Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(37,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.i (of order \(3\), degree \(2\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 11x^{6} + 4x^{5} + 91x^{4} - 6x^{3} + 129x^{2} + 36x + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(-1.30177 - 2.25473i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.37 |
Dual form | 804.2.i.d.565.1 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.60354 | −1.16434 | −0.582169 | − | 0.813068i | \(-0.697796\pi\) | ||||
−0.582169 | + | 0.813068i | \(0.697796\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.30177 | + | 2.25473i | −0.492023 | + | 0.852208i | −0.999958 | − | 0.00918719i | \(-0.997076\pi\) |
0.507935 | + | 0.861395i | \(0.330409\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.19098 | + | 3.79488i | 0.607667 | + | 1.05251i | 0.991624 | + | 0.129160i | \(0.0412280\pi\) |
−0.383956 | + | 0.923351i | \(0.625439\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.60354 | 0.672231 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.69098 | − | 2.92886i | −0.410122 | − | 0.710352i | 0.584781 | − | 0.811191i | \(-0.301181\pi\) |
−0.994903 | + | 0.100839i | \(0.967847\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.38921 | − | 2.40618i | −0.318706 | − | 0.552015i | 0.661512 | − | 0.749934i | \(-0.269915\pi\) |
−0.980218 | + | 0.197919i | \(0.936582\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30177 | − | 2.25473i | 0.284069 | − | 0.492023i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.798983 | − | 1.38388i | −0.166599 | − | 0.288559i | 0.770623 | − | 0.637292i | \(-0.219945\pi\) |
−0.937222 | + | 0.348733i | \(0.886612\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.77841 | 0.355683 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.10075 | − | 3.63861i | 0.390100 | − | 0.675673i | −0.602362 | − | 0.798223i | \(-0.705774\pi\) |
0.992462 | + | 0.122550i | \(0.0391071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.90252 | − | 8.49142i | 0.880519 | − | 1.52510i | 0.0297538 | − | 0.999557i | \(-0.490528\pi\) |
0.850765 | − | 0.525546i | \(-0.176139\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | + | 1.73205i | −0.174078 | + | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.38921 | − | 5.87028i | 0.572880 | − | 0.992258i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.89199 | − | 3.27703i | −0.311042 | − | 0.538740i | 0.667546 | − | 0.744568i | \(-0.267345\pi\) |
−0.978588 | + | 0.205828i | \(0.934011\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.19098 | − | 3.79488i | −0.350837 | − | 0.607667i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.48996 | − | 7.77684i | 0.701214 | − | 1.21454i | −0.266827 | − | 0.963744i | \(-0.585975\pi\) |
0.968041 | − | 0.250793i | \(-0.0806915\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.1870 | −1.70600 | −0.853000 | − | 0.521910i | \(-0.825220\pi\) | ||||
−0.853000 | + | 0.521910i | \(0.825220\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.60354 | −0.388113 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.48996 | − | 7.77684i | 0.654928 | − | 1.13437i | −0.326984 | − | 0.945030i | \(-0.606032\pi\) |
0.981912 | − | 0.189338i | \(-0.0606343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.110793 | + | 0.191900i | 0.0158276 | + | 0.0274142i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.69098 | + | 2.92886i | 0.236784 | + | 0.410122i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.618048 | 0.0848954 | 0.0424477 | − | 0.999099i | \(-0.486484\pi\) | ||||
0.0424477 | + | 0.999099i | \(0.486484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.60354 | + | 4.50946i | −0.351061 | + | 0.608056i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.38921 | + | 2.40618i | 0.184005 | + | 0.318706i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.18045 | 0.414059 | 0.207030 | − | 0.978335i | \(-0.433620\pi\) | ||||
0.207030 | + | 0.978335i | \(0.433620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.38474 | + | 12.7907i | 0.945519 | + | 1.63769i | 0.754709 | + | 0.656060i | \(0.227778\pi\) |
0.190810 | + | 0.981627i | \(0.438889\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.30177 | + | 2.25473i | −0.164008 | + | 0.284069i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.70429 | − | 9.88012i | −0.707530 | − | 1.22548i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.38642 | − | 6.91081i | −0.535887 | − | 0.844290i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.798983 | + | 1.38388i | 0.0961862 | + | 0.166599i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.40809 | + | 5.90299i | −0.404466 | + | 0.700556i | −0.994259 | − | 0.106998i | \(-0.965876\pi\) |
0.589793 | + | 0.807555i | \(0.299209\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.613580 | − | 1.06275i | −0.0718141 | − | 0.124386i | 0.827882 | − | 0.560902i | \(-0.189545\pi\) |
−0.899696 | + | 0.436516i | \(0.856212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.77841 | −0.205353 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.60354 | + | 4.50946i | 0.296701 | + | 0.513901i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.01610 | − | 8.68814i | 0.564355 | − | 0.977492i | −0.432754 | − | 0.901512i | \(-0.642458\pi\) |
0.997109 | − | 0.0759802i | \(-0.0242086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.69098 | − | 4.66091i | −0.295373 | − | 0.511601i | 0.679699 | − | 0.733492i | \(-0.262111\pi\) |
−0.975072 | + | 0.221890i | \(0.928777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.40252 | + | 7.62539i | 0.477521 | + | 0.827090i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.10075 | + | 3.63861i | −0.225224 | + | 0.390100i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00557 | −0.318590 | −0.159295 | − | 0.987231i | \(-0.550922\pi\) | ||||
−0.159295 | + | 0.987231i | \(0.550922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.4086 | −1.19594 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.90252 | + | 8.49142i | −0.508368 | + | 0.880519i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.61685 | + | 6.26457i | 0.371081 | + | 0.642732i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.99721 | + | 3.45928i | 0.202786 | + | 0.351236i | 0.949425 | − | 0.313993i | \(-0.101667\pi\) |
−0.746639 | + | 0.665230i | \(0.768334\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | − | 1.73205i | 0.100504 | − | 0.174078i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.07293 | − | 12.2507i | 0.703783 | − | 1.21899i | −0.263346 | − | 0.964701i | \(-0.584826\pi\) |
0.967129 | − | 0.254286i | \(-0.0818404\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.99275 | − | 3.45154i | 0.196351 | − | 0.340090i | −0.750992 | − | 0.660312i | \(-0.770424\pi\) |
0.947343 | + | 0.320222i | \(0.103757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.38921 | + | 5.87028i | −0.330753 | + | 0.572880i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.81062 | −0.948428 | −0.474214 | − | 0.880410i | \(-0.657268\pi\) | ||||
−0.474214 | + | 0.880410i | \(0.657268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.79053 | 0.554633 | 0.277316 | − | 0.960779i | \(-0.410555\pi\) | ||||
0.277316 | + | 0.960779i | \(0.410555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.89199 | + | 3.27703i | 0.179580 | + | 0.311042i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.52336 | − | 2.63853i | 0.143305 | − | 0.248212i | −0.785434 | − | 0.618945i | \(-0.787560\pi\) |
