Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(151,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 42x^{6} + 771x^{4} - 7098x^{2} + 28561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.3 | ||
Root | \(-3.52946 + 0.736813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.151 |
Dual form | 475.3.c.f.151.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.47363i | − | 0.736813i | −0.929665 | − | 0.368406i | \(-0.879903\pi\) | ||
0.929665 | − | 0.368406i | \(-0.120097\pi\) | |||||||
\(3\) | − | 3.55765i | − | 1.18588i | −0.805246 | − | 0.592941i | \(-0.797967\pi\) | ||
0.805246 | − | 0.592941i | \(-0.202033\pi\) | |||||||
\(4\) | 1.82843 | 0.457107 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.24264 | −0.873773 | ||||||||
\(7\) | −7.05893 | −1.00842 | −0.504209 | − | 0.863582i | \(-0.668216\pi\) | ||||
−0.504209 | + | 0.863582i | \(0.668216\pi\) | |||||||
\(8\) | − | 8.58892i | − | 1.07362i | ||||||
\(9\) | −3.65685 | −0.406317 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.24264 | 0.203876 | 0.101938 | − | 0.994791i | \(-0.467496\pi\) | ||||
0.101938 | + | 0.994791i | \(0.467496\pi\) | |||||||
\(12\) | − | 6.50490i | − | 0.542075i | ||||||
\(13\) | − | 6.86246i | − | 0.527882i | −0.964539 | − | 0.263941i | \(-0.914978\pi\) | ||
0.964539 | − | 0.263941i | \(-0.0850224\pi\) | |||||||
\(14\) | 10.4022i | 0.743015i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.34315 | −0.333947 | ||||||||
\(17\) | −11.1939 | −0.658468 | −0.329234 | − | 0.944248i | \(-0.606790\pi\) | ||||
−0.329234 | + | 0.944248i | \(0.606790\pi\) | |||||||
\(18\) | 5.38883i | 0.299380i | ||||||||
\(19\) | −15.8995 | − | 10.4022i | −0.836816 | − | 0.547485i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 25.1132i | 1.19587i | ||||||||
\(22\) | − | 3.30481i | − | 0.150219i | ||||||
\(23\) | −21.1768 | −0.920729 | −0.460365 | − | 0.887730i | \(-0.652281\pi\) | ||||
−0.460365 | + | 0.887730i | \(0.652281\pi\) | |||||||
\(24\) | −30.5563 | −1.27318 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −10.1127 | −0.388950 | ||||||||
\(27\) | − | 19.0090i | − | 0.704038i | ||||||
\(28\) | −12.9067 | −0.460955 | ||||||||
\(29\) | 45.9176i | 1.58337i | 0.610933 | + | 0.791683i | \(0.290795\pi\) | ||||
−0.610933 | + | 0.791683i | \(0.709205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 14.7110i | − | 0.474547i | −0.971443 | − | 0.237273i | \(-0.923746\pi\) | ||
0.971443 | − | 0.237273i | \(-0.0762537\pi\) | |||||||
\(32\) | − | 26.4819i | − | 0.827559i | ||||||
\(33\) | − | 7.97852i | − | 0.241773i | ||||||
\(34\) | 16.4957i | 0.485167i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.68629 | −0.185730 | ||||||||
\(37\) | 25.0083i | 0.675899i | 0.941164 | + | 0.337949i | \(0.109733\pi\) | ||||
−0.941164 | + | 0.337949i | \(0.890267\pi\) | |||||||
\(38\) | −15.3290 | + | 23.4299i | −0.403394 | + | 0.616576i | ||||
\(39\) | −24.4142 | −0.626005 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 64.9373i | − | 1.58384i | −0.610627 | − | 0.791918i | \(-0.709083\pi\) | ||
0.610627 | − | 0.791918i | \(-0.290917\pi\) | |||||||
\(42\) | 37.0074 | 0.881129 | ||||||||
\(43\) | 44.0663 | 1.02480 | 0.512399 | − | 0.858747i | \(-0.328757\pi\) | ||||
0.512399 | + | 0.858747i | \(0.328757\pi\) | |||||||
\(44\) | 4.10051 | 0.0931933 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 31.2066i | 0.678405i | ||||||||
\(47\) | 34.0835 | 0.725181 | 0.362590 | − | 0.931949i | \(-0.381892\pi\) | ||||
0.362590 | + | 0.931949i | \(0.381892\pi\) | |||||||
\(48\) | 19.0090i | 0.396021i | ||||||||
\(49\) | 0.828427 | 0.0169067 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 39.8241i | 0.780865i | ||||||||
\(52\) | − | 12.5475i | − | 0.241298i | ||||||
\(53\) | 20.8836i | 0.394030i | 0.980400 | + | 0.197015i | \(0.0631248\pi\) | ||||
−0.980400 | + | 0.197015i | \(0.936875\pi\) | |||||||
\(54\) | −28.0122 | −0.518744 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 60.6285i | 1.08265i | ||||||||
\(57\) | −37.0074 | + | 56.5648i | −0.649253 | + | 0.992365i | ||||
\(58\) | 67.6654 | 1.16664 | ||||||||
\(59\) | − | 69.2460i | − | 1.17366i | −0.809710 | − | 0.586831i | \(-0.800375\pi\) | ||
0.809710 | − | 0.586831i | \(-0.199625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.4142 | 0.383840 | 0.191920 | − | 0.981411i | \(-0.438529\pi\) | ||||
0.191920 | + | 0.981411i | \(0.438529\pi\) | |||||||
\(62\) | −21.6784 | −0.349652 | ||||||||
\(63\) | 25.8135 | 0.409737 | ||||||||
\(64\) | −60.3970 | −0.943703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.7574 | −0.178142 | ||||||||
\(67\) | 79.3843i | 1.18484i | 0.805629 | + | 0.592420i | \(0.201827\pi\) | ||||
−0.805629 | + | 0.592420i | \(0.798173\pi\) | |||||||
\(68\) | −20.4673 | −0.300990 | ||||||||
\(69\) | 75.3395i | 1.09188i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 26.8979i | − | 0.378844i | −0.981896 | − | 0.189422i | \(-0.939339\pi\) | ||
0.981896 | − | 0.189422i | \(-0.0606614\pi\) | |||||||
\(72\) | 31.4084i | 0.436228i | ||||||||
\(73\) | 99.3266 | 1.36064 | 0.680319 | − | 0.732916i | \(-0.261841\pi\) | ||||
0.680319 | + | 0.732916i | \(0.261841\pi\) | |||||||
\(74\) | 36.8528 | 0.498011 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −29.0711 | − | 19.0197i | −0.382514 | − | 0.250259i | ||||
\(77\) | −15.8306 | −0.205593 | ||||||||
\(78\) | 35.9774i | 0.461249i | ||||||||
\(79\) | 109.070i | 1.38063i | 0.723507 | + | 0.690317i | \(0.242529\pi\) | ||||
−0.723507 | + | 0.690317i | \(0.757471\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −100.539 | −1.24122 | ||||||||
\(82\) | −95.6933 | −1.16699 | ||||||||
\(83\) | −124.638 | −1.50167 | −0.750834 | − | 0.660491i | \(-0.770348\pi\) | ||||
−0.750834 | + | 0.660491i | \(0.770348\pi\) | |||||||
\(84\) | 45.9176i | 0.546638i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 64.9373i | − | 0.755085i | ||||||
\(87\) | 163.359 | 1.87769 | ||||||||
\(88\) | − | 19.2619i | − | 0.218885i | ||||||
\(89\) | − | 85.7417i | − | 0.963390i | −0.876339 | − | 0.481695i | \(-0.840021\pi\) | ||
0.876339 | − | 0.481695i | \(-0.159979\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 48.4416i | 0.532325i | ||||||||
\(92\) | −38.7202 | −0.420872 | ||||||||
\(93\) | −52.3364 | −0.562757 | ||||||||
\(94\) | − | 50.2263i | − | 0.534323i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −94.2132 | −0.981388 | ||||||||
\(97\) | 35.5765i | 0.366768i | 0.983041 | + | 0.183384i | \(0.0587051\pi\) | ||||
−0.983041 | + | 0.183384i | \(0.941295\pi\) | |||||||
\(98\) | − | 1.22079i | − | 0.0124571i | ||||||
\(99\) | −8.20101 | −0.0828385 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 200.492 | 1.98507 | 0.992537 | − | 0.121946i | \(-0.0389134\pi\) | ||||
0.992537 | + | 0.121946i | \(0.0389134\pi\) | |||||||
\(102\) | 58.6858 | 0.575351 | ||||||||
\(103\) | − | 48.5249i | − | 0.471116i | −0.971860 | − | 0.235558i | \(-0.924308\pi\) | ||
0.971860 | − | 0.235558i | \(-0.0756917\pi\) | |||||||
\(104\) | −58.9411 | −0.566742 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 30.7746 | 0.290326 | ||||||||
\(107\) | − | 173.104i | − | 1.61779i | −0.587951 | − | 0.808897i | \(-0.700065\pi\) | ||
0.587951 | − | 0.808897i | \(-0.299935\pi\) | |||||||
\(108\) | − | 34.7566i | − | 0.321821i | ||||||
\(109\) | − | 96.1439i | − | 0.882054i | −0.897494 | − | 0.441027i | \(-0.854614\pi\) | ||
