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: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 31x^{5} + 50x^{4} + 272x^{3} - 322x^{2} - 704x + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.70507\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.70507 | 1.30994 | 0.654970 | − | 0.755655i | \(-0.272681\pi\) | ||||
0.654970 | + | 0.755655i | \(0.272681\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 5.72754 | 0.715943 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −11.1152 | −0.756294 | ||||||||
\(7\) | 30.9104 | 1.66900 | 0.834502 | − | 0.551004i | \(-0.185755\pi\) | ||||
0.834502 | + | 0.551004i | \(0.185755\pi\) | |||||||
\(8\) | −8.41961 | −0.372098 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −17.1826 | −0.413350 | ||||||||
\(13\) | 39.2828 | 0.838083 | 0.419042 | − | 0.907967i | \(-0.362366\pi\) | ||||
0.419042 | + | 0.907967i | \(0.362366\pi\) | |||||||
\(14\) | 114.525 | 2.18630 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −77.0156 | −1.20337 | ||||||||
\(17\) | −83.0298 | −1.18457 | −0.592285 | − | 0.805729i | \(-0.701774\pi\) | ||||
−0.592285 | + | 0.805729i | \(0.701774\pi\) | |||||||
\(18\) | 33.3456 | 0.436647 | ||||||||
\(19\) | 49.6019 | 0.598918 | 0.299459 | − | 0.954109i | \(-0.403194\pi\) | ||||
0.299459 | + | 0.954109i | \(0.403194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −92.7312 | −0.963600 | ||||||||
\(22\) | 40.7558 | 0.394962 | ||||||||
\(23\) | 10.7536 | 0.0974902 | 0.0487451 | − | 0.998811i | \(-0.484478\pi\) | ||||
0.0487451 | + | 0.998811i | \(0.484478\pi\) | |||||||
\(24\) | 25.2588 | 0.214831 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 145.545 | 1.09784 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 177.041 | 1.19491 | ||||||||
\(29\) | 198.890 | 1.27355 | 0.636775 | − | 0.771050i | \(-0.280268\pi\) | ||||
0.636775 | + | 0.771050i | \(0.280268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 229.071 | 1.32717 | 0.663586 | − | 0.748100i | \(-0.269034\pi\) | ||||
0.663586 | + | 0.748100i | \(0.269034\pi\) | |||||||
\(32\) | −217.991 | −1.20424 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | −307.631 | −1.55171 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 51.5479 | 0.238648 | ||||||||
\(37\) | 348.562 | 1.54874 | 0.774368 | − | 0.632736i | \(-0.218068\pi\) | ||||
0.774368 | + | 0.632736i | \(0.218068\pi\) | |||||||
\(38\) | 183.778 | 0.784547 | ||||||||
\(39\) | −117.848 | −0.483867 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −459.643 | −1.75083 | −0.875416 | − | 0.483370i | \(-0.839413\pi\) | ||||
−0.875416 | + | 0.483370i | \(0.839413\pi\) | |||||||
\(42\) | −343.576 | −1.26226 | ||||||||
\(43\) | −461.300 | −1.63599 | −0.817995 | − | 0.575226i | \(-0.804914\pi\) | ||||
−0.817995 | + | 0.575226i | \(0.804914\pi\) | |||||||
\(44\) | 63.0030 | 0.215865 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 39.8427 | 0.127706 | ||||||||
\(47\) | 272.390 | 0.845365 | 0.422682 | − | 0.906278i | \(-0.361089\pi\) | ||||
0.422682 | + | 0.906278i | \(0.361089\pi\) | |||||||
\(48\) | 231.047 | 0.694765 | ||||||||
\(49\) | 612.453 | 1.78558 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 249.089 | 0.683911 | ||||||||
\(52\) | 224.994 | 0.600020 | ||||||||
\(53\) | 360.420 | 0.934104 | 0.467052 | − | 0.884230i | \(-0.345316\pi\) | ||||
0.467052 | + | 0.884230i | \(0.345316\pi\) | |||||||
\(54\) | −100.037 | −0.252098 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −260.253 | −0.621033 | ||||||||
\(57\) | −148.806 | −0.345786 | ||||||||
\(58\) | 736.901 | 1.66827 | ||||||||
\(59\) | −215.424 | −0.475352 | −0.237676 | − | 0.971345i | \(-0.576386\pi\) | ||||
−0.237676 | + | 0.971345i | \(0.576386\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 367.967 | 0.772350 | 0.386175 | − | 0.922426i | \(-0.373796\pi\) | ||||
0.386175 | + | 0.922426i | \(0.373796\pi\) | |||||||
\(62\) | 848.723 | 1.73851 | ||||||||
\(63\) | 278.194 | 0.556335 | ||||||||
\(64\) | −191.548 | −0.374118 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −122.267 | −0.228031 | ||||||||
\(67\) | 929.374 | 1.69464 | 0.847322 | − | 0.531079i | \(-0.178213\pi\) | ||||
0.847322 | + | 0.531079i | \(0.178213\pi\) | |||||||
\(68\) | −475.557 | −0.848084 | ||||||||
\(69\) | −32.2607 | −0.0562860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 126.531 | 0.211499 | 0.105750 | − | 0.994393i | \(-0.466276\pi\) | ||||
0.105750 | + | 0.994393i | \(0.466276\pi\) | |||||||
\(72\) | −75.7765 | −0.124033 | ||||||||
\(73\) | 509.402 | 0.816726 | 0.408363 | − | 0.912820i | \(-0.366100\pi\) | ||||
0.408363 | + | 0.912820i | \(0.366100\pi\) | |||||||
\(74\) | 1291.45 | 2.02875 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 284.097 | 0.428791 | ||||||||
\(77\) | 340.014 | 0.503224 | ||||||||
\(78\) | −436.636 | −0.633837 | ||||||||
\(79\) | 719.755 | 1.02505 | 0.512524 | − | 0.858673i | \(-0.328711\pi\) | ||||
0.512524 | + | 0.858673i | \(0.328711\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1703.01 | −2.29349 | ||||||||
\(83\) | −865.128 | −1.14410 | −0.572049 | − | 0.820220i | \(-0.693851\pi\) | ||||
−0.572049 | + | 0.820220i | \(0.693851\pi\) | |||||||
\(84\) | −531.122 | −0.689883 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1709.15 | −2.14305 | ||||||||
\(87\) | −596.670 | −0.735284 | ||||||||
\(88\) | −92.6157 | −0.112192 | ||||||||
\(89\) | 528.684 | 0.629668 | 0.314834 | − | 0.949147i | \(-0.398051\pi\) | ||||
0.314834 | + | 0.949147i | \(0.398051\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1214.25 | 1.39876 | ||||||||
\(92\) | 61.5915 | 0.0697974 | ||||||||
\(93\) | −687.212 | −0.766243 | ||||||||
\(94\) | 1009.22 | 1.10738 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 653.974 | 0.695270 | ||||||||
\(97\) | 858.037 | 0.898149 | 0.449075 | − | 0.893494i | \(-0.351754\pi\) | ||||
0.449075 | + | 0.893494i | \(0.351754\pi\) | |||||||
\(98\) | 2269.18 | 2.33900 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −48.7808 | −0.0480582 | −0.0240291 | − | 0.999711i | \(-0.507649\pi\) | ||||
−0.0240291 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(102\) | 922.893 | 0.895883 | ||||||||
\(103\) | 525.103 | 0.502329 | 0.251165 | − | 0.967944i | \(-0.419186\pi\) | ||||
0.251165 | + | 0.967944i | \(0.419186\pi\) | |||||||
\(104\) | −330.746 | −0.311849 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1335.38 | 1.22362 | ||||||||
\(107\) | 986.489 | 0.891285 | 0.445643 | − | 0.895211i | \(-0.352975\pi\) | ||||
0.445643 | + | 0.895211i | \(0.352975\pi\) | |||||||
\(108\) | −154.644 | −0.137783 | ||||||||
\(109\) | −55.2903 | −0.0485858 | −0.0242929 | − | 0.999705i | \(-0.507733\pi\) | ||||
−0.0242929 | + | 0.999705i | \(0.507733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1045.69 | −0.894163 | ||||||||
\(112\) | −2380.58 | −2.00843 | ||||||||
\(113\) | 459.760 | 0.382748 | 0.191374 | − | 0.981517i | \(-0.438706\pi\) | ||||