0.928739 | + | 0.370733i | \(0.120894\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.08018 | + | 3.60298i | 0.193978 | + | 0.335980i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.19098 | + | 3.79488i | 0.202556 | + | 0.350837i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.80504 | 0.807157 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.48996 | + | 7.77684i | −0.404846 | + | 0.701214i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.38753 | 0.750203 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.08465 | + | 5.34277i | −0.273719 | + | 0.474094i | −0.969811 | − | 0.243858i | \(-0.921587\pi\) |
0.696093 | + | 0.717952i | \(0.254920\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.1870 | 0.984960 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.1313 | −1.58414 | −0.792072 | − | 0.610428i | \(-0.790997\pi\) | ||||
−0.792072 | + | 0.610428i | \(0.790997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.23371 | 0.627242 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.60354 | 0.224077 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.9911 | 0.939030 | 0.469515 | − | 0.882925i | \(-0.344429\pi\) | ||||
0.469515 | + | 0.882925i | \(0.344429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.21265 | 0.272493 | 0.136247 | − | 0.990675i | \(-0.456496\pi\) | ||||
0.136247 | + | 0.990675i | \(0.456496\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.48996 | + | 7.77684i | −0.378123 | + | 0.654928i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.76390 | 0.732874 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.46939 | + | 9.47326i | −0.454208 | + | 0.786711i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.110793 | − | 0.191900i | −0.00913807 | − | 0.0158276i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.0588 | −1.56136 | −0.780680 | − | 0.624931i | \(-0.785127\pi\) | ||||
−0.780680 | + | 0.624931i | \(0.785127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.87470 | − | 11.9073i | −0.559455 | − | 0.969004i | −0.997542 | − | 0.0700718i | \(-0.977677\pi\) |
0.438087 | − | 0.898933i | \(-0.355656\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.69098 | − | 2.92886i | −0.136707 | − | 0.236784i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.7639 | + | 22.1077i | −1.02522 | + | 1.77574i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.00557 | − | 6.93786i | −0.319680 | − | 0.553701i | 0.660742 | − | 0.750613i | \(-0.270242\pi\) |
−0.980421 | + | 0.196912i | \(0.936909\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.618048 | −0.0490144 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.16037 | 0.327883 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.17815 | + | 15.8970i | −0.718888 | + | 1.24515i | 0.242553 | + | 0.970138i | \(0.422015\pi\) |
−0.961441 | + | 0.275012i | \(0.911318\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.60354 | − | 4.50946i | 0.202685 | − | 0.351061i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.11964 | − | 10.5995i | 0.473552 | − | 0.820216i | −0.525990 | − | 0.850491i | \(-0.676305\pi\) |
0.999542 | + | 0.0302749i | \(0.00963828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.10075 | + | 5.37066i | −0.238519 | + | 0.413128i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.38921 | − | 2.40618i | −0.106235 | − | 0.184005i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.30177 | + | 9.18293i | 0.403086 | + | 0.698166i | 0.994097 | − | 0.108498i | \(-0.0346042\pi\) |
−0.591011 | + | 0.806664i | \(0.701271\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.31508 | + | 4.00984i | −0.175004 | + | 0.303116i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.18045 | −0.239057 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.4086 | −1.00220 | −0.501102 | − | 0.865388i | \(-0.667072\pi\) | ||||
−0.501102 | + | 0.865388i | \(0.667072\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.68651 | − | 6.38522i | 0.274016 | − | 0.474610i | −0.695870 | − | 0.718167i | \(-0.744981\pi\) |
0.969886 | + | 0.243558i | \(0.0783145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.38474 | − | 12.7907i | −0.545896 | − | 0.945519i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.92588 | + | 8.53187i | 0.362158 | + | 0.627276i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.76390 | −0.494626 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.30177 | − | 2.25473i | 0.0946898 | − | 0.164008i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.5818 | − | 21.7923i | −0.910385 | − | 1.57683i | −0.813521 | − | 0.581536i | \(-0.802452\pi\) |
−0.0968646 | − | 0.995298i | \(-0.530881\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5634 | 0.832350 | 0.416175 | − | 0.909285i | \(-0.363370\pi\) | ||||
0.416175 | + | 0.909285i | \(0.363370\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.70429 | + | 9.88012i | 0.408493 | + | 0.707530i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7566 | + | 22.0952i | −0.908874 | + | 1.57422i | −0.0932423 | + | 0.995643i | \(0.529723\pi\) |
−0.815631 | + | 0.578572i | \(0.803610\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.18372 | + | 10.7105i | 0.438352 | + | 0.759249i | 0.997563 | − | 0.0697773i | \(-0.0222289\pi\) |
−0.559210 | + | 0.829026i | \(0.688896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.38642 | + | 6.91081i | 0.309394 | + | 0.487451i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.46939 | + | 9.47326i | 0.383876 | + | 0.664893i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.6898 | + | 20.2473i | −0.816450 | + | 1.41413i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.798983 | − | 1.38388i | −0.0555331 | − | 0.0961862i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.55683 | −0.384374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.69544 | − | 6.40070i | −0.254405 | − | 0.440642i | 0.710329 | − | 0.703870i | \(-0.248546\pi\) |
−0.964734 | + | 0.263228i | \(0.915213\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.40809 | − | 5.90299i | 0.233519 | − | 0.404466i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.1258 | 1.98636 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.7639 | + | 22.1077i | 0.866470 | + | 1.50077i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.613580 | + | 1.06275i | 0.0414619 | + | 0.0718141i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.40978 | − | 12.8341i | 0.498435 | − | 0.863316i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.83963 | −0.190156 | −0.0950780 | − | 0.995470i | \(-0.530310\pi\) | ||||
−0.0950780 | + | 0.995470i | \(0.530310\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.77841 | 0.118561 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0923 | − | 20.9445i | 0.802594 | − | 1.39013i | −0.115309 | − | 0.993330i | \(-0.536786\pi\) |
0.917903 | − | 0.396804i | \(-0.129881\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.593010 | + | 1.02712i | 0.0391872 | + | 0.0678743i | 0.884954 | − | 0.465679i | \(-0.154190\pi\) |
−0.845767 | + | 0.533553i | \(0.820856\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.60354 | − | 4.50946i | −0.171300 | − | 0.296701i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.49602 | + | 12.9835i | −0.491081 | + | 0.850576i | −0.999947 | − | 0.0102689i | \(-0.996731\pi\) |
0.508867 | + | 0.860845i | \(0.330065\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.6898 | + | 20.2473i | −0.762557 | + | 1.32079i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.01610 | + | 8.68814i | −0.325831 | + | 0.564355i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.00725462 | + | 0.0125654i | −0.000469262 | + | 0.000812786i | −0.866260 | − | 0.499594i | \(-0.833483\pi\) |
