Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,54,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 54, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 54);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 54 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(160.112796847\) |
Analytic rank: | \(0\) |
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: | \( x^{4} - x^{3} - 2315873743412x^{2} - 421178019174503472x + 612167648493870378955584 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{27}\cdot 3^{11}\cdot 5^{3}\cdot 7\cdot 13 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(447512.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58420e7 | −0.272290 | −0.136145 | − | 0.990689i | \(-0.543471\pi\) | ||||
−0.136145 | + | 0.990689i | \(0.543471\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.33939e15 | −0.925858 | ||||||||
\(5\) | −5.38136e18 | −1.61505 | −0.807527 | − | 0.589831i | \(-0.799194\pi\) | ||||
−0.807527 | + | 0.589831i | \(0.799194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.33436e22 | 0.939874 | 0.469937 | − | 0.882700i | \(-0.344277\pi\) | ||||
0.469937 | + | 0.882700i | \(0.344277\pi\) | |||||||
\(8\) | 4.48271e23 | 0.524392 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.39065e26 | 0.439763 | ||||||||
\(11\) | 3.50807e27 | 0.887487 | 0.443744 | − | 0.896154i | \(-0.353650\pi\) | ||||
0.443744 | + | 0.896154i | \(0.353650\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.76599e28 | −0.113862 | −0.0569312 | − | 0.998378i | \(-0.518132\pi\) | ||||
−0.0569312 | + | 0.998378i | \(0.518132\pi\) | |||||||
\(14\) | −6.03245e29 | −0.255918 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.35303e31 | 0.783072 | ||||||||
\(17\) | 5.80067e32 | 1.43411 | 0.717053 | − | 0.697018i | \(-0.245490\pi\) | ||||
0.717053 | + | 0.697018i | \(0.245490\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.40144e33 | −1.21962 | −0.609809 | − | 0.792548i | \(-0.708754\pi\) | ||||
−0.609809 | + | 0.792548i | \(0.708754\pi\) | |||||||
\(20\) | 4.48772e34 | 1.49531 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.06556e34 | −0.241654 | ||||||||
\(23\) | 5.69353e35 | 0.467298 | 0.233649 | − | 0.972321i | \(-0.424933\pi\) | ||||
0.233649 | + | 0.972321i | \(0.424933\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.78568e37 | 1.60840 | ||||||||
\(26\) | 9.73207e35 | 0.0310035 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.94671e38 | −0.870190 | ||||||||
\(29\) | 2.46957e38 | 0.435587 | 0.217794 | − | 0.975995i | \(-0.430114\pi\) | ||||
0.217794 | + | 0.975995i | \(0.430114\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.25695e39 | −1.28237 | −0.641185 | − | 0.767386i | \(-0.721557\pi\) | ||||
−0.641185 | + | 0.767386i | \(0.721557\pi\) | |||||||
\(32\) | −5.67942e39 | −0.737614 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.49901e40 | −0.390493 | ||||||||
\(35\) | −1.25620e41 | −1.51795 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.85991e41 | −1.62385 | −0.811924 | − | 0.583764i | \(-0.801580\pi\) | ||||
−0.811924 | + | 0.583764i | \(0.801580\pi\) | |||||||
\(38\) | 2.42952e41 | 0.332090 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.41231e42 | −0.846920 | ||||||||
\(41\) | −5.37725e42 | −0.981269 | −0.490634 | − | 0.871366i | \(-0.663235\pi\) | ||||
−0.490634 | + | 0.871366i | \(0.663235\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.54488e43 | 0.797961 | 0.398981 | − | 0.916959i | \(-0.369364\pi\) | ||||
0.398981 | + | 0.916959i | \(0.369364\pi\) | |||||||
\(44\) | −2.92552e43 | −0.821687 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.47132e43 | −0.127241 | ||||||||
\(47\) | 1.14085e44 | 0.557999 | 0.279000 | − | 0.960291i | \(-0.409997\pi\) | ||||
0.279000 | + | 0.960291i | \(0.409997\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.19501e43 | −0.116637 | ||||||||
\(50\) | −4.61455e44 | −0.437950 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.14060e44 | 0.105420 | ||||||||
\(53\) | −8.51129e44 | −0.172459 | −0.0862293 | − | 0.996275i | \(-0.527482\pi\) | ||||
−0.0862293 | + | 0.996275i | \(0.527482\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.88782e46 | −1.43334 | ||||||||
\(56\) | 1.04643e46 | 0.492862 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.38187e45 | −0.118606 | ||||||||
\(59\) | 9.48774e46 | 1.12095 | 0.560473 | − | 0.828173i | \(-0.310620\pi\) | ||||
0.560473 | + | 0.828173i | \(0.310620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.37366e47 | 1.64764 | 0.823818 | − | 0.566854i | \(-0.191840\pi\) | ||||
0.823818 | + | 0.566854i | \(0.191840\pi\) | |||||||
\(62\) | 1.10008e47 | 0.349176 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.25463e47 | −0.582227 | ||||||||
\(65\) | 2.02661e47 | 0.183894 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.70994e48 | −1.50794 | −0.753971 | − | 0.656908i | \(-0.771864\pi\) | ||||
−0.753971 | + | 0.656908i | \(0.771864\pi\) | |||||||
\(68\) | −4.83740e48 | −1.32778 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.24628e48 | 0.413321 | ||||||||
\(71\) | −2.16582e48 | −0.189355 | −0.0946774 | − | 0.995508i | \(-0.530182\pi\) | ||||
−0.0946774 | + | 0.995508i | \(0.530182\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.03616e49 | −0.433882 | −0.216941 | − | 0.976185i | \(-0.569608\pi\) | ||||
−0.216941 | + | 0.976185i | \(0.569608\pi\) | |||||||
\(74\) | 1.51432e49 | 0.442157 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.84022e49 | 1.12919 | ||||||||
\(77\) | 8.18910e49 | 0.834126 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.02034e49 | 0.259188 | 0.129594 | − | 0.991567i | \(-0.458633\pi\) | ||||
0.129594 | + | 0.991567i | \(0.458633\pi\) | |||||||
\(80\) | −3.41879e50 | −1.26470 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.38959e50 | 0.267189 | ||||||||
\(83\) | 3.18305e50 | 0.443889 | 0.221944 | − | 0.975059i | \(-0.428760\pi\) | ||||
0.221944 | + | 0.975059i | \(0.428760\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.12155e51 | −2.31616 | ||||||||
\(86\) | −3.99229e50 | −0.217277 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.57257e51 | 0.465391 | ||||||||
\(89\) | −3.04162e51 | −0.667222 | −0.333611 | − | 0.942711i | \(-0.608267\pi\) | ||||
−0.333611 | + | 0.942711i | \(0.608267\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.79117e50 | −0.107016 | ||||||||
\(92\) | −4.74806e51 | −0.432652 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.94817e51 | −0.151938 | ||||||||
\(95\) | 5.05925e52 | 1.96975 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.29374e52 | 0.962465 | 0.481232 | − | 0.876593i | \(-0.340189\pi\) | ||||
0.481232 | + | 0.876593i | \(0.340189\pi\) | |||||||
\(98\) | 1.85933e51 | 0.0317590 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.48915e53 | −1.48915 | ||||||||
\(101\) | −2.40879e53 | −1.85047 | −0.925236 | − | 0.379392i | \(-0.876133\pi\) | ||||
−0.925236 | + | 0.379392i | \(0.876133\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.77425e52 | 0.263821 | 0.131910 | − | 0.991262i | \(-0.457889\pi\) | ||||