0.191374 | + | 0.981517i | \(0.438706\pi\) | |||||||
\(114\) | −551.335 | −0.452959 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1139.15 | 0.911789 | ||||||||
\(117\) | 353.545 | 0.279361 | ||||||||
\(118\) | −798.160 | −0.622683 | ||||||||
\(119\) | −2566.48 | −1.97705 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1363.34 | 1.01173 | ||||||||
\(123\) | 1378.93 | 1.01084 | ||||||||
\(124\) | 1312.01 | 0.950179 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1030.73 | 0.728765 | ||||||||
\(127\) | −1959.31 | −1.36898 | −0.684492 | − | 0.729020i | \(-0.739976\pi\) | ||||
−0.684492 | + | 0.729020i | \(0.739976\pi\) | |||||||
\(128\) | 1034.23 | 0.714171 | ||||||||
\(129\) | 1383.90 | 0.944539 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.2654 | 0.0108482 | 0.00542412 | − | 0.999985i | \(-0.498273\pi\) | ||||
0.00542412 | + | 0.999985i | \(0.498273\pi\) | |||||||
\(132\) | −189.009 | −0.124630 | ||||||||
\(133\) | 1533.21 | 0.999598 | ||||||||
\(134\) | 3443.40 | 2.21988 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 699.078 | 0.440775 | ||||||||
\(137\) | 941.492 | 0.587132 | 0.293566 | − | 0.955939i | \(-0.405158\pi\) | ||||
0.293566 | + | 0.955939i | \(0.405158\pi\) | |||||||
\(138\) | −119.528 | −0.0737313 | ||||||||
\(139\) | −1975.04 | −1.20518 | −0.602591 | − | 0.798050i | \(-0.705865\pi\) | ||||
−0.602591 | + | 0.798050i | \(0.705865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −817.169 | −0.488072 | ||||||||
\(142\) | 468.805 | 0.277051 | ||||||||
\(143\) | 432.110 | 0.252692 | ||||||||
\(144\) | −693.140 | −0.401123 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1887.37 | 1.06986 | ||||||||
\(147\) | −1837.36 | −1.03090 | ||||||||
\(148\) | 1996.40 | 1.10881 | ||||||||
\(149\) | −2958.51 | −1.62665 | −0.813325 | − | 0.581810i | \(-0.802345\pi\) | ||||
−0.813325 | + | 0.581810i | \(0.802345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3453.22 | −1.86105 | −0.930526 | − | 0.366227i | \(-0.880650\pi\) | ||||
−0.930526 | + | 0.366227i | \(0.880650\pi\) | |||||||
\(152\) | −417.628 | −0.222856 | ||||||||
\(153\) | −747.268 | −0.394856 | ||||||||
\(154\) | 1259.78 | 0.659193 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −674.981 | −0.346422 | ||||||||
\(157\) | 738.890 | 0.375604 | 0.187802 | − | 0.982207i | \(-0.439864\pi\) | ||||
0.187802 | + | 0.982207i | \(0.439864\pi\) | |||||||
\(158\) | 2666.74 | 1.34275 | ||||||||
\(159\) | −1081.26 | −0.539305 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 332.397 | 0.162712 | ||||||||
\(162\) | 300.111 | 0.145549 | ||||||||
\(163\) | 242.527 | 0.116541 | 0.0582705 | − | 0.998301i | \(-0.481441\pi\) | ||||
0.0582705 | + | 0.998301i | \(0.481441\pi\) | |||||||
\(164\) | −2632.62 | −1.25350 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3205.36 | −1.49870 | ||||||||
\(167\) | 2447.06 | 1.13389 | 0.566944 | − | 0.823756i | \(-0.308126\pi\) | ||||
0.566944 | + | 0.823756i | \(0.308126\pi\) | |||||||
\(168\) | 780.760 | 0.358553 | ||||||||
\(169\) | −653.864 | −0.297617 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 446.417 | 0.199639 | ||||||||
\(172\) | −2642.11 | −1.17127 | ||||||||
\(173\) | −878.419 | −0.386040 | −0.193020 | − | 0.981195i | \(-0.561828\pi\) | ||||
−0.193020 | + | 0.981195i | \(0.561828\pi\) | |||||||
\(174\) | −2210.70 | −0.963178 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −847.172 | −0.362829 | ||||||||
\(177\) | 646.271 | 0.274445 | ||||||||
\(178\) | 1958.81 | 0.824827 | ||||||||
\(179\) | −2473.19 | −1.03271 | −0.516354 | − | 0.856375i | \(-0.672711\pi\) | ||||
−0.516354 | + | 0.856375i | \(0.672711\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 49.4762 | 0.0203179 | 0.0101589 | − | 0.999948i | \(-0.496766\pi\) | ||||
0.0101589 | + | 0.999948i | \(0.496766\pi\) | |||||||
\(182\) | 4498.87 | 1.83230 | ||||||||
\(183\) | −1103.90 | −0.445916 | ||||||||
\(184\) | −90.5408 | −0.0362759 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2546.17 | −1.00373 | ||||||||
\(187\) | −913.327 | −0.357161 | ||||||||
\(188\) | 1560.12 | 0.605233 | ||||||||
\(189\) | −834.581 | −0.321200 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1945.54 | −0.737037 | −0.368518 | − | 0.929620i | \(-0.620135\pi\) | ||||
−0.368518 | + | 0.929620i | \(0.620135\pi\) | |||||||
\(192\) | 574.645 | 0.215997 | ||||||||
\(193\) | −3064.50 | −1.14294 | −0.571470 | − | 0.820623i | \(-0.693627\pi\) | ||||
−0.571470 | + | 0.820623i | \(0.693627\pi\) | |||||||
\(194\) | 3179.09 | 1.17652 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3507.85 | 1.27837 | ||||||||
\(197\) | −1659.71 | −0.600251 | −0.300125 | − | 0.953900i | \(-0.597029\pi\) | ||||
−0.300125 | + | 0.953900i | \(0.597029\pi\) | |||||||
\(198\) | 366.802 | 0.131654 | ||||||||
\(199\) | −3230.11 | −1.15063 | −0.575317 | − | 0.817930i | \(-0.695121\pi\) | ||||
−0.575317 | + | 0.817930i | \(0.695121\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2788.12 | −0.978403 | ||||||||
\(202\) | −180.736 | −0.0629533 | ||||||||
\(203\) | 6147.77 | 2.12556 | ||||||||
\(204\) | 1426.67 | 0.489642 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1945.54 | 0.658021 | ||||||||
\(207\) | 96.7821 | 0.0324967 | ||||||||
\(208\) | −3025.39 | −1.00852 | ||||||||
\(209\) | 545.621 | 0.180581 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2543.86 | −0.829983 | −0.414991 | − | 0.909825i | \(-0.636215\pi\) | ||||
−0.414991 | + | 0.909825i | \(0.636215\pi\) | |||||||
\(212\) | 2064.32 | 0.668766 | ||||||||
\(213\) | −379.592 | −0.122109 | ||||||||
\(214\) | 3655.01 | 1.16753 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 227.329 | 0.0716102 | ||||||||
\(217\) | 7080.67 | 2.21506 | ||||||||
\(218\) | −204.854 | −0.0636445 | ||||||||
\(219\) | −1528.21 | −0.471537 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3261.64 | −0.992767 | ||||||||
\(222\) | −3874.34 | −1.17130 | ||||||||
\(223\) | 1189.64 | 0.357240 | 0.178620 | − | 0.983918i | \(-0.442837\pi\) | ||||
0.178620 | + | 0.983918i | \(0.442837\pi\) | |||||||
\(224\) | −6738.20 | −2.00989 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1703.44 | 0.501378 | ||||||||
\(227\) | 4897.90 | 1.43209 | 0.716047 | − | 0.698053i | \(-0.245950\pi\) | ||||
0.716047 | + | 0.698053i | \(0.245950\pi\) | |||||||
\(228\) | −852.291 | −0.247563 | ||||||||
\(229\) | −2415.61 | −0.697065 | −0.348533 | − | 0.937297i | \(-0.613320\pi\) | ||||
−0.348533 | + | 0.937297i | \(0.613320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1020.04 | −0.290536 | ||||||||
\(232\) | −1674.58 | −0.473885 | ||||||||
\(233\) | −524.258 | −0.147405 | −0.0737023 | − | 0.997280i | \(-0.523481\pi\) | ||||
−0.0737023 | + | 0.997280i | \(0.523481\pi\) | |||||||
\(234\) | 1309.91 | 0.365946 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1233.85 | −0.340325 | ||||||||
\(237\) | −2159.27 | −0.591812 | ||||||||
\(238\) | −9509.00 | −2.58982 | ||||||||