0.865791 | + | 0.500406i | \(0.166816\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.36426 | 0.0878796 | 0.0439398 | − | 0.999034i | \(-0.486009\pi\) | ||||
0.0439398 | + | 0.999034i | \(0.486009\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.288455 | − | 0.499618i | −0.0184287 | − | 0.0319194i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.08744 | − | 10.5438i | 0.387334 | − | 0.670883i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.69098 | + | 4.66091i | 0.170534 | + | 0.295373i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.817871 | + | 1.41659i | 0.0516235 | + | 0.0894146i | 0.890682 | − | 0.454626i | \(-0.150227\pi\) |
−0.839059 | + | 0.544041i | \(0.816894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.19593 | −0.200926 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.40252 | − | 7.62539i | −0.275697 | − | 0.477521i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.946034 | − | 1.63858i | 0.0590120 | − | 0.102212i | −0.835010 | − | 0.550234i | \(-0.814538\pi\) |
0.894022 | + | 0.448023i | \(0.147872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.85175 | 0.612158 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.10075 | − | 3.63861i | 0.130033 | − | 0.225224i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.42309 | −0.211077 | −0.105538 | − | 0.994415i | \(-0.533657\pi\) | ||||
−0.105538 | + | 0.994415i | \(0.533657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.60911 | −0.0988469 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.00557 | 0.183938 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.48431 | 0.151471 | 0.0757356 | − | 0.997128i | \(-0.475870\pi\) | ||||
0.0757356 | + | 0.997128i | \(0.475870\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0533 | 1.03591 | 0.517956 | − | 0.855407i | \(-0.326693\pi\) | ||||
0.517956 | + | 0.855407i | \(0.326693\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.4086 | 0.690479 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.77841 | − | 3.08030i | 0.107242 | − | 0.185749i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.17487 | −0.431096 | −0.215548 | − | 0.976493i | \(-0.569154\pi\) | ||||
−0.215548 | + | 0.976493i | \(0.569154\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.90252 | − | 8.49142i | 0.293506 | − | 0.508368i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1664 | − | 28.0011i | −0.964408 | − | 1.67040i | −0.711197 | − | 0.702993i | \(-0.751847\pi\) |
−0.253211 | − | 0.967411i | \(-0.581487\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.737275 | −0.0438264 | −0.0219132 | − | 0.999760i | \(-0.506976\pi\) | ||||
−0.0219132 | + | 0.999760i | \(0.506976\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.61685 | − | 6.26457i | −0.214244 | − | 0.371081i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6898 | + | 20.2473i | 0.690026 | + | 1.19516i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.78120 | − | 4.81718i | 0.163600 | − | 0.283364i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.99721 | − | 3.45928i | −0.117079 | − | 0.202786i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.9444 | −1.63253 | −0.816263 | − | 0.577680i | \(-0.803958\pi\) | ||||
−0.816263 | + | 0.577680i | \(0.803958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.28042 | −0.482105 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.50110 | − | 6.06409i | 0.202474 | − | 0.350695i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.5629 | − | 25.2237i | 0.839391 | − | 1.45387i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.07293 | + | 12.2507i | −0.406329 | + | 0.703783i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.2265 | − | 33.3012i | −1.10090 | − | 1.90682i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.69376 | + | 6.39778i | 0.210814 | + | 0.365141i | 0.951970 | − | 0.306193i | \(-0.0990552\pi\) |
−0.741155 | + | 0.671333i | \(0.765722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.99275 | + | 3.45154i | −0.113363 | + | 0.196351i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.94214 | 0.393653 | 0.196826 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196826 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.2303 | −1.31306 | −0.656528 | − | 0.754301i | \(-0.727976\pi\) | ||||
−0.656528 | + | 0.754301i | \(0.727976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.38921 | − | 5.87028i | 0.190960 | − | 0.330753i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.972176 | + | 1.68386i | 0.0546028 | + | 0.0945749i | 0.892035 | − | 0.451967i | \(-0.149277\pi\) |
−0.837432 | + | 0.546542i | \(0.815944\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.20150 | − | 7.27722i | −0.235239 | − | 0.407446i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.81062 | 0.547575 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.69823 | + | 8.13757i | −0.261417 | + | 0.452787i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.89646 | + | 6.74887i | 0.216137 | + | 0.374360i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.79053 | −0.320217 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.6898 | + | 20.2473i | 0.644479 | + | 1.11627i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.93592 | + | 5.08516i | −0.161373 | + | 0.279506i | −0.935361 | − | 0.353694i | \(-0.884925\pi\) |
0.773989 | + | 0.633200i | \(0.218259\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.89199 | − | 3.27703i | −0.103681 | − | 0.179580i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.4202 | + | 17.9926i | 0.623953 | + | 0.983039i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.67974 | − | 15.0338i | −0.472816 | − | 0.818941i | 0.526700 | − | 0.850051i | \(-0.323429\pi\) |
−0.999516 | + | 0.0311104i | \(0.990096\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.52336 | + | 2.63853i | −0.0827373 | + | 0.143305i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.80504 | − | 16.9828i | −0.530973 | − | 0.919672i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8017 | −1.01520 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.08018 | − | 3.60298i | −0.111993 | − | 0.193978i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0116 | − | 17.3407i | 0.537453 | − | 0.930895i | −0.461588 | − | 0.887095i | \(-0.652720\pi\) |
0.999040 | − | 0.0438007i | \(-0.0139466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.36187 | −0.179957 | −0.0899784 | − | 0.995944i | \(-0.528680\pi\) | ||||
−0.0899784 | + | 0.995944i | \(0.528680\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.19098 | − | 3.79488i | −0.116946 | − | 0.202556i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.4008 | + | 21.4789i | 0.660030 | + | 1.14321i | 0.980607 | + | 0.195983i | \(0.0627898\pi\) |
−0.320577 | + | 0.947222i | \(0.603877\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.87311 | − | 15.3687i | 0.470936 | − | 0.815684i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.80504 | −0.466012 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.6769 | 1.24962 | 0.624809 | − | 0.780778i | \(-0.285177\pi\) | ||||
0.624809 | + | 0.780778i | \(0.285177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.64021 | − | 9.76913i | 0.296853 | − | 0.514165i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.50000 | − | 6.06218i | −0.183702 | − | 0.318182i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.59748 | + | 2.76691i | 0.0836158 | + | 0.144827i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0734 | − | 20.9118i | 0.630227 | − | 1.09159i | −0.357278 | − | 0.933998i | \(-0.616295\pi\) |
