Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,4,Mod(1,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1225.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.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: | \(72.2773397570\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 32x^{2} - 35x + 120 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 175) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.50478\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.504784 | 0.178468 | 0.0892340 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892340 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(3\) | 4.26379 | 0.820567 | 0.410284 | − | 0.911958i | \(-0.365430\pi\) | ||||
0.410284 | + | 0.911958i | \(0.365430\pi\) | |||||||
\(4\) | −7.74519 | −0.968149 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.15229 | 0.146445 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −7.94792 | −0.351252 | ||||||||
\(9\) | −8.82008 | −0.326670 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 54.8800 | 1.50427 | 0.752134 | − | 0.659010i | \(-0.229025\pi\) | ||||
0.752134 | + | 0.659010i | \(0.229025\pi\) | |||||||
\(12\) | −33.0239 | −0.794431 | ||||||||
\(13\) | 16.0073 | 0.341510 | 0.170755 | − | 0.985313i | \(-0.445379\pi\) | ||||
0.170755 | + | 0.985313i | \(0.445379\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 57.9496 | 0.905462 | ||||||||
\(17\) | −0.422056 | −0.00602139 | −0.00301069 | − | 0.999995i | \(-0.500958\pi\) | ||||
−0.00301069 | + | 0.999995i | \(0.500958\pi\) | |||||||
\(18\) | −4.45223 | −0.0583000 | ||||||||
\(19\) | −127.501 | −1.53952 | −0.769758 | − | 0.638336i | \(-0.779623\pi\) | ||||
−0.769758 | + | 0.638336i | \(0.779623\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 27.7025 | 0.268464 | ||||||||
\(23\) | −51.1101 | −0.463357 | −0.231678 | − | 0.972792i | \(-0.574422\pi\) | ||||
−0.231678 | + | 0.972792i | \(0.574422\pi\) | |||||||
\(24\) | −33.8883 | −0.288226 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.08024 | 0.0609487 | ||||||||
\(27\) | −152.729 | −1.08862 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 41.4750 | 0.265576 | 0.132788 | − | 0.991144i | \(-0.457607\pi\) | ||||
0.132788 | + | 0.991144i | \(0.457607\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −192.354 | −1.11445 | −0.557224 | − | 0.830362i | \(-0.688134\pi\) | ||||
−0.557224 | + | 0.830362i | \(0.688134\pi\) | |||||||
\(32\) | 92.8353 | 0.512848 | ||||||||
\(33\) | 233.997 | 1.23435 | ||||||||
\(34\) | −0.213047 | −0.00107462 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 68.3132 | 0.316265 | ||||||||
\(37\) | 189.232 | 0.840801 | 0.420400 | − | 0.907339i | \(-0.361890\pi\) | ||||
0.420400 | + | 0.907339i | \(0.361890\pi\) | |||||||
\(38\) | −64.3605 | −0.274754 | ||||||||
\(39\) | 68.2519 | 0.280232 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 76.3187 | 0.290707 | 0.145353 | − | 0.989380i | \(-0.453568\pi\) | ||||
0.145353 | + | 0.989380i | \(0.453568\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −294.499 | −1.04443 | −0.522216 | − | 0.852813i | \(-0.674895\pi\) | ||||
−0.522216 | + | 0.852813i | \(0.674895\pi\) | |||||||
\(44\) | −425.056 | −1.45636 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −25.7996 | −0.0826943 | ||||||||
\(47\) | 540.297 | 1.67682 | 0.838408 | − | 0.545043i | \(-0.183487\pi\) | ||||
0.838408 | + | 0.545043i | \(0.183487\pi\) | |||||||
\(48\) | 247.085 | 0.742992 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.79956 | −0.00494095 | ||||||||
\(52\) | −123.980 | −0.330633 | ||||||||
\(53\) | 661.316 | 1.71394 | 0.856969 | − | 0.515368i | \(-0.172345\pi\) | ||||
0.856969 | + | 0.515368i | \(0.172345\pi\) | |||||||
\(54\) | −77.0953 | −0.194284 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −543.639 | −1.26328 | ||||||||
\(58\) | 20.9359 | 0.0473969 | ||||||||
\(59\) | −410.312 | −0.905390 | −0.452695 | − | 0.891665i | \(-0.649537\pi\) | ||||
−0.452695 | + | 0.891665i | \(0.649537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −46.0495 | −0.0966563 | −0.0483281 | − | 0.998832i | \(-0.515389\pi\) | ||||
−0.0483281 | + | 0.998832i | \(0.515389\pi\) | |||||||
\(62\) | −97.0974 | −0.198893 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −416.735 | −0.813935 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 118.118 | 0.220292 | ||||||||
\(67\) | −10.4074 | −0.0189771 | −0.00948854 | − | 0.999955i | \(-0.503020\pi\) | ||||
−0.00948854 | + | 0.999955i | \(0.503020\pi\) | |||||||
\(68\) | 3.26890 | 0.00582960 | ||||||||
\(69\) | −217.923 | −0.380215 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −491.117 | −0.820913 | −0.410456 | − | 0.911880i | \(-0.634631\pi\) | ||||
−0.410456 | + | 0.911880i | \(0.634631\pi\) | |||||||
\(72\) | 70.1012 | 0.114743 | ||||||||
\(73\) | −814.540 | −1.30595 | −0.652977 | − | 0.757378i | \(-0.726480\pi\) | ||||
−0.652977 | + | 0.757378i | \(0.726480\pi\) | |||||||
\(74\) | 95.5215 | 0.150056 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 987.522 | 1.49048 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 34.4525 | 0.0500125 | ||||||||
\(79\) | −858.725 | −1.22296 | −0.611482 | − | 0.791258i | \(-0.709426\pi\) | ||||
−0.611482 | + | 0.791258i | \(0.709426\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −413.064 | −0.566617 | ||||||||
\(82\) | 38.5244 | 0.0518818 | ||||||||
\(83\) | −1055.80 | −1.39626 | −0.698129 | − | 0.715972i | \(-0.745984\pi\) | ||||
−0.698129 | + | 0.715972i | \(0.745984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −148.658 | −0.186398 | ||||||||
\(87\) | 176.841 | 0.217923 | ||||||||
\(88\) | −436.182 | −0.528376 | ||||||||
\(89\) | −341.567 | −0.406809 | −0.203405 | − | 0.979095i | \(-0.565201\pi\) | ||||
−0.203405 | + | 0.979095i | \(0.565201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 395.858 | 0.448598 | ||||||||
\(93\) | −820.159 | −0.914479 | ||||||||
\(94\) | 272.733 | 0.299258 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 395.831 | 0.420826 | ||||||||
\(97\) | −1417.21 | −1.48346 | −0.741731 | − | 0.670697i | \(-0.765995\pi\) | ||||
−0.741731 | + | 0.670697i | \(0.765995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −484.046 | −0.491398 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 121.051 | 0.119258 | 0.0596289 | − | 0.998221i | \(-0.481008\pi\) | ||||
0.0596289 | + | 0.998221i | \(0.481008\pi\) | |||||||
\(102\) | −0.908388 | −0.000881802 0 | ||||||||
\(103\) | −655.594 | −0.627161 | −0.313581 | − | 0.949562i | \(-0.601529\pi\) | ||||
−0.313581 | + | 0.949562i | \(0.601529\pi\) | |||||||
\(104\) | −127.225 | −0.119956 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 333.821 | 0.305883 | ||||||||