\(239\) | −4165.12 | −1.12728 | −0.563638 | − | 0.826022i | \(-0.690599\pi\) | ||||
−0.563638 | + | 0.826022i | \(0.690599\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1908.80 | 0.510194 | 0.255097 | − | 0.966915i | \(-0.417893\pi\) | ||||
0.255097 | + | 0.966915i | \(0.417893\pi\) | |||||||
\(242\) | 448.313 | 0.119085 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 2107.55 | 0.552958 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5109.03 | 1.32414 | ||||||||
\(247\) | 1948.50 | 0.501943 | ||||||||
\(248\) | −1928.69 | −0.493837 | ||||||||
\(249\) | 2595.38 | 0.660545 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2503.63 | 0.629592 | 0.314796 | − | 0.949159i | \(-0.398064\pi\) | ||||
0.314796 | + | 0.949159i | \(0.398064\pi\) | |||||||
\(252\) | 1593.37 | 0.398304 | ||||||||
\(253\) | 118.289 | 0.0293944 | ||||||||
\(254\) | −7259.39 | −1.79329 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5364.28 | 1.30964 | ||||||||
\(257\) | −2985.91 | −0.724731 | −0.362365 | − | 0.932036i | \(-0.618031\pi\) | ||||
−0.362365 | + | 0.932036i | \(0.618031\pi\) | |||||||
\(258\) | 5127.44 | 1.23729 | ||||||||
\(259\) | 10774.2 | 2.58485 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1790.01 | 0.424517 | ||||||||
\(262\) | 60.2646 | 0.0142105 | ||||||||
\(263\) | 2213.20 | 0.518903 | 0.259452 | − | 0.965756i | \(-0.416458\pi\) | ||||
0.259452 | + | 0.965756i | \(0.416458\pi\) | |||||||
\(264\) | 277.847 | 0.0647739 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5680.66 | 1.30941 | ||||||||
\(267\) | −1586.05 | −0.363539 | ||||||||
\(268\) | 5323.03 | 1.21327 | ||||||||
\(269\) | −630.921 | −0.143003 | −0.0715017 | − | 0.997440i | \(-0.522779\pi\) | ||||
−0.0715017 | + | 0.997440i | \(0.522779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5781.90 | −1.29603 | −0.648017 | − | 0.761626i | \(-0.724402\pi\) | ||||
−0.648017 | + | 0.761626i | \(0.724402\pi\) | |||||||
\(272\) | 6394.59 | 1.42547 | ||||||||
\(273\) | −3642.74 | −0.807577 | ||||||||
\(274\) | 3488.29 | 0.769108 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −184.775 | −0.0402976 | ||||||||
\(277\) | −3365.10 | −0.729925 | −0.364962 | − | 0.931022i | \(-0.618918\pi\) | ||||
−0.364962 | + | 0.931022i | \(0.618918\pi\) | |||||||
\(278\) | −7317.64 | −1.57872 | ||||||||
\(279\) | 2061.64 | 0.442390 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 622.308 | 0.132113 | 0.0660566 | − | 0.997816i | \(-0.478958\pi\) | ||||
0.0660566 | + | 0.997816i | \(0.478958\pi\) | |||||||
\(282\) | −3027.67 | −0.639344 | ||||||||
\(283\) | −1629.44 | −0.342263 | −0.171131 | − | 0.985248i | \(-0.554742\pi\) | ||||
−0.171131 | + | 0.985248i | \(0.554742\pi\) | |||||||
\(284\) | 724.710 | 0.151421 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1601.00 | 0.331011 | ||||||||
\(287\) | −14207.7 | −2.92215 | ||||||||
\(288\) | −1961.92 | −0.401414 | ||||||||
\(289\) | 1980.94 | 0.403204 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2574.11 | −0.518547 | ||||||||
\(292\) | 2917.62 | 0.584729 | ||||||||
\(293\) | −5845.09 | −1.16544 | −0.582720 | − | 0.812673i | \(-0.698012\pi\) | ||||
−0.582720 | + | 0.812673i | \(0.698012\pi\) | |||||||
\(294\) | −6807.54 | −1.35042 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2934.75 | −0.576281 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | −10961.5 | −2.13081 | ||||||||
\(299\) | 422.430 | 0.0817049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14259.0 | −2.73047 | ||||||||
\(302\) | −12794.4 | −2.43787 | ||||||||
\(303\) | 146.343 | 0.0277464 | ||||||||
\(304\) | −3820.12 | −0.720720 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2768.68 | −0.517238 | ||||||||
\(307\) | −4452.12 | −0.827674 | −0.413837 | − | 0.910351i | \(-0.635812\pi\) | ||||
−0.413837 | + | 0.910351i | \(0.635812\pi\) | |||||||
\(308\) | 1947.45 | 0.360280 | ||||||||
\(309\) | −1575.31 | −0.290020 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7340.61 | −1.33842 | −0.669209 | − | 0.743074i | \(-0.733367\pi\) | ||||
−0.669209 | + | 0.743074i | \(0.733367\pi\) | |||||||
\(312\) | 992.237 | 0.180046 | ||||||||
\(313\) | 4302.99 | 0.777059 | 0.388530 | − | 0.921436i | \(-0.372983\pi\) | ||||
0.388530 | + | 0.921436i | \(0.372983\pi\) | |||||||
\(314\) | 2737.64 | 0.492019 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4122.43 | 0.733876 | ||||||||
\(317\) | 5631.72 | 0.997821 | 0.498910 | − | 0.866654i | \(-0.333734\pi\) | ||||
0.498910 | + | 0.866654i | \(0.333734\pi\) | |||||||
\(318\) | −4006.15 | −0.706458 | ||||||||
\(319\) | 2187.79 | 0.383990 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2959.47 | −0.514584 | ||||||||
\(322\) | 1231.55 | 0.213142 | ||||||||
\(323\) | −4118.43 | −0.709460 | ||||||||
\(324\) | 463.931 | 0.0795492 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 898.579 | 0.152662 | ||||||||
\(327\) | 165.871 | 0.0280510 | ||||||||
\(328\) | 3870.01 | 0.651481 | ||||||||
\(329\) | 8419.68 | 1.41092 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11290.4 | 1.87485 | 0.937424 | − | 0.348190i | \(-0.113204\pi\) | ||||
0.937424 | + | 0.348190i | \(0.113204\pi\) | |||||||
\(332\) | −4955.06 | −0.819109 | ||||||||
\(333\) | 3137.06 | 0.516245 | ||||||||
\(334\) | 9066.53 | 1.48533 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7141.75 | 1.15957 | ||||||||
\(337\) | −4323.61 | −0.698878 | −0.349439 | − | 0.936959i | \(-0.613628\pi\) | ||||
−0.349439 | + | 0.936959i | \(0.613628\pi\) | |||||||
\(338\) | −2422.61 | −0.389860 | ||||||||
\(339\) | −1379.28 | −0.220980 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2519.78 | 0.400157 | ||||||||
\(342\) | 1654.01 | 0.261516 | ||||||||
\(343\) | 8328.90 | 1.31113 | ||||||||
\(344\) | 3883.96 | 0.608748 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3254.60 | −0.505689 | ||||||||
\(347\) | 7693.25 | 1.19019 | 0.595094 | − | 0.803656i | \(-0.297115\pi\) | ||||
0.595094 | + | 0.803656i | \(0.297115\pi\) | |||||||
\(348\) | −3417.45 | −0.526422 | ||||||||
\(349\) | 2791.91 | 0.428217 | 0.214108 | − | 0.976810i | \(-0.431315\pi\) | ||||
0.214108 | + | 0.976810i | \(0.431315\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1060.63 | −0.161289 | ||||||||
\(352\) | −2397.90 | −0.363093 | ||||||||
\(353\) | −5310.27 | −0.800672 | −0.400336 | − | 0.916368i | \(-0.631107\pi\) | ||||
−0.400336 | + | 0.916368i | \(0.631107\pi\) | |||||||
\(354\) | 2394.48 | 0.359506 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3028.06 | 0.450806 | ||||||||
\(357\) | 7699.45 | 1.14145 | ||||||||
\(358\) | −9163.33 | −1.35278 | ||||||||
\(359\) | 7008.05 | 1.03028 | 0.515140 | − | 0.857106i | \(-0.327740\pi\) | ||||
0.515140 | + | 0.857106i | \(0.327740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4398.65 | −0.641297 | ||||||||
\(362\) | 183.313 | 0.0266152 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | 6954.65 | 1.00144 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4090.03 | −0.584124 | ||||||||