0.987505 | − | 0.157587i | \(-0.0503716\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.48996 | − | 7.77684i | 0.233738 | − | 0.404846i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.804556 | + | 1.39353i | −0.0417705 | + | 0.0723485i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.11517 | − | 12.3238i | 0.368410 | − | 0.638104i | −0.620907 | − | 0.783884i | \(-0.713236\pi\) |
0.989317 | + | 0.145780i | \(0.0465691\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.38753 | −0.433130 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.4108 | 0.948204 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.607520 | − | 1.05225i | −0.0312062 | − | 0.0540507i | 0.850001 | − | 0.526782i | \(-0.176602\pi\) |
−0.881207 | + | 0.472731i | \(0.843268\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.08465 | − | 5.34277i | 0.158031 | − | 0.273719i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.320657 | − | 0.555394i | −0.0163848 | − | 0.0283793i | 0.857717 | − | 0.514123i | \(-0.171882\pi\) |
−0.874102 | + | 0.485743i | \(0.838549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.77841 | − | 11.7406i | −0.345460 | − | 0.598354i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.1870 | −0.568667 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.98549 | − | 6.90307i | −0.202072 | − | 0.350000i | 0.747124 | − | 0.664685i | \(-0.231434\pi\) |
−0.949196 | + | 0.314685i | \(0.898101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.70212 | + | 4.68021i | −0.136652 | + | 0.236689i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.1313 | 0.914605 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0596 | + | 22.6199i | −0.657100 | + | 1.13813i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.99106 | 0.501437 | 0.250719 | − | 0.968060i | \(-0.419333\pi\) | ||||
0.250719 | + | 0.968060i | \(0.419333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.23371 | −0.362138 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.4197 | 0.770024 | 0.385012 | − | 0.922911i | \(-0.374197\pi\) | ||||
0.385012 | + | 0.922911i | \(0.374197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.9652 | 2.14025 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.60354 | −0.129371 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.56797 | −0.375130 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.11190 | + | 7.12202i | −0.203320 | + | 0.352161i | −0.949596 | − | 0.313476i | \(-0.898507\pi\) |
0.746276 | + | 0.665637i | \(0.231840\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.9911 | −0.542149 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.14021 | + | 7.17105i | −0.203726 | + | 0.352864i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.00606 | + | 12.1349i | 0.343914 | + | 0.595676i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.21265 | −0.157324 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.32791 | − | 7.49616i | −0.211432 | − | 0.366212i | 0.740731 | − | 0.671802i | \(-0.234479\pi\) |
−0.952163 | + | 0.305591i | \(0.901146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9682 | − | 32.8539i | −0.924453 | − | 1.60120i | −0.792438 | − | 0.609952i | \(-0.791189\pi\) |
−0.132015 | − | 0.991248i | \(-0.542145\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.48996 | − | 7.77684i | 0.218309 | − | 0.378123i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00725 | − | 5.20872i | −0.145873 | − | 0.252660i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.4529 | −1.86087 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.76390 | −0.423125 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.75100 | + | 13.4251i | −0.373353 | + | 0.646666i | −0.990079 | − | 0.140512i | \(-0.955125\pi\) |
0.616726 | + | 0.787178i | \(0.288459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8222 | − | 25.6729i | 0.712312 | − | 1.23376i | −0.251675 | − | 0.967812i | \(-0.580982\pi\) |
0.963987 | − | 0.265949i | \(-0.0856851\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.46939 | − | 9.47326i | 0.262237 | − | 0.454208i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.21990 | + | 3.84499i | −0.106192 | + | 0.183931i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.9013 | − | 25.8099i | −0.711202 | − | 1.23184i | −0.964406 | − | 0.264425i | \(-0.914818\pi\) |
0.253205 | − | 0.967413i | \(-0.418515\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.110793 | + | 0.191900i | 0.00527587 | + | 0.00913807i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.07461 | + | 5.32538i | −0.146079 | + | 0.253016i | −0.929775 | − | 0.368128i | \(-0.879999\pi\) |
0.783696 | + | 0.621145i | \(0.213332\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.82513 | 0.370947 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.0588 | 0.901452 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3941 | + | 24.9313i | −0.679298 | + | 1.17658i | 0.295894 | + | 0.955221i | \(0.404382\pi\) |
−0.975193 | + | 0.221358i | \(0.928951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.97992 | − | 15.5537i | −0.422848 | − | 0.732394i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.87470 | + | 11.9073i | 0.323001 | + | 0.559455i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 29.7027 | 1.39248 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.52057 | − | 14.7581i | 0.398575 | − | 0.690353i | −0.594975 | − | 0.803744i | \(-0.702838\pi\) |
0.993550 | + | 0.113391i | \(0.0361714\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.69098 | + | 2.92886i | 0.0789280 | + | 0.136707i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.1781 | −1.07951 | −0.539755 | − | 0.841822i | \(-0.681483\pi\) | ||||
−0.539755 | + | 0.841822i | \(0.681483\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.26104 | + | 14.3085i | 0.383923 | + | 0.664975i | 0.991619 | − | 0.129195i | \(-0.0412394\pi\) |
−0.607696 | + | 0.794170i | \(0.707906\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.7639 | − | 22.1077i | 0.591912 | − | 1.02522i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.60403 | + | 7.97441i | 0.213049 | + | 0.369012i | 0.952667 | − | 0.304015i | \(-0.0983273\pi\) |
−0.739618 | + | 0.673027i | \(0.764994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.2921 | − | 0.893914i | 0.983179 | − | 0.0412771i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.00557 | + | 6.93786i | 0.184567 | + | 0.319680i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.1870 | + | 19.3764i | −0.514379 | + | 0.890930i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.47058 | − | 4.27918i | −0.113358 | − | 0.196342i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.618048 | 0.0282985 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.9260 | + | 20.6564i | 0.544911 | + | 0.943813i | 0.998613 | + | 0.0526594i | \(0.0167698\pi\) |
−0.453702 | + | 0.891154i | \(0.649897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.29062 | − | 14.3598i | 0.378020 | − | 0.654750i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.16037 | −0.189303 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.19982 | − | 9.00636i | −0.236112 | − | 0.408958i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.9081 | + | 29.2857i | 0.766179 | + | 1.32706i | 0.939621 | + | 0.342217i | \(0.111178\pi\) |
−0.173442 | + | 0.984844i | \(0.555489\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.17815 | − | 15.8970i | 0.415050 | − | 0.718888i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.41195 | −0.424755 | −0.212378 | − | 0.977188i | \(-0.568121\pi\) | ||||