0.131910 | + | 0.991262i | \(0.457889\pi\) | |||||||
\(104\) | −1.68818e52 | −0.0597084 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.19949e52 | 0.0469587 | ||||||||
\(107\) | 2.30554e53 | 0.383797 | 0.191899 | − | 0.981415i | \(-0.438535\pi\) | ||||
0.191899 | + | 0.981415i | \(0.438535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.84013e53 | 0.595142 | 0.297571 | − | 0.954700i | \(-0.403824\pi\) | ||||
0.297571 | + | 0.954700i | \(0.403824\pi\) | |||||||
\(110\) | 4.87850e53 | 0.390284 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.48303e54 | 0.735989 | ||||||||
\(113\) | 4.64679e53 | 0.182211 | 0.0911055 | − | 0.995841i | \(-0.470960\pi\) | ||||
0.0911055 | + | 0.995841i | \(0.470960\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.06389e54 | −0.754711 | ||||||||
\(116\) | −2.05947e54 | −0.403292 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.45182e54 | −0.305222 | ||||||||
\(119\) | 1.35408e55 | 1.34788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.31816e54 | −0.212366 | ||||||||
\(122\) | −8.71823e54 | −0.448634 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.55003e55 | 1.18729 | ||||||||
\(125\) | −3.63487e55 | −0.982593 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.05751e54 | 0.0187709 | 0.00938545 | − | 0.999956i | \(-0.497012\pi\) | ||||
0.00938545 | + | 0.999956i | \(0.497012\pi\) | |||||||
\(128\) | 6.21504e55 | 0.896149 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.23717e54 | −0.0500724 | ||||||||
\(131\) | −9.48285e55 | −0.740031 | −0.370015 | − | 0.929026i | \(-0.620648\pi\) | ||||
−0.370015 | + | 0.929026i | \(0.620648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.19463e56 | −1.14629 | ||||||||
\(134\) | 9.58722e55 | 0.410597 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.60027e56 | 0.752034 | ||||||||
\(137\) | −1.67624e56 | −0.399248 | −0.199624 | − | 0.979873i | \(-0.563972\pi\) | ||||
−0.199624 | + | 0.979873i | \(0.563972\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.36794e55 | −0.103301 | −0.0516507 | − | 0.998665i | \(-0.516448\pi\) | ||||
−0.0516507 | + | 0.998665i | \(0.516448\pi\) | |||||||
\(140\) | 1.04760e57 | 1.40540 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.59692e55 | 0.0515594 | ||||||||
\(143\) | −1.32113e56 | −0.101051 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.32897e57 | −0.703496 | ||||||||
\(146\) | 2.67765e56 | 0.118142 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.88681e57 | 1.50345 | ||||||||
\(149\) | −5.30162e55 | −0.0136450 | −0.00682249 | − | 0.999977i | \(-0.502172\pi\) | ||||
−0.00682249 | + | 0.999977i | \(0.502172\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.81438e56 | −0.0689500 | −0.0344750 | − | 0.999406i | \(-0.510976\pi\) | ||||
−0.0344750 | + | 0.999406i | \(0.510976\pi\) | |||||||
\(152\) | −4.21439e57 | −0.639557 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.11623e57 | −0.227124 | ||||||||
\(155\) | 2.29082e58 | 2.07110 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.25055e57 | −0.144860 | −0.0724298 | − | 0.997374i | \(-0.523075\pi\) | ||||
−0.0724298 | + | 0.997374i | \(0.523075\pi\) | |||||||
\(158\) | −1.29736e57 | −0.0705744 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.05630e58 | 1.19129 | ||||||||
\(161\) | 1.32907e58 | 0.439201 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.68137e58 | 1.35357 | 0.676786 | − | 0.736180i | \(-0.263372\pi\) | ||||
0.676786 | + | 0.736180i | \(0.263372\pi\) | |||||||
\(164\) | 4.48430e58 | 0.908516 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.22564e57 | −0.120866 | ||||||||
\(167\) | 5.90727e58 | 0.740288 | 0.370144 | − | 0.928974i | \(-0.379308\pi\) | ||||
0.370144 | + | 0.928974i | \(0.379308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.07977e59 | −0.987035 | ||||||||
\(170\) | 8.06670e58 | 0.630666 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.28834e59 | −0.738799 | ||||||||
\(173\) | −5.53658e58 | −0.272282 | −0.136141 | − | 0.990689i | \(-0.543470\pi\) | ||||
−0.136141 | + | 0.990689i | \(0.543470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.16842e59 | 1.51169 | ||||||||
\(176\) | 2.22869e59 | 0.694966 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.86016e58 | 0.181678 | ||||||||
\(179\) | 7.91775e59 | 1.57760 | 0.788799 | − | 0.614651i | \(-0.210703\pi\) | ||||
0.788799 | + | 0.614651i | \(0.210703\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.76480e59 | 1.00409 | 0.502045 | − | 0.864841i | \(-0.332581\pi\) | ||||
0.502045 | + | 0.864841i | \(0.332581\pi\) | |||||||
\(182\) | 2.27181e58 | 0.0291394 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.55224e59 | 0.245047 | ||||||||
\(185\) | 3.15343e60 | 2.62260 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.03491e60 | 1.27275 | ||||||||
\(188\) | −9.51396e59 | −0.516628 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.30741e60 | −0.536342 | ||||||||
\(191\) | −5.29979e59 | −0.189180 | −0.0945899 | − | 0.995516i | \(-0.530154\pi\) | ||||
−0.0945899 | + | 0.995516i | \(0.530154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.36608e59 | −0.253682 | −0.126841 | − | 0.991923i | \(-0.540484\pi\) | ||||
−0.126841 | + | 0.991923i | \(0.540484\pi\) | |||||||
\(194\) | −1.10959e60 | −0.262069 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.00020e59 | 0.107989 | ||||||||
\(197\) | 1.14277e61 | 1.79723 | 0.898615 | − | 0.438737i | \(-0.144574\pi\) | ||||
0.898615 | + | 0.438737i | \(0.144574\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.32212e59 | 0.0881110 | 0.0440555 | − | 0.999029i | \(-0.485972\pi\) | ||||
0.0440555 | + | 0.999029i | \(0.485972\pi\) | |||||||
\(200\) | 8.00468e60 | 0.843430 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.22480e60 | 0.503865 | ||||||||
\(203\) | 5.76487e60 | 0.409397 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.89369e61 | 1.58480 | ||||||||
\(206\) | −1.49218e60 | −0.0718357 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.39254e60 | −0.0891624 | ||||||||
\(209\) | −3.29809e61 | −1.08240 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.50377e61 | −1.91335 | −0.956676 | − | 0.291156i | \(-0.905960\pi\) | ||||
−0.956676 | + | 0.291156i | \(0.905960\pi\) | |||||||
\(212\) | 7.09790e60 | 0.159672 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.95797e60 | −0.104504 | ||||||||
\(215\) | −8.31358e61 | −1.28875 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.93724e61 | −1.20527 | ||||||||
\(218\) | −1.50921e61 | −0.162051 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.57433e62 | 1.32707 | ||||||||
\(221\) | −2.18452e61 | −0.163291 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.22197e61 | −0.0719419 | −0.0359710 | − | 0.999353i | \(-0.511452\pi\) | ||||
−0.0359710 | + | 0.999353i | \(0.511452\pi\) | |||||||
\(224\) | −1.32578e62 | −0.693264 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.20082e61 | −0.0496142 | ||||||||