\(107\) | −2069.81 | −1.87006 | −0.935031 | − | 0.354567i | \(-0.884628\pi\) | ||||
−0.935031 | + | 0.354567i | \(0.884628\pi\) | |||||||
\(108\) | 1182.92 | 1.05395 | ||||||||
\(109\) | 904.218 | 0.794573 | 0.397286 | − | 0.917695i | \(-0.369952\pi\) | ||||
0.397286 | + | 0.917695i | \(0.369952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 806.848 | 0.689934 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 843.350 | 0.702086 | 0.351043 | − | 0.936359i | \(-0.385827\pi\) | ||||
0.351043 | + | 0.936359i | \(0.385827\pi\) | |||||||
\(114\) | −274.420 | −0.225454 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −321.232 | −0.257117 | ||||||||
\(117\) | −141.186 | −0.111561 | ||||||||
\(118\) | −207.119 | −0.161583 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1680.81 | 1.26282 | ||||||||
\(122\) | −23.2450 | −0.0172501 | ||||||||
\(123\) | 325.407 | 0.238544 | ||||||||
\(124\) | 1489.82 | 1.07895 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2030.50 | −1.41872 | −0.709362 | − | 0.704845i | \(-0.751017\pi\) | ||||
−0.709362 | + | 0.704845i | \(0.751017\pi\) | |||||||
\(128\) | −953.043 | −0.658109 | ||||||||
\(129\) | −1255.68 | −0.857027 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2872.47 | −1.91579 | −0.957897 | − | 0.287113i | \(-0.907305\pi\) | ||||
−0.957897 | + | 0.287113i | \(0.907305\pi\) | |||||||
\(132\) | −1812.35 | −1.19504 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.25348 | −0.00338680 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.35446 | 0.00211502 | ||||||||
\(137\) | 1621.62 | 1.01127 | 0.505636 | − | 0.862747i | \(-0.331258\pi\) | ||||
0.505636 | + | 0.862747i | \(0.331258\pi\) | |||||||
\(138\) | −110.004 | −0.0678562 | ||||||||
\(139\) | −2617.72 | −1.59735 | −0.798677 | − | 0.601760i | \(-0.794466\pi\) | ||||
−0.798677 | + | 0.601760i | \(0.794466\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2303.71 | 1.37594 | ||||||||
\(142\) | −247.908 | −0.146507 | ||||||||
\(143\) | 878.482 | 0.513723 | ||||||||
\(144\) | −511.120 | −0.295787 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −411.166 | −0.233071 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1465.64 | −0.814021 | ||||||||
\(149\) | 2252.63 | 1.23854 | 0.619270 | − | 0.785178i | \(-0.287429\pi\) | ||||
0.619270 | + | 0.785178i | \(0.287429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1849.61 | −0.996813 | −0.498407 | − | 0.866943i | \(-0.666081\pi\) | ||||
−0.498407 | + | 0.866943i | \(0.666081\pi\) | |||||||
\(152\) | 1013.37 | 0.540757 | ||||||||
\(153\) | 3.72257 | 0.00196700 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −528.624 | −0.271307 | ||||||||
\(157\) | −3337.59 | −1.69661 | −0.848307 | − | 0.529505i | \(-0.822378\pi\) | ||||
−0.848307 | + | 0.529505i | \(0.822378\pi\) | |||||||
\(158\) | −433.471 | −0.218260 | ||||||||
\(159\) | 2819.71 | 1.40640 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −208.508 | −0.101123 | ||||||||
\(163\) | 471.099 | 0.226376 | 0.113188 | − | 0.993574i | \(-0.463894\pi\) | ||||
0.113188 | + | 0.993574i | \(0.463894\pi\) | |||||||
\(164\) | −591.103 | −0.281447 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −532.952 | −0.249187 | ||||||||
\(167\) | −3676.72 | −1.70367 | −0.851836 | − | 0.523809i | \(-0.824511\pi\) | ||||
−0.851836 | + | 0.523809i | \(0.824511\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1940.77 | −0.883371 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1124.57 | 0.502913 | ||||||||
\(172\) | 2280.95 | 1.01117 | ||||||||
\(173\) | 1009.11 | 0.443475 | 0.221737 | − | 0.975106i | \(-0.428827\pi\) | ||||
0.221737 | + | 0.975106i | \(0.428827\pi\) | |||||||
\(174\) | 89.2663 | 0.0388923 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3180.27 | 1.36206 | ||||||||
\(177\) | −1749.48 | −0.742934 | ||||||||
\(178\) | −172.417 | −0.0726024 | ||||||||
\(179\) | 3201.27 | 1.33673 | 0.668364 | − | 0.743835i | \(-0.266995\pi\) | ||||
0.668364 | + | 0.743835i | \(0.266995\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1970.14 | 0.809056 | 0.404528 | − | 0.914526i | \(-0.367436\pi\) | ||||
0.404528 | + | 0.914526i | \(0.367436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −196.345 | −0.0793130 | ||||||||
\(184\) | 406.219 | 0.162755 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −414.003 | −0.163205 | ||||||||
\(187\) | −23.1624 | −0.00905778 | ||||||||
\(188\) | −4184.70 | −1.62341 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3953.39 | 1.49768 | 0.748842 | − | 0.662749i | \(-0.230610\pi\) | ||||
0.748842 | + | 0.662749i | \(0.230610\pi\) | |||||||
\(192\) | −1776.87 | −0.667888 | ||||||||
\(193\) | −2425.45 | −0.904598 | −0.452299 | − | 0.891866i | \(-0.649396\pi\) | ||||
−0.452299 | + | 0.891866i | \(0.649396\pi\) | |||||||
\(194\) | −715.385 | −0.264751 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3126.50 | −1.13073 | −0.565366 | − | 0.824840i | \(-0.691265\pi\) | ||||
−0.565366 | + | 0.824840i | \(0.691265\pi\) | |||||||
\(198\) | −244.338 | −0.0876989 | ||||||||
\(199\) | 3566.13 | 1.27033 | 0.635166 | − | 0.772376i | \(-0.280932\pi\) | ||||
0.635166 | + | 0.772376i | \(0.280932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −44.3749 | −0.0155720 | ||||||||
\(202\) | 61.1046 | 0.0212837 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 13.9379 | 0.00478358 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −330.933 | −0.111928 | ||||||||
\(207\) | 450.795 | 0.151364 | ||||||||
\(208\) | 927.618 | 0.309225 | ||||||||
\(209\) | −6997.27 | −2.31584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3699.18 | −1.20693 | −0.603465 | − | 0.797389i | \(-0.706214\pi\) | ||||
−0.603465 | + | 0.797389i | \(0.706214\pi\) | |||||||
\(212\) | −5122.02 | −1.65935 | ||||||||
\(213\) | −2094.02 | −0.673614 | ||||||||
\(214\) | −1044.81 | −0.333746 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1213.88 | 0.382380 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 456.435 | 0.141806 | ||||||||
\(219\) | −3473.03 | −1.07162 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.75599 | −0.00205637 | ||||||||
\(222\) | 407.284 | 0.123131 | ||||||||
\(223\) | −102.041 | −0.0306419 | −0.0153210 | − | 0.999883i | \(-0.504877\pi\) | ||||
−0.0153210 | + | 0.999883i | \(0.504877\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 425.709 | 0.125300 | ||||||||
\(227\) | 5739.91 | 1.67829 | 0.839144 | − | 0.543909i | \(-0.183057\pi\) | ||||
0.839144 | + | 0.543909i | \(0.183057\pi\) | |||||||
\(228\) | 4210.59 | 1.22304 | ||||||||
\(229\) | 843.125 | 0.243298 | 0.121649 | − | 0.992573i | \(-0.461182\pi\) | ||||