−0.212378 | + | 0.977188i | \(0.568121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.2093 | −0.639954 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.60354 | + | 4.50946i | −0.117020 | + | 0.202685i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.87311 | − | 15.3687i | −0.398013 | − | 0.689379i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.40301 | − | 11.0903i | −0.286638 | − | 0.496472i | 0.686367 | − | 0.727255i | \(-0.259204\pi\) |
−0.973005 | + | 0.230784i | \(0.925871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.11964 | + | 10.5995i | −0.273405 | + | 0.473552i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.0741226 | + | 0.128384i | −0.00330496 | + | 0.00572437i | −0.867673 | − | 0.497135i | \(-0.834385\pi\) |
0.864368 | + | 0.502859i | \(0.167719\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.4146 | + | 31.8951i | −0.819441 | + | 1.41931i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.10075 | − | 5.37066i | 0.137709 | − | 0.238519i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.84282 | −0.126006 | −0.0630029 | − | 0.998013i | \(-0.520068\pi\) | ||||
−0.0630029 | + | 0.998013i | \(0.520068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.19496 | 0.141337 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.38921 | + | 2.40618i | 0.0613350 | + | 0.106235i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.18819 | + | 8.98621i | −0.228619 | + | 0.395980i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.97992 | − | 15.5537i | −0.394936 | − | 0.684050i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.30177 | − | 9.18293i | −0.232722 | − | 0.403086i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.78399 | −0.341023 | −0.170511 | − | 0.985356i | \(-0.554542\pi\) | ||||
−0.170511 | + | 0.985356i | \(0.554542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.38244 | + | 16.2509i | 0.410265 | + | 0.710601i | 0.994919 | − | 0.100683i | \(-0.0321027\pi\) |
−0.584653 | + | 0.811283i | \(0.698769\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.31508 | − | 4.00984i | 0.101039 | − | 0.175004i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.1602 | −1.44448 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.2233 | − | 17.7072i | 0.444489 | − | 0.769878i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.18045 | 0.138020 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.3496 | 1.70442 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.5423 | 1.10429 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.4086 | 0.578623 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.443173 | 0.0190888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.80186 | −0.292435 | −0.146217 | − | 0.989252i | \(-0.546710\pi\) | ||||
−0.146217 | + | 0.989252i | \(0.546710\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.68651 | + | 6.38522i | −0.158203 | + | 0.274016i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.0759 | −0.645780 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.8863 | − | 34.4441i | 0.850278 | − | 1.47272i | −0.0306793 | − | 0.999529i | \(-0.509767\pi\) |
0.880957 | − | 0.473196i | \(-0.156900\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.38474 | + | 12.7907i | 0.315173 | + | 0.545896i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.6735 | −0.497309 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.0596 | + | 22.6199i | 0.555351 | + | 0.961897i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.92588 | − | 8.53187i | −0.209092 | − | 0.362158i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.24055 | − | 12.5410i | 0.306792 | − | 0.531379i | −0.670867 | − | 0.741578i | \(-0.734078\pi\) |
0.977659 | + | 0.210199i | \(0.0674111\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.5104 | − | 42.4533i | −1.03668 | − | 1.79558i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.76390 | 0.285572 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.13374 | −0.174216 | −0.0871081 | − | 0.996199i | \(-0.527763\pi\) | ||||
−0.0871081 | + | 0.996199i | \(0.527763\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.96612 | + | 6.86951i | −0.166856 | + | 0.289003i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.30177 | + | 2.25473i | −0.0546692 | + | 0.0946898i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.0456 | + | 31.2559i | −0.756511 | + | 1.31031i | 0.188109 | + | 0.982148i | \(0.439764\pi\) |
−0.944620 | + | 0.328167i | \(0.893569\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.9275 | − | 39.7115i | 0.959485 | − | 1.66188i | 0.235731 | − | 0.971818i | \(-0.424252\pi\) |
0.723754 | − | 0.690058i | \(-0.242415\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.5818 | + | 21.7923i | 0.525611 | + | 0.910385i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.42092 | − | 2.46111i | −0.0592565 | − | 0.102635i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.1079 | + | 24.4356i | −0.587320 | + | 1.01727i | 0.407262 | + | 0.913312i | \(0.366484\pi\) |
−0.994582 | + | 0.103957i | \(0.966850\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.5634 | −0.480557 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.0121 | 0.581321 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.618048 | − | 1.07049i | 0.0255969 | − | 0.0443352i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.70429 | − | 9.88012i | −0.235843 | − | 0.408493i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.3006 | + | 24.7693i | 0.590248 | + | 1.02234i | 0.994199 | + | 0.107559i | \(0.0343033\pi\) |
−0.403951 | + | 0.914781i | \(0.632363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.2425 | −1.12251 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.7566 | − | 22.0952i | 0.524738 | − | 0.908874i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.0177 | − | 22.5473i | −0.534573 | − | 0.925907i | −0.999184 | − | 0.0403922i | \(-0.987139\pi\) |
0.464611 | − | 0.885515i | \(-0.346194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.9243 | −0.939803 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.18372 | − | 10.7105i | −0.253083 | − | 0.438352i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.1063 | + | 36.5572i | −0.862381 | + | 1.49369i | 0.00724324 | + | 0.999974i | \(0.497694\pi\) |
−0.869624 | + | 0.493714i | \(0.835639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.35860 | − | 14.4775i | −0.340954 | − | 0.590550i | 0.643656 | − | 0.765315i | \(-0.277417\pi\) |
−0.984610 | + | 0.174765i | \(0.944083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.38642 | − | 6.91081i | −0.178629 | − | 0.281430i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.11239 | − | 15.7831i | −0.370471 | − | 0.641675i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.15758 | − | 8.93319i | 0.209340 | − | 0.362587i | −0.742167 | − | 0.670215i | \(-0.766202\pi\) |
0.951507 | + | 0.307628i | \(0.0995352\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.46939 | − | 9.47326i | −0.221631 | − | 0.383876i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.3496 | 1.59191 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.6129 | + | 30.5064i | 0.711377 | + | 1.23214i | 0.964340 | + | 0.264666i | \(0.0852616\pi\) |
−0.252963 | + | 0.967476i | \(0.581405\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.6898 | − | 20.2473i | 0.471377 | − | 0.816450i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.8685 | 0.679099 | 0.339550 | − | 0.940588i | \(-0.389725\pi\) | ||||