\(227\) | 5.02981e61 | 0.184870 | 0.0924350 | − | 0.995719i | \(-0.470535\pi\) | ||||
0.0924350 | + | 0.995719i | \(0.470535\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.41310e62 | −0.994281 | −0.497140 | − | 0.867670i | \(-0.665617\pi\) | ||||
−0.497140 | + | 0.867670i | \(0.665617\pi\) | |||||||
\(230\) | 7.91771e61 | 0.205500 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.10704e62 | 0.228418 | ||||||||
\(233\) | −5.82407e62 | −1.07225 | −0.536123 | − | 0.844140i | \(-0.680112\pi\) | ||||
−0.536123 | + | 0.844140i | \(0.680112\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.13930e62 | −0.901198 | ||||||||
\(236\) | −7.91219e62 | −1.03784 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.49923e62 | −0.367014 | ||||||||
\(239\) | −1.01634e63 | −0.953879 | −0.476939 | − | 0.878936i | \(-0.658254\pi\) | ||||
−0.476939 | + | 0.878936i | \(0.658254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.10470e63 | 1.58394 | 0.791970 | − | 0.610560i | \(-0.209056\pi\) | ||||
0.791970 | + | 0.610560i | \(0.209056\pi\) | |||||||
\(242\) | 8.57480e61 | 0.0578252 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.81343e63 | −1.52548 | ||||||||
\(245\) | 3.87189e62 | 0.188374 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.54057e62 | 0.138868 | ||||||||
\(248\) | −1.90826e63 | −0.672464 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.39324e62 | 0.267550 | ||||||||
\(251\) | 3.46671e63 | 0.888309 | 0.444154 | − | 0.895950i | \(-0.353504\pi\) | ||||
0.444154 | + | 0.895950i | \(0.353504\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.99733e63 | 0.414721 | ||||||||
\(254\) | −2.73281e61 | −0.00511113 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.22614e63 | 0.338215 | ||||||||
\(257\) | 7.98120e63 | 1.09355 | 0.546777 | − | 0.837278i | \(-0.315854\pi\) | ||||
0.546777 | + | 0.837278i | \(0.315854\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.36791e64 | −1.52621 | ||||||||
\(260\) | −1.69007e63 | −0.170259 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.45056e63 | 0.201503 | ||||||||
\(263\) | 6.73466e63 | 0.500597 | 0.250299 | − | 0.968169i | \(-0.419471\pi\) | ||||
0.250299 | + | 0.968169i | \(0.419471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.58023e63 | 0.278530 | ||||||||
\(266\) | 5.67137e63 | 0.312122 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.09386e64 | 1.39614 | ||||||||
\(269\) | −1.44464e64 | −0.590640 | −0.295320 | − | 0.955398i | \(-0.595426\pi\) | ||||
−0.295320 | + | 0.955398i | \(0.595426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.71685e64 | 0.912810 | 0.456405 | − | 0.889772i | \(-0.349137\pi\) | ||||
0.456405 | + | 0.889772i | \(0.349137\pi\) | |||||||
\(272\) | 3.68518e64 | 1.12301 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.33175e63 | 0.108711 | ||||||||
\(275\) | 6.26429e64 | 1.42743 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.80661e64 | 0.527798 | 0.263899 | − | 0.964550i | \(-0.414991\pi\) | ||||
0.263899 | + | 0.964550i | \(0.414991\pi\) | |||||||
\(278\) | 1.64560e63 | 0.0281279 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.63119e64 | −0.795998 | ||||||||
\(281\) | 2.78031e64 | 0.357582 | 0.178791 | − | 0.983887i | \(-0.442781\pi\) | ||||
0.178791 | + | 0.983887i | \(0.442781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.35233e64 | −0.677006 | −0.338503 | − | 0.940965i | \(-0.609920\pi\) | ||||
−0.338503 | + | 0.940965i | \(0.609920\pi\) | |||||||
\(284\) | 1.80616e64 | 0.175316 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.41408e63 | 0.0275153 | ||||||||
\(287\) | −1.25524e65 | −0.922269 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.72874e65 | 1.05666 | ||||||||
\(290\) | 3.43432e64 | 0.191555 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.64095e64 | 0.401713 | ||||||||
\(293\) | 1.18763e65 | 0.504300 | 0.252150 | − | 0.967688i | \(-0.418862\pi\) | ||||
0.252150 | + | 0.967688i | \(0.418862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.10569e65 | −1.81039 | ||||||||
\(296\) | −2.62683e65 | −0.851532 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.37005e63 | 0.00371539 | ||||||||
\(299\) | −2.14418e64 | −0.0532076 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.60632e65 | 0.749983 | ||||||||
\(302\) | 9.85711e63 | 0.0187744 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.97276e65 | −0.955048 | ||||||||
\(305\) | −1.81549e66 | −2.66102 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.02441e65 | −0.126271 | −0.0631357 | − | 0.998005i | \(-0.520110\pi\) | ||||
−0.0631357 | + | 0.998005i | \(0.520110\pi\) | |||||||
\(308\) | −6.82921e65 | −0.772283 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.91993e65 | −0.563938 | ||||||||
\(311\) | 2.08869e66 | 1.82694 | 0.913469 | − | 0.406909i | \(-0.133393\pi\) | ||||
0.913469 | + | 0.406909i | \(0.133393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.41675e65 | 0.621183 | 0.310591 | − | 0.950543i | \(-0.399473\pi\) | ||||
0.310591 | + | 0.950543i | \(0.399473\pi\) | |||||||
\(314\) | 5.81587e64 | 0.0394438 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.18666e65 | −0.239972 | ||||||||
\(317\) | −1.89204e66 | −0.997378 | −0.498689 | − | 0.866781i | \(-0.666185\pi\) | ||||
−0.498689 | + | 0.866781i | \(0.666185\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.66344e65 | 0.386578 | ||||||||
\(320\) | 2.28957e66 | 0.940328 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.43460e65 | −0.119590 | ||||||||
\(323\) | −5.45346e66 | −1.74906 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.72484e65 | −0.183136 | ||||||||
\(326\) | −1.46818e66 | −0.368564 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.41046e66 | −0.514569 | ||||||||
\(329\) | 2.66314e66 | 0.524449 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.72579e66 | −0.624850 | −0.312425 | − | 0.949942i | \(-0.601141\pi\) | ||||
−0.312425 | + | 0.949942i | \(0.601141\pi\) | |||||||
\(332\) | −2.65447e66 | −0.410978 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.52656e66 | −0.201573 | ||||||||
\(335\) | 1.99645e67 | 2.43540 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.36606e66 | 0.975808 | 0.487904 | − | 0.872897i | \(-0.337762\pi\) | ||||
0.487904 | + | 0.872897i | \(0.337762\pi\) | |||||||
\(338\) | 2.79034e66 | 0.268760 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.60318e67 | 2.14443 | ||||||||
\(341\) | −1.49337e67 | −1.13809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.60796e67 | −1.04950 | ||||||||
\(344\) | 6.92526e66 | 0.418444 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.43076e66 | 0.0741397 | ||||||||
\(347\) | 2.74862e67 | 1.31942 | 0.659711 | − | 0.751520i | \(-0.270679\pi\) | ||||
0.659711 | + | 0.751520i | \(0.270679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.18632e67 | 0.489024 | 0.244512 | − | 0.969646i | \(-0.421372\pi\) | ||||
0.244512 | + | 0.969646i | \(0.421372\pi\) | |||||||
\(350\) | −1.07720e67 | −0.411618 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.99238e67 | −0.654623 | ||||||||