0.121649 | + | 0.992573i | \(0.461182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −329.640 | −0.0932841 | ||||||||
\(233\) | 2017.65 | 0.567300 | 0.283650 | − | 0.958928i | \(-0.408455\pi\) | ||||
0.283650 | + | 0.958928i | \(0.408455\pi\) | |||||||
\(234\) | −71.2683 | −0.0199101 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3177.94 | 0.876553 | ||||||||
\(237\) | −3661.43 | −1.00352 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 243.685 | 0.0659526 | 0.0329763 | − | 0.999456i | \(-0.489501\pi\) | ||||
0.0329763 | + | 0.999456i | \(0.489501\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3060.58 | 0.818048 | 0.409024 | − | 0.912524i | \(-0.365869\pi\) | ||||
0.409024 | + | 0.912524i | \(0.365869\pi\) | |||||||
\(242\) | 848.448 | 0.225373 | ||||||||
\(243\) | 2362.47 | 0.623674 | ||||||||
\(244\) | 356.662 | 0.0935777 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 164.260 | 0.0425725 | ||||||||
\(247\) | −2040.95 | −0.525760 | ||||||||
\(248\) | 1528.82 | 0.391452 | ||||||||
\(249\) | −4501.72 | −1.14572 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6594.14 | 1.65824 | 0.829120 | − | 0.559070i | \(-0.188842\pi\) | ||||
0.829120 | + | 0.559070i | \(0.188842\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2804.92 | −0.697012 | ||||||||
\(254\) | −1024.96 | −0.253197 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2852.80 | 0.696484 | ||||||||
\(257\) | 512.646 | 0.124428 | 0.0622139 | − | 0.998063i | \(-0.480184\pi\) | ||||
0.0622139 | + | 0.998063i | \(0.480184\pi\) | |||||||
\(258\) | −633.847 | −0.152952 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −365.813 | −0.0867557 | ||||||||
\(262\) | −1449.98 | −0.341908 | ||||||||
\(263\) | 3560.04 | 0.834681 | 0.417341 | − | 0.908750i | \(-0.362962\pi\) | ||||
0.417341 | + | 0.908750i | \(0.362962\pi\) | |||||||
\(264\) | −1859.79 | −0.433568 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1456.37 | −0.333814 | ||||||||
\(268\) | 80.6072 | 0.0183726 | ||||||||
\(269\) | 549.744 | 0.124604 | 0.0623020 | − | 0.998057i | \(-0.480156\pi\) | ||||
0.0623020 | + | 0.998057i | \(0.480156\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3944.91 | 0.884267 | 0.442134 | − | 0.896949i | \(-0.354222\pi\) | ||||
0.442134 | + | 0.896949i | \(0.354222\pi\) | |||||||
\(272\) | −24.4580 | −0.00545214 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 818.567 | 0.180480 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1687.86 | 0.368105 | ||||||||
\(277\) | 1254.67 | 0.272150 | 0.136075 | − | 0.990699i | \(-0.456551\pi\) | ||||
0.136075 | + | 0.990699i | \(0.456551\pi\) | |||||||
\(278\) | −1321.38 | −0.285077 | ||||||||
\(279\) | 1696.58 | 0.364056 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −681.496 | −0.144679 | −0.0723393 | − | 0.997380i | \(-0.523046\pi\) | ||||
−0.0723393 | + | 0.997380i | \(0.523046\pi\) | |||||||
\(282\) | 1162.88 | 0.245561 | ||||||||
\(283\) | −5946.88 | −1.24914 | −0.624568 | − | 0.780970i | \(-0.714725\pi\) | ||||
−0.624568 | + | 0.780970i | \(0.714725\pi\) | |||||||
\(284\) | 3803.79 | 0.794766 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 443.444 | 0.0916831 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −818.815 | −0.167532 | ||||||||
\(289\) | −4912.82 | −0.999964 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6042.69 | −1.21728 | ||||||||
\(292\) | 6308.77 | 1.26436 | ||||||||
\(293\) | 2171.03 | 0.432877 | 0.216438 | − | 0.976296i | \(-0.430556\pi\) | ||||
0.216438 | + | 0.976296i | \(0.430556\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1504.00 | −0.295333 | ||||||||
\(297\) | −8381.79 | −1.63758 | ||||||||
\(298\) | 1137.09 | 0.221040 | ||||||||
\(299\) | −818.137 | −0.158241 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −933.651 | −0.177899 | ||||||||
\(303\) | 516.137 | 0.0978590 | ||||||||
\(304\) | −7388.64 | −1.39397 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.87909 | 0.000351047 0 | ||||||||
\(307\) | −3644.59 | −0.677549 | −0.338775 | − | 0.940868i | \(-0.610012\pi\) | ||||
−0.338775 | + | 0.940868i | \(0.610012\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2795.32 | −0.514628 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2584.19 | −0.471177 | −0.235589 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235589 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(312\) | −542.461 | −0.0984320 | ||||||||
\(313\) | 6693.63 | 1.20878 | 0.604388 | − | 0.796690i | \(-0.293418\pi\) | ||||
0.604388 | + | 0.796690i | \(0.293418\pi\) | |||||||
\(314\) | −1684.76 | −0.302791 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6650.99 | 1.18401 | ||||||||
\(317\) | 3843.36 | 0.680962 | 0.340481 | − | 0.940251i | \(-0.389410\pi\) | ||||
0.340481 | + | 0.940251i | \(0.389410\pi\) | |||||||
\(318\) | 1423.35 | 0.250998 | ||||||||
\(319\) | 2276.15 | 0.399498 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8825.26 | −1.53451 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 53.8126 | 0.00927002 | ||||||||
\(324\) | 3199.26 | 0.548570 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 237.803 | 0.0404009 | ||||||||
\(327\) | 3855.40 | 0.652000 | ||||||||
\(328\) | −606.575 | −0.102111 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −821.922 | −0.136486 | −0.0682431 | − | 0.997669i | \(-0.521739\pi\) | ||||
−0.0682431 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(332\) | 8177.39 | 1.35179 | ||||||||
\(333\) | −1669.05 | −0.274664 | ||||||||
\(334\) | −1855.95 | −0.304051 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1032.55 | −0.166904 | −0.0834520 | − | 0.996512i | \(-0.526595\pi\) | ||||
−0.0834520 | + | 0.996512i | \(0.526595\pi\) | |||||||
\(338\) | −979.667 | −0.157653 | ||||||||
\(339\) | 3595.87 | 0.576108 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10556.4 | −1.67643 | ||||||||
\(342\) | 567.665 | 0.0897538 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2340.65 | 0.366859 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 509.382 | 0.0791461 | ||||||||
\(347\) | 2587.70 | 0.400332 | 0.200166 | − | 0.979762i | \(-0.435852\pi\) | ||||
0.200166 | + | 0.979762i | \(0.435852\pi\) | |||||||
\(348\) | −1369.67 | −0.210982 | ||||||||
\(349\) | 8454.24 | 1.29669 | 0.648345 | − | 0.761346i | \(-0.275461\pi\) | ||||
0.648345 | + | 0.761346i | \(0.275461\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2444.79 | −0.371776 | ||||||||
\(352\) | 5094.80 | 0.771460 | ||||||||
\(353\) | −4129.63 | −0.622658 | −0.311329 | − | 0.950302i | \(-0.600774\pi\) | ||||
−0.311329 | + | 0.950302i | \(0.600774\pi\) | |||||||
\(354\) | −883.111 | −0.132590 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2645.50 | 0.393852 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1615.95 | 0.238563 | ||||||||