0.339550 | + | 0.940588i | \(0.389725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.02336 | + | 13.8969i | 0.322486 | + | 0.558562i | 0.981000 | − | 0.194006i | \(-0.0621482\pi\) |
−0.658514 | + | 0.752568i | \(0.728815\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.798983 | + | 1.38388i | 0.0320621 | + | 0.0555331i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.91256 | − | 6.77676i | 0.156754 | − | 0.271505i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7293 | −1.22917 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.55683 | 0.221918 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.39863 | + | 11.0828i | −0.255130 | + | 0.441898i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.737762 | + | 1.27784i | 0.0293698 | + | 0.0508701i | 0.880337 | − | 0.474349i | \(-0.157317\pi\) |
−0.850967 | + | 0.525219i | \(0.823983\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.69544 | + | 6.40070i | 0.146881 | + | 0.254405i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.03101 | − | 13.9101i | 0.318701 | − | 0.552006i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.485491 | + | 0.840895i | −0.0192358 | + | 0.0333175i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.40809 | + | 5.90299i | −0.134822 | + | 0.233519i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.0640 | + | 27.8237i | −0.634490 | + | 1.09897i | 0.352134 | + | 0.935950i | \(0.385456\pi\) |
−0.986623 | + | 0.163018i | \(0.947877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.1202 | −0.714591 | −0.357295 | − | 0.933991i | \(-0.616301\pi\) | ||||
−0.357295 | + | 0.933991i | \(0.616301\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −29.1258 | −1.14683 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.7966 | − | 37.7528i | −0.856913 | − | 1.48422i | −0.874859 | − | 0.484377i | \(-0.839046\pi\) |
0.0179468 | − | 0.999839i | \(-0.494287\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.18045 | − | 5.50870i | 0.124843 | − | 0.216235i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.7639 | − | 22.1077i | −0.500257 | − | 0.866470i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.58783 | + | 16.6066i | 0.375201 | + | 0.649867i | 0.990357 | − | 0.138538i | \(-0.0442404\pi\) |
−0.615156 | + | 0.788405i | \(0.710907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 47.2057 | 1.84448 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.613580 | − | 1.06275i | −0.0239380 | − | 0.0414619i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.9932 | + | 39.8254i | −0.895689 | + | 1.55138i | −0.0627398 | + | 0.998030i | \(0.519984\pi\) |
−0.832949 | + | 0.553349i | \(0.813349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.1113 | 1.87131 | 0.935656 | − | 0.352914i | \(-0.114809\pi\) | ||||
0.935656 | + | 0.352914i | \(0.114809\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.40978 | + | 12.8341i | −0.287772 | + | 0.498435i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.8332 | −0.730322 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.71386 | −0.259962 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.83963 | 0.109787 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.5390 | 1.14034 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6380 | 0.756987 | 0.378494 | − | 0.925604i | \(-0.376442\pi\) | ||||
0.378494 | + | 0.925604i | \(0.376442\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.77841 | −0.0684512 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5757 | − | 28.7100i | 0.637056 | − | 1.10341i | −0.349019 | − | 0.937116i | \(-0.613485\pi\) |
0.986075 | − | 0.166299i | \(-0.0531815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.3996 | −0.399102 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0923 | + | 20.9445i | −0.463378 | + | 0.802594i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.407607 | − | 0.705996i | −0.0155967 | − | 0.0270142i | 0.858122 | − | 0.513446i | \(-0.171631\pi\) |
−0.873718 | + | 0.486432i | \(0.838298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.6157 | −1.09335 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.593010 | − | 1.02712i | −0.0226248 | − | 0.0391872i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.35413 | + | 2.34542i | 0.0515882 | + | 0.0893533i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.2928 | + | 28.2200i | −0.619809 | + | 1.07354i | 0.369712 | + | 0.929146i | \(0.379456\pi\) |
−0.989520 | + | 0.144393i | \(0.953877\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.60354 | + | 4.50946i | 0.0989003 | + | 0.171300i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.36426 | −0.317274 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.3697 | −1.15033 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.49602 | − | 12.9835i | 0.283525 | − | 0.491081i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1730 | − | 40.1368i | 0.875231 | − | 1.51594i | 0.0187148 | − | 0.999825i | \(-0.494043\pi\) |
0.856516 | − | 0.516120i | \(-0.172624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.25674 | + | 9.10494i | −0.198262 | + | 0.343399i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.6898 | − | 20.2473i | 0.440263 | − | 0.762557i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.4146 | + | 31.8951i | 0.692554 | + | 1.19954i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.57452 | + | 16.5836i | 0.359579 | + | 0.622808i | 0.987890 | − | 0.155153i | \(-0.0495871\pi\) |
−0.628312 | + | 0.777962i | \(0.716254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.01610 | − | 8.68814i | 0.188118 | − | 0.325831i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.6681 | −0.586776 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.8172 | −0.853314 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.00725462 | − | 0.0125654i | 0.000270929 | − | 0.000469262i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.4292 | + | 31.9204i | 0.687294 | + | 1.19043i | 0.972710 | + | 0.232025i | \(0.0745350\pi\) |
−0.285416 | + | 0.958404i | \(0.592132\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.18819 | + | 8.98621i | 0.193218 | + | 0.334664i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.36426 | −0.0507373 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.73601 | − | 6.47095i | 0.138752 | − | 0.240325i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.6592 | + | 44.4430i | 0.951646 | + | 1.64830i | 0.741863 | + | 0.670551i | \(0.233942\pi\) |
0.209783 | + | 0.977748i | \(0.432724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.9169 | + | 32.7651i | 0.699668 | + | 1.21186i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.44157 | − | 9.42507i | 0.200989 | − | 0.348123i | −0.747858 | − | 0.663858i | \(-0.768918\pi\) |
0.948847 | + | 0.315735i | \(0.102251\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.288455 | + | 0.499618i | 0.0106398 | + | 0.0184287i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.3563 | + | 0.686691i | −0.602492 | + | 0.0252946i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.1101 | + | 38.2958i | 0.813333 | + | 1.40873i | 0.910519 | + | 0.413467i | \(0.135682\pi\) |
−0.0971863 | + | 0.995266i | \(0.530984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.08744 | + | 10.5438i | −0.223628 | + | 0.387334i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.29403 | − | 9.16952i | −0.194219 | − | 0.336397i | 0.752425 | − | 0.658678i | \(-0.228884\pi\) |