\(367\) | 2101.70 | 0.298932 | 0.149466 | − | 0.988767i | \(-0.452245\pi\) | ||||
0.149466 | + | 0.988767i | \(0.452245\pi\) | |||||||
\(368\) | −828.192 | −0.117317 | ||||||||
\(369\) | −4136.78 | −0.583611 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11140.7 | 1.55902 | ||||||||
\(372\) | −3936.04 | −0.548586 | ||||||||
\(373\) | 8782.22 | 1.21910 | 0.609552 | − | 0.792746i | \(-0.291349\pi\) | ||||
0.609552 | + | 0.792746i | \(0.291349\pi\) | |||||||
\(374\) | −3383.94 | −0.467860 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2293.42 | −0.314558 | ||||||||
\(377\) | 7812.95 | 1.06734 | ||||||||
\(378\) | −3092.18 | −0.420753 | ||||||||
\(379\) | 3038.99 | 0.411879 | 0.205940 | − | 0.978565i | \(-0.433975\pi\) | ||||
0.205940 | + | 0.978565i | \(0.433975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5877.94 | 0.790383 | ||||||||
\(382\) | −7208.35 | −0.965474 | ||||||||
\(383\) | 14611.0 | 1.94932 | 0.974658 | − | 0.223700i | \(-0.0718137\pi\) | ||||
0.974658 | + | 0.223700i | \(0.0718137\pi\) | |||||||
\(384\) | −3102.69 | −0.412327 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11354.2 | −1.49718 | ||||||||
\(387\) | −4151.70 | −0.545330 | ||||||||
\(388\) | 4914.45 | 0.643024 | ||||||||
\(389\) | −173.498 | −0.0226136 | −0.0113068 | − | 0.999936i | \(-0.503599\pi\) | ||||
−0.0113068 | + | 0.999936i | \(0.503599\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −892.866 | −0.115484 | ||||||||
\(392\) | −5156.61 | −0.664409 | ||||||||
\(393\) | −48.7963 | −0.00626323 | ||||||||
\(394\) | −6149.34 | −0.786292 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 567.027 | 0.0719550 | ||||||||
\(397\) | 1369.79 | 0.173168 | 0.0865841 | − | 0.996245i | \(-0.472405\pi\) | ||||
0.0865841 | + | 0.996245i | \(0.472405\pi\) | |||||||
\(398\) | −11967.8 | −1.50726 | ||||||||
\(399\) | −4599.64 | −0.577118 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14595.4 | 1.81760 | 0.908801 | − | 0.417230i | \(-0.136999\pi\) | ||||
0.908801 | + | 0.417230i | \(0.136999\pi\) | |||||||
\(402\) | −10330.2 | −1.28165 | ||||||||
\(403\) | 8998.53 | 1.11228 | ||||||||
\(404\) | −279.394 | −0.0344069 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22777.9 | 2.78436 | ||||||||
\(407\) | 3834.18 | 0.466961 | ||||||||
\(408\) | −2097.23 | −0.254482 | ||||||||
\(409\) | −9903.11 | −1.19726 | −0.598628 | − | 0.801027i | \(-0.704287\pi\) | ||||
−0.598628 | + | 0.801027i | \(0.704287\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2824.48 | −0.338981 | ||||||||
\(412\) | 3007.55 | 0.359639 | ||||||||
\(413\) | −6658.83 | −0.793365 | ||||||||
\(414\) | 358.584 | 0.0425688 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8563.30 | −1.00926 | ||||||||
\(417\) | 5925.11 | 0.695812 | ||||||||
\(418\) | 2021.56 | 0.236550 | ||||||||
\(419\) | −10648.7 | −1.24159 | −0.620794 | − | 0.783974i | \(-0.713190\pi\) | ||||
−0.620794 | + | 0.783974i | \(0.713190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14573.7 | 1.68713 | 0.843563 | − | 0.537030i | \(-0.180454\pi\) | ||||
0.843563 | + | 0.537030i | \(0.180454\pi\) | |||||||
\(422\) | −9425.17 | −1.08723 | ||||||||
\(423\) | 2451.51 | 0.281788 | ||||||||
\(424\) | −3034.60 | −0.347578 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1406.42 | −0.159956 | ||||||||
\(427\) | 11374.0 | 1.28906 | ||||||||
\(428\) | 5650.16 | 0.638110 | ||||||||
\(429\) | −1296.33 | −0.145892 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2825.70 | −0.315799 | −0.157899 | − | 0.987455i | \(-0.550472\pi\) | ||||
−0.157899 | + | 0.987455i | \(0.550472\pi\) | |||||||
\(432\) | 2079.42 | 0.231588 | ||||||||
\(433\) | −14814.8 | −1.64423 | −0.822116 | − | 0.569320i | \(-0.807206\pi\) | ||||
−0.822116 | + | 0.569320i | \(0.807206\pi\) | |||||||
\(434\) | 26234.4 | 2.90159 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −316.678 | −0.0347847 | ||||||||
\(437\) | 533.397 | 0.0583887 | ||||||||
\(438\) | −5662.11 | −0.617685 | ||||||||
\(439\) | 12452.4 | 1.35381 | 0.676904 | − | 0.736071i | \(-0.263321\pi\) | ||||
0.676904 | + | 0.736071i | \(0.263321\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5512.08 | 0.595192 | ||||||||
\(442\) | −12084.6 | −1.30047 | ||||||||
\(443\) | −7989.73 | −0.856892 | −0.428446 | − | 0.903567i | \(-0.640939\pi\) | ||||
−0.428446 | + | 0.903567i | \(0.640939\pi\) | |||||||
\(444\) | −5989.21 | −0.640170 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4407.71 | 0.467963 | ||||||||
\(447\) | 8875.54 | 0.939147 | ||||||||
\(448\) | −5920.83 | −0.624404 | ||||||||
\(449\) | 7874.23 | 0.827635 | 0.413817 | − | 0.910360i | \(-0.364195\pi\) | ||||
0.413817 | + | 0.910360i | \(0.364195\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5056.07 | −0.527896 | ||||||||
\(452\) | 2633.30 | 0.274026 | ||||||||
\(453\) | 10359.6 | 1.07448 | ||||||||
\(454\) | 18147.1 | 1.87596 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1252.88 | 0.128666 | ||||||||
\(457\) | −10376.8 | −1.06216 | −0.531078 | − | 0.847323i | \(-0.678213\pi\) | ||||
−0.531078 | + | 0.847323i | \(0.678213\pi\) | |||||||
\(458\) | −8950.00 | −0.913114 | ||||||||
\(459\) | 2241.80 | 0.227970 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7935.15 | −0.801685 | −0.400843 | − | 0.916147i | \(-0.631283\pi\) | ||||
−0.400843 | + | 0.916147i | \(0.631283\pi\) | |||||||
\(462\) | −3779.33 | −0.380585 | ||||||||
\(463\) | −4036.46 | −0.405163 | −0.202581 | − | 0.979265i | \(-0.564933\pi\) | ||||
−0.202581 | + | 0.979265i | \(0.564933\pi\) | |||||||
\(464\) | −15317.6 | −1.53255 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1942.41 | −0.193091 | ||||||||
\(467\) | −9548.40 | −0.946140 | −0.473070 | − | 0.881025i | \(-0.656854\pi\) | ||||
−0.473070 | + | 0.881025i | \(0.656854\pi\) | |||||||
\(468\) | 2024.94 | 0.200007 | ||||||||
\(469\) | 28727.3 | 2.82837 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2216.67 | −0.216855 | ||||||||
\(472\) | 1813.78 | 0.176877 | ||||||||
\(473\) | −5074.30 | −0.493269 | ||||||||
\(474\) | −8000.23 | −0.775238 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14699.6 | −1.41546 | ||||||||
\(477\) | 3243.78 | 0.311368 | ||||||||
\(478\) | −15432.1 | −1.47667 | ||||||||
\(479\) | −15208.5 | −1.45072 | −0.725358 | − | 0.688372i | \(-0.758326\pi\) | ||||
−0.725358 | + | 0.688372i | \(0.758326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13692.5 | 1.29797 | ||||||||
\(482\) | 7072.25 | 0.668324 | ||||||||
\(483\) | −997.191 | −0.0939416 | ||||||||
\(484\) | 693.033 | 0.0650857 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −900.332 | −0.0840327 | ||||||||
\(487\) | 12284.0 | 1.14300 | 0.571502 | − | 0.820601i | \(-0.306361\pi\) | ||||
0.571502 | + | 0.820601i | \(0.306361\pi\) | |||||||
\(488\) | −3098.14 | −0.287390 | ||||||||
\(489\) | −727.581 | −0.0672849 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15310.6 | −1.40725 | −0.703623 | − | 0.710574i | \(-0.748436\pi\) | ||||