0.897494 | − | 0.441027i | \(-0.145386\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 88.9706 | 0.801537 | ||||||||
\(112\) | 37.7169 | 0.336758 | ||||||||
\(113\) | − | 112.057i | − | 0.991654i | −0.868421 | − | 0.495827i | \(-0.834865\pi\) | ||
0.868421 | − | 0.495827i | \(-0.165135\pi\) | |||||||
\(114\) | 83.3553 | + | 54.5351i | 0.731187 | + | 0.478378i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 83.9570i | 0.723767i | ||||||||
\(117\) | 25.0950i | 0.214487i | ||||||||
\(118\) | −102.043 | −0.864769 | ||||||||
\(119\) | 79.0172 | 0.664010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −115.971 | −0.958434 | ||||||||
\(122\) | − | 34.5038i | − | 0.282818i | ||||||
\(123\) | −231.024 | −1.87824 | ||||||||
\(124\) | − | 26.8979i | − | 0.216919i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 38.0394i | − | 0.301900i | ||||||
\(127\) | − | 162.727i | − | 1.28132i | −0.767826 | − | 0.640658i | \(-0.778662\pi\) | ||
0.767826 | − | 0.640658i | \(-0.221338\pi\) | |||||||
\(128\) | − | 16.9250i | − | 0.132227i | ||||||
\(129\) | − | 156.772i | − | 1.21529i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 122.593 | 0.935824 | 0.467912 | − | 0.883775i | \(-0.345006\pi\) | ||||
0.467912 | + | 0.883775i | \(0.345006\pi\) | |||||||
\(132\) | − | 14.5882i | − | 0.110516i | ||||||
\(133\) | 112.233 | + | 73.4285i | 0.843860 | + | 0.552094i | ||||
\(134\) | 116.983 | 0.873006 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 96.1439i | 0.706941i | ||||||||
\(137\) | 66.2464 | 0.483551 | 0.241775 | − | 0.970332i | \(-0.422270\pi\) | ||||
0.241775 | + | 0.970332i | \(0.422270\pi\) | |||||||
\(138\) | 111.022 | 0.804509 | ||||||||
\(139\) | 176.191 | 1.26756 | 0.633780 | − | 0.773513i | \(-0.281502\pi\) | ||||
0.633780 | + | 0.773513i | \(0.281502\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 121.257i | − | 0.859979i | ||||||
\(142\) | −39.6374 | −0.279137 | ||||||||
\(143\) | − | 15.3900i | − | 0.107623i | ||||||
\(144\) | 19.5391 | 0.135688 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 146.370i | − | 1.00254i | ||||||
\(147\) | − | 2.94725i | − | 0.0200493i | ||||||
\(148\) | 45.7258i | 0.308958i | ||||||||
\(149\) | 8.94618 | 0.0600415 | 0.0300207 | − | 0.999549i | \(-0.490443\pi\) | ||||
0.0300207 | + | 0.999549i | \(0.490443\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 263.319i | − | 1.74383i | −0.489656 | − | 0.871916i | \(-0.662877\pi\) | ||
0.489656 | − | 0.871916i | \(-0.337123\pi\) | |||||||
\(152\) | −89.3438 | + | 136.559i | −0.587788 | + | 0.898418i | ||||
\(153\) | 40.9346 | 0.267547 | ||||||||
\(154\) | 23.3284i | 0.151483i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −44.6396 | −0.286151 | ||||||||
\(157\) | −218.619 | −1.39248 | −0.696239 | − | 0.717811i | \(-0.745144\pi\) | ||||
−0.696239 | + | 0.717811i | \(0.745144\pi\) | |||||||
\(158\) | 160.729 | 1.01727 | ||||||||
\(159\) | 74.2965 | 0.467273 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 149.485 | 0.928480 | ||||||||
\(162\) | 148.157i | 0.914549i | ||||||||
\(163\) | −56.7653 | −0.348253 | −0.174127 | − | 0.984723i | \(-0.555710\pi\) | ||||
−0.174127 | + | 0.984723i | \(0.555710\pi\) | |||||||
\(164\) | − | 118.733i | − | 0.723982i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 183.670i | 1.10645i | ||||||||
\(167\) | − | 89.4035i | − | 0.535350i | −0.963509 | − | 0.267675i | \(-0.913745\pi\) | ||
0.963509 | − | 0.267675i | \(-0.0862554\pi\) | |||||||
\(168\) | 215.695 | 1.28390 | ||||||||
\(169\) | 121.907 | 0.721341 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 58.1421 | + | 38.0394i | 0.340012 | + | 0.222453i | ||||
\(172\) | 80.5721 | 0.468442 | ||||||||
\(173\) | 105.090i | 0.607455i | 0.952759 | + | 0.303728i | \(0.0982312\pi\) | ||||
−0.952759 | + | 0.303728i | \(0.901769\pi\) | |||||||
\(174\) | − | 240.729i | − | 1.38350i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.9828 | −0.0680838 | ||||||||
\(177\) | −246.353 | −1.39182 | ||||||||
\(178\) | −126.351 | −0.709838 | ||||||||
\(179\) | − | 65.9828i | − | 0.368619i | −0.982868 | − | 0.184309i | \(-0.940995\pi\) | ||
0.982868 | − | 0.184309i | \(-0.0590048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 129.875i | 0.717539i | 0.933426 | + | 0.358770i | \(0.116804\pi\) | ||||
−0.933426 | + | 0.358770i | \(0.883196\pi\) | |||||||
\(182\) | 71.3848 | 0.392224 | ||||||||
\(183\) | − | 83.2995i | − | 0.455189i | ||||||
\(184\) | 181.886i | 0.988509i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 77.1242i | 0.414646i | ||||||||
\(187\) | −25.1040 | −0.134246 | ||||||||
\(188\) | 62.3192 | 0.331485 | ||||||||
\(189\) | 134.183i | 0.709965i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −172.012 | −0.900587 | −0.450294 | − | 0.892880i | \(-0.648681\pi\) | ||||
−0.450294 | + | 0.892880i | \(0.648681\pi\) | |||||||
\(192\) | 214.871i | 1.11912i | ||||||||
\(193\) | 230.810i | 1.19591i | 0.801531 | + | 0.597954i | \(0.204019\pi\) | ||||
−0.801531 | + | 0.597954i | \(0.795981\pi\) | |||||||
\(194\) | 52.4264 | 0.270239 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.51472 | 0.00772816 | ||||||||
\(197\) | −44.0663 | −0.223687 | −0.111843 | − | 0.993726i | \(-0.535676\pi\) | ||||
−0.111843 | + | 0.993726i | \(0.535676\pi\) | |||||||
\(198\) | 12.0852i | 0.0610365i | ||||||||
\(199\) | −15.1493 | −0.0761270 | −0.0380635 | − | 0.999275i | \(-0.512119\pi\) | ||||
−0.0380635 | + | 0.999275i | \(0.512119\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 282.421 | 1.40508 | ||||||||
\(202\) | − | 295.451i | − | 1.46263i | ||||||
\(203\) | − | 324.129i | − | 1.59669i | ||||||
\(204\) | 72.8155i | 0.356939i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −71.5076 | −0.347124 | ||||||||
\(207\) | 77.4404 | 0.374108 | ||||||||
\(208\) | 36.6671i | 0.176284i | ||||||||
\(209\) | −35.6569 | − | 23.3284i | −0.170607 | − | 0.111619i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 332.565i | − | 1.57614i | −0.615588 | − | 0.788068i | \(-0.711082\pi\) | ||
0.615588 | − | 0.788068i | \(-0.288918\pi\) | |||||||
\(212\) | 38.1841i | 0.180114i | ||||||||
\(213\) | −95.6933 | −0.449264 | ||||||||
\(214\) | −255.090 | −1.19201 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −163.267 | −0.755866 | ||||||||
\(217\) | 103.844i | 0.478542i | ||||||||
\(218\) | −141.680 | −0.649909 | ||||||||
\(219\) | − | 353.369i | − | 1.61356i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 76.8180i | 0.347593i | ||||||||
\(222\) | − | 131.109i | − | 0.590582i | ||||||
\(223\) | 135.400i | 0.607175i | 0.952804 | + | 0.303588i | \(0.0981845\pi\) | ||||
−0.952804 | + | 0.303588i | \(0.901816\pi\) | |||||||
\(224\) | 186.934i | 0.834525i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −165.130 | −0.730663 | ||||||||
\(227\) | − | 313.683i | − | 1.38187i | −0.722919 | − | 0.690933i | \(-0.757200\pi\) | ||
0.722919 | − | 0.690933i | \(-0.242800\pi\) | |||||||
\(228\) | −67.6654 | + | 103.425i | −0.296778 | + | 0.453617i | ||||
\(229\) | −221.373 | −0.966693 | −0.483346 | − | 0.875429i | \(-0.660579\pi\) | ||||
−0.483346 | + | 0.875429i | \(0.660579\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 56.3198i | 0.243809i | ||||||||
\(232\) | 394.383 | 1.69992 | ||||||||
\(233\) | 344.261 | 1.47751 | 0.738757 | − | 0.673972i | \(-0.235413\pi\) | ||||
0.738757 | + | 0.673972i | \(0.235413\pi\) | |||||||