−0.946644 | + | 0.322280i | \(0.895551\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 49.6204 | 1.81795 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.69098 | − | 4.66091i | −0.0984577 | − | 0.170534i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.7712 | − | 22.1203i | 0.466648 | − | 0.808258i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.7848 | −1.19633 | −0.598167 | − | 0.801372i | \(-0.704104\pi\) | ||||
−0.598167 | + | 0.801372i | \(0.704104\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.817871 | − | 1.41659i | −0.0298049 | − | 0.0516235i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.8985 | + | 31.0012i | 0.651395 | + | 1.12825i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.02949 | + | 12.1754i | −0.255491 | + | 0.442524i | −0.965029 | − | 0.262144i | \(-0.915571\pi\) |
0.709538 | + | 0.704668i | \(0.248904\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.19593 | 0.116005 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.07237 | 0.328873 | 0.164437 | − | 0.986388i | \(-0.447419\pi\) | ||||
0.164437 | + | 0.986388i | \(0.447419\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.53794 | + | 13.0561i | −0.272892 | + | 0.472662i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.40252 | + | 7.62539i | 0.159174 | + | 0.275697i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.96828 | + | 12.0694i | 0.251610 | + | 0.435802i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.91654 | − | 5.05160i | 0.105173 | − | 0.182165i | −0.808636 | − | 0.588310i | \(-0.799794\pi\) |
0.913809 | + | 0.406144i | \(0.133127\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.946034 | + | 1.63858i | −0.0340706 | + | 0.0590120i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.2594 | + | 19.5019i | −0.404974 | + | 0.701435i | −0.994318 | − | 0.106447i | \(-0.966053\pi\) |
0.589345 | + | 0.807882i | \(0.299386\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.71871 | − | 15.1012i | 0.313185 | − | 0.542453i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.85175 | −0.353430 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.9499 | −0.893924 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.81619 | + | 11.8060i | 0.243902 | + | 0.422451i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.10075 | + | 3.63861i | −0.0750748 | + | 0.130033i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.4287 | + | 18.0630i | 0.372215 | + | 0.644695i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.4815 | − | 30.2789i | −0.623149 | − | 1.07932i | −0.988896 | − | 0.148611i | \(-0.952520\pi\) |
0.365747 | − | 0.930714i | \(-0.380813\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.42309 | 0.121865 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.96612 | + | 6.86951i | 0.141019 | + | 0.244252i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.3596 | + | 56.0484i | −1.14912 | + | 1.99034i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.60911 | 0.0570693 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.1129 | + | 26.1763i | −0.535325 | + | 0.927211i | 0.463822 | + | 0.885928i | \(0.346478\pi\) |
−0.999148 | + | 0.0412825i | \(0.986856\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.3697 | −1.07440 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00557 | −0.106197 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.45432 | −0.0866110 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.8317 | −0.381766 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.48431 | −0.0874519 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.3652 | −0.575371 | −0.287685 | − | 0.957725i | \(-0.592886\pi\) | ||||
−0.287685 | + | 0.957725i | \(0.592886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7209 | + | 32.4255i | −0.657379 | + | 1.13861i | 0.323913 | + | 0.946087i | \(0.395002\pi\) |
−0.981292 | + | 0.192527i | \(0.938332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.0533 | −0.598084 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.8957 | − | 41.3885i | 0.837029 | − | 1.44978i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.5410 | + | 26.9179i | 0.543712 | + | 0.941738i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.4086 | −0.398648 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.2933 | + | 35.1491i | 0.708242 | + | 1.22671i | 0.965509 | + | 0.260370i | \(0.0838447\pi\) |
−0.257267 | + | 0.966340i | \(0.582822\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.1813 | + | 29.7589i | 0.598904 | + | 1.03733i | 0.992983 | + | 0.118255i | \(0.0377301\pi\) |
−0.394080 | + | 0.919076i | \(0.628937\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.77841 | + | 3.08030i | −0.0619164 | + | 0.107242i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.77771 | + | 16.9355i | 0.340004 | + | 0.588904i | 0.984433 | − | 0.175760i | \(-0.0562382\pi\) |
−0.644429 | + | 0.764664i | \(0.722905\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.4833 | −1.54497 | −0.772485 | − | 0.635034i | \(-0.780986\pi\) | ||||
−0.772485 | + | 0.635034i | \(0.780986\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.17487 | 0.248894 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.374698 | − | 0.648995i | 0.0129825 | − | 0.0224863i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.9327 | + | 27.5963i | −0.551374 | + | 0.955009i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.90252 | + | 8.49142i | −0.169456 | + | 0.293506i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.32840 | + | 2.30085i | −0.0458614 | + | 0.0794343i | −0.888045 | − | 0.459757i | \(-0.847937\pi\) |
0.842183 | + | 0.539191i | \(0.181270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.67368 | + | 9.82710i | 0.195644 | + | 0.338866i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.1664 | + | 28.0011i | 0.556801 | + | 0.964408i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.07293 | − | 13.9827i | 0.277717 | − | 0.481020i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.2248 | −0.626211 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.737275 | 0.0253032 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.02334 | + | 5.23658i | −0.103639 | + | 0.179508i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.2615 | + | 43.7542i | 0.864938 | + | 1.49812i | 0.867109 | + | 0.498119i | \(0.165976\pi\) |
−0.00217110 | + | 0.999998i | \(0.500691\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.61685 | + | 6.26457i | 0.123694 | + | 0.214244i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.8460 | −1.15616 | −0.578079 | − | 0.815981i | \(-0.696197\pi\) | ||||
−0.578079 | + | 0.815981i | \(0.696197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.754570 | − | 1.30695i | 0.0257456 | − | 0.0445927i | −0.852866 | − | 0.522131i | \(-0.825137\pi\) |
0.878611 | + | 0.477538i | \(0.158471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6898 | − | 20.2473i | −0.398387 | − | 0.690026i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.85830 | 0.233459 | 0.116730 | − | 0.993164i | \(-0.462759\pi\) | ||||
0.116730 | + | 0.993164i | \(0.462759\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.8034 | − | 23.9081i | −0.469328 | − | 0.812901i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.78120 | + | 4.81718i | −0.0944545 | + | 0.163600i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.0322 | − | 17.3763i | −0.340319 | − | 0.589450i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.6152 | − | 31.7874i | 0.562984 | − | 1.07707i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.99721 | + | 3.45928i | 0.0675954 | + | 0.117079i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.9186 | + | 18.9116i | −0.369117 | + | 0.639329i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.4114 | − | 45.7458i | −0.891849 | − | 1.54473i | −0.837657 | − | 0.546196i | \(-0.816075\pi\) |