\(353\) | 2.74837e67 | 0.837618 | 0.418809 | − | 0.908074i | \(-0.362448\pi\) | ||||
0.418809 | + | 0.908074i | \(0.362448\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.16551e67 | 0.305818 | ||||||||
\(356\) | 2.53653e67 | 0.617753 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.04610e67 | −0.429564 | ||||||||
\(359\) | −3.20694e67 | −0.625299 | −0.312649 | − | 0.949869i | \(-0.601216\pi\) | ||||
−0.312649 | + | 0.949869i | \(0.601216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.89659e67 | 0.487468 | ||||||||
\(362\) | −1.74816e67 | −0.273404 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.33130e66 | 0.0990819 | ||||||||
\(365\) | 5.57595e67 | 0.700742 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.14979e67 | 0.668666 | 0.334333 | − | 0.942455i | \(-0.391489\pi\) | ||||
0.334333 | + | 0.942455i | \(0.391489\pi\) | |||||||
\(368\) | 3.61712e67 | 0.365928 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.14909e67 | −0.714107 | ||||||||
\(371\) | −1.98684e67 | −0.162089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.08656e68 | 0.768723 | 0.384362 | − | 0.923183i | \(-0.374422\pi\) | ||||
0.384362 | + | 0.923183i | \(0.374422\pi\) | |||||||
\(374\) | −5.25863e67 | −0.346557 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.11408e67 | 0.292610 | ||||||||
\(377\) | −9.30038e66 | −0.0495970 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.80807e68 | −1.30158 | −0.650788 | − | 0.759259i | \(-0.725561\pi\) | ||||
−0.650788 | + | 0.759259i | \(0.725561\pi\) | |||||||
\(380\) | −4.21911e68 | −1.82371 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.36957e67 | 0.0515117 | ||||||||
\(383\) | −4.61965e68 | −1.62122 | −0.810610 | − | 0.585586i | \(-0.800864\pi\) | ||||
−0.810610 | + | 0.585586i | \(0.800864\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.40685e68 | −1.34716 | ||||||||
\(386\) | 2.42038e67 | 0.0690749 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.58072e68 | −0.891106 | ||||||||
\(389\) | 3.34377e68 | 0.777271 | 0.388636 | − | 0.921392i | \(-0.372947\pi\) | ||||
0.388636 | + | 0.921392i | \(0.372947\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.30263e68 | 0.670155 | ||||||||
\(392\) | −3.22531e67 | −0.0611633 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.95315e68 | −0.489368 | ||||||||
\(395\) | −2.70163e68 | −0.418603 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.89097e68 | 0.391827 | 0.195914 | − | 0.980621i | \(-0.437233\pi\) | ||||
0.195914 | + | 0.980621i | \(0.437233\pi\) | |||||||
\(398\) | −1.89218e67 | −0.0239917 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.13445e69 | 1.25949 | ||||||||
\(401\) | −4.66806e67 | −0.0485077 | −0.0242538 | − | 0.999706i | \(-0.507721\pi\) | ||||
−0.0242538 | + | 0.999706i | \(0.507721\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.60316e68 | 0.146014 | ||||||||
\(404\) | 2.00878e69 | 1.71327 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.48976e68 | −0.111475 | ||||||||
\(407\) | −2.05570e69 | −1.44114 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.42643e68 | −0.334077 | −0.167039 | − | 0.985950i | \(-0.553420\pi\) | ||||
−0.167039 | + | 0.985950i | \(0.553420\pi\) | |||||||
\(410\) | −7.47788e68 | −0.431525 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.81537e68 | −0.244261 | ||||||||
\(413\) | 2.21478e69 | 1.05355 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.71291e69 | −0.716904 | ||||||||
\(416\) | 2.13886e68 | 0.0839864 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.52293e68 | 0.294725 | ||||||||
\(419\) | −2.80482e69 | −0.910403 | −0.455202 | − | 0.890388i | \(-0.650433\pi\) | ||||
−0.455202 | + | 0.890388i | \(0.650433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.47945e69 | 1.28159 | 0.640795 | − | 0.767712i | \(-0.278605\pi\) | ||||
0.640795 | + | 0.767712i | \(0.278605\pi\) | |||||||
\(422\) | 1.93913e69 | 0.520986 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.81536e68 | −0.0904359 | ||||||||
\(425\) | 1.03581e70 | 2.30661 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.87535e69 | 1.54857 | ||||||||
\(428\) | −1.92268e69 | −0.355342 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.14840e69 | 0.350914 | ||||||||
\(431\) | 1.07297e70 | 1.64793 | 0.823967 | − | 0.566638i | \(-0.191756\pi\) | ||||
0.823967 | + | 0.566638i | \(0.191756\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.28857e70 | −1.75057 | −0.875286 | − | 0.483606i | \(-0.839327\pi\) | ||||
−0.875286 | + | 0.483606i | \(0.839327\pi\) | |||||||
\(434\) | 2.56798e69 | 0.328182 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.87031e69 | −0.551017 | ||||||||
\(437\) | −5.35274e69 | −0.569925 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.10965e69 | 0.199022 | 0.0995111 | − | 0.995036i | \(-0.468272\pi\) | ||||
0.0995111 | + | 0.995036i | \(0.468272\pi\) | |||||||
\(440\) | −8.46254e69 | −0.751631 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.64525e68 | 0.0444624 | ||||||||
\(443\) | −1.77505e70 | −1.31678 | −0.658389 | − | 0.752678i | \(-0.728762\pi\) | ||||
−0.658389 | + | 0.752678i | \(0.728762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.63681e70 | 1.07760 | ||||||||
\(446\) | 3.15782e68 | 0.0195891 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.93183e69 | −0.547220 | ||||||||
\(449\) | 7.87557e69 | 0.409029 | 0.204515 | − | 0.978864i | \(-0.434438\pi\) | ||||
0.204515 | + | 0.978864i | \(0.434438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.88638e70 | −0.870863 | ||||||||
\(452\) | −3.87514e69 | −0.168702 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.29980e69 | −0.0503382 | ||||||||
\(455\) | 4.73084e69 | 0.172837 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.48981e70 | 1.13507 | 0.567536 | − | 0.823349i | \(-0.307897\pi\) | ||||
0.567536 | + | 0.823349i | \(0.307897\pi\) | |||||||
\(458\) | 8.82014e69 | 0.270733 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.55510e70 | 0.698756 | ||||||||
\(461\) | −4.79728e70 | −1.23857 | −0.619286 | − | 0.785166i | \(-0.712578\pi\) | ||||
−0.619286 | + | 0.785166i | \(0.712578\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.09571e70 | −1.17303 | −0.586514 | − | 0.809939i | \(-0.699500\pi\) | ||||
−0.586514 | + | 0.809939i | \(0.699500\pi\) | |||||||
\(464\) | 1.56893e70 | 0.341096 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.50506e70 | 0.291962 | ||||||||
\(467\) | −8.74085e70 | −1.60198 | −0.800989 | − | 0.598680i | \(-0.795692\pi\) | ||||
−0.800989 | + | 0.598680i | \(0.795692\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.66033e70 | −1.41727 | ||||||||
\(470\) | 1.58652e70 | 0.245387 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.25307e70 | 0.587814 | ||||||||
\(473\) | 5.41956e70 | 0.708181 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.67879e71 | −1.96163 | ||||||||
\(476\) | −1.12922e71 | −1.24795 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.62642e70 | 0.259732 | ||||||||