\(234\) | 36.9807 | 0.158037 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 126.611i | − | 0.536489i | ||||||
\(237\) | 388.033 | 1.63727 | ||||||||
\(238\) | − | 116.442i | − | 0.489251i | ||||||
\(239\) | 403.825 | 1.68965 | 0.844823 | − | 0.535046i | \(-0.179706\pi\) | ||||
0.844823 | + | 0.535046i | \(0.179706\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 233.897i | 0.970526i | 0.874368 | + | 0.485263i | \(0.161276\pi\) | ||||
−0.874368 | + | 0.485263i | \(0.838724\pi\) | |||||||
\(242\) | 170.897i | 0.706187i | ||||||||
\(243\) | 186.601i | 0.767907i | ||||||||
\(244\) | 42.8112 | 0.175456 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 340.443i | 1.38391i | ||||||||
\(247\) | −71.3848 | + | 109.110i | −0.289007 | + | 0.441739i | ||||
\(248\) | −126.351 | −0.509481 | ||||||||
\(249\) | 443.420i | 1.78080i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 183.816 | 0.732336 | 0.366168 | − | 0.930549i | \(-0.380670\pi\) | ||||
0.366168 | + | 0.930549i | \(0.380670\pi\) | |||||||
\(252\) | 47.1980 | 0.187294 | ||||||||
\(253\) | −47.4919 | −0.187715 | ||||||||
\(254\) | −239.799 | −0.944091 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −266.529 | −1.04113 | ||||||||
\(257\) | 190.867i | 0.742672i | 0.928499 | + | 0.371336i | \(0.121100\pi\) | ||||
−0.928499 | + | 0.371336i | \(0.878900\pi\) | |||||||
\(258\) | −231.024 | −0.895442 | ||||||||
\(259\) | − | 176.531i | − | 0.681589i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 167.914i | − | 0.643348i | ||||||
\(262\) | − | 180.656i | − | 0.689527i | ||||||
\(263\) | −123.220 | −0.468515 | −0.234258 | − | 0.972175i | \(-0.575266\pi\) | ||||
−0.234258 | + | 0.972175i | \(0.575266\pi\) | |||||||
\(264\) | −68.5269 | −0.259572 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 108.206 | − | 165.390i | 0.406790 | − | 0.621767i | ||||
\(267\) | −305.039 | −1.14247 | ||||||||
\(268\) | 145.148i | 0.541599i | ||||||||
\(269\) | 3.56948i | 0.0132694i | 0.999978 | + | 0.00663471i | \(0.00211191\pi\) | ||||
−0.999978 | + | 0.00663471i | \(0.997888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 122.983 | 0.453811 | 0.226905 | − | 0.973917i | \(-0.427139\pi\) | ||||
0.226905 | + | 0.973917i | \(0.427139\pi\) | |||||||
\(272\) | 59.8109 | 0.219893 | ||||||||
\(273\) | 172.338 | 0.631275 | ||||||||
\(274\) | − | 97.6225i | − | 0.356286i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 137.753i | 0.499104i | ||||||||
\(277\) | 103.669 | 0.374258 | 0.187129 | − | 0.982335i | \(-0.440082\pi\) | ||||
0.187129 | + | 0.982335i | \(0.440082\pi\) | |||||||
\(278\) | − | 259.639i | − | 0.933955i | ||||||
\(279\) | 53.7958i | 0.192817i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 362.726i | − | 1.29084i | −0.763828 | − | 0.645420i | \(-0.776683\pi\) | ||
0.763828 | − | 0.645420i | \(-0.223317\pi\) | |||||||
\(282\) | −178.688 | −0.633644 | ||||||||
\(283\) | −123.220 | −0.435405 | −0.217702 | − | 0.976015i | \(-0.569856\pi\) | ||||
−0.217702 | + | 0.976015i | \(0.569856\pi\) | |||||||
\(284\) | − | 49.1809i | − | 0.173172i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.6791 | −0.0792977 | ||||||||
\(287\) | 458.387i | 1.59717i | ||||||||
\(288\) | 96.8404i | 0.336251i | ||||||||
\(289\) | −163.696 | −0.566421 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 126.569 | 0.434943 | ||||||||
\(292\) | 181.611 | 0.621957 | ||||||||
\(293\) | 30.4764i | 0.104015i | 0.998647 | + | 0.0520075i | \(0.0165620\pi\) | ||||
−0.998647 | + | 0.0520075i | \(0.983438\pi\) | |||||||
\(294\) | −4.34315 | −0.0147726 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 214.794 | 0.725655 | ||||||||
\(297\) | − | 42.6304i | − | 0.143537i | ||||||
\(298\) | − | 13.1833i | − | 0.0442393i | ||||||
\(299\) | 145.325i | 0.486036i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −311.061 | −1.03343 | ||||||||
\(302\) | −388.033 | −1.28488 | ||||||||
\(303\) | − | 713.281i | − | 2.35406i | ||||||
\(304\) | 84.9533 | + | 55.5805i | 0.279452 | + | 0.182831i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 60.3223i | − | 0.197132i | ||||||
\(307\) | 214.557i | 0.698883i | 0.936958 | + | 0.349441i | \(0.113629\pi\) | ||||
−0.936958 | + | 0.349441i | \(0.886371\pi\) | |||||||
\(308\) | −28.9452 | −0.0939778 | ||||||||
\(309\) | −172.635 | −0.558688 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 178.345 | 0.573457 | 0.286729 | − | 0.958012i | \(-0.407432\pi\) | ||||
0.286729 | + | 0.958012i | \(0.407432\pi\) | |||||||
\(312\) | 209.692i | 0.672089i | ||||||||
\(313\) | 377.255 | 1.20529 | 0.602643 | − | 0.798011i | \(-0.294114\pi\) | ||||
0.602643 | + | 0.798011i | \(0.294114\pi\) | |||||||
\(314\) | 322.162i | 1.02599i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 199.427i | 0.631097i | ||||||||
\(317\) | − | 448.813i | − | 1.41581i | −0.706306 | − | 0.707906i | \(-0.749640\pi\) | ||
0.706306 | − | 0.707906i | \(-0.250360\pi\) | |||||||
\(318\) | − | 109.485i | − | 0.344293i | ||||||
\(319\) | 102.977i | 0.322811i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −615.843 | −1.91851 | ||||||||
\(322\) | − | 220.285i | − | 0.684116i | ||||||
\(323\) | 177.978 | + | 116.442i | 0.551016 | + | 0.360501i | ||||
\(324\) | −183.828 | −0.567372 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 83.6508i | 0.256597i | ||||||||
\(327\) | −342.046 | −1.04601 | ||||||||
\(328\) | −557.741 | −1.70043 | ||||||||
\(329\) | −240.593 | −0.731285 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 590.835i | 1.78500i | 0.451047 | + | 0.892500i | \(0.351051\pi\) | ||||
−0.451047 | + | 0.892500i | \(0.648949\pi\) | |||||||
\(332\) | −227.892 | −0.686422 | ||||||||
\(333\) | − | 91.4516i | − | 0.274629i | ||||||
\(334\) | −131.747 | −0.394453 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 134.183i | − | 0.399355i | ||||||
\(337\) | 515.902i | 1.53087i | 0.643515 | + | 0.765434i | \(0.277475\pi\) | ||||
−0.643515 | + | 0.765434i | \(0.722525\pi\) | |||||||
\(338\) | − | 179.645i | − | 0.531493i | ||||||
\(339\) | −398.659 | −1.17599 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 32.9914i | − | 0.0967489i | ||||||
\(342\) | 56.0558 | − | 85.6797i | 0.163906 | − | 0.250526i | ||||
\(343\) | 340.040 | 0.991369 | ||||||||
\(344\) | − | 378.482i | − | 1.10024i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 154.863 | 0.447581 | ||||||||
\(347\) | 114.362 | 0.329573 | 0.164786 | − | 0.986329i | \(-0.447307\pi\) | ||||
0.164786 | + | 0.986329i | \(0.447307\pi\) | |||||||
\(348\) | 298.689 | 0.858303 | ||||||||
\(349\) | 37.5980 | 0.107731 | 0.0538653 | − | 0.998548i | \(-0.482846\pi\) | ||||
0.0538653 | + | 0.998548i | \(0.482846\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −130.449 | −0.371649 | ||||||||
\(352\) | − | 59.3894i | − | 0.168720i | ||||||
\(353\) | −207.841 | −0.588783 | −0.294392 | − | 0.955685i | \(-0.595117\pi\) | ||||
−0.294392 | + | 0.955685i | \(0.595117\pi\) | |||||||
\(354\) | 363.032i | 1.02551i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 156.772i | − | 0.440372i | ||||||
\(357\) | − | 281.115i | − | 0.787438i | ||||||
\(358\) | −97.2339 | −0.271603 | ||||||||
\(359\) | −355.444 | −0.990094 | −0.495047 | − | 0.868866i | \(-0.664849\pi\) | ||||
−0.495047 | + | 0.868866i | \(0.664849\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 144.588 | + | 330.780i | 0.400520 | + | 0.916288i | ||||
\(362\) | 191.387 | 0.528692 | ||||||||
\(363\) | 412.582i | 1.13659i | ||||||||
