||||
\(597\) | 9670.69 | 0.662973 | ||||||||
\(598\) | 282.852 | 0.0193423 | ||||||||
\(599\) | −11678.3 | −0.796601 | −0.398300 | − | 0.917255i | \(-0.630400\pi\) | ||||
−0.398300 | + | 0.917255i | \(0.630400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17335.0 | 1.17655 | 0.588277 | − | 0.808660i | \(-0.299807\pi\) | ||||
0.588277 | + | 0.808660i | \(0.299807\pi\) | |||||||
\(602\) | −6875.29 | −0.465475 | ||||||||
\(603\) | 3764.27 | 0.254217 | ||||||||
\(604\) | −20047.0 | −1.35050 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 21428.4 | 1.43642 | ||||||||
\(607\) | −10259.9 | −0.686057 | −0.343028 | − | 0.939325i | \(-0.611453\pi\) | ||||
−0.343028 | + | 0.939325i | \(0.611453\pi\) | |||||||
\(608\) | −15898.3 | −1.06046 | ||||||||
\(609\) | 5195.31 | 0.345689 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3497.75 | −0.231594 | ||||||||
\(612\) | −481.693 | −0.0318158 | ||||||||
\(613\) | −8691.75 | −0.572686 | −0.286343 | − | 0.958127i | \(-0.592440\pi\) | ||||
−0.286343 | + | 0.958127i | \(0.592440\pi\) | |||||||
\(614\) | −17777.0 | −1.16844 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1799.71 | 0.117715 | ||||||||
\(617\) | −7438.86 | −0.485377 | −0.242688 | − | 0.970104i | \(-0.578029\pi\) | ||||
−0.242688 | + | 0.970104i | \(0.578029\pi\) | |||||||
\(618\) | −14773.5 | −0.961613 | ||||||||
\(619\) | −8091.72 | −0.525418 | −0.262709 | − | 0.964875i | \(-0.584616\pi\) | ||||
−0.262709 | + | 0.964875i | \(0.584616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −274.437 | −0.0177340 | ||||||||
\(622\) | −202.132 | −0.0130301 | ||||||||
\(623\) | 18458.7 | 1.18705 | ||||||||
\(624\) | −1671.30 | −0.107220 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17549.8 | −1.12050 | ||||||||
\(627\) | 2300.11 | 0.146503 | ||||||||
\(628\) | −15352.1 | −0.975503 | ||||||||
\(629\) | −917.639 | −0.0581696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10374.5 | 0.654518 | 0.327259 | − | 0.944935i | \(-0.393875\pi\) | ||||
0.327259 | + | 0.944935i | \(0.393875\pi\) | |||||||
\(632\) | 378.462 | 0.0238202 | ||||||||
\(633\) | −5038.14 | −0.316347 | ||||||||
\(634\) | 32606.3 | 2.04253 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3797.37 | 0.236754 | ||||||||
\(637\) | −1593.47 | −0.0991142 | ||||||||
\(638\) | 3033.29 | 0.188228 | ||||||||
\(639\) | −4556.96 | −0.282113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25560.8 | 1.57502 | 0.787511 | − | 0.616300i | \(-0.211369\pi\) | ||||
0.787511 | + | 0.616300i | \(0.211369\pi\) | |||||||
\(642\) | −2332.93 | −0.143416 | ||||||||
\(643\) | 22746.6 | 1.39508 | 0.697541 | − | 0.716544i | \(-0.254277\pi\) | ||||
0.697541 | + | 0.716544i | \(0.254277\pi\) | |||||||
\(644\) | 1479.71 | 0.0905415 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2278.78 | −0.138789 | ||||||||
\(647\) | −24638.3 | −1.49711 | −0.748555 | − | 0.663073i | \(-0.769252\pi\) | ||||
−0.748555 | + | 0.663073i | \(0.769252\pi\) | |||||||
\(648\) | 560.779 | 0.0339961 | ||||||||
\(649\) | 3632.87 | 0.219727 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20628.7 | 1.24194 | ||||||||
\(652\) | 4974.66 | 0.298808 | ||||||||