\(479\) | 9.38882e70 | 0.878455 | 0.439228 | − | 0.898376i | \(-0.355252\pi\) | ||||
0.439228 | + | 0.898376i | \(0.355252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.20683e70 | 0.184895 | ||||||||
\(482\) | −5.43897e70 | −0.431291 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.76715e70 | 0.196621 | ||||||||
\(485\) | −2.31062e71 | −1.55443 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.27176e71 | 1.97362 | 0.986810 | − | 0.161885i | \(-0.0517573\pi\) | ||||
0.986810 | + | 0.161885i | \(0.0517573\pi\) | |||||||
\(488\) | 1.51232e71 | 0.864006 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.00057e70 | −0.0512924 | ||||||||
\(491\) | 2.76660e71 | 1.34365 | 0.671826 | − | 0.740709i | \(-0.265510\pi\) | ||||
0.671826 | + | 0.740709i | \(0.265510\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.43252e71 | 0.624679 | ||||||||
\(494\) | −9.14954e69 | −0.0378125 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.70445e71 | −1.00419 | ||||||||
\(497\) | −5.05580e70 | −0.177970 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.81364e71 | −1.52338 | −0.761692 | − | 0.647939i | \(-0.775631\pi\) | ||||
−0.761692 | + | 0.647939i | \(0.775631\pi\) | |||||||
\(500\) | 3.03126e71 | 0.909742 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.95868e70 | −0.241877 | ||||||||
\(503\) | 4.97279e71 | 1.27364 | 0.636822 | − | 0.771011i | \(-0.280249\pi\) | ||||
0.636822 | + | 0.771011i | \(0.280249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.29626e72 | 2.98861 | ||||||||
\(506\) | −5.16150e70 | −0.112924 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.81898e69 | −0.0173792 | ||||||||
\(509\) | 4.86664e71 | 0.910349 | 0.455174 | − | 0.890402i | \(-0.349577\pi\) | ||||
0.455174 | + | 0.890402i | \(0.349577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.41877e71 | −0.407794 | ||||||||
\(512\) | −6.17329e71 | −0.988241 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.06250e71 | −0.297764 | ||||||||
\(515\) | −3.10733e71 | −0.426084 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00217e71 | 0.495217 | ||||||||
\(518\) | 3.53496e71 | 0.415572 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.08471e70 | 0.0964323 | ||||||||
\(521\) | 1.04553e72 | 1.05472 | 0.527358 | − | 0.849643i | \(-0.323183\pi\) | ||||
0.527358 | + | 0.849643i | \(0.323183\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.01240e71 | −0.183408 | −0.0917042 | − | 0.995786i | \(-0.529231\pi\) | ||||
−0.0917042 | + | 0.995786i | \(0.529231\pi\) | |||||||
\(524\) | 7.90812e71 | 0.685163 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.74037e71 | −0.136308 | ||||||||
\(527\) | −2.46931e72 | −1.83906 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.16032e72 | −0.781633 | ||||||||
\(530\) | −1.18362e71 | −0.0758409 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.83019e72 | 1.06130 | ||||||||
\(533\) | 2.02506e71 | 0.111730 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.24069e72 | −0.619853 | ||||||||
\(536\) | −1.66306e72 | −0.790752 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.73323e71 | 0.160825 | ||||||||
\(539\) | −2.52406e71 | −0.103514 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.67923e72 | −0.996053 | −0.498026 | − | 0.867162i | \(-0.665942\pi\) | ||||
−0.498026 | + | 0.867162i | \(0.665942\pi\) | |||||||
\(542\) | −7.02090e71 | −0.248549 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.29444e72 | −1.05782 | ||||||||
\(545\) | −3.14278e72 | −0.961186 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.99196e72 | 1.10795 | 0.553977 | − | 0.832532i | \(-0.313110\pi\) | ||||
0.553977 | + | 0.832532i | \(0.313110\pi\) | |||||||
\(548\) | 1.39789e72 | 0.369647 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.61882e72 | −0.388675 | ||||||||
\(551\) | −2.32175e72 | −0.531250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.17193e72 | 0.243604 | ||||||||
\(554\) | −7.25284e71 | −0.143714 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.31047e71 | 0.0956425 | ||||||||
\(557\) | 4.75050e72 | 0.815786 | 0.407893 | − | 0.913030i | \(-0.366264\pi\) | ||||
0.407893 | + | 0.913030i | \(0.366264\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.81801e71 | −0.0908577 | ||||||||
\(560\) | −7.98070e72 | −1.18866 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.18488e71 | −0.0973660 | ||||||||
\(563\) | −2.08122e72 | −0.269058 | −0.134529 | − | 0.990910i | \(-0.542952\pi\) | ||||
−0.134529 | + | 0.990910i | \(0.542952\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.50061e72 | −0.294280 | ||||||||
\(566\) | 1.64157e72 | 0.184342 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.70874e71 | −0.0992961 | ||||||||
\(569\) | 8.16033e72 | 0.796586 | 0.398293 | − | 0.917258i | \(-0.369603\pi\) | ||||
0.398293 | + | 0.917258i | \(0.369603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.30282e72 | −0.471683 | −0.235841 | − | 0.971792i | \(-0.575785\pi\) | ||||
−0.235841 | + | 0.971792i | \(0.575785\pi\) | |||||||
\(572\) | 1.10175e72 | 0.0935592 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.24380e72 | 0.251124 | ||||||||
\(575\) | 1.01668e73 | 0.751601 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.14077e73 | 1.44348 | 0.721740 | − | 0.692164i | \(-0.243343\pi\) | ||||
0.721740 | + | 0.692164i | \(0.243343\pi\) | |||||||
\(578\) | −4.46741e72 | −0.287718 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.10828e73 | 0.651338 | ||||||||
\(581\) | 7.43039e72 | 0.417200 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.98582e72 | −0.153055 | ||||||||
\(584\) | −4.64481e72 | −0.227524 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.06907e72 | −0.137316 | ||||||||
\(587\) | 1.26033e73 | 0.538981 | 0.269490 | − | 0.963003i | \(-0.413145\pi\) | ||||
0.269490 | + | 0.963003i | \(0.413145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00214e73 | 1.56400 | ||||||||
\(590\) | 1.31941e73 | 0.492950 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.72282e73 | −1.27159 | ||||||||
\(593\) | 3.38540e73 | 1.10576 | 0.552880 | − | 0.833261i | \(-0.313529\pi\) | ||||
0.552880 | + | 0.833261i | \(0.313529\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.28681e73 | −2.17690 | ||||||||
\(596\) | 4.42123e71 | 0.0126333 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.54098e71 | 0.0144879 | ||||||||
\(599\) | −4.50976e73 | −1.12809 | −0.564043 | − | 0.825745i | \(-0.690755\pi\) | ||||
−0.564043 | + | 0.825745i | \(0.690755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.21159e73 | 1.19343 | 0.596714 | − | 0.802454i | \(-0.296473\pi\) | ||||
0.596714 | + | 0.802454i | \(0.296473\pi\) | |||||||
\(602\) | −9.31944e72 | −0.204213 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.18096e72 | 0.0638379 | ||||||||
\(605\) | 1.78562e73 | 0.342983 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.40353e72 | 0.0247015 | 0.0123507 | − | 0.999924i | \(-0.496069\pi\) | ||||
0.0123507 | + | 0.999924i | \(0.496069\pi\) | |||||||