−0.703623 | + | 0.710574i | \(0.748436\pi\) | |||||||
\(492\) | 7897.87 | 0.723707 | ||||||||
\(493\) | −16513.8 | −1.50861 | ||||||||
\(494\) | 7219.32 | 0.657516 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17642.0 | −1.59708 | ||||||||
\(497\) | 3911.12 | 0.352993 | ||||||||
\(498\) | 9616.08 | 0.865274 | ||||||||
\(499\) | 2024.99 | 0.181665 | 0.0908325 | − | 0.995866i | \(-0.471047\pi\) | ||||
0.0908325 | + | 0.995866i | \(0.471047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7341.18 | −0.654651 | ||||||||
\(502\) | 9276.11 | 0.824728 | ||||||||
\(503\) | −9262.81 | −0.821090 | −0.410545 | − | 0.911840i | \(-0.634661\pi\) | ||||
−0.410545 | + | 0.911840i | \(0.634661\pi\) | |||||||
\(504\) | −2342.28 | −0.207011 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 438.270 | 0.0385049 | ||||||||
\(507\) | 1961.59 | 0.171829 | ||||||||
\(508\) | −11222.1 | −0.980115 | ||||||||
\(509\) | −15354.4 | −1.33707 | −0.668537 | − | 0.743679i | \(-0.733079\pi\) | ||||
−0.668537 | + | 0.743679i | \(0.733079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15745.8 | 1.36312 | ||||||||
\(512\) | 11601.2 | 1.00138 | ||||||||
\(513\) | −1339.25 | −0.115262 | ||||||||
\(514\) | −11063.0 | −0.949354 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7926.34 | 0.676236 | ||||||||
\(517\) | 2996.29 | 0.254887 | ||||||||
\(518\) | 39919.1 | 3.38599 | ||||||||
\(519\) | 2635.26 | 0.222880 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1155.39 | −0.0971562 | −0.0485781 | − | 0.998819i | \(-0.515469\pi\) | ||||
−0.0485781 | + | 0.998819i | \(0.515469\pi\) | |||||||
\(522\) | 6632.11 | 0.556091 | ||||||||
\(523\) | 3705.49 | 0.309808 | 0.154904 | − | 0.987930i | \(-0.450493\pi\) | ||||
0.154904 | + | 0.987930i | \(0.450493\pi\) | |||||||
\(524\) | 93.1611 | 0.00776672 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8200.05 | 0.679732 | ||||||||
\(527\) | −19019.7 | −1.57213 | ||||||||
\(528\) | 2541.51 | 0.209480 | ||||||||
\(529\) | −12051.4 | −0.990496 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1938.81 | −0.158451 | ||||||||
\(532\) | 8781.55 | 0.715655 | ||||||||
\(533\) | −18056.0 | −1.46734 | ||||||||
\(534\) | −5876.44 | −0.476214 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7824.97 | −0.630573 | ||||||||
\(537\) | 7419.56 | 0.596234 | ||||||||
\(538\) | −2337.61 | −0.187326 | ||||||||
\(539\) | 6736.98 | 0.538372 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13354.8 | 1.06131 | 0.530653 | − | 0.847589i | \(-0.321947\pi\) | ||||
0.530653 | + | 0.847589i | \(0.321947\pi\) | |||||||
\(542\) | −21422.3 | −1.69773 | ||||||||
\(543\) | −148.429 | −0.0117305 | ||||||||
\(544\) | 18099.8 | 1.42651 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13496.6 | −1.05788 | ||||||||
\(547\) | 18996.8 | 1.48491 | 0.742454 | − | 0.669897i | \(-0.233662\pi\) | ||||
0.742454 | + | 0.669897i | \(0.233662\pi\) | |||||||
\(548\) | 5392.44 | 0.420353 | ||||||||
\(549\) | 3311.70 | 0.257450 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9865.31 | 0.762752 | ||||||||
\(552\) | 271.622 | 0.0209439 | ||||||||
\(553\) | 22247.9 | 1.71081 | ||||||||
\(554\) | −12467.9 | −0.956158 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11312.1 | −0.862842 | ||||||||
\(557\) | 8518.26 | 0.647990 | 0.323995 | − | 0.946059i | \(-0.394974\pi\) | ||||
0.323995 | + | 0.946059i | \(0.394974\pi\) | |||||||
\(558\) | 7638.51 | 0.579505 | ||||||||
\(559\) | −18121.1 | −1.37109 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2739.98 | 0.206207 | ||||||||
\(562\) | 2305.70 | 0.173060 | ||||||||
\(563\) | −10311.5 | −0.771900 | −0.385950 | − | 0.922520i | \(-0.626126\pi\) | ||||
−0.385950 | + | 0.922520i | \(0.626126\pi\) | |||||||
\(564\) | −4680.37 | −0.349431 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6037.20 | −0.448344 | ||||||||
\(567\) | 2503.74 | 0.185445 | ||||||||
\(568\) | −1065.34 | −0.0786983 | ||||||||
\(569\) | −14997.9 | −1.10500 | −0.552498 | − | 0.833514i | \(-0.686325\pi\) | ||||
−0.552498 | + | 0.833514i | \(0.686325\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12160.9 | 0.891274 | 0.445637 | − | 0.895214i | \(-0.352977\pi\) | ||||
0.445637 | + | 0.895214i | \(0.352977\pi\) | |||||||
\(572\) | 2474.93 | 0.180913 | ||||||||
\(573\) | 5836.61 | 0.425528 | ||||||||
\(574\) | −52640.7 | −3.82784 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1723.93 | −0.124706 | ||||||||
\(577\) | −16898.7 | −1.21924 | −0.609619 | − | 0.792694i | \(-0.708678\pi\) | ||||
−0.609619 | + | 0.792694i | \(0.708678\pi\) | |||||||
\(578\) | 7339.53 | 0.528174 | ||||||||
\(579\) | 9193.50 | 0.659877 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26741.4 | −1.90950 | ||||||||
\(582\) | −9537.26 | −0.679265 | ||||||||
\(583\) | 3964.62 | 0.281643 | ||||||||
\(584\) | −4288.96 | −0.303902 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21656.5 | −1.52666 | ||||||||
\(587\) | −18702.0 | −1.31502 | −0.657508 | − | 0.753448i | \(-0.728389\pi\) | ||||
−0.657508 | + | 0.753448i | \(0.728389\pi\) | |||||||
\(588\) | −10523.6 | −0.738068 | ||||||||
\(589\) | 11362.3 | 0.794867 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4979.13 | 0.346555 | ||||||||
\(592\) | −26844.7 | −1.86370 | ||||||||
\(593\) | −198.418 | −0.0137404 | −0.00687019 | − | 0.999976i | \(-0.502187\pi\) | ||||
−0.00687019 | + | 0.999976i | \(0.502187\pi\) | |||||||
\(594\) | −1100.41 | −0.0760104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16945.0 | −1.16459 | ||||||||
\(597\) | 9690.32 | 0.664319 | ||||||||
\(598\) | 1565.13 | 0.107028 | ||||||||
\(599\) | 13958.3 | 0.952119 | 0.476060 | − | 0.879413i | \(-0.342065\pi\) | ||||
0.476060 | + | 0.879413i | \(0.342065\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14279.5 | 0.969173 | 0.484587 | − | 0.874743i | \(-0.338970\pi\) | ||||
0.484587 | + | 0.874743i | \(0.338970\pi\) | |||||||
\(602\) | −52830.4 | −3.57676 | ||||||||
\(603\) | 8364.37 | 0.564881 | ||||||||
\(604\) | −19778.4 | −1.33241 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 542.209 | 0.0363461 | ||||||||
\(607\) | −435.160 | −0.0290982 | −0.0145491 | − | 0.999894i | \(-0.504631\pi\) | ||||
−0.0145491 | + | 0.999894i | \(0.504631\pi\) | |||||||
\(608\) | −10812.8 | −0.721243 | ||||||||
\(609\) | −18443.3 | −1.22719 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10700.2 | 0.708486 | ||||||||
\(612\) | −4280.01 | −0.282695 | ||||||||
\(613\) | 1032.63 | 0.0680384 | 0.0340192 | − | 0.999421i | \(-0.489169\pi\) | ||||
0.0340192 | + | 0.999421i | \(0.489169\pi\) | |||||||
\(614\) | −16495.4 | −1.08420 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2862.79 | −0.187248 | ||||||||
\(617\) | 1793.68 | 0.117035 | 0.0585176 | − | 0.998286i | \(-0.481363\pi\) | ||||
0.0585176 | + | 0.998286i | \(0.481363\pi\) | |||||||
\(618\) | −5836.63 | −0.379909 | ||||||||
\(619\) | −21282.0 | −1.38190 | −0.690948 | − | 0.722904i | \(-0.742807\pi\) | ||||