\(364\) | 88.5719i | 0.243329i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −122.752 | −0.335389 | ||||||||
\(367\) | 288.793 | 0.786901 | 0.393450 | − | 0.919346i | \(-0.371281\pi\) | ||||
0.393450 | + | 0.919346i | \(0.371281\pi\) | |||||||
\(368\) | 113.151 | 0.307474 | ||||||||
\(369\) | 237.466i | 0.643540i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 147.416i | − | 0.397347i | ||||||
\(372\) | −95.6933 | −0.257240 | ||||||||
\(373\) | 480.221i | 1.28746i | 0.765254 | + | 0.643728i | \(0.222613\pi\) | ||||
−0.765254 | + | 0.643728i | \(0.777387\pi\) | |||||||
\(374\) | 36.9939i | 0.0989142i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 292.741i | − | 0.778565i | ||||||
\(377\) | 315.108 | 0.835829 | ||||||||
\(378\) | 197.736 | 0.523111 | ||||||||
\(379\) | 186.934i | 0.493229i | 0.969114 | + | 0.246614i | \(0.0793181\pi\) | ||||
−0.969114 | + | 0.246614i | \(0.920682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −578.926 | −1.51949 | ||||||||
\(382\) | 253.482i | 0.663564i | ||||||||
\(383\) | 424.292i | 1.10781i | 0.832579 | + | 0.553906i | \(0.186863\pi\) | ||||
−0.832579 | + | 0.553906i | \(0.813137\pi\) | |||||||
\(384\) | −60.2132 | −0.156805 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 340.128 | 0.881160 | ||||||||
\(387\) | −161.144 | −0.416393 | ||||||||
\(388\) | 65.0490i | 0.167652i | ||||||||
\(389\) | −283.757 | −0.729453 | −0.364727 | − | 0.931115i | \(-0.618838\pi\) | ||||
−0.364727 | + | 0.931115i | \(0.618838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 237.052 | 0.606270 | ||||||||
\(392\) | − | 7.11529i | − | 0.0181513i | ||||||
\(393\) | − | 436.142i | − | 1.10978i | ||||||
\(394\) | 64.9373i | 0.164815i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −14.9949 | −0.0378660 | ||||||||
\(397\) | 569.143 | 1.43361 | 0.716805 | − | 0.697274i | \(-0.245604\pi\) | ||||
0.716805 | + | 0.697274i | \(0.245604\pi\) | |||||||
\(398\) | 22.3244i | 0.0560914i | ||||||||
\(399\) | 261.233 | − | 399.287i | 0.654718 | − | 1.00072i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 475.365i | 1.18545i | 0.805405 | + | 0.592725i | \(0.201948\pi\) | ||||
−0.805405 | + | 0.592725i | \(0.798052\pi\) | |||||||
\(402\) | − | 416.183i | − | 1.03528i | ||||||
\(403\) | −100.953 | −0.250505 | ||||||||
\(404\) | 366.586 | 0.907391 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −477.645 | −1.17646 | ||||||||
\(407\) | 56.0845i | 0.137800i | ||||||||
\(408\) | 342.046 | 0.838348 | ||||||||
\(409\) | 581.479i | 1.42171i | 0.703340 | + | 0.710854i | \(0.251691\pi\) | ||||
−0.703340 | + | 0.710854i | \(0.748309\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 235.681i | − | 0.573434i | ||||||
\(412\) | − | 88.7243i | − | 0.215350i | ||||||
\(413\) | 488.803i | 1.18354i | ||||||||
\(414\) | − | 114.118i | − | 0.275648i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −181.731 | −0.436853 | ||||||||
\(417\) | − | 626.825i | − | 1.50318i | ||||||
\(418\) | −34.3774 | + | 52.5449i | −0.0822425 | + | 0.125705i | ||||
\(419\) | 227.508 | 0.542978 | 0.271489 | − | 0.962442i | \(-0.412484\pi\) | ||||
0.271489 | + | 0.962442i | \(0.412484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 106.240i | − | 0.252351i | −0.992008 | − | 0.126176i | \(-0.959730\pi\) | ||
0.992008 | − | 0.126176i | \(-0.0402703\pi\) | |||||||
\(422\) | −490.076 | −1.16132 | ||||||||
\(423\) | −124.638 | −0.294653 | ||||||||
\(424\) | 179.368 | 0.423037 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 141.016i | 0.331024i | ||||||||
\(427\) | −165.279 | −0.387071 | ||||||||
\(428\) | − | 316.508i | − | 0.739504i | ||||||
\(429\) | −54.7523 | −0.127628 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 236.421i | − | 0.548540i | −0.961653 | − | 0.274270i | \(-0.911564\pi\) | ||
0.961653 | − | 0.274270i | \(-0.0884362\pi\) | |||||||
\(432\) | 101.568i | 0.235111i | ||||||||
\(433\) | 405.561i | 0.936631i | 0.883561 | + | 0.468316i | \(0.155139\pi\) | ||||
−0.883561 | + | 0.468316i | \(0.844861\pi\) | |||||||
\(434\) | 153.026 | 0.352596 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 175.792i | − | 0.403193i | ||||||
\(437\) | 336.700 | + | 220.285i | 0.770481 | + | 0.504085i | ||||
\(438\) | −520.734 | −1.18889 | ||||||||
\(439\) | − | 415.043i | − | 0.945428i | −0.881216 | − | 0.472714i | \(-0.843274\pi\) | ||
0.881216 | − | 0.472714i | \(-0.156726\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.02944 | −0.00686947 | ||||||||
\(442\) | 113.201 | 0.256111 | ||||||||
\(443\) | −372.790 | −0.841513 | −0.420756 | − | 0.907174i | \(-0.638235\pi\) | ||||
−0.420756 | + | 0.907174i | \(0.638235\pi\) | |||||||
\(444\) | 162.676 | 0.366388 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 199.529 | 0.447374 | ||||||||
\(447\) | − | 31.8273i | − | 0.0712021i | ||||||
\(448\) | 426.338 | 0.951647 | ||||||||
\(449\) | − | 297.789i | − | 0.663226i | −0.943415 | − | 0.331613i | \(-0.892407\pi\) | ||
0.943415 | − | 0.331613i | \(-0.107593\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 145.631i | − | 0.322907i | ||||||
\(452\) | − | 204.888i | − | 0.453292i | ||||||
\(453\) | −936.795 | −2.06798 | ||||||||
\(454\) | −462.252 | −1.01818 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 485.831 | + | 317.854i | 1.06542 | + | 0.697048i | ||||
\(457\) | −111.022 | −0.242937 | −0.121469 | − | 0.992595i | \(-0.538760\pi\) | ||||
−0.121469 | + | 0.992595i | \(0.538760\pi\) | |||||||
\(458\) | 326.220i | 0.712271i | ||||||||
\(459\) | 212.786i | 0.463586i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 692.531 | 1.50224 | 0.751118 | − | 0.660168i | \(-0.229515\pi\) | ||||
0.751118 | + | 0.660168i | \(0.229515\pi\) | |||||||
\(462\) | 82.9943 | 0.179641 | ||||||||
\(463\) | 460.213 | 0.993981 | 0.496991 | − | 0.867756i | \(-0.334438\pi\) | ||||
0.496991 | + | 0.867756i | \(0.334438\pi\) | |||||||
\(464\) | − | 245.344i | − | 0.528759i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 507.311i | − | 1.08865i | ||||||
\(467\) | −581.548 | −1.24528 | −0.622642 | − | 0.782507i | \(-0.713941\pi\) | ||||
−0.622642 | + | 0.782507i | \(0.713941\pi\) | |||||||
\(468\) | 45.8844i | 0.0980436i | ||||||||
\(469\) | − | 560.368i | − | 1.19481i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 777.769i | 1.65131i | ||||||||
\(472\) | −594.749 | −1.26006 | ||||||||
\(473\) | 98.8250 | 0.208932 | ||||||||
\(474\) | − | 571.816i | − | 1.20636i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 144.477 | 0.303524 | ||||||||
\(477\) | − | 76.3683i | − | 0.160101i | ||||||
\(478\) | − | 595.088i | − | 1.24495i | ||||||
\(479\) | 290.686 | 0.606861 | 0.303430 | − | 0.952854i | \(-0.401868\pi\) | ||||
0.303430 | + | 0.952854i | \(0.401868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 171.618 | 0.356795 | ||||||||
\(482\) | 344.676 | 0.715096 | ||||||||
\(483\) | − | 531.816i | − | 1.10107i | ||||||
\(484\) | −212.044 | −0.438107 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 274.981 | 0.565804 | ||||||||
\(487\) | 402.206i | 0.825884i | 0.910757 | + | 0.412942i | \(0.135499\pi\) | ||||
−0.910757 | + | 0.412942i | \(0.864501\pi\) | |||||||
\(488\) | − | 201.103i | − | 0.412096i | ||||||
\(489\) | 201.951i | 0.412987i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −568.222 | −1.15728 | −0.578638 | − | 0.815585i | \(-0.696416\pi\) | ||||
−0.578638 | + | 0.815585i | \(0.696416\pi\) | |||||||