\(608\) | 5.33947e73 | 0.899607 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.69159e73 | 0.724569 | ||||||||
\(611\) | −4.29641e72 | −0.0635351 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.09089e73 | 1.23283 | 0.616416 | − | 0.787421i | \(-0.288584\pi\) | ||||
0.616416 | + | 0.787421i | \(0.288584\pi\) | |||||||
\(614\) | 2.64727e72 | 0.0343824 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.67093e73 | 0.437409 | ||||||||
\(617\) | 1.15906e74 | 1.32297 | 0.661486 | − | 0.749957i | \(-0.269926\pi\) | ||||
0.661486 | + | 0.749957i | \(0.269926\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.53802e74 | −1.61124 | −0.805621 | − | 0.592432i | \(-0.798168\pi\) | ||||
−0.805621 | + | 0.592432i | \(0.798168\pi\) | |||||||
\(620\) | −1.91040e74 | −1.91754 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.39760e73 | −0.497457 | ||||||||
\(623\) | −7.10024e73 | −0.627104 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.64476e72 | −0.0214568 | ||||||||
\(626\) | −2.17506e73 | −0.169142 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.87682e73 | 0.134119 | ||||||||
\(629\) | −3.39914e74 | −2.32877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.90940e74 | −1.20259 | −0.601297 | − | 0.799025i | \(-0.705349\pi\) | ||||
−0.601297 | + | 0.799025i | \(0.705349\pi\) | |||||||
\(632\) | 2.25047e73 | 0.135916 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.88941e73 | 0.271576 | ||||||||
\(635\) | −5.69083e72 | −0.0303160 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.70963e72 | 0.0132805 | ||||||||
\(638\) | −2.23881e73 | −0.105261 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.34454e74 | −1.44733 | ||||||||
\(641\) | 2.13596e74 | 0.886860 | 0.443430 | − | 0.896309i | \(-0.353761\pi\) | ||||
0.443430 | + | 0.896309i | \(0.353761\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.06521e74 | 0.407235 | 0.203617 | − | 0.979051i | \(-0.434730\pi\) | ||||
0.203617 | + | 0.979051i | \(0.434730\pi\) | |||||||
\(644\) | −1.10837e74 | −0.406638 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.40928e74 | 0.476252 | ||||||||
\(647\) | 3.74264e74 | 1.21399 | 0.606995 | − | 0.794706i | \(-0.292375\pi\) | ||||
0.606995 | + | 0.794706i | \(0.292375\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.32836e74 | 0.994824 | ||||||||
\(650\) | 1.73783e73 | 0.0498660 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.73791e74 | −1.25322 | ||||||||
\(653\) | 5.40144e73 | 0.137186 | 0.0685930 | − | 0.997645i | \(-0.478149\pi\) | ||||
0.0685930 | + | 0.997645i | \(0.478149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.10306e74 | 1.19519 | ||||||||
\(656\) | −3.41618e74 | −0.768404 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.88210e73 | −0.142802 | ||||||||
\(659\) | −7.60313e74 | −1.51541 | −0.757703 | − | 0.652599i | \(-0.773678\pi\) | ||||
−0.757703 | + | 0.652599i | \(0.773678\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.63286e72 | −0.00484272 | −0.00242136 | − | 0.999997i | \(-0.500771\pi\) | ||||
−0.00242136 | + | 0.999997i | \(0.500771\pi\) | |||||||
\(662\) | 9.62818e73 | 0.170140 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.42687e74 | 0.232772 | ||||||||
\(665\) | 1.18101e75 | 1.85131 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.40606e74 | 0.203549 | ||||||||
\(668\) | −4.92630e74 | −0.685401 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.15923e74 | −0.663136 | ||||||||
\(671\) | 1.18351e75 | 1.46226 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.59799e74 | −0.753378 | −0.376689 | − | 0.926340i | \(-0.622937\pi\) | ||||
−0.376689 | + | 0.926340i | \(0.622937\pi\) | |||||||
\(674\) | −2.42038e74 | −0.265703 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.00460e74 | 0.913855 | ||||||||
\(677\) | 9.68261e74 | 0.944915 | 0.472457 | − | 0.881354i | \(-0.343367\pi\) | ||||
0.472457 | + | 0.881354i | \(0.343367\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.00231e75 | 0.904596 | ||||||||
\(680\) | −1.39930e75 | −1.21457 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.85916e74 | 0.309890 | ||||||||
\(683\) | 2.38917e75 | 1.84543 | 0.922715 | − | 0.385483i | \(-0.125965\pi\) | ||||
0.922715 | + | 0.385483i | \(0.125965\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.02047e74 | 0.644806 | ||||||||
\(686\) | 4.15530e74 | 0.285768 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.81470e74 | 0.624861 | ||||||||
\(689\) | 3.20534e73 | 0.0196365 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.74982e74 | −0.156004 | −0.0780020 | − | 0.996953i | \(-0.524854\pi\) | ||||
−0.0780020 | + | 0.996953i | \(0.524854\pi\) | |||||||
\(692\) | 4.61717e74 | 0.252095 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.10298e74 | −0.359265 | ||||||||
\(695\) | 3.42681e74 | 0.166837 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.11916e75 | −1.40724 | ||||||||
\(698\) | −3.06570e74 | −0.133156 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.47621e75 | −1.39961 | ||||||||
\(701\) | −5.35713e74 | −0.207685 | −0.103842 | − | 0.994594i | \(-0.533114\pi\) | ||||
−0.103842 | + | 0.994594i | \(0.533114\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.50916e75 | 1.98047 | ||||||||
\(704\) | −1.49255e75 | −0.516719 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.10235e74 | −0.228075 | ||||||||
\(707\) | −5.62298e75 | −1.73921 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.32161e75 | −0.953287 | −0.476644 | − | 0.879097i | \(-0.658147\pi\) | ||||
−0.476644 | + | 0.879097i | \(0.658147\pi\) | |||||||
\(710\) | −3.01190e74 | −0.0832711 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.36347e75 | −0.349885 | ||||||||
\(713\) | −2.42371e75 | −0.599249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.10950e74 | 0.163203 | ||||||||
\(716\) | −6.60292e75 | −1.46063 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.28737e74 | 0.170262 | ||||||||
\(719\) | 6.15825e75 | 1.21939 | 0.609694 | − | 0.792637i | \(-0.291292\pi\) | ||||
0.609694 | + | 0.792637i | \(0.291292\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.34792e75 | 0.247958 | ||||||||
\(722\) | −7.48536e74 | −0.132732 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.64143e75 | −0.929645 | ||||||||
\(725\) | 4.40987e75 | 0.700597 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.07750e76 | 1.59131 | 0.795657 | − | 0.605747i | \(-0.207126\pi\) | ||||
0.795657 | + | 0.605747i | \(0.207126\pi\) | |||||||
\(728\) | −3.94082e74 | −0.0561184 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.44094e75 | −0.190805 | ||||||||
\(731\) | 8.96136e75 | 1.14436 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.46870e75 | −0.174453 | −0.0872263 | − | 0.996189i | \(-0.527800\pi\) | ||||
−0.0872263 | + | 0.996189i | \(0.527800\pi\) | |||||||
\(734\) | −1.58923e75 | −0.182071 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.23359e75 | −0.344686 | ||||||||
\(737\) | −1.30147e76 | −1.33828 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.45777e75 | −0.713726 | −0.356863 | − | 0.934157i | \(-0.616154\pi\) | ||||