−0.690948 | + | 0.722904i | \(0.742807\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −290.346 | −0.0187620 | ||||||||
\(622\) | −27197.5 | −1.75325 | ||||||||
\(623\) | 16341.8 | 1.05092 | ||||||||
\(624\) | 9076.16 | 0.582271 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15942.9 | 1.01790 | ||||||||
\(627\) | −1636.86 | −0.104258 | ||||||||
\(628\) | 4232.03 | 0.268911 | ||||||||
\(629\) | −28941.0 | −1.83458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20393.2 | −1.28660 | −0.643298 | − | 0.765616i | \(-0.722434\pi\) | ||||
−0.643298 | + | 0.765616i | \(0.722434\pi\) | |||||||
\(632\) | −6060.06 | −0.381418 | ||||||||
\(633\) | 7631.57 | 0.479191 | ||||||||
\(634\) | 20865.9 | 1.30709 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6192.97 | −0.386112 | ||||||||
\(637\) | 24058.8 | 1.49646 | ||||||||
\(638\) | 8105.91 | 0.503003 | ||||||||
\(639\) | 1138.78 | 0.0704997 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1068.76 | −0.0658559 | −0.0329280 | − | 0.999458i | \(-0.510483\pi\) | ||||
−0.0329280 | + | 0.999458i | \(0.510483\pi\) | |||||||
\(642\) | −10965.0 | −0.674074 | ||||||||
\(643\) | 6293.52 | 0.385991 | 0.192995 | − | 0.981200i | \(-0.438180\pi\) | ||||
0.192995 | + | 0.981200i | \(0.438180\pi\) | |||||||
\(644\) | 1903.82 | 0.116492 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15259.1 | −0.929351 | ||||||||
\(647\) | 14233.7 | 0.864888 | 0.432444 | − | 0.901661i | \(-0.357651\pi\) | ||||
0.432444 | + | 0.901661i | \(0.357651\pi\) | |||||||
\(648\) | −681.988 | −0.0413442 | ||||||||
\(649\) | −2369.66 | −0.143324 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21242.0 | −1.27886 | ||||||||
\(652\) | 1389.08 | 0.0834367 | ||||||||
\(653\) | −7671.06 | −0.459712 | −0.229856 | − | 0.973225i | \(-0.573825\pi\) | ||||
−0.229856 | + | 0.973225i | \(0.573825\pi\) | |||||||
\(654\) | 614.563 | 0.0367452 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 35399.7 | 2.10690 | ||||||||
\(657\) | 4584.62 | 0.272242 | ||||||||
\(658\) | 31195.5 | 1.84822 | ||||||||
\(659\) | 18783.6 | 1.11033 | 0.555165 | − | 0.831741i | \(-0.312655\pi\) | ||||
0.555165 | + | 0.831741i | \(0.312655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21814.3 | −1.28363 | −0.641815 | − | 0.766859i | \(-0.721818\pi\) | ||||
−0.641815 | + | 0.766859i | \(0.721818\pi\) | |||||||
\(662\) | 41831.6 | 2.45594 | ||||||||
\(663\) | 9784.92 | 0.573175 | ||||||||
\(664\) | 7284.04 | 0.425716 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11623.0 | 0.676250 | ||||||||
\(667\) | 2138.78 | 0.124159 | ||||||||
\(668\) | 14015.7 | 0.811799 | ||||||||
\(669\) | −3568.93 | −0.206252 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4047.64 | 0.232872 | ||||||||
\(672\) | 20214.6 | 1.16041 | ||||||||
\(673\) | 4320.84 | 0.247483 | 0.123742 | − | 0.992314i | \(-0.460511\pi\) | ||||
0.123742 | + | 0.992314i | \(0.460511\pi\) | |||||||
\(674\) | −16019.3 | −0.915488 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3745.03 | −0.213077 | ||||||||
\(677\) | −8173.49 | −0.464007 | −0.232004 | − | 0.972715i | \(-0.574528\pi\) | ||||
−0.232004 | + | 0.972715i | \(0.574528\pi\) | |||||||
\(678\) | −5110.33 | −0.289470 | ||||||||
\(679\) | 26522.3 | 1.49902 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14693.7 | −0.826819 | ||||||||
\(682\) | 9335.95 | 0.524182 | ||||||||
\(683\) | −11387.1 | −0.637945 | −0.318973 | − | 0.947764i | \(-0.603338\pi\) | ||||
−0.318973 | + | 0.947764i | \(0.603338\pi\) | |||||||
\(684\) | 2556.87 | 0.142930 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 30859.2 | 1.71750 | ||||||||
\(687\) | 7246.83 | 0.402451 | ||||||||
\(688\) | 35527.3 | 1.96870 | ||||||||
\(689\) | 14158.3 | 0.782857 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7445.76 | 0.409913 | 0.204957 | − | 0.978771i | \(-0.434295\pi\) | ||||
0.204957 | + | 0.978771i | \(0.434295\pi\) | |||||||
\(692\) | −5031.18 | −0.276383 | ||||||||
\(693\) | 3060.13 | 0.167741 | ||||||||
\(694\) | 28504.0 | 1.55907 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5023.73 | 0.273598 | ||||||||
\(697\) | 38164.0 | 2.07398 | ||||||||
\(698\) | 10344.2 | 0.560938 | ||||||||
\(699\) | 1572.77 | 0.0851041 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35574.7 | −1.91674 | −0.958372 | − | 0.285523i | \(-0.907833\pi\) | ||||
−0.958372 | + | 0.285523i | \(0.907833\pi\) | |||||||
\(702\) | −3929.73 | −0.211279 | ||||||||
\(703\) | 17289.3 | 0.927566 | ||||||||
\(704\) | −2107.03 | −0.112801 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19674.9 | −1.04883 | ||||||||
\(707\) | −1507.84 | −0.0802093 | ||||||||
\(708\) | 3701.54 | 0.196487 | ||||||||
\(709\) | 12878.9 | 0.682199 | 0.341099 | − | 0.940027i | \(-0.389201\pi\) | ||||
0.341099 | + | 0.940027i | \(0.389201\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6477.80 | 0.341683 | ||||||||
\(712\) | −4451.31 | −0.234298 | ||||||||
\(713\) | 2463.33 | 0.129386 | ||||||||
\(714\) | 28527.0 | 1.49523 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14165.3 | −0.739359 | ||||||||
\(717\) | 12495.4 | 0.650834 | ||||||||
\(718\) | 25965.3 | 1.34961 | ||||||||
\(719\) | −19103.3 | −0.990867 | −0.495434 | − | 0.868646i | \(-0.664991\pi\) | ||||
−0.495434 | + | 0.868646i | \(0.664991\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16231.1 | 0.838390 | ||||||||
\(722\) | −16297.3 | −0.840060 | ||||||||
\(723\) | −5726.41 | −0.294561 | ||||||||
\(724\) | 283.377 | 0.0145465 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1344.94 | −0.0687540 | ||||||||
\(727\) | −1059.06 | −0.0540281 | −0.0270141 | − | 0.999635i | \(-0.508600\pi\) | ||||
−0.0270141 | + | 0.999635i | \(0.508600\pi\) | |||||||
\(728\) | −10223.5 | −0.520477 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38301.6 | 1.93794 | ||||||||
\(732\) | −6322.64 | −0.319251 | ||||||||
\(733\) | −24503.8 | −1.23475 | −0.617373 | − | 0.786670i | \(-0.711803\pi\) | ||||
−0.617373 | + | 0.786670i | \(0.711803\pi\) | |||||||
\(734\) | 7786.96 | 0.391583 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2344.18 | −0.117402 | ||||||||
\(737\) | 10223.1 | 0.510954 | ||||||||
\(738\) | −15327.1 | −0.764495 | ||||||||
\(739\) | 23488.3 | 1.16919 | 0.584595 | − | 0.811325i | \(-0.301253\pi\) | ||||
0.584595 | + | 0.811325i | \(0.301253\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5845.50 | −0.289797 | ||||||||
\(742\) | 41277.2 | 2.04223 | ||||||||
\(743\) | 33500.5 | 1.65413 | 0.827063 | − | 0.562109i | \(-0.190010\pi\) | ||||
0.827063 | + | 0.562109i | \(0.190010\pi\) | |||||||
\(744\) | 5786.06 | 0.285117 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32538.7 | 1.59695 | ||||||||
\(747\) | −7786.15 | −0.381366 | ||||||||
\(748\) | −5231.12 | −0.255707 | ||||||||
\(749\) | 30492.8 | 1.48756 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26937.5 | −1.30887 | −0.654436 | − | 0.756117i | \(-0.727094\pi\) | ||||