\(653\) | 17926.1 | 1.07428 | 0.537139 | − | 0.843493i | \(-0.319505\pi\) | ||||
0.537139 | + | 0.843493i | \(0.319505\pi\) | |||||||
\(654\) | 6724.87 | 0.402085 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3051.82 | −0.181637 | ||||||||
\(657\) | −5512.47 | −0.327339 | ||||||||
\(658\) | −42061.1 | −2.49197 | ||||||||
\(659\) | −28662.2 | −1.69426 | −0.847132 | − | 0.531382i | \(-0.821673\pi\) | ||||
−0.847132 | + | 0.531382i | \(0.821673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13447.8 | 0.791312 | 0.395656 | − | 0.918399i | \(-0.370517\pi\) | ||||
0.395656 | + | 0.918399i | \(0.370517\pi\) | |||||||
\(662\) | 12879.0 | 0.756129 | ||||||||
\(663\) | −192.752 | −0.0112909 | ||||||||
\(664\) | −3731.35 | −0.218079 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3576.97 | −0.208115 | ||||||||
\(667\) | −744.847 | −0.0432392 | ||||||||
\(668\) | −11293.4 | −0.654123 | ||||||||
\(669\) | −18365.3 | −1.06135 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10251.9 | −0.589822 | ||||||||
\(672\) | −16171.1 | −0.928294 | ||||||||
\(673\) | 9621.01 | 0.551059 | 0.275529 | − | 0.961293i | \(-0.411147\pi\) | ||||
0.275529 | + | 0.961293i | \(0.411147\pi\) | |||||||
\(674\) | 447.283 | 0.0255619 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13197.1 | −0.750857 | ||||||||
\(677\) | −15901.5 | −0.902723 | −0.451361 | − | 0.892341i | \(-0.649061\pi\) | ||||
−0.451361 | + | 0.892341i | \(0.649061\pi\) | |||||||
\(678\) | −17080.3 | −0.967501 | ||||||||
\(679\) | 12566.7 | 0.710257 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5280.68 | −0.297145 | ||||||||
\(682\) | 12044.1 | 0.676236 | ||||||||
\(683\) | −611.084 | −0.0342350 | −0.0171175 | − | 0.999853i | \(-0.505449\pi\) | ||||
−0.0171175 | + | 0.999853i | \(0.505449\pi\) | |||||||
\(684\) | −3864.30 | −0.216017 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11340.4 | 0.631162 | ||||||||
\(687\) | 17341.7 | 0.963069 | ||||||||
\(688\) | −5824.29 | −0.322745 | ||||||||
\(689\) | 1519.54 | 0.0840201 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24067.1 | 1.32497 | 0.662487 | − | 0.749074i | \(-0.269501\pi\) | ||||
0.662487 | + | 0.749074i | \(0.269501\pi\) | |||||||
\(692\) | 6448.09 | 0.354219 | ||||||||
\(693\) | 2339.58 | 0.128244 | ||||||||
\(694\) | −39265.9 | −2.14771 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1522.00 | 0.0828899 | ||||||||
\(697\) | −351.969 | −0.0191274 | ||||||||
\(698\) | −28331.3 | −1.53633 | ||||||||
\(699\) | 16301.8 | 0.882105 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10093.5 | 0.543834 | 0.271917 | − | 0.962321i | \(-0.412342\pi\) | ||||
0.271917 | + | 0.962321i | \(0.412342\pi\) | |||||||
\(702\) | −751.352 | −0.0403959 | ||||||||
\(703\) | −7361.61 | −0.394948 | ||||||||
\(704\) | −2812.19 | −0.150551 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −810.753 | −0.0432197 | ||||||||
\(707\) | 44857.6 | 2.38620 | ||||||||
\(708\) | −6103.41 | −0.323984 | ||||||||
\(709\) | −4970.98 | −0.263313 | −0.131657 | − | 0.991295i | \(-0.542030\pi\) | ||||
−0.131657 | + | 0.991295i | \(0.542030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 491.991 | 0.0259509 | ||||||||