−0.356863 | + | 0.934157i | \(0.616154\pi\) | |||||||
\(740\) | −2.62977e76 | −2.42816 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.13440e74 | 0.0441353 | ||||||||
\(743\) | 2.17472e76 | 1.80385 | 0.901923 | − | 0.431897i | \(-0.142155\pi\) | ||||
0.901923 | + | 0.431897i | \(0.142155\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.85299e74 | 0.0220374 | ||||||||
\(746\) | −2.80789e75 | −0.209316 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.69699e76 | −1.17839 | ||||||||
\(749\) | 5.38195e75 | 0.360721 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.74960e75 | 0.546424 | 0.273212 | − | 0.961954i | \(-0.411914\pi\) | ||||
0.273212 | + | 0.961954i | \(0.411914\pi\) | |||||||
\(752\) | 7.24783e75 | 0.436953 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.40341e74 | 0.0135047 | ||||||||
\(755\) | 2.05265e75 | 0.111358 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.13811e76 | 1.08141 | 0.540705 | − | 0.841212i | \(-0.318158\pi\) | ||||
0.540705 | + | 0.841212i | \(0.318158\pi\) | |||||||
\(758\) | 7.25663e75 | 0.354406 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.26791e76 | 1.03292 | ||||||||
\(761\) | 2.22724e76 | 0.979658 | 0.489829 | − | 0.871819i | \(-0.337059\pi\) | ||||
0.489829 | + | 0.871819i | \(0.337059\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.36330e76 | 0.559358 | ||||||||
\(764\) | 4.41970e75 | 0.175154 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.19381e76 | 0.441442 | ||||||||
\(767\) | −3.57307e75 | −0.127633 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.21344e75 | −0.0404548 | −0.0202274 | − | 0.999795i | \(-0.506439\pi\) | ||||
−0.0202274 | + | 0.999795i | \(0.506439\pi\) | |||||||
\(770\) | 1.13882e76 | 0.366817 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.81074e75 | 0.234873 | ||||||||
\(773\) | −8.70709e75 | −0.252998 | −0.126499 | − | 0.991967i | \(-0.540374\pi\) | ||||
−0.126499 | + | 0.991967i | \(0.540374\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.60154e76 | −2.06256 | ||||||||
\(776\) | 1.92476e76 | 0.504709 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.64098e75 | −0.211643 | ||||||||
\(779\) | 5.05539e76 | 1.19677 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.59785e75 | −0.168050 | ||||||||
\(782\) | −8.53465e75 | −0.182476 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.57101e75 | −0.0913349 | ||||||||
\(785\) | 1.21110e76 | 0.233956 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.21858e76 | 1.30353 | 0.651766 | − | 0.758420i | \(-0.274029\pi\) | ||||
0.651766 | + | 0.758420i | \(0.274029\pi\) | |||||||
\(788\) | −9.53000e76 | −1.66398 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.98155e75 | 0.113981 | ||||||||
\(791\) | 1.08473e76 | 0.171255 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.27052e76 | −0.187604 | ||||||||
\(794\) | −7.47084e75 | −0.106691 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.10620e75 | −0.0815783 | ||||||||
\(797\) | 7.22104e76 | 0.933155 | 0.466578 | − | 0.884480i | \(-0.345487\pi\) | ||||
0.466578 | + | 0.884480i | \(0.345487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.61767e76 | 0.800231 | ||||||||
\(800\) | −1.01416e77 | −1.18638 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.20632e75 | 0.0132082 | ||||||||
\(803\) | −3.63493e76 | −0.385065 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.15223e76 | −0.709334 | ||||||||
\(806\) | −4.14289e75 | −0.0397580 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.07979e77 | −0.970372 | ||||||||
\(809\) | 1.58042e77 | 1.37447 | 0.687235 | − | 0.726435i | \(-0.258824\pi\) | ||||
0.687235 | + | 0.726435i | \(0.258824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.16585e77 | 0.949707 | 0.474853 | − | 0.880065i | \(-0.342501\pi\) | ||||
0.474853 | + | 0.880065i | \(0.342501\pi\) | |||||||
\(812\) | −4.80755e76 | −0.379044 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.31234e76 | 0.392409 | ||||||||
\(815\) | −3.05735e77 | −2.18609 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.45241e77 | −0.973208 | ||||||||
\(818\) | 1.40230e76 | 0.0909658 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.41316e77 | −1.46730 | ||||||||
\(821\) | −2.60575e77 | −1.53405 | −0.767023 | − | 0.641619i | \(-0.778263\pi\) | ||||
−0.767023 | + | 0.641619i | \(0.778263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.34341e76 | 0.184541 | 0.0922707 | − | 0.995734i | \(-0.470588\pi\) | ||||
0.0922707 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(824\) | 2.58843e76 | 0.138345 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.72343e76 | −0.286870 | ||||||||
\(827\) | 1.56452e77 | 0.759426 | 0.379713 | − | 0.925104i | \(-0.376023\pi\) | ||||
0.379713 | + | 0.925104i | \(0.376023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.97591e77 | 1.35495 | 0.677477 | − | 0.735544i | \(-0.263073\pi\) | ||||
0.677477 | + | 0.735544i | \(0.263073\pi\) | |||||||
\(830\) | 4.42651e76 | 0.195206 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.60229e76 | 0.0662937 | ||||||||
\(833\) | −4.17359e76 | −0.167269 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.17891e77 | −1.19560 | ||||||||
\(836\) | 2.75041e77 | 1.00214 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.24822e76 | 0.247893 | ||||||||
\(839\) | −2.75386e77 | −0.912535 | −0.456267 | − | 0.889843i | \(-0.650814\pi\) | ||||
−0.456267 | + | 0.889843i | \(0.650814\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.60448e77 | −0.810264 | ||||||||
\(842\) | −1.15758e77 | −0.348964 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.25769e77 | 1.77149 | ||||||||
\(845\) | 5.81062e77 | 1.59411 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.74579e76 | −0.199598 | ||||||||
\(848\) | −5.40725e76 | −0.135048 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.67675e77 | −0.628067 | ||||||||
\(851\) | −3.33636e77 | −0.758821 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.83575e77 | 1.46096 | 0.730478 | − | 0.682936i | \(-0.239297\pi\) | ||||
0.730478 | + | 0.682936i | \(0.239297\pi\) | |||||||
\(854\) | −2.03515e77 | −0.421660 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.03350e77 | 0.201260 | ||||||||
\(857\) | 6.22171e77 | 1.17467 | 0.587337 | − | 0.809342i | \(-0.300176\pi\) | ||||
0.587337 | + | 0.809342i | \(0.300176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.11261e77 | −0.729960 | −0.364980 | − | 0.931015i | \(-0.618924\pi\) | ||||
−0.364980 | + | 0.931015i | \(0.618924\pi\) | |||||||
\(860\) | 6.93302e77 | 1.19320 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.77277e77 | −0.448716 | ||||||||
\(863\) | 3.72761e77 | 0.584984 | 0.292492 | − | 0.956268i | \(-0.405516\pi\) | ||||
0.292492 | + | 0.956268i | \(0.405516\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.97943e77 | 0.439751 | ||||||||
\(866\) | 3.32993e77 | 0.476663 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.28706e77 | 1.11591 | ||||||||
\(869\) | 1.76117e77 | 0.230026 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.39716e77 | 0.171698 | ||||||||