−0.654436 | + | 0.756117i | \(0.727094\pi\) | |||||||
\(752\) | −20978.3 | −1.01729 | ||||||||
\(753\) | −7510.88 | −0.363495 | ||||||||
\(754\) | 28947.5 | 1.39815 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4780.10 | −0.229961 | ||||||||
\(757\) | 8869.39 | 0.425843 | 0.212922 | − | 0.977069i | \(-0.431702\pi\) | ||||
0.212922 | + | 0.977069i | \(0.431702\pi\) | |||||||
\(758\) | 11259.7 | 0.539537 | ||||||||
\(759\) | −354.868 | −0.0169709 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12433.6 | 0.592271 | 0.296135 | − | 0.955146i | \(-0.404302\pi\) | ||||
0.296135 | + | 0.955146i | \(0.404302\pi\) | |||||||
\(762\) | 21778.2 | 1.03535 | ||||||||
\(763\) | −1709.05 | −0.0810899 | ||||||||
\(764\) | −11143.1 | −0.527676 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 54134.8 | 2.55349 | ||||||||
\(767\) | −8462.44 | −0.398384 | ||||||||
\(768\) | −16092.8 | −0.756121 | ||||||||
\(769\) | 24551.5 | 1.15130 | 0.575650 | − | 0.817696i | \(-0.304749\pi\) | ||||
0.575650 | + | 0.817696i | \(0.304749\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8957.72 | 0.418424 | ||||||||
\(772\) | −17552.1 | −0.818280 | ||||||||
\(773\) | 21858.5 | 1.01707 | 0.508535 | − | 0.861041i | \(-0.330187\pi\) | ||||
0.508535 | + | 0.861041i | \(0.330187\pi\) | |||||||
\(774\) | −15382.3 | −0.714349 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7224.34 | −0.334199 | ||||||||
\(777\) | −32322.6 | −1.49236 | ||||||||
\(778\) | −642.821 | −0.0296224 | ||||||||
\(779\) | −22799.1 | −1.04861 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1391.84 | 0.0637694 | ||||||||
\(782\) | −3308.13 | −0.151277 | ||||||||
\(783\) | −5370.03 | −0.245095 | ||||||||
\(784\) | −47168.4 | −2.14871 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −180.794 | −0.00820446 | ||||||||
\(787\) | 3488.56 | 0.158010 | 0.0790048 | − | 0.996874i | \(-0.474826\pi\) | ||||
0.0790048 | + | 0.996874i | \(0.474826\pi\) | |||||||
\(788\) | −9506.06 | −0.429745 | ||||||||
\(789\) | −6639.59 | −0.299589 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14211.4 | 0.638809 | ||||||||
\(792\) | −833.541 | −0.0373972 | ||||||||
\(793\) | 14454.8 | 0.647293 | ||||||||
\(794\) | 5075.16 | 0.226840 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18500.6 | −0.823789 | ||||||||
\(797\) | 19467.5 | 0.865212 | 0.432606 | − | 0.901583i | \(-0.357594\pi\) | ||||
0.432606 | + | 0.901583i | \(0.357594\pi\) | |||||||
\(798\) | −17042.0 | −0.755990 | ||||||||
\(799\) | −22616.5 | −1.00139 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4758.16 | 0.209889 | ||||||||
\(802\) | 54076.9 | 2.38095 | ||||||||
\(803\) | 5603.42 | 0.246252 | ||||||||
\(804\) | −15969.1 | −0.700481 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 33340.2 | 1.45702 | ||||||||
\(807\) | 1892.76 | 0.0825631 | ||||||||
\(808\) | 410.716 | 0.0178823 | ||||||||
\(809\) | −3078.16 | −0.133773 | −0.0668866 | − | 0.997761i | \(-0.521307\pi\) | ||||
−0.0668866 | + | 0.997761i | \(0.521307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31711.1 | 1.37303 | 0.686516 | − | 0.727115i | \(-0.259139\pi\) | ||||
0.686516 | + | 0.727115i | \(0.259139\pi\) | |||||||
\(812\) | 35211.6 | 1.52178 | ||||||||
\(813\) | 17345.7 | 0.748266 | ||||||||
\(814\) | 14205.9 | 0.611691 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −19183.8 | −0.822998 | ||||||||
\(817\) | −22881.3 | −0.979824 | ||||||||
\(818\) | −36691.7 | −1.56833 | ||||||||
\(819\) | 10928.2 | 0.466255 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31485.7 | −1.33844 | −0.669219 | − | 0.743065i | \(-0.733371\pi\) | ||||
−0.669219 | + | 0.743065i | \(0.733371\pi\) | |||||||
\(822\) | −10464.9 | −0.444045 | ||||||||
\(823\) | 19306.7 | 0.817726 | 0.408863 | − | 0.912596i | \(-0.365925\pi\) | ||||
0.408863 | + | 0.912596i | \(0.365925\pi\) | |||||||
\(824\) | −4421.16 | −0.186916 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24671.4 | −1.03926 | ||||||||
\(827\) | 7147.76 | 0.300546 | 0.150273 | − | 0.988645i | \(-0.451985\pi\) | ||||
0.150273 | + | 0.988645i | \(0.451985\pi\) | |||||||
\(828\) | 554.324 | 0.0232658 | ||||||||
\(829\) | −35630.4 | −1.49276 | −0.746378 | − | 0.665522i | \(-0.768209\pi\) | ||||
−0.746378 | + | 0.665522i | \(0.768209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10095.3 | 0.421422 | ||||||||
\(832\) | −7524.55 | −0.313542 | ||||||||
\(833\) | −50851.8 | −2.11514 | ||||||||
\(834\) | 21952.9 | 0.911472 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3125.07 | 0.129285 | ||||||||
\(837\) | −6184.91 | −0.255414 | ||||||||
\(838\) | −39454.3 | −1.62640 | ||||||||
\(839\) | 27513.3 | 1.13214 | 0.566070 | − | 0.824357i | \(-0.308463\pi\) | ||||
0.566070 | + | 0.824357i | \(0.308463\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15168.2 | 0.621929 | ||||||||
\(842\) | 53996.7 | 2.21003 | ||||||||
\(843\) | −1866.92 | −0.0762756 | ||||||||
\(844\) | −14570.1 | −0.594220 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9083.01 | 0.369126 | ||||||||
\(847\) | 3740.16 | 0.151728 | ||||||||
\(848\) | −27758.0 | −1.12407 | ||||||||
\(849\) | 4888.33 | 0.197605 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3748.28 | 0.150986 | ||||||||
\(852\) | −2174.13 | −0.0874231 | ||||||||
\(853\) | −21498.2 | −0.862935 | −0.431467 | − | 0.902129i | \(-0.642004\pi\) | ||||
−0.431467 | + | 0.902129i | \(0.642004\pi\) | |||||||
\(854\) | 42141.5 | 1.68859 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8305.85 | −0.331645 | ||||||||
\(857\) | −7144.96 | −0.284792 | −0.142396 | − | 0.989810i | \(-0.545481\pi\) | ||||
−0.142396 | + | 0.989810i | \(0.545481\pi\) | |||||||
\(858\) | −4803.00 | −0.191109 | ||||||||
\(859\) | −5734.28 | −0.227766 | −0.113883 | − | 0.993494i | \(-0.536329\pi\) | ||||
−0.113883 | + | 0.993494i | \(0.536329\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 42623.2 | 1.68710 | ||||||||
\(862\) | −10469.4 | −0.413677 | ||||||||
\(863\) | −5032.50 | −0.198503 | −0.0992516 | − | 0.995062i | \(-0.531645\pi\) | ||||
−0.0992516 | + | 0.995062i | \(0.531645\pi\) | |||||||
\(864\) | 5885.76 | 0.231757 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −54889.8 | −2.15385 | ||||||||
\(867\) | −5942.83 | −0.232790 | ||||||||
\(868\) | 40554.8 | 1.58585 | ||||||||
\(869\) | 7917.31 | 0.309064 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36508.4 | 1.42025 | ||||||||
\(872\) | 465.523 | 0.0180787 | ||||||||
\(873\) | 7722.33 | 0.299383 | ||||||||
\(874\) | 1976.27 | 0.0764856 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8752.86 | −0.337593 | ||||||||
\(877\) | −29097.4 | −1.12035 | −0.560177 | − | 0.828373i | \(-0.689267\pi\) | ||||
−0.560177 | + | 0.828373i | \(0.689267\pi\) | |||||||
\(878\) | 46137.1 | 1.77341 | ||||||||
\(879\) | 17535.3 | 0.672867 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6899.21 | 0.263837 | 0.131918 | − | 0.991261i | \(-0.457886\pi\) | ||||