\(359\) | −4536.69 | −0.666957 | −0.333478 | − | 0.942758i | \(-0.608222\pi\) | ||||
−0.333478 | + | 0.942758i | \(0.608222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9397.56 | 1.37011 | ||||||||
\(362\) | 994.492 | 0.144390 | ||||||||
\(363\) | 7166.65 | 1.03623 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −99.1120 | −0.0141548 | ||||||||
\(367\) | 1643.00 | 0.233689 | 0.116844 | − | 0.993150i | \(-0.462722\pi\) | ||||
0.116844 | + | 0.993150i | \(0.462722\pi\) | |||||||
\(368\) | −2961.81 | −0.419552 | ||||||||
\(369\) | −673.137 | −0.0949650 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6352.29 | 0.885352 | ||||||||
\(373\) | −9019.53 | −1.25205 | −0.626024 | − | 0.779804i | \(-0.715319\pi\) | ||||
−0.626024 | + | 0.779804i | \(0.715319\pi\) | |||||||
\(374\) | −11.6920 | −0.00161652 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4294.23 | −0.588984 | ||||||||
\(377\) | 663.904 | 0.0906971 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2463.63 | −0.333900 | −0.166950 | − | 0.985965i | \(-0.553392\pi\) | ||||
−0.166950 | + | 0.985965i | \(0.553392\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8657.63 | −1.16416 | ||||||||
\(382\) | 1995.61 | 0.267289 | ||||||||
\(383\) | −11007.2 | −1.46852 | −0.734261 | − | 0.678867i | \(-0.762471\pi\) | ||||
−0.734261 | + | 0.678867i | \(0.762471\pi\) | |||||||
\(384\) | −4063.58 | −0.540023 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1224.33 | −0.161442 | ||||||||
\(387\) | 2597.50 | 0.341184 | ||||||||
\(388\) | 10976.6 | 1.43621 | ||||||||
\(389\) | 6162.79 | 0.803254 | 0.401627 | − | 0.915803i | \(-0.368445\pi\) | ||||
0.401627 | + | 0.915803i | \(0.368445\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.5713 | 0.00279005 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12247.6 | −1.57204 | ||||||||
\(394\) | −1578.21 | −0.201799 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3749.03 | 0.475747 | ||||||||
\(397\) | −15137.9 | −1.91373 | −0.956864 | − | 0.290537i | \(-0.906166\pi\) | ||||
−0.956864 | + | 0.290537i | \(0.906166\pi\) | |||||||
\(398\) | 1800.12 | 0.226714 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3302.29 | 0.411243 | 0.205622 | − | 0.978632i | \(-0.434078\pi\) | ||||
0.205622 | + | 0.978632i | \(0.434078\pi\) | |||||||
\(402\) | −22.3997 | −0.00277910 | ||||||||
\(403\) | −3079.08 | −0.380596 | ||||||||
\(404\) | −937.564 | −0.115459 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10385.1 | 1.26479 | ||||||||
\(408\) | 14.3027 | 0.00173552 | ||||||||
\(409\) | −4576.40 | −0.553273 | −0.276636 | − | 0.960975i | \(-0.589220\pi\) | ||||
−0.276636 | + | 0.960975i | \(0.589220\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6914.25 | 0.829817 | ||||||||
\(412\) | 5077.70 | 0.607186 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 227.554 | 0.0270137 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1486.05 | 0.175143 | ||||||||
\(417\) | −11161.4 | −1.31074 | ||||||||
\(418\) | −3532.11 | −0.413304 | ||||||||
\(419\) | 6778.05 | 0.790285 | 0.395142 | − | 0.918620i | \(-0.370695\pi\) | ||||
0.395142 | + | 0.918620i | \(0.370695\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3952.68 | −0.457582 | −0.228791 | − | 0.973476i | \(-0.573477\pi\) | ||||
−0.228791 | + | 0.973476i | \(0.573477\pi\) | |||||||
\(422\) | −1867.29 | −0.215398 | ||||||||
\(423\) | −4765.46 | −0.547765 | ||||||||
\(424\) | −5256.08 | −0.602024 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1057.03 | −0.120219 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16031.1 | 1.81050 | ||||||||
\(429\) | 3745.67 | 0.421544 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3435.10 | −0.383905 | −0.191952 | − | 0.981404i | \(-0.561482\pi\) | ||||
−0.191952 | + | 0.981404i | \(0.561482\pi\) | |||||||
\(432\) | −8850.60 | −0.985705 | ||||||||
\(433\) | −5457.82 | −0.605742 | −0.302871 | − | 0.953032i | \(-0.597945\pi\) | ||||
−0.302871 | + | 0.953032i | \(0.597945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7003.35 | −0.769265 | ||||||||
\(437\) | 6516.61 | 0.713344 | ||||||||
\(438\) | −1753.13 | −0.191250 | ||||||||
\(439\) | −4188.10 | −0.455323 | −0.227662 | − | 0.973740i | \(-0.573108\pi\) | ||||
−0.227662 | + | 0.973740i | \(0.573108\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.41031 | −0.000366996 0 | ||||||||
\(443\) | −2097.50 | −0.224955 | −0.112478 | − | 0.993654i | \(-0.535879\pi\) | ||||
−0.112478 | + | 0.993654i | \(0.535879\pi\) | |||||||
\(444\) | −6249.19 | −0.667959 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −51.5085 | −0.00546860 | ||||||||
\(447\) | 9604.74 | 1.01631 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11318.2 | 1.18962 | 0.594809 | − | 0.803867i | \(-0.297228\pi\) | ||||
0.594809 | + | 0.803867i | \(0.297228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4188.37 | 0.437301 | ||||||||
\(452\) | −6531.91 | −0.679724 | ||||||||
\(453\) | −7886.34 | −0.817952 | ||||||||
\(454\) | 2897.41 | 0.299521 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4320.79 | 0.443728 | ||||||||
\(457\) | 11696.4 | 1.19723 | 0.598617 | − | 0.801036i | \(-0.295717\pi\) | ||||
0.598617 | + | 0.801036i | \(0.295717\pi\) | |||||||
\(458\) | 425.596 | 0.0434209 | ||||||||
\(459\) | 64.4603 | 0.00655501 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10685.0 | −1.07951 | −0.539753 | − | 0.841823i | \(-0.681482\pi\) | ||||
−0.539753 | + | 0.841823i | \(0.681482\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10407.2 | 1.04463 | 0.522315 | − | 0.852752i | \(-0.325068\pi\) | ||||
0.522315 | + | 0.852752i | \(0.325068\pi\) | |||||||
\(464\) | 2403.46 | 0.240469 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1018.48 | 0.101245 | ||||||||
\(467\) | −2978.24 | −0.295111 | −0.147555 | − | 0.989054i | \(-0.547140\pi\) | ||||
−0.147555 | + | 0.989054i | \(0.547140\pi\) | |||||||
\(468\) | 1093.51 | 0.108008 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14230.8 | −1.39219 | ||||||||
\(472\) | 3261.12 | 0.318020 | ||||||||
\(473\) | −16162.1 | −1.57111 | ||||||||
\(474\) | −1848.23 | −0.179097 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5832.86 | −0.559892 | ||||||||
\(478\) | 123.008 | 0.0117704 | ||||||||
\(479\) | 14214.3 | 1.35588 | 0.677940 | − | 0.735117i | \(-0.262873\pi\) | ||||
0.677940 | + | 0.735117i | \(0.262873\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3029.11 | 0.287142 | ||||||||
\(482\) | 1544.93 | 0.145995 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13018.2 | −1.22260 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1192.54 | 0.111306 | ||||||||