\(712\) | 5407.61 | 0.284633 | ||||||||
\(713\) | −2957.52 | −0.155343 | ||||||||
\(714\) | −2317.89 | −0.121491 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11586.1 | 0.604737 | ||||||||
\(717\) | −1751.48 | −0.0912277 | ||||||||
\(718\) | −34262.2 | −1.78086 | ||||||||
\(719\) | −35411.6 | −1.83676 | −0.918381 | − | 0.395698i | \(-0.870503\pi\) | ||||
−0.918381 | + | 0.395698i | \(0.870503\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30926.4 | −1.59745 | ||||||||
\(722\) | 7529.30 | 0.388105 | ||||||||
\(723\) | −12653.6 | −0.650888 | ||||||||
\(724\) | −11838.8 | −0.607715 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1365.97 | 0.0698291 | ||||||||
\(727\) | −34598.6 | −1.76505 | −0.882525 | − | 0.470266i | \(-0.844158\pi\) | ||||
−0.882525 | + | 0.470266i | \(0.844158\pi\) | |||||||
\(728\) | −1209.91 | −0.0615966 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −671.719 | −0.0339869 | ||||||||
\(732\) | 17223.7 | 0.869683 | ||||||||
\(733\) | 32108.2 | 1.61793 | 0.808966 | − | 0.587856i | \(-0.200028\pi\) | ||||
0.808966 | + | 0.587856i | \(0.200028\pi\) | |||||||
\(734\) | 14160.4 | 0.712085 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2318.44 | 0.116112 | ||||||||
\(737\) | 4600.78 | 0.229948 | ||||||||
\(738\) | −1371.98 | −0.0684326 | ||||||||
\(739\) | −27536.9 | −1.37072 | −0.685359 | − | 0.728206i | \(-0.740355\pi\) | ||||
−0.685359 | + | 0.728206i | \(0.740355\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1546.32 | −0.0766608 | ||||||||
\(742\) | 18272.8 | 0.904062 | ||||||||
\(743\) | −2437.44 | −0.120351 | −0.0601757 | − | 0.998188i | \(-0.519166\pi\) | ||||
−0.0601757 | + | 0.998188i | \(0.519166\pi\) | |||||||
\(744\) | 6043.32 | 0.297794 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1414.85 | 0.0694386 | ||||||||
\(747\) | −4850.67 | −0.237586 | ||||||||
\(748\) | −588.736 | −0.0287785 | ||||||||
\(749\) | −4883.69 | −0.238246 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29534.7 | −1.43507 | −0.717534 | − | 0.696523i | \(-0.754729\pi\) | ||||
−0.717534 | + | 0.696523i | \(0.754729\pi\) | |||||||
\(752\) | −35631.4 | −1.72785 | ||||||||
\(753\) | 14510.3 | 0.702235 | ||||||||
\(754\) | −2039.23 | −0.0984940 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3930.62 | −0.189094 | ||||||||
\(757\) | −747.476 | −0.0358883 | −0.0179442 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179442 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(758\) | −11166.6 | −0.535079 | ||||||||
\(759\) | −335.423 | −0.0160410 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21031.2 | −1.00181 | −0.500906 | − | 0.865502i | \(-0.667000\pi\) | ||||
−0.500906 | + | 0.865502i | \(0.667000\pi\) | |||||||
\(762\) | −879.749 | −0.0418241 | ||||||||
\(763\) | 14077.7 | 0.667950 | ||||||||
\(764\) | 1254.93 | 0.0594264 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5836.15 | −0.275286 | ||||||||
\(767\) | −2442.32 | −0.114976 | ||||||||
\(768\) | −15875.1 | −0.745890 | ||||||||
\(769\) | 23107.4 | 1.08358 | 0.541790 | − | 0.840514i | \(-0.317747\pi\) | ||||
0.541790 | + | 0.840514i | \(0.317747\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13962.4 | −0.652197 | ||||||||