\(492\) | −422.410 | −0.858558 | ||||||||
\(493\) | − | 513.999i | − | 1.04259i | ||||||
\(494\) | 160.787 | + | 105.194i | 0.325479 | + | 0.212944i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 78.6028i | 0.158473i | ||||||||
\(497\) | 189.870i | 0.382033i | ||||||||
\(498\) | 653.434 | 1.31212 | ||||||||
\(499\) | 536.237 | 1.07462 | 0.537311 | − | 0.843384i | \(-0.319440\pi\) | ||||
0.537311 | + | 0.843384i | \(0.319440\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −318.066 | −0.634862 | ||||||||
\(502\) | − | 270.876i | − | 0.539594i | ||||||
\(503\) | 167.787 | 0.333574 | 0.166787 | − | 0.985993i | \(-0.446661\pi\) | ||||
0.166787 | + | 0.985993i | \(0.446661\pi\) | |||||||
\(504\) | − | 221.710i | − | 0.439900i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 69.9853i | 0.138311i | ||||||||
\(507\) | − | 433.701i | − | 0.855426i | ||||||
\(508\) | − | 297.535i | − | 0.585698i | ||||||
\(509\) | 622.042i | 1.22209i | 0.791597 | + | 0.611043i | \(0.209250\pi\) | ||||
−0.791597 | + | 0.611043i | \(0.790750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −701.139 | −1.37209 | ||||||||
\(512\) | 325.064i | 0.634891i | ||||||||
\(513\) | −197.736 | + | 302.234i | −0.385450 | + | 0.589150i | ||||
\(514\) | 281.266 | 0.547210 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 286.647i | − | 0.555518i | ||||||
\(517\) | 76.4371 | 0.147847 | ||||||||
\(518\) | −260.141 | −0.502203 | ||||||||
\(519\) | 373.872 | 0.720370 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 805.100i | − | 1.54530i | −0.634834 | − | 0.772649i | \(-0.718931\pi\) | ||
0.634834 | − | 0.772649i | \(-0.281069\pi\) | |||||||
\(522\) | −247.442 | −0.474027 | ||||||||
\(523\) | − | 283.164i | − | 0.541422i | −0.962661 | − | 0.270711i | \(-0.912741\pi\) | ||
0.962661 | − | 0.270711i | \(-0.0872587\pi\) | |||||||
\(524\) | 224.152 | 0.427771 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 181.579i | 0.345208i | ||||||||
\(527\) | 164.674i | 0.312474i | ||||||||
\(528\) | 42.6304i | 0.0807394i | ||||||||
\(529\) | −80.5442 | −0.152257 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 253.223i | 0.476879i | ||||||||
\(532\) | 205.210 | + | 134.259i | 0.385734 | + | 0.252366i | ||||
\(533\) | −445.630 | −0.836078 | ||||||||
\(534\) | 449.513i | 0.841785i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 681.825 | 1.27206 | ||||||||
\(537\) | −234.743 | −0.437139 | ||||||||
\(538\) | 5.26007 | 0.00977708 | ||||||||
\(539\) | 1.85786 | 0.00344687 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −296.551 | −0.548154 | −0.274077 | − | 0.961708i | \(-0.588372\pi\) | ||||
−0.274077 | + | 0.961708i | \(0.588372\pi\) | |||||||
\(542\) | − | 181.231i | − | 0.334374i | ||||||
\(543\) | 462.048 | 0.850917 | ||||||||
\(544\) | 296.437i | 0.544921i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 253.962i | − | 0.465132i | ||||||
\(547\) | 368.218i | 0.673159i | 0.941655 | + | 0.336580i | \(0.109270\pi\) | ||||
−0.941655 | + | 0.336580i | \(0.890730\pi\) | |||||||
\(548\) | 121.127 | 0.221034 | ||||||||
\(549\) | −85.6224 | −0.155961 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 477.645 | − | 730.067i | 0.866869 | − | 1.32498i | ||||
\(552\) | 647.085 | 1.17226 | ||||||||
\(553\) | − | 769.918i | − | 1.39226i | ||||||
\(554\) | − | 152.770i | − | 0.275758i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 322.152 | 0.579410 | ||||||||
\(557\) | 718.764 | 1.29042 | 0.645210 | − | 0.764006i | \(-0.276770\pi\) | ||||
0.645210 | + | 0.764006i | \(0.276770\pi\) | |||||||
\(558\) | 79.2749 | 0.142070 | ||||||||
\(559\) | − | 302.403i | − | 0.540972i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 89.3112i | 0.159200i | ||||||||
\(562\) | −534.522 | −0.951107 | ||||||||
\(563\) | − | 50.1751i | − | 0.0891210i | −0.999007 | − | 0.0445605i | \(-0.985811\pi\) | ||
0.999007 | − | 0.0445605i | \(-0.0141888\pi\) | |||||||
\(564\) | − | 221.710i | − | 0.393102i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 181.579i | 0.320812i | ||||||||
\(567\) | 709.698 | 1.25167 | ||||||||
\(568\) | −231.024 | −0.406732 | ||||||||
\(569\) | − | 356.632i | − | 0.626770i | −0.949626 | − | 0.313385i | \(-0.898537\pi\) | ||
0.949626 | − | 0.313385i | \(-0.101463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −434.831 | −0.761526 | −0.380763 | − | 0.924673i | \(-0.624339\pi\) | ||||
−0.380763 | + | 0.924673i | \(0.624339\pi\) | |||||||
\(572\) | − | 28.1396i | − | 0.0491950i | ||||||
\(573\) | 611.959i | 1.06799i | ||||||||
\(574\) | 675.492 | 1.17681 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 220.863 | 0.383443 | ||||||||
\(577\) | −1000.20 | −1.73345 | −0.866727 | − | 0.498782i | \(-0.833781\pi\) | ||||
−0.866727 | + | 0.498782i | \(0.833781\pi\) | |||||||
\(578\) | 241.226i | 0.417346i | ||||||||
\(579\) | 821.141 | 1.41821 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 879.813 | 1.51431 | ||||||||
\(582\) | − | 186.515i | − | 0.320472i | ||||||
\(583\) | 46.8344i | 0.0803334i | ||||||||
\(584\) | − | 853.108i | − | 1.46080i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 44.9108 | 0.0766396 | ||||||||
\(587\) | 402.860 | 0.686304 | 0.343152 | − | 0.939280i | \(-0.388505\pi\) | ||||
0.343152 | + | 0.939280i | \(0.388505\pi\) | |||||||
\(588\) | − | 5.38883i | − | 0.00916468i | ||||||
\(589\) | −153.026 | + | 233.897i | −0.259807 | + | 0.397108i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 156.772i | 0.265266i | ||||||||
\(592\) | − | 133.623i | − | 0.225714i | ||||||
\(593\) | 640.735 | 1.08050 | 0.540249 | − | 0.841505i | \(-0.318330\pi\) | ||||
0.540249 | + | 0.841505i | \(0.318330\pi\) | |||||||
\(594\) | −62.8213 | −0.105760 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.3574 | 0.0274454 | ||||||||
\(597\) | 53.8958i | 0.0902777i | ||||||||
\(598\) | 214.154 | 0.358118 | ||||||||
\(599\) | − | 735.727i | − | 1.22826i | −0.789205 | − | 0.614129i | \(-0.789507\pi\) | ||
0.789205 | − | 0.614129i | \(-0.210493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 204.042i | 0.339504i | 0.985487 | + | 0.169752i | \(0.0542966\pi\) | ||||
−0.985487 | + | 0.169752i | \(0.945703\pi\) | |||||||
\(602\) | 458.387i | 0.761441i | ||||||||
\(603\) | − | 290.297i | − | 0.481421i | ||||||
\(604\) | − | 481.459i | − | 0.797117i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1051.11 | −1.73450 | ||||||||
\(607\) | 169.424i | 0.279116i | 0.990214 | + | 0.139558i | \(0.0445682\pi\) | ||||
−0.990214 | + | 0.139558i | \(0.955432\pi\) | |||||||
\(608\) | −275.470 | + | 421.049i | −0.453076 | + | 0.692514i | ||||
\(609\) | −1153.14 | −1.89349 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 233.897i | − | 0.382810i | ||||||
\(612\) | 74.8460 | 0.122297 | ||||||||
\(613\) | −132.615 | −0.216337 | −0.108169 | − | 0.994133i | \(-0.534499\pi\) | ||||
−0.108169 | + | 0.994133i | \(0.534499\pi\) | |||||||
\(614\) | 316.177 | 0.514946 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 135.968i | 0.220727i | ||||||||
\(617\) | 109.517 | 0.177500 | 0.0887498 | − | 0.996054i | \(-0.471713\pi\) | ||||
0.0887498 | + | 0.996054i | \(0.471713\pi\) | |||||||
\(618\) | 254.399i | 0.411648i | ||||||||
\(619\) | 841.414 | 1.35931 | 0.679656 | − | 0.733531i | \(-0.262129\pi\) | ||||
0.679656 | + | 0.733531i | \(0.262129\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 402.550i | 0.648229i | ||||||||