0.131918 | + | 0.991261i | \(0.457886\pi\) | |||||||
\(882\) | 20422.6 | 0.779666 | ||||||||
\(883\) | −13094.5 | −0.499054 | −0.249527 | − | 0.968368i | \(-0.580275\pi\) | ||||
−0.249527 | + | 0.968368i | \(0.580275\pi\) | |||||||
\(884\) | −18681.2 | −0.710765 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29602.5 | −1.12248 | ||||||||
\(887\) | −27043.9 | −1.02373 | −0.511863 | − | 0.859067i | \(-0.671044\pi\) | ||||
−0.511863 | + | 0.859067i | \(0.671044\pi\) | |||||||
\(888\) | 8804.26 | 0.332716 | ||||||||
\(889\) | −60563.2 | −2.28484 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | 6813.74 | 0.255763 | ||||||||
\(893\) | 13511.0 | 0.506304 | ||||||||
\(894\) | 32884.5 | 1.23023 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 31968.5 | 1.19196 | ||||||||
\(897\) | −1267.29 | −0.0471723 | ||||||||
\(898\) | 29174.6 | 1.08415 | ||||||||
\(899\) | 45559.9 | 1.69022 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29925.6 | −1.10651 | ||||||||
\(902\) | −18733.1 | −0.691512 | ||||||||
\(903\) | 42776.9 | 1.57644 | ||||||||
\(904\) | −3871.00 | −0.142420 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 38383.2 | 1.40750 | ||||||||
\(907\) | −375.753 | −0.0137560 | −0.00687799 | − | 0.999976i | \(-0.502189\pi\) | ||||
−0.00687799 | + | 0.999976i | \(0.502189\pi\) | |||||||
\(908\) | 28052.9 | 1.02530 | ||||||||
\(909\) | −439.028 | −0.0160194 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7303.70 | 0.265623 | 0.132811 | − | 0.991141i | \(-0.457600\pi\) | ||||
0.132811 | + | 0.991141i | \(0.457600\pi\) | |||||||
\(912\) | 11460.4 | 0.416108 | ||||||||
\(913\) | −9516.40 | −0.344958 | ||||||||
\(914\) | −38446.7 | −1.39136 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13835.5 | −0.499059 | ||||||||
\(917\) | 502.772 | 0.0181058 | ||||||||
\(918\) | 8306.04 | 0.298628 | ||||||||
\(919\) | 3492.12 | 0.125348 | 0.0626738 | − | 0.998034i | \(-0.480037\pi\) | ||||
0.0626738 | + | 0.998034i | \(0.480037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13356.4 | 0.477858 | ||||||||
\(922\) | −29400.3 | −1.05016 | ||||||||
\(923\) | 4970.48 | 0.177254 | ||||||||
\(924\) | −5842.34 | −0.208008 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14955.4 | −0.530739 | ||||||||
\(927\) | 4725.93 | 0.167443 | ||||||||
\(928\) | −43356.3 | −1.53366 | ||||||||
\(929\) | 16961.2 | 0.599009 | 0.299504 | − | 0.954095i | \(-0.403179\pi\) | ||||
0.299504 | + | 0.954095i | \(0.403179\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30378.8 | 1.06941 | ||||||||
\(932\) | −3002.71 | −0.105533 | ||||||||
\(933\) | 22021.8 | 0.772736 | ||||||||
\(934\) | −35377.5 | −1.23939 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2976.71 | −0.103950 | ||||||||
\(937\) | 3401.53 | 0.118595 | 0.0592973 | − | 0.998240i | \(-0.481114\pi\) | ||||
0.0592973 | + | 0.998240i | \(0.481114\pi\) | |||||||
\(938\) | 106437. | 3.70499 | ||||||||
\(939\) | −12909.0 | −0.448635 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39517.5 | −1.36901 | −0.684503 | − | 0.729010i | \(-0.739981\pi\) | ||||
−0.684503 | + | 0.729010i | \(0.739981\pi\) | |||||||
\(942\) | −8212.92 | −0.284067 | ||||||||
\(943\) | −4942.80 | −0.170689 | ||||||||
\(944\) | 16591.0 | 0.572024 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18800.6 | −0.646153 | ||||||||
\(947\) | 39781.6 | 1.36508 | 0.682538 | − | 0.730850i | \(-0.260876\pi\) | ||||
0.682538 | + | 0.730850i | \(0.260876\pi\) | |||||||
\(948\) | −12367.3 | −0.423703 | ||||||||
\(949\) | 20010.7 | 0.684484 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16895.2 | −0.576092 | ||||||||
\(952\) | 21608.8 | 0.735656 | ||||||||
\(953\) | −19941.5 | −0.677826 | −0.338913 | − | 0.940818i | \(-0.610059\pi\) | ||||
−0.338913 | + | 0.940818i | \(0.610059\pi\) | |||||||
\(954\) | 12018.4 | 0.407874 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −23855.9 | −0.807066 | ||||||||
\(957\) | −6563.37 | −0.221697 | ||||||||
\(958\) | −56348.5 | −1.90035 | ||||||||
\(959\) | 29101.9 | 0.979926 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22682.4 | 0.761384 | ||||||||
\(962\) | 50731.6 | 1.70026 | ||||||||
\(963\) | 8878.41 | 0.297095 | ||||||||
\(964\) | 10932.8 | 0.365270 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3694.66 | −0.123058 | ||||||||
\(967\) | 22672.9 | 0.753992 | 0.376996 | − | 0.926215i | \(-0.376957\pi\) | ||||
0.376996 | + | 0.926215i | \(0.376957\pi\) | |||||||
\(968\) | −1018.77 | −0.0338271 | ||||||||
\(969\) | 12355.3 | 0.409607 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15739.4 | 0.520186 | 0.260093 | − | 0.965584i | \(-0.416247\pi\) | ||||
0.260093 | + | 0.965584i | \(0.416247\pi\) | |||||||
\(972\) | −1391.79 | −0.0459278 | ||||||||
\(973\) | −61049.1 | −2.01145 | ||||||||
\(974\) | 45513.2 | 1.49727 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28339.2 | −0.929422 | ||||||||
\(977\) | −55085.0 | −1.80381 | −0.901906 | − | 0.431933i | \(-0.857832\pi\) | ||||
−0.901906 | + | 0.431933i | \(0.857832\pi\) | |||||||
\(978\) | −2695.74 | −0.0881392 | ||||||||
\(979\) | 5815.53 | 0.189852 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −497.613 | −0.0161953 | ||||||||
\(982\) | −56726.8 | −1.84341 | ||||||||
\(983\) | 3826.41 | 0.124154 | 0.0620770 | − | 0.998071i | \(-0.480228\pi\) | ||||
0.0620770 | + | 0.998071i | \(0.480228\pi\) | |||||||
\(984\) | −11610.0 | −0.376133 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −61184.7 | −1.97619 | ||||||||
\(987\) | −25259.0 | −0.814594 | ||||||||
\(988\) | 11160.1 | 0.359363 | ||||||||
\(989\) | −4960.62 | −0.159493 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10873.3 | 0.348538 | 0.174269 | − | 0.984698i | \(-0.444244\pi\) | ||||
0.174269 | + | 0.984698i | \(0.444244\pi\) | |||||||
\(992\) | −49935.4 | −1.59824 | ||||||||
\(993\) | −33871.1 | −1.08244 | ||||||||
\(994\) | 14491.0 | 0.462400 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14865.2 | 0.472913 | ||||||||
\(997\) | −40064.9 | −1.27269 | −0.636343 | − | 0.771406i | \(-0.719554\pi\) | ||||
−0.636343 | + | 0.771406i | \(0.719554\pi\) | |||||||
\(998\) | 7502.72 | 0.237970 | ||||||||
\(999\) | −9411.17 | −0.298054 |
(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.bd.1.6 | 7 | ||
3.2 | odd | 2 | 2475.4.a.bo.1.2 | 7 | |||
5.2 | odd | 4 | 165.4.c.b.34.13 | yes | 14 | ||
5.3 | odd | 4 | 165.4.c.b.34.2 | ✓ | 14 | ||
5.4 | even | 2 | 825.4.a.ba.1.2 | 7 | |||
15.2 | even | 4 | 495.4.c.d.199.2 | 14 | |||
15.8 | even | 4 | 495.4.c.d.199.13 | 14 | |||
15.14 | odd | 2 | 2475.4.a.bs.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.c.b.34.2 | ✓ | 14 | 5.3 | odd | 4 | ||
165.4.c.b.34.13 | yes | 14 | 5.2 | odd | 4 | ||
495.4.c.d.199.2 | 14 | 15.2 | even | 4 | |||
495.4.c.d.199.13 | 14 | 15.8 | even | 4 | |||
825.4.a.ba.1.2 | 7 | 5.4 | even | 2 | |||
825.4.a.bd.1.6 | 7 | 1.1 | even | 1 | trivial | ||
2475.4.a.bo.1.2 | 7 | 3.2 | odd | 2 | |||
2475.4.a.bs.1.6 | 7 | 15.14 | odd | 2 |