\(487\) | −18097.0 | −1.68389 | −0.841946 | − | 0.539562i | \(-0.818590\pi\) | ||||
−0.841946 | + | 0.539562i | \(0.818590\pi\) | |||||||
\(488\) | 365.998 | 0.0339507 | ||||||||
\(489\) | 2008.67 | 0.185757 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13750.8 | −1.26388 | −0.631940 | − | 0.775017i | \(-0.717741\pi\) | ||||
−0.631940 | + | 0.775017i | \(0.717741\pi\) | |||||||
\(492\) | −2520.34 | −0.230947 | ||||||||
\(493\) | −17.5048 | −0.00159914 | ||||||||
\(494\) | −1030.24 | −0.0938314 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11146.9 | −1.00909 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2272.40 | −0.204475 | ||||||||
\(499\) | 15684.2 | 1.40706 | 0.703528 | − | 0.710667i | \(-0.251607\pi\) | ||||
0.703528 | + | 0.710667i | \(0.251607\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15676.8 | −1.39798 | ||||||||
\(502\) | 3328.61 | 0.295943 | ||||||||
\(503\) | 977.937 | 0.0866880 | 0.0433440 | − | 0.999060i | \(-0.486199\pi\) | ||||
0.0433440 | + | 0.999060i | \(0.486199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1415.88 | −0.124394 | ||||||||
\(507\) | −8275.02 | −0.724865 | ||||||||
\(508\) | 15726.6 | 1.37354 | ||||||||
\(509\) | 19664.6 | 1.71242 | 0.856208 | − | 0.516632i | \(-0.172814\pi\) | ||||
0.856208 | + | 0.516632i | \(0.172814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 9064.39 | 0.782409 | ||||||||
\(513\) | 19473.2 | 1.67595 | ||||||||
\(514\) | 258.775 | 0.0222064 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9725.49 | 0.829730 | ||||||||
\(517\) | 29651.5 | 2.52238 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4302.63 | 0.363901 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12522.8 | −1.05304 | −0.526519 | − | 0.850163i | \(-0.676503\pi\) | ||||
−0.526519 | + | 0.850163i | \(0.676503\pi\) | |||||||
\(522\) | −184.656 | −0.0154831 | ||||||||
\(523\) | 1104.42 | 0.0923382 | 0.0461691 | − | 0.998934i | \(-0.485299\pi\) | ||||
0.0461691 | + | 0.998934i | \(0.485299\pi\) | |||||||
\(524\) | 22247.8 | 1.85477 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1797.05 | 0.148964 | ||||||||
\(527\) | 81.1843 | 0.00671052 | ||||||||
\(528\) | 13560.0 | 1.11766 | ||||||||
\(529\) | −9554.75 | −0.785301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3618.98 | 0.295763 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1221.66 | 0.0992794 | ||||||||
\(534\) | −735.152 | −0.0595751 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 82.7170 | 0.00666573 | ||||||||
\(537\) | 13649.5 | 1.09687 | ||||||||
\(538\) | 277.502 | 0.0222378 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2126.45 | −0.168989 | −0.0844945 | − | 0.996424i | \(-0.526928\pi\) | ||||
−0.0844945 | + | 0.996424i | \(0.526928\pi\) | |||||||
\(542\) | 1991.33 | 0.157813 | ||||||||
\(543\) | 8400.25 | 0.663884 | ||||||||
\(544\) | −39.1817 | −0.00308805 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2137.04 | 0.167044 | 0.0835220 | − | 0.996506i | \(-0.473383\pi\) | ||||
0.0835220 | + | 0.996506i | \(0.473383\pi\) | |||||||
\(548\) | −12559.8 | −0.979063 | ||||||||
\(549\) | 406.160 | 0.0315747 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5288.11 | −0.408859 | ||||||||
\(552\) | 1732.03 | 0.133551 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 633.335 | 0.0485701 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20274.8 | 1.54648 | ||||||||
\(557\) | 19435.1 | 1.47844 | 0.739219 | − | 0.673465i | \(-0.235195\pi\) | ||||
0.739219 | + | 0.673465i | \(0.235195\pi\) | |||||||
\(558\) | 856.407 | 0.0649724 | ||||||||
\(559\) | −4714.14 | −0.356685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −98.7598 | −0.00743252 | ||||||||
\(562\) | −344.008 | −0.0258205 | ||||||||
\(563\) | 1467.52 | 0.109855 | 0.0549276 | − | 0.998490i | \(-0.482507\pi\) | ||||
0.0549276 | + | 0.998490i | \(0.482507\pi\) | |||||||
\(564\) | −17842.7 | −1.33212 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3001.89 | −0.222931 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3903.35 | 0.288347 | ||||||||
\(569\) | 15080.3 | 1.11107 | 0.555536 | − | 0.831493i | \(-0.312513\pi\) | ||||
0.555536 | + | 0.831493i | \(0.312513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15800.8 | 1.15804 | 0.579022 | − | 0.815312i | \(-0.303435\pi\) | ||||
0.579022 | + | 0.815312i | \(0.303435\pi\) | |||||||
\(572\) | −6804.02 | −0.497361 | ||||||||
\(573\) | 16856.5 | 1.22895 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3675.63 | 0.265888 | ||||||||
\(577\) | 6165.64 | 0.444851 | 0.222425 | − | 0.974950i | \(-0.428603\pi\) | ||||
0.222425 | + | 0.974950i | \(0.428603\pi\) | |||||||
\(578\) | −2479.91 | −0.178461 | ||||||||
\(579\) | −10341.6 | −0.742283 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3050.25 | −0.217246 | ||||||||
\(583\) | 36293.0 | 2.57822 | ||||||||
\(584\) | 6473.89 | 0.458719 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1095.90 | 0.0772547 | ||||||||
\(587\) | 23104.0 | 1.62454 | 0.812268 | − | 0.583285i | \(-0.198233\pi\) | ||||
0.812268 | + | 0.583285i | \(0.198233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24525.4 | 1.71571 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13330.8 | −0.927841 | ||||||||
\(592\) | 10965.9 | 0.761313 | ||||||||
\(593\) | 6544.43 | 0.453200 | 0.226600 | − | 0.973988i | \(-0.427239\pi\) | ||||
0.226600 | + | 0.973988i | \(0.427239\pi\) | |||||||
\(594\) | −4230.99 | −0.292255 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17447.0 | −1.19909 | ||||||||
\(597\) | 15205.2 | 1.04239 | ||||||||
\(598\) | −412.982 | −0.0282410 | ||||||||
\(599\) | 3215.71 | 0.219349 | 0.109675 | − | 0.993968i | \(-0.465019\pi\) | ||||
0.109675 | + | 0.993968i | \(0.465019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 234.653 | 0.0159263 | 0.00796313 | − | 0.999968i | \(-0.497465\pi\) | ||||
0.00796313 | + | 0.999968i | \(0.497465\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 91.7939 | 0.00619923 | ||||||||
\(604\) | 14325.6 | 0.965064 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 260.537 | 0.0174647 | ||||||||
\(607\) | −14528.7 | −0.971501 | −0.485750 | − | 0.874098i | \(-0.661454\pi\) | ||||
−0.485750 | + | 0.874098i | \(0.661454\pi\) | |||||||
\(608\) | −11836.6 | −0.789537 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8648.71 | 0.572650 | ||||||||
\(612\) | −28.8320 | −0.00190435 | ||||||||
\(613\) | −11332.7 | −0.746696 | −0.373348 | − | 0.927691i | \(-0.621790\pi\) | ||||
−0.373348 | + | 0.927691i | \(0.621790\pi\) | |||||||
\(614\) | −1839.73 | −0.120921 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17400.2 | 1.13534 | 0.567672 | − | 0.823255i | \(-0.307844\pi\) | ||||