\(622\) | − | 262.814i | − | 0.422531i | ||||||
\(623\) | 605.244i | 0.971500i | ||||||||
\(624\) | 130.449 | 0.209052 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 555.932i | − | 0.888071i | ||||||
\(627\) | −82.9943 | + | 126.855i | −0.132367 | + | 0.202320i | ||||
\(628\) | −399.729 | −0.636511 | ||||||||
\(629\) | − | 279.941i | − | 0.445057i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 699.661 | 1.10881 | 0.554407 | − | 0.832246i | \(-0.312945\pi\) | ||||
0.554407 | + | 0.832246i | \(0.312945\pi\) | |||||||
\(632\) | 936.795 | 1.48227 | ||||||||
\(633\) | −1183.15 | −1.86911 | ||||||||
\(634\) | −661.382 | −1.04319 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 135.846 | 0.213594 | ||||||||
\(637\) | − | 5.68505i | − | 0.00892472i | ||||||
\(638\) | 151.749 | 0.237851 | ||||||||
\(639\) | 98.3617i | 0.153931i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1163.39i | 1.81496i | 0.420094 | + | 0.907481i | \(0.361997\pi\) | ||||
−0.420094 | + | 0.907481i | \(0.638003\pi\) | |||||||
\(642\) | 907.522i | 1.41359i | ||||||||
\(643\) | 32.0769 | 0.0498862 | 0.0249431 | − | 0.999689i | \(-0.492060\pi\) | ||||
0.0249431 | + | 0.999689i | \(0.492060\pi\) | |||||||
\(644\) | 273.323 | 0.424415 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 171.592 | − | 262.273i | 0.265622 | − | 0.405996i | ||||
\(647\) | −324.087 | −0.500908 | −0.250454 | − | 0.968129i | \(-0.580580\pi\) | ||||
−0.250454 | + | 0.968129i | \(0.580580\pi\) | |||||||
\(648\) | 863.522i | 1.33260i | ||||||||
\(649\) | − | 155.294i | − | 0.239282i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 369.439 | 0.567494 | ||||||||
\(652\) | −103.791 | −0.159189 | ||||||||
\(653\) | 245.436 | 0.375859 | 0.187929 | − | 0.982183i | \(-0.439822\pi\) | ||||
0.187929 | + | 0.982183i | \(0.439822\pi\) | |||||||
\(654\) | 504.048i | 0.770716i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 346.969i | 0.528917i | ||||||||
\(657\) | −363.223 | −0.552851 | ||||||||
\(658\) | 354.544i | 0.538821i | ||||||||
\(659\) | 959.655i | 1.45623i | 0.685456 | + | 0.728114i | \(0.259603\pi\) | ||||
−0.685456 | + | 0.728114i | \(0.740397\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 172.835i | − | 0.261475i | −0.991417 | − | 0.130738i | \(-0.958265\pi\) | ||
0.991417 | − | 0.130738i | \(-0.0417345\pi\) | |||||||
\(662\) | 870.670 | 1.31521 | ||||||||
\(663\) | 273.291 | 0.412204 | ||||||||
\(664\) | 1070.51i | 1.61221i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −134.765 | −0.202350 | ||||||||
\(667\) | − | 972.387i | − | 1.45785i | ||||||
\(668\) | − | 163.468i | − | 0.244712i | ||||||
\(669\) | 481.706 | 0.720038 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.5097 | 0.0782558 | ||||||||
\(672\) | 665.044 | 0.989649 | ||||||||
\(673\) | − | 866.672i | − | 1.28777i | −0.765121 | − | 0.643887i | \(-0.777321\pi\) | ||
0.765121 | − | 0.643887i | \(-0.222679\pi\) | |||||||
\(674\) | 760.247 | 1.12796 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 222.897 | 0.329730 | ||||||||
\(677\) | − | 232.811i | − | 0.343886i | −0.985107 | − | 0.171943i | \(-0.944996\pi\) | ||
0.985107 | − | 0.171943i | \(-0.0550044\pi\) | |||||||
\(678\) | 587.474i | 0.866481i | ||||||||
\(679\) | − | 251.132i | − | 0.369855i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1115.97 | −1.63873 | ||||||||
\(682\) | −48.6169 | −0.0712858 | ||||||||
\(683\) | − | 1.51701i | − | 0.00222109i | −0.999999 | − | 0.00111055i | \(-0.999647\pi\) | ||
0.999999 | − | 0.00111055i | \(-0.000353498\pi\) | |||||||
\(684\) | 106.309 | + | 69.5522i | 0.155422 | + | 0.101685i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 501.091i | − | 0.730453i | ||||||
\(687\) | 787.566i | 1.14638i | ||||||||
\(688\) | −235.453 | −0.342228 | ||||||||
\(689\) | 143.313 | 0.208001 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −584.049 | −0.845223 | −0.422611 | − | 0.906311i | \(-0.638886\pi\) | ||||
−0.422611 | + | 0.906311i | \(0.638886\pi\) | |||||||
\(692\) | 192.149i | 0.277672i | ||||||||
\(693\) | 57.8903 | 0.0835358 | ||||||||
\(694\) | − | 168.526i | − | 0.242833i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 1403.07i | − | 2.01591i | ||||||
\(697\) | 726.905i | 1.04290i | ||||||||
\(698\) | − | 55.4054i | − | 0.0793773i | ||||||
\(699\) | − | 1224.76i | − | 1.75216i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −861.671 | −1.22920 | −0.614601 | − | 0.788838i | \(-0.710683\pi\) | ||||
−0.614601 | + | 0.788838i | \(0.710683\pi\) | |||||||
\(702\) | 192.233i | 0.273836i | ||||||||
\(703\) | 260.141 | − | 397.619i | 0.370044 | − | 0.565603i | ||||
\(704\) | −135.449 | −0.192399 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 306.279i | 0.433823i | ||||||||
\(707\) | −1415.26 | −2.00178 | ||||||||
\(708\) | −450.438 | −0.636212 | ||||||||
\(709\) | −808.916 | −1.14093 | −0.570463 | − | 0.821324i | \(-0.693236\pi\) | ||||
−0.570463 | + | 0.821324i | \(0.693236\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 398.854i | − | 0.560976i | ||||||
\(712\) | −736.429 | −1.03431 | ||||||||
\(713\) | 311.531i | 0.436929i | ||||||||
\(714\) | −414.259 | −0.580195 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 120.645i | − | 0.168498i | ||||||
\(717\) | − | 1436.67i | − | 2.00372i | ||||||
\(718\) | 523.791i | 0.729514i | ||||||||
\(719\) | −364.836 | −0.507422 | −0.253711 | − | 0.967280i | \(-0.581651\pi\) | ||||
−0.253711 | + | 0.967280i | \(0.581651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 342.534i | 0.475082i | ||||||||
\(722\) | 487.446 | − | 213.068i | 0.675133 | − | 0.295109i | ||||
\(723\) | 832.122 | 1.15093 | ||||||||
\(724\) | 237.466i | 0.327992i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 607.992 | 0.837455 | ||||||||
\(727\) | 786.551 | 1.08191 | 0.540956 | − | 0.841051i | \(-0.318062\pi\) | ||||
0.540956 | + | 0.841051i | \(0.318062\pi\) | |||||||
\(728\) | 416.061 | 0.571512 | ||||||||
\(729\) | −240.990 | −0.330576 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −493.276 | −0.674797 | ||||||||
\(732\) | − | 152.307i | − | 0.208070i | ||||||
\(733\) | 471.493 | 0.643238 | 0.321619 | − | 0.946869i | \(-0.395773\pi\) | ||||
0.321619 | + | 0.946869i | \(0.395773\pi\) | |||||||
\(734\) | − | 425.572i | − | 0.579799i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 560.801i | 0.761958i | ||||||||
\(737\) | 178.030i | 0.241561i | ||||||||
\(738\) | 349.936 | 0.474168 | ||||||||
\(739\) | −492.673 | −0.666676 | −0.333338 | − | 0.942807i | \(-0.608175\pi\) | ||||
−0.333338 | + | 0.942807i | \(0.608175\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 388.174 | + | 253.962i | 0.523851 | + | 0.342729i | ||||
\(742\) | −217.236 | −0.292770 | ||||||||
\(743\) | − | 437.843i | − | 0.589291i | −0.955607 | − | 0.294646i | \(-0.904798\pi\) | ||
0.955607 | − | 0.294646i | \(-0.0952016\pi\) | |||||||
\(744\) | 449.513i | 0.604184i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 707.666 | 0.948614 | ||||||||
\(747\) | 455.785 | 0.610153 | ||||||||
\(748\) | −45.9008 | −0.0613648 | ||||||||
\(749\) | 1221.93i | 1.63141i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 690.549i | 0.919506i | 0.888047 | + | 0.459753i | \(0.152062\pi\) | ||||
−0.888047 | + | 0.459753i | \(0.847938\pi\) | |||||||
\(752\) | −182.113 | −0.242172 | ||||||||
\(753\) | − | 653.953i | − | 0.868464i | ||||||