\(772\) | −17608.1 | −0.820892 | ||||||||
\(773\) | 24367.7 | 1.13382 | 0.566912 | − | 0.823778i | \(-0.308138\pi\) | ||||
0.566912 | + | 0.823778i | \(0.308138\pi\) | |||||||
\(774\) | −2618.37 | −0.121596 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3681.49 | 0.170307 | ||||||||
\(777\) | −7487.94 | −0.345725 | ||||||||
\(778\) | 28266.3 | 1.30256 | ||||||||
\(779\) | −2823.61 | −0.129867 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5569.62 | −0.255181 | ||||||||
\(782\) | 332.313 | 0.0151963 | ||||||||
\(783\) | 1978.57 | 0.0903043 | ||||||||
\(784\) | −16232.6 | −0.739460 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −97.1095 | −0.00440685 | ||||||||
\(787\) | 11308.1 | 0.512188 | 0.256094 | − | 0.966652i | \(-0.417564\pi\) | ||||
0.256094 | + | 0.966652i | \(0.417564\pi\) | |||||||
\(788\) | 7026.14 | 0.317634 | ||||||||
\(789\) | 15306.3 | 0.690647 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35755.5 | −1.60723 | ||||||||
\(792\) | 685.397 | 0.0307506 | ||||||||
\(793\) | 6892.18 | 0.308636 | ||||||||
\(794\) | 41863.9 | 1.87115 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19857.8 | −0.884221 | ||||||||
\(797\) | 43620.5 | 1.93867 | 0.969333 | − | 0.245752i | \(-0.0790350\pi\) | ||||
0.969333 | + | 0.245752i | \(0.0790350\pi\) | |||||||
\(798\) | −18594.8 | −0.824875 | ||||||||
\(799\) | −4109.39 | −0.181952 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7029.77 | 0.310093 | ||||||||
\(802\) | 50717.7 | 2.23305 | ||||||||
\(803\) | −6737.47 | −0.296090 | ||||||||
\(804\) | −7729.55 | −0.339055 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8097.06 | −0.353854 | ||||||||
\(807\) | −13425.4 | −0.585623 | ||||||||
\(808\) | 13141.4 | 0.572168 | ||||||||
\(809\) | −7491.05 | −0.325551 | −0.162776 | − | 0.986663i | \(-0.552045\pi\) | ||||
−0.162776 | + | 0.986663i | \(0.552045\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7335.75 | −0.317624 | −0.158812 | − | 0.987309i | \(-0.550766\pi\) | ||||
−0.158812 | + | 0.987309i | \(0.550766\pi\) | |||||||
\(812\) | −10668.0 | −0.461052 | ||||||||
\(813\) | 23488.2 | 1.01324 | ||||||||
\(814\) | −4371.85 | −0.188247 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1963.56 | −0.0842380 | ||||||||
\(817\) | −5388.76 | −0.230757 | ||||||||
\(818\) | −48585.7 | −2.07672 | ||||||||
\(819\) | −1572.86 | −0.0671064 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37482.9 | −1.59338 | −0.796689 | − | 0.604390i | \(-0.793417\pi\) | ||||
−0.796689 | + | 0.604390i | \(0.793417\pi\) | |||||||
\(822\) | 7509.01 | 0.318621 | ||||||||
\(823\) | 1213.87 | 0.0514128 | 0.0257064 | − | 0.999670i | \(-0.491816\pi\) | ||||
0.0257064 | + | 0.999670i | \(0.491816\pi\) | |||||||
\(824\) | −9060.12 | −0.383039 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29369.4 | −1.23716 | ||||||||
\(827\) | −7999.10 | −0.336343 | −0.168172 | − | 0.985758i | \(-0.553786\pi\) | ||||
−0.168172 | + | 0.985758i | \(0.553786\pi\) | |||||||
\(828\) | 563.529 | 0.0236522 | ||||||||
\(829\) | −14809.5 | −0.620451 | −0.310225 | − | 0.950663i | \(-0.600405\pi\) | ||||