0.567672 | + | 0.823255i | \(0.307844\pi\) | |||||||
\(618\) | −1411.03 | −0.0918446 | ||||||||
\(619\) | 11987.8 | 0.778402 | 0.389201 | − | 0.921153i | \(-0.372751\pi\) | ||||
0.389201 | + | 0.921153i | \(0.372751\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7806.02 | 0.504420 | ||||||||
\(622\) | −1304.46 | −0.0840900 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3955.17 | 0.253740 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3378.84 | 0.215728 | ||||||||
\(627\) | −29834.9 | −1.90030 | ||||||||
\(628\) | 25850.3 | 1.64258 | ||||||||
\(629\) | −79.8667 | −0.00506279 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3800.38 | −0.239764 | −0.119882 | − | 0.992788i | \(-0.538252\pi\) | ||||
−0.119882 | + | 0.992788i | \(0.538252\pi\) | |||||||
\(632\) | 6825.08 | 0.429568 | ||||||||
\(633\) | −15772.6 | −0.990368 | ||||||||
\(634\) | 1940.07 | 0.121530 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −21839.2 | −1.36161 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1148.96 | 0.0712976 | ||||||||
\(639\) | 4331.69 | 0.268167 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12294.2 | 0.757552 | 0.378776 | − | 0.925488i | \(-0.376345\pi\) | ||||
0.378776 | + | 0.925488i | \(0.376345\pi\) | |||||||
\(642\) | −4454.85 | −0.273861 | ||||||||
\(643\) | 14615.4 | 0.896382 | 0.448191 | − | 0.893938i | \(-0.352068\pi\) | ||||
0.448191 | + | 0.893938i | \(0.352068\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.1637 | 0.00165440 | ||||||||
\(647\) | −16047.0 | −0.975071 | −0.487536 | − | 0.873103i | \(-0.662104\pi\) | ||||
−0.487536 | + | 0.873103i | \(0.662104\pi\) | |||||||
\(648\) | 3283.00 | 0.199025 | ||||||||
\(649\) | −22517.9 | −1.36195 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3648.75 | −0.219166 | ||||||||
\(653\) | −623.425 | −0.0373607 | −0.0186803 | − | 0.999826i | \(-0.505946\pi\) | ||||
−0.0186803 | + | 0.999826i | \(0.505946\pi\) | |||||||
\(654\) | 1946.14 | 0.116361 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4422.63 | 0.263224 | ||||||||
\(657\) | 7184.30 | 0.426616 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 963.459 | 0.0569515 | 0.0284758 | − | 0.999594i | \(-0.490935\pi\) | ||||
0.0284758 | + | 0.999594i | \(0.490935\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24183.6 | −1.42304 | −0.711522 | − | 0.702664i | \(-0.751994\pi\) | ||||
−0.711522 | + | 0.702664i | \(0.751994\pi\) | |||||||
\(662\) | −414.893 | −0.0243584 | ||||||||
\(663\) | −28.8061 | −0.00168739 | ||||||||
\(664\) | 8391.43 | 0.490438 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −842.507 | −0.0490187 | ||||||||
\(667\) | −2119.79 | −0.123057 | ||||||||
\(668\) | 28476.9 | 1.64941 | ||||||||
\(669\) | −435.080 | −0.0251438 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2527.20 | −0.145397 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14167.0 | −0.811437 | −0.405718 | − | 0.913998i | \(-0.632979\pi\) | ||||
−0.405718 | + | 0.913998i | \(0.632979\pi\) | |||||||
\(674\) | −521.215 | −0.0297870 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15031.6 | 0.855235 | ||||||||
\(677\) | −19397.1 | −1.10117 | −0.550584 | − | 0.834780i | \(-0.685595\pi\) | ||||
−0.550584 | + | 0.834780i | \(0.685595\pi\) | |||||||
\(678\) | 1815.14 | 0.102817 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24473.8 | 1.37715 | ||||||||
\(682\) | −5328.71 | −0.299189 | ||||||||
\(683\) | −20984.8 | −1.17564 | −0.587820 | − | 0.808992i | \(-0.700014\pi\) | ||||
−0.587820 | + | 0.808992i | \(0.700014\pi\) | |||||||
\(684\) | −8710.02 | −0.486895 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3594.91 | 0.199643 | ||||||||
\(688\) | −17066.1 | −0.945694 | ||||||||
\(689\) | 10585.9 | 0.585328 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18079.2 | 0.995320 | 0.497660 | − | 0.867372i | \(-0.334193\pi\) | ||||
0.497660 | + | 0.867372i | \(0.334193\pi\) | |||||||
\(692\) | −7815.75 | −0.429350 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1306.23 | 0.0714465 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1405.52 | −0.0765459 | ||||||||
\(697\) | −32.2107 | −0.00175046 | ||||||||
\(698\) | 4267.56 | 0.231418 | ||||||||
\(699\) | 8602.86 | 0.465508 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18660.6 | 1.00542 | 0.502711 | − | 0.864455i | \(-0.332336\pi\) | ||||
0.502711 | + | 0.864455i | \(0.332336\pi\) | |||||||
\(702\) | −1234.09 | −0.0663500 | ||||||||
\(703\) | −24127.4 | −1.29443 | ||||||||
\(704\) | −22870.4 | −1.22438 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2084.57 | −0.111125 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13550.1 | 0.719271 | ||||||||
\(709\) | −24545.4 | −1.30017 | −0.650085 | − | 0.759862i | \(-0.725267\pi\) | ||||
−0.650085 | + | 0.759862i | \(0.725267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7574.02 | 0.399505 | ||||||||
\(712\) | 2714.74 | 0.142892 | ||||||||
\(713\) | 9831.26 | 0.516387 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24794.5 | −1.29415 | ||||||||
\(717\) | 1039.02 | 0.0541185 | ||||||||
\(718\) | −2290.05 | −0.119030 | ||||||||
\(719\) | 7300.32 | 0.378659 | 0.189330 | − | 0.981914i | \(-0.439369\pi\) | ||||
0.189330 | + | 0.981914i | \(0.439369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4743.74 | 0.244520 | ||||||||
\(723\) | 13049.7 | 0.671263 | ||||||||
\(724\) | −15259.1 | −0.783286 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3617.61 | 0.184934 | ||||||||
\(727\) | 15466.0 | 0.788998 | 0.394499 | − | 0.918896i | \(-0.370918\pi\) | ||||
0.394499 | + | 0.918896i | \(0.370918\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21225.8 | 1.07838 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 124.295 | 0.00628893 | ||||||||
\(732\) | 1520.73 | 0.0767868 | ||||||||
\(733\) | −13830.5 | −0.696917 | −0.348459 | − | 0.937324i | \(-0.613295\pi\) | ||||
−0.348459 | + | 0.937324i | \(0.613295\pi\) | |||||||
\(734\) | 829.358 | 0.0417060 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4744.83 | −0.237631 | ||||||||
\(737\) | −571.157 | −0.0285466 | ||||||||
\(738\) | −339.788 | −0.0169482 | ||||||||
\(739\) | 11714.5 | 0.583118 | 0.291559 | − | 0.956553i | \(-0.405826\pi\) | ||||
0.291559 | + | 0.956553i | \(0.405826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8702.20 | −0.431422 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28963.4 | −1.43010 | −0.715050 | − | 0.699074i | \(-0.753596\pi\) | ||||
−0.715050 | + | 0.699074i | \(0.753596\pi\) | |||||||
\(744\) | 6518.56 | 0.321212 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4552.91 | −0.223450 | ||||||||
\(747\) | 9312.26 | 0.456115 | ||||||||