\(754\) | − | 464.351i | − | 0.615850i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 245.344i | 0.324530i | ||||||||
\(757\) | −386.442 | −0.510491 | −0.255246 | − | 0.966876i | \(-0.582156\pi\) | ||||
−0.255246 | + | 0.966876i | \(0.582156\pi\) | |||||||
\(758\) | 275.470 | 0.363417 | ||||||||
\(759\) | 168.959i | 0.222608i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1032.01 | −1.35613 | −0.678064 | − | 0.735003i | \(-0.737181\pi\) | ||||
−0.678064 | + | 0.735003i | \(0.737181\pi\) | |||||||
\(762\) | 853.120i | 1.11958i | ||||||||
\(763\) | 678.673i | 0.889479i | ||||||||
\(764\) | −314.512 | −0.411665 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 625.248 | 0.816250 | ||||||||
\(767\) | −475.198 | −0.619554 | ||||||||
\(768\) | 948.216i | 1.23466i | ||||||||
\(769\) | −562.421 | −0.731367 | −0.365684 | − | 0.930739i | \(-0.619165\pi\) | ||||
−0.365684 | + | 0.930739i | \(0.619165\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 679.037 | 0.880722 | ||||||||
\(772\) | 422.020i | 0.546658i | ||||||||
\(773\) | − | 503.048i | − | 0.650774i | −0.945581 | − | 0.325387i | \(-0.894505\pi\) | ||
0.945581 | − | 0.325387i | \(-0.105495\pi\) | |||||||
\(774\) | 237.466i | 0.306804i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 305.563 | 0.393767 | ||||||||
\(777\) | −628.037 | −0.808284 | ||||||||
\(778\) | 418.152i | 0.537471i | ||||||||
\(779\) | −675.492 | + | 1032.47i | −0.867127 | + | 1.32538i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 60.3223i | − | 0.0772373i | ||||||
\(782\) | − | 349.326i | − | 0.446708i | ||||||
\(783\) | 872.849 | 1.11475 | ||||||||
\(784\) | −4.42641 | −0.00564593 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −642.711 | −0.817698 | ||||||||
\(787\) | − | 1453.47i | − | 1.84685i | −0.383774 | − | 0.923427i | \(-0.625376\pi\) | ||
0.383774 | − | 0.923427i | \(-0.374624\pi\) | |||||||
\(788\) | −80.5721 | −0.102249 | ||||||||
\(789\) | 438.372i | 0.555604i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 791.001i | 1.00000i | ||||||||
\(792\) | 70.4378i | 0.0889366i | ||||||||
\(793\) | − | 160.679i | − | 0.202622i | ||||||
\(794\) | − | 838.704i | − | 1.05630i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.6994 | −0.0347982 | ||||||||
\(797\) | 754.127i | 0.946207i | 0.881007 | + | 0.473104i | \(0.156866\pi\) | ||||
−0.881007 | + | 0.473104i | \(0.843134\pi\) | |||||||
\(798\) | −588.399 | − | 384.959i | −0.737342 | − | 0.482405i | ||||
\(799\) | −381.529 | −0.477508 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 313.545i | 0.391442i | ||||||||
\(802\) | 700.511 | 0.873455 | ||||||||
\(803\) | 222.754 | 0.277402 | ||||||||
\(804\) | 516.387 | 0.642272 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 148.767i | 0.184575i | ||||||||
\(807\) | 12.6989 | 0.0157360 | ||||||||
\(808\) | − | 1722.01i | − | 2.13120i | ||||||
\(809\) | 57.1136 | 0.0705977 | 0.0352989 | − | 0.999377i | \(-0.488762\pi\) | ||||
0.0352989 | + | 0.999377i | \(0.488762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 899.332i | − | 1.10892i | −0.832211 | − | 0.554459i | \(-0.812925\pi\) | ||
0.832211 | − | 0.554459i | \(-0.187075\pi\) | |||||||
\(812\) | − | 592.646i | − | 0.729860i | ||||||
\(813\) | − | 437.529i | − | 0.538166i | ||||||
\(814\) | 82.6476 | 0.101533 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 212.786i | − | 0.260767i | ||||||
\(817\) | −700.632 | − | 458.387i | −0.857567 | − | 0.561062i | ||||
\(818\) | 856.882 | 1.04753 | ||||||||
\(819\) | − | 177.144i | − | 0.216293i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −524.303 | −0.638615 | −0.319307 | − | 0.947651i | \(-0.603450\pi\) | ||||
−0.319307 | + | 0.947651i | \(0.603450\pi\) | |||||||
\(822\) | −347.306 | −0.422514 | ||||||||
\(823\) | −1107.42 | −1.34559 | −0.672795 | − | 0.739829i | \(-0.734906\pi\) | ||||
−0.672795 | + | 0.739829i | \(0.734906\pi\) | |||||||
\(824\) | −416.777 | −0.505797 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 720.312 | 0.872048 | ||||||||
\(827\) | − | 549.290i | − | 0.664196i | −0.943245 | − | 0.332098i | \(-0.892244\pi\) | ||
0.943245 | − | 0.332098i | \(-0.107756\pi\) | |||||||
\(828\) | 141.594 | 0.171007 | ||||||||
\(829\) | 676.577i | 0.816136i | 0.912951 | + | 0.408068i | \(0.133797\pi\) | ||||
−0.912951 | + | 0.408068i | \(0.866203\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 368.819i | − | 0.443826i | ||||||
\(832\) | 414.472i | 0.498163i | ||||||||
\(833\) | −9.27337 | −0.0111325 | ||||||||
\(834\) | −923.706 | −1.10756 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −65.1960 | − | 42.6543i | −0.0779856 | − | 0.0510219i | ||||
\(837\) | −279.641 | −0.334099 | ||||||||
\(838\) | − | 335.261i | − | 0.400073i | ||||||
\(839\) | − | 196.723i | − | 0.234474i | −0.993104 | − | 0.117237i | \(-0.962596\pi\) | ||
0.993104 | − | 0.117237i | \(-0.0374037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1267.43 | −1.50705 | ||||||||
\(842\) | −156.558 | −0.185936 | ||||||||
\(843\) | −1290.45 | −1.53078 | ||||||||
\(844\) | − | 608.070i | − | 0.720462i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 183.670i | 0.217104i | ||||||||
\(847\) | 818.628 | 0.966502 | ||||||||
\(848\) | − | 111.584i | − | 0.131585i | ||||||
\(849\) | 438.372i | 0.516339i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 529.594i | − | 0.622320i | ||||||
\(852\) | −174.968 | −0.205362 | ||||||||
\(853\) | −1124.34 | −1.31810 | −0.659050 | − | 0.752099i | \(-0.729042\pi\) | ||||
−0.659050 | + | 0.752099i | \(0.729042\pi\) | |||||||
\(854\) | 243.560i | 0.285199i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1486.78 | −1.73689 | ||||||||
\(857\) | − | 1634.72i | − | 1.90749i | −0.300616 | − | 0.953745i | \(-0.597192\pi\) | ||
0.300616 | − | 0.953745i | \(-0.402808\pi\) | |||||||
\(858\) | 80.6844i | 0.0940378i | ||||||||
\(859\) | 325.977 | 0.379484 | 0.189742 | − | 0.981834i | \(-0.439235\pi\) | ||||
0.189742 | + | 0.981834i | \(0.439235\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1630.78 | 1.89405 | ||||||||
\(862\) | −348.396 | −0.404171 | ||||||||
\(863\) | − | 330.052i | − | 0.382447i | −0.981547 | − | 0.191224i | \(-0.938754\pi\) | ||
0.981547 | − | 0.191224i | \(-0.0612455\pi\) | |||||||
\(864\) | −503.395 | −0.582633 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 597.646 | 0.690122 | ||||||||
\(867\) | 582.371i | 0.671708i | ||||||||
\(868\) | 189.870i | 0.218745i | ||||||||
\(869\) | 244.605i | 0.281479i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 544.772 | 0.625455 | ||||||||
\(872\) | −825.773 | −0.946987 | ||||||||
\(873\) | − | 130.098i | − | 0.149024i | ||||||
\(874\) | 324.618 | − | 496.170i | 0.371417 | − | 0.567700i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 646.110i | − | 0.737568i | ||||||
\(877\) | 415.606i | 0.473895i | 0.971522 | + | 0.236947i | \(0.0761469\pi\) | ||||
−0.971522 | + | 0.236947i | \(0.923853\pi\) | |||||||
\(878\) | −611.618 | −0.696604 | ||||||||
\(879\) | 108.424 | 0.123350 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1411.11 | −1.60172 | −0.800859 | − | 0.598854i | \(-0.795623\pi\) | ||||
−0.800859 | + | 0.598854i | \(0.795623\pi\) | |||||||
\(882\) | 4.46426i | 0.00506152i | ||||||||
\(883\) | −811.984 | −0.919574 | −0.459787 | − | 0.888029i | \(-0.652074\pi\) | ||||
−0.459787 | + | 0.888029i | \(0.652074\pi\) | |||||||
\(884\) | 140.456i | 0.158887i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 549.353i | 0.620038i | ||||||||