−0.310225 | + | 0.950663i | \(0.600405\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11077.5 | 0.462425 | ||||||||
\(832\) | 1890.58 | 0.0787791 | ||||||||
\(833\) | −1872.12 | −0.0778693 | ||||||||
\(834\) | 8417.74 | 0.349499 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4723.04 | −0.195394 | ||||||||
\(837\) | 7856.18 | 0.324432 | ||||||||
\(838\) | 33514.8 | 1.38156 | ||||||||
\(839\) | −44598.1 | −1.83516 | −0.917578 | − | 0.397555i | \(-0.869859\pi\) | ||||
−0.917578 | + | 0.397555i | \(0.869859\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19019.0 | −0.779819 | ||||||||
\(842\) | −6970.45 | −0.285294 | ||||||||
\(843\) | 3888.62 | 0.158875 | ||||||||
\(844\) | 10345.3 | 0.421919 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −16018.5 | −0.650977 | ||||||||
\(847\) | 2859.49 | 0.116001 | ||||||||
\(848\) | 15479.5 | 0.626848 | ||||||||
\(849\) | 3505.50 | 0.141706 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1073.54 | 0.0432438 | ||||||||
\(852\) | 9357.25 | 0.376261 | ||||||||
\(853\) | 28250.2 | 1.13396 | 0.566980 | − | 0.823732i | \(-0.308112\pi\) | ||||
0.566980 | + | 0.823732i | \(0.308112\pi\) | |||||||
\(854\) | 82879.9 | 3.32095 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1430.71 | −0.0571270 | ||||||||
\(857\) | 28018.4 | 1.11679 | 0.558395 | − | 0.829575i | \(-0.311417\pi\) | ||||
0.558395 | + | 0.829575i | \(0.311417\pi\) | |||||||
\(858\) | −918.319 | −0.0365395 | ||||||||
\(859\) | 17367.5 | 0.689837 | 0.344919 | − | 0.938633i | \(-0.387906\pi\) | ||||
0.344919 | + | 0.938633i | \(0.387906\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2872.07 | −0.113681 | ||||||||
\(862\) | 15393.4 | 0.608240 | ||||||||
\(863\) | −49064.8 | −1.93532 | −0.967662 | − | 0.252252i | \(-0.918829\pi\) | ||||
−0.967662 | + | 0.252252i | \(0.918829\pi\) | |||||||
\(864\) | −6158.56 | −0.242498 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 31059.6 | 1.21876 | ||||||||
\(867\) | 14512.5 | 0.568480 | ||||||||
\(868\) | −42358.9 | −1.65640 | ||||||||
\(869\) | 601.323 | 0.0234735 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3093.02 | −0.120325 | ||||||||
\(872\) | 4124.15 | 0.160162 | ||||||||
\(873\) | 4785.86 | 0.185540 | ||||||||
\(874\) | 2665.93 | 0.103177 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11319.3 | 0.436579 | ||||||||
\(877\) | 42355.0 | 1.63082 | 0.815409 | − | 0.578885i | \(-0.196512\pi\) | ||||
0.815409 | + | 0.578885i | \(0.196512\pi\) | |||||||
\(878\) | −3684.89 | −0.141639 | ||||||||
\(879\) | −26638.3 | −1.02217 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36424.8 | −1.39294 | −0.696472 | − | 0.717584i | \(-0.745248\pi\) | ||||
−0.696472 | + | 0.717584i | \(0.745248\pi\) | |||||||
\(882\) | −7297.55 | −0.278596 | ||||||||
\(883\) | −27158.6 | −1.03506 | −0.517532 | − | 0.855664i | \(-0.673149\pi\) | ||||
−0.517532 | + | 0.855664i | \(0.673149\pi\) | |||||||
\(884\) | 395.797 | 0.0150589 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 336.862 | 0.0127732 | ||||||||
\(887\) | 45832.2 | 1.73494 | 0.867472 | − | 0.497486i | \(-0.165743\pi\) | ||||
0.867472 | + | 0.497486i | \(0.165743\pi\) | |||||||