\(748\) | 179.397 | 0.00876928 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6331.99 | 0.307667 | 0.153833 | − | 0.988097i | \(-0.450838\pi\) | ||||
0.153833 | + | 0.988097i | \(0.450838\pi\) | |||||||
\(752\) | 31310.0 | 1.51829 | ||||||||
\(753\) | 28116.0 | 1.36070 | ||||||||
\(754\) | 335.128 | 0.0161865 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6256.80 | 0.300406 | 0.150203 | − | 0.988655i | \(-0.452007\pi\) | ||||
0.150203 | + | 0.988655i | \(0.452007\pi\) | |||||||
\(758\) | −1243.60 | −0.0595905 | ||||||||
\(759\) | −11959.6 | −0.571945 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13953.7 | −0.664679 | −0.332340 | − | 0.943160i | \(-0.607838\pi\) | ||||
−0.332340 | + | 0.943160i | \(0.607838\pi\) | |||||||
\(762\) | −4370.23 | −0.207765 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −30619.8 | −1.44998 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5556.28 | −0.262084 | ||||||||
\(767\) | −6568.00 | −0.309200 | ||||||||
\(768\) | 12163.7 | 0.571512 | ||||||||
\(769\) | −34278.1 | −1.60741 | −0.803707 | − | 0.595025i | \(-0.797142\pi\) | ||||
−0.803707 | + | 0.595025i | \(0.797142\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2185.82 | 0.102101 | ||||||||
\(772\) | 18785.5 | 0.875786 | ||||||||
\(773\) | 8769.31 | 0.408034 | 0.204017 | − | 0.978967i | \(-0.434600\pi\) | ||||
0.204017 | + | 0.978967i | \(0.434600\pi\) | |||||||
\(774\) | 1311.18 | 0.0608905 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11263.9 | 0.521069 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3110.88 | 0.143355 | ||||||||
\(779\) | −9730.73 | −0.447547 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26952.5 | −1.23487 | ||||||||
\(782\) | 10.8889 | 0.000497934 0 | ||||||||
\(783\) | −6334.45 | −0.289112 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6182.40 | −0.280558 | ||||||||
\(787\) | −3546.15 | −0.160618 | −0.0803092 | − | 0.996770i | \(-0.525591\pi\) | ||||
−0.0803092 | + | 0.996770i | \(0.525591\pi\) | |||||||
\(788\) | 24215.4 | 1.09472 | ||||||||
\(789\) | 15179.3 | 0.684912 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3847.16 | 0.172604 | ||||||||
\(793\) | −737.130 | −0.0330091 | ||||||||
\(794\) | −7641.37 | −0.341539 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27620.3 | −1.22987 | ||||||||
\(797\) | −18169.4 | −0.807520 | −0.403760 | − | 0.914865i | \(-0.632297\pi\) | ||||
−0.403760 | + | 0.914865i | \(0.632297\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −228.035 | −0.0100968 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3012.65 | 0.132892 | ||||||||
\(802\) | 1666.94 | 0.0733938 | ||||||||
\(803\) | −44702.0 | −1.96451 | ||||||||
\(804\) | 343.692 | 0.0150760 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1554.27 | −0.0679241 | ||||||||
\(807\) | 2343.99 | 0.102246 | ||||||||
\(808\) | −962.104 | −0.0418895 | ||||||||
\(809\) | 11853.0 | 0.515115 | 0.257557 | − | 0.966263i | \(-0.417082\pi\) | ||||
0.257557 | + | 0.966263i | \(0.417082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11921.1 | 0.516161 | 0.258080 | − | 0.966123i | \(-0.416910\pi\) | ||||
0.258080 | + | 0.966123i | \(0.416910\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16820.3 | 0.725601 | ||||||||
\(814\) | 5242.22 | 0.225724 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −104.284 | −0.00447384 | ||||||||
\(817\) | 37548.9 | 1.60792 | ||||||||
\(818\) | −2310.09 | −0.0987415 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42094.1 | −1.78940 | −0.894698 | − | 0.446671i | \(-0.852610\pi\) | ||||
−0.894698 | + | 0.446671i | \(0.852610\pi\) | |||||||
\(822\) | 3490.20 | 0.148096 | ||||||||
\(823\) | −1622.17 | −0.0687064 | −0.0343532 | − | 0.999410i | \(-0.510937\pi\) | ||||
−0.0343532 | + | 0.999410i | \(0.510937\pi\) | |||||||
\(824\) | 5210.61 | 0.220291 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28171.7 | −1.18455 | −0.592277 | − | 0.805735i | \(-0.701771\pi\) | ||||
−0.592277 | + | 0.805735i | \(0.701771\pi\) | |||||||
\(828\) | −3491.50 | −0.146543 | ||||||||
\(829\) | 9244.23 | 0.387293 | 0.193646 | − | 0.981071i | \(-0.437969\pi\) | ||||
0.193646 | + | 0.981071i | \(0.437969\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5349.63 | 0.223317 | ||||||||
\(832\) | −6670.81 | −0.277967 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5634.10 | −0.233924 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 54195.2 | 2.24208 | ||||||||
\(837\) | 29378.2 | 1.21321 | ||||||||
\(838\) | 3421.45 | 0.141041 | ||||||||
\(839\) | 43012.5 | 1.76991 | 0.884956 | − | 0.465674i | \(-0.154188\pi\) | ||||
0.884956 | + | 0.465674i | \(0.154188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22668.8 | −0.929469 | ||||||||
\(842\) | −1995.25 | −0.0816637 | ||||||||
\(843\) | −2905.76 | −0.118718 | ||||||||
\(844\) | 28650.9 | 1.16849 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2405.53 | −0.0977585 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 38323.0 | 1.55191 | ||||||||
\(849\) | −25356.3 | −1.02500 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9671.70 | −0.389591 | ||||||||
\(852\) | 16218.6 | 0.652159 | ||||||||
\(853\) | −19756.9 | −0.793041 | −0.396521 | − | 0.918026i | \(-0.629783\pi\) | ||||
−0.396521 | + | 0.918026i | \(0.629783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16450.7 | 0.656862 | ||||||||
\(857\) | 325.658 | 0.0129805 | 0.00649024 | − | 0.999979i | \(-0.497934\pi\) | ||||
0.00649024 | + | 0.999979i | \(0.497934\pi\) | |||||||
\(858\) | 1890.75 | 0.0752321 | ||||||||
\(859\) | −3275.22 | −0.130092 | −0.0650461 | − | 0.997882i | \(-0.520719\pi\) | ||||
−0.0650461 | + | 0.997882i | \(0.520719\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1733.98 | −0.0685147 | ||||||||
\(863\) | −44585.0 | −1.75862 | −0.879311 | − | 0.476247i | \(-0.841997\pi\) | ||||
−0.879311 | + | 0.476247i | \(0.841997\pi\) | |||||||
\(864\) | −14178.7 | −0.558297 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2755.02 | −0.108106 | ||||||||
\(867\) | −20947.3 | −0.820537 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47126.9 | −1.83967 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −166.594 | −0.00648087 | ||||||||
\(872\) | −7186.65 | −0.279095 | ||||||||
\(873\) | 12499.9 | 0.484602 | ||||||||
\(874\) | 3289.48 | 0.127309 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 26899.3 | 1.03749 | ||||||||
\(877\) | −16433.8 | −0.632761 | −0.316380 | − | 0.948632i | \(-0.602468\pi\) | ||||
−0.316380 | + | 0.948632i | \(0.602468\pi\) | |||||||
\(878\) | −2114.08 | −0.0812607 | ||||||||
\(879\) | 9256.82 | 0.355205 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39080.2 | 1.49449 | 0.747245 | − | 0.664549i | \(-0.231376\pi\) | ||||