\(887\) | 534.735i | 0.602858i | 0.953489 | + | 0.301429i | \(0.0974636\pi\) | ||||
−0.953489 | + | 0.301429i | \(0.902536\pi\) | |||||||
\(888\) | − | 764.161i | − | 0.860542i | ||||||
\(889\) | 1148.68i | 1.29210i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −225.473 | −0.253056 | ||||||||
\(892\) | 247.569i | 0.277544i | ||||||||
\(893\) | −541.911 | − | 354.544i | −0.606843 | − | 0.397026i | ||||
\(894\) | −46.9016 | −0.0524626 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 119.472i | 0.133340i | ||||||||
\(897\) | 517.014 | 0.576382 | ||||||||
\(898\) | −438.829 | −0.488674 | ||||||||
\(899\) | 675.492 | 0.751381 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 233.770i | − | 0.259456i | ||||||
\(902\) | −214.606 | −0.237922 | ||||||||
\(903\) | 1106.65i | 1.22552i | ||||||||
\(904\) | −962.448 | −1.06465 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1380.48i | 1.52371i | ||||||||
\(907\) | − | 634.240i | − | 0.699272i | −0.936886 | − | 0.349636i | \(-0.886305\pi\) | ||
0.936886 | − | 0.349636i | \(-0.113695\pi\) | |||||||
\(908\) | − | 573.547i | − | 0.631660i | ||||||
\(909\) | −733.172 | −0.806569 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 931.405i | 1.02240i | 0.859462 | + | 0.511199i | \(0.170799\pi\) | ||||
−0.859462 | + | 0.511199i | \(0.829201\pi\) | |||||||
\(912\) | 197.736 | − | 302.234i | 0.216816 | − | 0.331397i | ||||
\(913\) | −279.519 | −0.306155 | ||||||||
\(914\) | 163.605i | 0.178999i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −404.764 | −0.441882 | ||||||||
\(917\) | −865.374 | −0.943702 | ||||||||
\(918\) | 313.567 | 0.341576 | ||||||||
\(919\) | 596.055 | 0.648591 | 0.324295 | − | 0.945956i | \(-0.394873\pi\) | ||||
0.324295 | + | 0.945956i | \(0.394873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 763.318 | 0.828793 | ||||||||
\(922\) | − | 1020.53i | − | 1.10687i | ||||||
\(923\) | −184.586 | −0.199985 | ||||||||
\(924\) | 102.977i | 0.111447i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 678.182i | − | 0.732378i | ||||||
\(927\) | 177.449i | 0.191422i | ||||||||
\(928\) | 1215.98 | 1.31033 | ||||||||
\(929\) | −953.514 | −1.02639 | −0.513194 | − | 0.858273i | \(-0.671538\pi\) | ||||
−0.513194 | + | 0.858273i | \(0.671538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.1716 | − | 8.61748i | −0.0141478 | − | 0.00925615i | ||||
\(932\) | 629.455 | 0.675381 | ||||||||
\(933\) | − | 634.489i | − | 0.680053i | ||||||
\(934\) | 856.984i | 0.917542i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 215.539 | 0.230277 | ||||||||
\(937\) | −248.360 | −0.265058 | −0.132529 | − | 0.991179i | \(-0.542310\pi\) | ||||
−0.132529 | + | 0.991179i | \(0.542310\pi\) | |||||||
\(938\) | −825.773 | −0.880355 | ||||||||
\(939\) | − | 1342.14i | − | 1.42933i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 736.899i | − | 0.783102i | −0.920156 | − | 0.391551i | \(-0.871939\pi\) | ||
0.920156 | − | 0.391551i | \(-0.128061\pi\) | |||||||
\(942\) | 1146.14 | 1.21671 | ||||||||
\(943\) | 1375.16i | 1.45828i | ||||||||
\(944\) | 369.992i | 0.391940i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 145.631i | − | 0.153944i | ||||||
\(947\) | 257.547 | 0.271961 | 0.135980 | − | 0.990712i | \(-0.456582\pi\) | ||||
0.135980 | + | 0.990712i | \(0.456582\pi\) | |||||||
\(948\) | 709.490 | 0.748407 | ||||||||
\(949\) | − | 681.625i | − | 0.718256i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1596.72 | −1.67899 | ||||||||
\(952\) | − | 678.673i | − | 0.712892i | ||||||
\(953\) | − | 251.242i | − | 0.263633i | −0.991274 | − | 0.131816i | \(-0.957919\pi\) | ||
0.991274 | − | 0.131816i | \(-0.0420809\pi\) | |||||||
\(954\) | −112.538 | −0.117965 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 738.365 | 0.772349 | ||||||||
\(957\) | 366.355 | 0.382816 | ||||||||
\(958\) | − | 428.363i | − | 0.447143i | ||||||
\(959\) | −467.629 | −0.487621 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 744.588 | 0.774805 | ||||||||
\(962\) | − | 252.901i | − | 0.262891i | ||||||
\(963\) | 633.016i | 0.657337i | ||||||||
\(964\) | 427.663i | 0.443634i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −783.698 | −0.811281 | ||||||||
\(967\) | 1508.95 | 1.56044 | 0.780221 | − | 0.625504i | \(-0.215107\pi\) | ||||
0.780221 | + | 0.625504i | \(0.215107\pi\) | |||||||
\(968\) | 996.062i | 1.02899i | ||||||||
\(969\) | 414.259 | − | 633.183i | 0.427512 | − | 0.653440i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 701.690i | 0.722647i | 0.932441 | + | 0.361323i | \(0.117675\pi\) | ||||
−0.932441 | + | 0.361323i | \(0.882325\pi\) | |||||||
\(972\) | 341.187i | 0.351016i | ||||||||
\(973\) | −1243.72 | −1.27823 | ||||||||
\(974\) | 592.701 | 0.608522 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −125.106 | −0.128182 | ||||||||
\(977\) | 485.382i | 0.496809i | 0.968656 | + | 0.248405i | \(0.0799062\pi\) | ||||
−0.968656 | + | 0.248405i | \(0.920094\pi\) | |||||||
\(978\) | 297.600 | 0.304294 | ||||||||
\(979\) | − | 192.288i | − | 0.196413i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 351.584i | 0.358394i | ||||||||
\(982\) | 837.347i | 0.852696i | ||||||||
\(983\) | 1015.25i | 1.03281i | 0.856344 | + | 0.516406i | \(0.172731\pi\) | ||||
−0.856344 | + | 0.516406i | \(0.827269\pi\) | |||||||
\(984\) | 1984.25i | 2.01651i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −757.442 | −0.768197 | ||||||||
\(987\) | 855.945i | 0.867219i | ||||||||
\(988\) | −130.522 | + | 199.499i | −0.132107 | + | 0.201922i | ||||
\(989\) | −933.183 | −0.943562 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 93.4931i | − | 0.0943422i | −0.998887 | − | 0.0471711i | \(-0.984979\pi\) | ||
0.998887 | − | 0.0471711i | \(-0.0150206\pi\) | |||||||
\(992\) | −389.574 | −0.392715 | ||||||||
\(993\) | 2101.98 | 2.11680 | ||||||||
\(994\) | 279.798 | 0.281487 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 810.760i | 0.814016i | ||||||||
\(997\) | 1088.79 | 1.09206 | 0.546032 | − | 0.837764i | \(-0.316138\pi\) | ||||
0.546032 | + | 0.837764i | \(0.316138\pi\) | |||||||
\(998\) | − | 790.212i | − | 0.791796i | ||||||
\(999\) | 475.383 | 0.475859 |
(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 | 475.3.c.f.151.3 | 8 | ||
5.2 | odd | 4 | 95.3.d.d.94.5 | yes | 8 | ||
5.3 | odd | 4 | 95.3.d.d.94.4 | yes | 8 | ||
5.4 | even | 2 | inner | 475.3.c.f.151.6 | 8 | ||
15.2 | even | 4 | 855.3.g.g.379.4 | 8 | |||
15.8 | even | 4 | 855.3.g.g.379.5 | 8 | |||
19.18 | odd | 2 | inner | 475.3.c.f.151.5 | 8 | ||
95.18 | even | 4 | 95.3.d.d.94.6 | yes | 8 | ||
95.37 | even | 4 | 95.3.d.d.94.3 | ✓ | 8 | ||
95.94 | odd | 2 | inner | 475.3.c.f.151.4 | 8 | ||
285.113 | odd | 4 | 855.3.g.g.379.3 | 8 | |||
285.227 | odd | 4 | 855.3.g.g.379.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.3.d.d.94.3 | ✓ | 8 | 95.37 | even | 4 | ||
95.3.d.d.94.4 | yes | 8 | 5.3 | odd | 4 | ||
95.3.d.d.94.5 | yes | 8 | 5.2 | odd | 4 | ||
95.3.d.d.94.6 | yes | 8 | 95.18 | even | 4 | ||
475.3.c.f.151.3 | 8 | 1.1 | even | 1 | trivial | ||
475.3.c.f.151.4 | 8 | 95.94 | odd | 2 | inner | ||
475.3.c.f.151.5 | 8 | 19.18 | odd | 2 | inner | ||
475.3.c.f.151.6 | 8 | 5.4 | even | 2 | inner | ||
855.3.g.g.379.3 | 8 | 285.113 | odd | 4 | |||
855.3.g.g.379.4 | 8 | 15.2 | even | 4 | |||
855.3.g.g.379.5 | 8 | 15.8 | even | 4 | |||
855.3.g.g.379.6 | 8 | 285.227 | odd | 4 |