\(888\) | −2193.64 | −0.0828985 | ||||||||
\(889\) | −1841.64 | −0.0694789 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | 37711.2 | 1.41554 | ||||||||
\(893\) | −32966.9 | −1.23538 | ||||||||
\(894\) | −27076.6 | −1.01295 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −20388.2 | −0.760183 | ||||||||
\(897\) | 225.500 | 0.00839377 | ||||||||
\(898\) | 64419.2 | 2.39387 | ||||||||
\(899\) | 21322.4 | 0.791035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1785.26 | 0.0660106 | ||||||||
\(902\) | −1676.86 | −0.0618996 | ||||||||
\(903\) | −5481.23 | −0.201998 | ||||||||
\(904\) | −10474.8 | −0.385384 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −36737.6 | −1.34716 | ||||||||
\(907\) | 42596.1 | 1.55940 | 0.779702 | − | 0.626151i | \(-0.215371\pi\) | ||||
0.779702 | + | 0.626151i | \(0.215371\pi\) | |||||||
\(908\) | 10843.3 | 0.396309 | ||||||||
\(909\) | 17083.5 | 0.623348 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45531.0 | 1.65588 | 0.827941 | − | 0.560816i | \(-0.189512\pi\) | ||||
0.827941 | + | 0.560816i | \(0.189512\pi\) | |||||||
\(912\) | −15752.3 | −0.571942 | ||||||||
\(913\) | −5928.60 | −0.214905 | ||||||||
\(914\) | −6701.80 | −0.242534 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35609.5 | −1.28447 | ||||||||
\(917\) | −203.286 | −0.00732073 | ||||||||
\(918\) | −882.738 | −0.0317372 | ||||||||
\(919\) | 14353.6 | 0.515215 | 0.257607 | − | 0.966250i | \(-0.417066\pi\) | ||||
0.257607 | + | 0.966250i | \(0.417066\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14172.4 | −0.507055 | ||||||||
\(922\) | 27154.3 | 0.969936 | ||||||||
\(923\) | 3744.36 | 0.133529 | ||||||||
\(924\) | −4804.09 | −0.171042 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35565.2 | 1.26214 | ||||||||
\(927\) | −11777.9 | −0.417302 | ||||||||
\(928\) | −16714.9 | −0.591263 | ||||||||
\(929\) | 38477.7 | 1.35890 | 0.679448 | − | 0.733724i | \(-0.262219\pi\) | ||||
0.679448 | + | 0.733724i | \(0.262219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15018.8 | −0.528701 | ||||||||
\(932\) | −33474.1 | −1.17648 | ||||||||
\(933\) | −161.147 | −0.00565456 | ||||||||
\(934\) | 27049.9 | 0.947645 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −460.780 | −0.0160909 | ||||||||
\(937\) | −6917.67 | −0.241185 | −0.120592 | − | 0.992702i | \(-0.538479\pi\) | ||||
−0.120592 | + | 0.992702i | \(0.538479\pi\) | |||||||
\(938\) | −37194.2 | −1.29471 | ||||||||
\(939\) | −13991.3 | −0.486250 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41270.2 | 1.42972 | 0.714862 | − | 0.699265i | \(-0.246489\pi\) | ||||
0.714862 | + | 0.699265i | \(0.246489\pi\) | |||||||
\(942\) | −28133.9 | −0.973091 | ||||||||
\(943\) | 411.766 | 0.0142194 | ||||||||
\(944\) | −24879.7 | −0.857803 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3200.23 | −0.109988 | ||||||||
\(947\) | −7099.57 | −0.243617 | −0.121808 | − | 0.992554i | \(-0.538869\pi\) | ||||
−0.121808 | + | 0.992554i | \(0.538869\pi\) | |||||||
\(948\) | −1010.25 | −0.0346113 | ||||||||
\(949\) | 4529.48 | 0.154935 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25994.9 | 0.886375 | ||||||||
\(952\) | −1421.49 | −0.0483935 | ||||||||