\(872\) | 2.61796e77 | 0.312087 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.38325e77 | 0.155185 | ||||||||
\(875\) | −8.48510e77 | −0.923514 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.87970e77 | 0.499924 | 0.249962 | − | 0.968256i | \(-0.419582\pi\) | ||||
0.249962 | + | 0.968256i | \(0.419582\pi\) | |||||||
\(878\) | −5.45177e76 | −0.0541917 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.19934e78 | −1.12241 | ||||||||
\(881\) | −1.30154e78 | −1.18194 | −0.590970 | − | 0.806693i | \(-0.701255\pi\) | ||||
−0.590970 | + | 0.806693i | \(0.701255\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.47958e77 | 0.297556 | 0.148778 | − | 0.988871i | \(-0.452466\pi\) | ||||
0.148778 | + | 0.988871i | \(0.452466\pi\) | |||||||
\(884\) | 1.82176e77 | 0.151184 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.58710e77 | 0.358545 | ||||||||
\(887\) | 1.85101e78 | 1.40421 | 0.702107 | − | 0.712071i | \(-0.252243\pi\) | ||||
0.702107 | + | 0.712071i | \(0.252243\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.46861e76 | 0.0176423 | ||||||||
\(890\) | −4.22984e77 | −0.293419 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.01905e77 | 0.0666080 | ||||||||
\(893\) | −1.07256e78 | −0.680546 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.26082e78 | −2.54790 | ||||||||
\(896\) | 1.45081e78 | 0.842267 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.03521e77 | −0.111374 | ||||||||
\(899\) | −1.05128e78 | −0.558584 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.93712e77 | −0.247324 | ||||||||
\(902\) | 4.87478e77 | 0.237127 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.08302e77 | 0.0955499 | ||||||||
\(905\) | −3.64038e78 | −1.62166 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.94140e78 | 0.815686 | 0.407843 | − | 0.913052i | \(-0.366281\pi\) | ||||
0.407843 | + | 0.913052i | \(0.366281\pi\) | |||||||
\(908\) | −4.19456e77 | −0.171163 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.22254e77 | −0.0470617 | ||||||||
\(911\) | −6.52188e75 | −0.00243857 | −0.00121929 | − | 0.999999i | \(-0.500388\pi\) | ||||
−0.00121929 | + | 0.999999i | \(0.500388\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.11664e78 | 0.393946 | ||||||||
\(914\) | −9.01838e77 | −0.309068 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.84632e78 | 0.920563 | ||||||||
\(917\) | −2.21364e78 | −0.695536 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.20106e78 | 0.356208 | 0.178104 | − | 0.984012i | \(-0.443004\pi\) | ||||
0.178104 | + | 0.984012i | \(0.443004\pi\) | |||||||
\(920\) | −1.37345e78 | −0.395764 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.23971e78 | 0.337250 | ||||||||
\(923\) | 8.15645e76 | 0.0215604 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.04639e79 | −2.61179 | ||||||||
\(926\) | 1.31683e78 | 0.319404 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.40257e78 | −0.321295 | ||||||||
\(929\) | 1.35743e78 | 0.302205 | 0.151103 | − | 0.988518i | \(-0.451718\pi\) | ||||
0.151103 | + | 0.988518i | \(0.451718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.76434e77 | 0.142252 | ||||||||
\(932\) | 4.85692e78 | 0.992748 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.25881e78 | 0.436202 | ||||||||
\(935\) | −1.09506e79 | −2.05556 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.78543e77 | −0.138097 | −0.0690483 | − | 0.997613i | \(-0.521996\pi\) | ||||
−0.0690483 | + | 0.997613i | \(0.521996\pi\) | |||||||
\(938\) | 2.23800e78 | 0.385909 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.11980e78 | 0.834382 | ||||||||
\(941\) | 8.40474e77 | 0.133168 | 0.0665839 | − | 0.997781i | \(-0.478790\pi\) | ||||
0.0665839 | + | 0.997781i | \(0.478790\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.06155e78 | −0.458545 | ||||||||
\(944\) | 6.02759e78 | 0.877780 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.40052e78 | −0.192830 | ||||||||
\(947\) | −6.73558e78 | −0.901780 | −0.450890 | − | 0.892579i | \(-0.648893\pi\) | ||||
−0.450890 | + | 0.892579i | \(0.648893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.90217e77 | 0.0494028 | ||||||||
\(950\) | 4.33834e78 | 0.534132 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.06996e78 | 0.706817 | ||||||||
\(953\) | 1.66845e79 | 1.88952 | 0.944758 | − | 0.327768i | \(-0.106296\pi\) | ||||
0.944758 | + | 0.327768i | \(0.106296\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.85201e78 | 0.305535 | ||||||||
\(956\) | 8.47563e78 | 0.883157 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.42626e78 | −0.239194 | ||||||||
\(959\) | −3.91296e78 | −0.375242 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.10190e78 | 0.644473 | ||||||||
\(962\) | −5.70290e77 | −0.0503450 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.75519e79 | −1.46650 | ||||||||
\(965\) | 5.04022e78 | 0.409709 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.07490e79 | 1.59660 | 0.798301 | − | 0.602259i | \(-0.205733\pi\) | ||||
0.798301 | + | 0.602259i | \(0.205733\pi\) | |||||||
\(968\) | −1.48744e78 | −0.111363 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.97110e78 | 0.423256 | ||||||||
\(971\) | 7.04775e78 | 0.486117 | 0.243059 | − | 0.970012i | \(-0.421849\pi\) | ||||
0.243059 | + | 0.970012i | \(0.421849\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.48651e78 | −0.0970904 | ||||||||
\(974\) | −8.45487e78 | −0.537396 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.14330e79 | 1.29022 | ||||||||
\(977\) | −1.67318e79 | −0.980247 | −0.490123 | − | 0.871653i | \(-0.663048\pi\) | ||||
−0.490123 | + | 0.871653i | \(0.663048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.06702e79 | −0.592151 | ||||||||
\(980\) | −3.22892e78 | −0.174408 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.14945e78 | −0.365863 | ||||||||
\(983\) | 5.74735e78 | 0.286286 | 0.143143 | − | 0.989702i | \(-0.454279\pi\) | ||||
0.143143 | + | 0.989702i | \(0.454279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.14966e79 | −2.90262 | ||||||||
\(986\) | −3.70191e78 | −0.170094 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.95262e78 | −0.128573 | ||||||||
\(989\) | 8.79585e78 | 0.372886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.54858e79 | 1.02411 | 0.512055 | − | 0.858953i | \(-0.328885\pi\) | ||||
0.512055 | + | 0.858953i | \(0.328885\pi\) | |||||||
\(992\) | 2.41770e79 | 0.945894 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.30652e78 | 0.0484593 | ||||||||
\(995\) | −3.94029e78 | −0.142304 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.70743e79 | 1.61199 | 0.805994 | − | 0.591924i | \(-0.201631\pi\) | ||||
0.805994 | + | 0.591924i | \(0.201631\pi\) | |||||||
\(998\) | 1.24394e79 | 0.414802 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9.54.a.b.1.2 | 4 | ||
3.2 | odd | 2 | 1.54.a.a.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.54.a.a.1.3 | ✓ | 4 | 3.2 | odd | 2 | ||
9.54.a.b.1.2 | 4 | 1.1 | even | 1 | trivial |