0.747245 | + | 0.664549i | \(0.231376\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48548.2 | −1.85026 | −0.925129 | − | 0.379652i | \(-0.876044\pi\) | ||||
−0.925129 | + | 0.379652i | \(0.876044\pi\) | |||||||
\(884\) | 52.3264 | 0.00199087 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1058.78 | −0.0401473 | ||||||||
\(887\) | −13447.1 | −0.509029 | −0.254514 | − | 0.967069i | \(-0.581916\pi\) | ||||
−0.254514 | + | 0.967069i | \(0.581916\pi\) | |||||||
\(888\) | −6412.76 | −0.242340 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22669.0 | −0.852344 | ||||||||
\(892\) | 790.325 | 0.0296660 | ||||||||
\(893\) | −68888.5 | −2.58148 | ||||||||
\(894\) | 4848.32 | 0.181378 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3488.37 | −0.129847 | ||||||||
\(898\) | 5713.24 | 0.212309 | ||||||||
\(899\) | −7977.90 | −0.295971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −279.112 | −0.0103203 | ||||||||
\(902\) | 2114.22 | 0.0780442 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6702.87 | −0.246609 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3980.89 | −0.145978 | ||||||||
\(907\) | −15750.3 | −0.576604 | −0.288302 | − | 0.957539i | \(-0.593091\pi\) | ||||
−0.288302 | + | 0.957539i | \(0.593091\pi\) | |||||||
\(908\) | −44456.7 | −1.62483 | ||||||||
\(909\) | −1067.68 | −0.0389579 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31449.7 | 1.14377 | 0.571886 | − | 0.820333i | \(-0.306212\pi\) | ||||
0.571886 | + | 0.820333i | \(0.306212\pi\) | |||||||
\(912\) | −31503.6 | −1.14385 | ||||||||
\(913\) | −57942.4 | −2.10034 | ||||||||
\(914\) | 5904.16 | 0.213668 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6530.17 | −0.235549 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 32.5385 | 0.00116986 | ||||||||
\(919\) | −30355.6 | −1.08960 | −0.544798 | − | 0.838567i | \(-0.683394\pi\) | ||||
−0.544798 | + | 0.838567i | \(0.683394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15539.8 | −0.555975 | ||||||||
\(922\) | −5393.64 | −0.192657 | ||||||||
\(923\) | −7861.46 | −0.280350 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5253.39 | 0.186433 | ||||||||
\(927\) | 5782.39 | 0.204874 | ||||||||
\(928\) | 3850.34 | 0.136200 | ||||||||
\(929\) | 28533.8 | 1.00771 | 0.503856 | − | 0.863788i | \(-0.331914\pi\) | ||||
0.503856 | + | 0.863788i | \(0.331914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15627.1 | −0.549231 | ||||||||
\(933\) | −11018.5 | −0.386632 | ||||||||
\(934\) | −1503.37 | −0.0526678 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1122.13 | 0.0391860 | ||||||||
\(937\) | −19269.1 | −0.671817 | −0.335908 | − | 0.941895i | \(-0.609043\pi\) | ||||
−0.335908 | + | 0.941895i | \(0.609043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28540.3 | 0.991881 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2097.84 | 0.0726756 | 0.0363378 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363378 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(942\) | −7183.46 | −0.248461 | ||||||||
\(943\) | −3900.66 | −0.134701 | ||||||||
\(944\) | −23777.4 | −0.819797 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8158.36 | −0.280392 | ||||||||
\(947\) | −5072.14 | −0.174047 | −0.0870235 | − | 0.996206i | \(-0.527736\pi\) | ||||
−0.0870235 | + | 0.996206i | \(0.527736\pi\) | |||||||
\(948\) | 28358.5 | 0.971561 | ||||||||
\(949\) | −13038.6 | −0.445997 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16387.3 | 0.558775 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23464.1 | 0.797564 | 0.398782 | − | 0.917046i | \(-0.369433\pi\) | ||||
0.398782 | + | 0.917046i | \(0.369433\pi\) | |||||||
\(954\) | −2944.33 | −0.0999227 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1887.39 | −0.0638519 | ||||||||
\(957\) | 9705.02 | 0.327815 | ||||||||
\(958\) | 7175.13 | 0.241981 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7209.24 | 0.241994 | ||||||||
\(962\) | 1529.04 | 0.0512457 | ||||||||
\(963\) | 18255.9 | 0.610892 | ||||||||
\(964\) | −23704.8 | −0.791992 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6994.27 | 0.232596 | 0.116298 | − | 0.993214i | \(-0.462897\pi\) | ||||
0.116298 | + | 0.993214i | \(0.462897\pi\) | |||||||
\(968\) | −13359.0 | −0.443568 | ||||||||
\(969\) | 229.446 | 0.00760667 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37752.5 | −1.24772 | −0.623860 | − | 0.781536i | \(-0.714436\pi\) | ||||
−0.623860 | + | 0.781536i | \(0.714436\pi\) | |||||||
\(972\) | −18297.8 | −0.603809 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9135.09 | −0.300521 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2668.55 | −0.0875186 | ||||||||
\(977\) | 6380.21 | 0.208926 | 0.104463 | − | 0.994529i | \(-0.466688\pi\) | ||||
0.104463 | + | 0.994529i | \(0.466688\pi\) | |||||||
\(978\) | 1013.94 | 0.0331517 | ||||||||
\(979\) | −18745.2 | −0.611950 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7975.28 | −0.259563 | ||||||||
\(982\) | −6941.18 | −0.225562 | ||||||||
\(983\) | 17330.0 | 0.562299 | 0.281150 | − | 0.959664i | \(-0.409284\pi\) | ||||
0.281150 | + | 0.959664i | \(0.409284\pi\) | |||||||
\(984\) | −2586.31 | −0.0837891 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.83612 | −0.000285395 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15807.6 | 0.509014 | ||||||||
\(989\) | 15051.9 | 0.483945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32191.8 | 1.03189 | 0.515947 | − | 0.856621i | \(-0.327440\pi\) | ||||
0.515947 | + | 0.856621i | \(0.327440\pi\) | |||||||
\(992\) | −17857.3 | −0.571542 | ||||||||
\(993\) | −3504.50 | −0.111996 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 34866.7 | 1.10923 | ||||||||
\(997\) | −2678.20 | −0.0850748 | −0.0425374 | − | 0.999095i | \(-0.513544\pi\) | ||||
−0.0425374 | + | 0.999095i | \(0.513544\pi\) | |||||||
\(998\) | 7917.13 | 0.251114 | ||||||||
\(999\) | −28901.4 | −0.915314 |
(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 | 1225.4.a.z.1.3 | 4 | ||
5.4 | even | 2 | 1225.4.a.bd.1.2 | 4 | |||
7.6 | odd | 2 | 175.4.a.g.1.3 | ✓ | 4 | ||
21.20 | even | 2 | 1575.4.a.bl.1.2 | 4 | |||
35.13 | even | 4 | 175.4.b.f.99.4 | 8 | |||
35.27 | even | 4 | 175.4.b.f.99.5 | 8 | |||
35.34 | odd | 2 | 175.4.a.h.1.2 | yes | 4 | ||
105.104 | even | 2 | 1575.4.a.bg.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.4.a.g.1.3 | ✓ | 4 | 7.6 | odd | 2 | ||
175.4.a.h.1.2 | yes | 4 | 35.34 | odd | 2 | ||
175.4.b.f.99.4 | 8 | 35.13 | even | 4 | |||
175.4.b.f.99.5 | 8 | 35.27 | even | 4 | |||
1225.4.a.z.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1225.4.a.bd.1.2 | 4 | 5.4 | even | 2 | |||
1575.4.a.bg.1.3 | 4 | 105.104 | even | 2 | |||
1575.4.a.bl.1.2 | 4 | 21.20 | even | 2 |