\(953\) | 27983.8 | 0.951191 | 0.475595 | − | 0.879664i | \(-0.342233\pi\) | ||||
0.475595 | + | 0.879664i | \(0.342233\pi\) | |||||||
\(954\) | 6958.96 | 0.236168 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3596.49 | 0.121672 | ||||||||
\(957\) | 2418.25 | 0.0816833 | ||||||||
\(958\) | 30950.2 | 1.04379 | ||||||||
\(959\) | 15719.2 | 0.529299 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54872.3 | 1.84191 | ||||||||
\(962\) | 2939.12 | 0.0985043 | ||||||||
\(963\) | −1859.89 | −0.0622370 | ||||||||
\(964\) | 25982.9 | 0.868103 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2711.68 | 0.0903176 | ||||||||
\(967\) | 22702.4 | 0.754972 | 0.377486 | − | 0.926015i | \(-0.376789\pi\) | ||||
0.377486 | + | 0.926015i | \(0.376789\pi\) | |||||||
\(968\) | 837.707 | 0.0278150 | ||||||||
\(969\) | −1816.73 | −0.0602287 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11642.7 | 0.384791 | 0.192396 | − | 0.981317i | \(-0.438374\pi\) | ||||
0.192396 | + | 0.981317i | \(0.438374\pi\) | |||||||
\(972\) | −1496.93 | −0.0493971 | ||||||||
\(973\) | 17621.5 | 0.580595 | ||||||||
\(974\) | −18128.2 | −0.596372 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 70210.2 | 2.30264 | ||||||||
\(977\) | −6166.32 | −0.201922 | −0.100961 | − | 0.994890i | \(-0.532192\pi\) | ||||
−0.100961 | + | 0.994890i | \(0.532192\pi\) | |||||||
\(978\) | 9116.44 | 0.298069 | ||||||||
\(979\) | 8591.94 | 0.280490 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5361.31 | 0.174489 | ||||||||
\(982\) | 18604.4 | 0.604573 | ||||||||
\(983\) | 18059.0 | 0.585953 | 0.292976 | − | 0.956120i | \(-0.405354\pi\) | ||||
0.292976 | + | 0.956120i | \(0.405354\pi\) | |||||||
\(984\) | −841.392 | −0.0272587 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2395.83 | −0.0773821 | ||||||||
\(987\) | −33532.6 | −1.08141 | ||||||||
\(988\) | 3175.22 | 0.102244 | ||||||||
\(989\) | 785.839 | 0.0252662 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62330.7 | −1.99798 | −0.998991 | − | 0.0449065i | \(-0.985701\pi\) | ||||
−0.998991 | + | 0.0449065i | \(0.985701\pi\) | |||||||
\(992\) | −66368.7 | −2.12420 | ||||||||
\(993\) | 10267.6 | 0.328130 | ||||||||
\(994\) | 45026.7 | 1.43678 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9960.36 | 0.316874 | ||||||||
\(997\) | 13560.3 | 0.430752 | 0.215376 | − | 0.976531i | \(-0.430902\pi\) | ||||
0.215376 | + | 0.976531i | \(0.430902\pi\) | |||||||
\(998\) | 13610.7 | 0.431702 | ||||||||
\(999\) | −2851.69 | −0.0903138 |
(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 | 825.4.a.q.1.1 | yes | 3 | |
3.2 | odd | 2 | 2475.4.a.v.1.3 | 3 | |||
5.2 | odd | 4 | 825.4.c.n.199.2 | 6 | |||
5.3 | odd | 4 | 825.4.c.n.199.5 | 6 | |||
5.4 | even | 2 | 825.4.a.o.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 2475.4.a.y.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.4.a.o.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
825.4.a.q.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
825.4.c.n.199.2 | 6 | 5.2 | odd | 4 | |||
825.4.c.n.199.5 | 6 | 5.3 | odd | 4 | |||
2475.4.a.v.1.3 | 3 | 3.2 | odd | 2 | |||
2475.4.a.y.1.1 | 3 | 15.14 | odd | 2 |