−0.0541914 | − | 0.998531i | \(-0.517258\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.9444 | 0.942540 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.1657 | − | 45.3204i | −0.881545 | − | 1.52688i | −0.849623 | − | 0.527391i | \(-0.823170\pi\) |
−0.0319229 | − | 0.999490i | \(-0.510163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.0617824 | + | 0.107010i | −0.00207914 | + | 0.00360118i | −0.867063 | − | 0.498198i | \(-0.833995\pi\) |
0.864984 | + | 0.501800i | \(0.167328\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.28042 | 0.278343 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.51730 | + | 14.7524i | 0.285983 | + | 0.495337i | 0.972847 | − | 0.231449i | \(-0.0743466\pi\) |
−0.686864 | + | 0.726786i | \(0.741013\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.03101 | − | 13.9101i | −0.269351 | − | 0.466530i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.9499 | −0.834917 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.9098 | 1.16690 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.50110 | + | 6.06409i | −0.116898 | + | 0.202474i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.5980 | − | 35.6767i | −0.686981 | − | 1.18989i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.04510 | − | 1.81017i | −0.0348175 | − | 0.0603056i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.5629 | + | 25.2237i | −0.484623 | + | 0.839391i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.59797 | + | 16.6242i | −0.319047 | + | 0.552606i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.7498 | − | 27.2795i | 0.522964 | − | 0.905800i | −0.476679 | − | 0.879077i | \(-0.658160\pi\) |
0.999643 | − | 0.0267225i | \(-0.00850704\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.07293 | − | 12.2507i | 0.234594 | − | 0.406329i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.3408 | 1.17089 | 0.585447 | − | 0.810711i | \(-0.300919\pi\) | ||||
0.585447 | + | 0.810711i | \(0.300919\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.7639 | −0.356233 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.2265 | + | 33.3012i | 0.635607 | + | 1.10090i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.6028 | − | 40.8813i | 0.779434 | − | 1.35002i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.35622 | + | 4.08110i | 0.0777246 | + | 0.134623i | 0.902268 | − | 0.431176i | \(-0.141901\pi\) |
−0.824543 | + | 0.565799i | \(0.808568\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.69376 | − | 6.39778i | −0.121714 | − | 0.210814i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.8682 | −0.983124 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.36475 | − | 5.82791i | −0.110632 | − | 0.191621i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.99275 | − | 3.45154i | 0.0654503 | − | 0.113363i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.5344 | −0.345621 | −0.172811 | − | 0.984955i | \(-0.555285\pi\) | ||||
−0.172811 | + | 0.984955i | \(0.555285\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.307829 | − | 0.533176i | 0.0100887 | − | 0.0174741i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.94214 | −0.227276 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.6101 | 0.575911 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.6936 | 0.447350 | 0.223675 | − | 0.974664i | \(-0.428195\pi\) | ||||
0.223675 | + | 0.974664i | \(0.428195\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.2303 | 0.758094 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.5055 | 1.28784 | 0.643922 | − | 0.765092i | \(-0.277306\pi\) | ||||
0.643922 | + | 0.765092i | \(0.277306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.3496 | −0.467287 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.38921 | + | 5.87028i | −0.110251 | + | 0.190960i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.2860 | −0.496728 | −0.248364 | − | 0.968667i | \(-0.579893\pi\) | ||||
−0.248364 | + | 0.968667i | \(0.579893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.68868 | − | 4.65692i | 0.0872781 | − | 0.151170i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.972176 | − | 1.68386i | −0.0315250 | − | 0.0546028i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.3875 | −1.04913 | −0.524567 | − | 0.851369i | \(-0.675773\pi\) | ||||
−0.524567 | + | 0.851369i | \(0.675773\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.7571 | + | 56.7370i | 1.06000 | + | 1.83597i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.20150 | + | 7.27722i | 0.135815 | + | 0.235239i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.3078 | + | 24.7819i | −0.462024 | + | 0.800249i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32.5694 | − | 56.4119i | −1.05063 | − | 1.81974i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.81062 | −0.316143 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.1057 | −0.969137 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.41305 | − | 4.17952i | 0.0775985 | − | 0.134404i | −0.824615 | − | 0.565695i | \(-0.808608\pi\) |
0.902213 | + | 0.431290i | \(0.141941\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.69823 | − | 8.13757i | 0.150929 | − | 0.261417i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.12181 | − | 10.6033i | 0.196458 | − | 0.340276i | −0.750919 | − | 0.660394i | \(-0.770389\pi\) |
0.947378 | + | 0.320118i | \(0.103723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.18213 | + | 7.24366i | −0.134073 | + | 0.232221i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.89646 | − | 6.74887i | −0.124787 | − | 0.216137i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.3490 | − | 35.2456i | −0.651024 | − | 1.12761i | −0.982875 | − | 0.184274i | \(-0.941007\pi\) |
0.331851 | − | 0.943332i | \(-0.392327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.00557 | + | 5.20580i | −0.0960585 | + | 0.166378i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.79053 | 0.184878 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.0387 | 1.21325 | 0.606624 | − | 0.794989i | \(-0.292523\pi\) | ||||
0.606624 | + | 0.794989i | \(0.292523\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.2124 | − | 57.5256i | 1.05824 | − | 1.83292i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.6898 | − | 20.2473i | −0.372090 | − | 0.644479i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.93822 | + | 15.4814i | 0.284219 | + | 0.492281i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.9074 | 1.42653 | 0.713265 | − | 0.700895i | \(-0.247216\pi\) | ||||
0.713265 | + | 0.700895i | \(0.247216\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.93592 | − | 5.08516i | 0.0931686 | − | 0.161373i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.0996 | − | 27.8853i | −0.510390 | − | 0.884022i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.11825 | 0.130426 | 0.0652132 | − | 0.997871i | \(-0.479227\pi\) | ||||
0.0652132 | + | 0.997871i | \(0.479227\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.89199 | + | 3.27703i | 0.0598600 | + | 0.103681i |
(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 | 804.2.i.d.37.1 | ✓ | 8 | |
3.2 | odd | 2 | 2412.2.l.e.37.4 | 8 | |||
67.29 | even | 3 | inner | 804.2.i.d.565.1 | yes | 8 | |
201.29 | odd | 6 | 2412.2.l.e.1369.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.i.d.37.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
804.2.i.d.565.1 | yes | 8 | 67.29 | even | 3 | inner | |
2412.2.l.e.37.4 | 8 | 3.2 | odd | 2 | |||
2412.2.l.e.1369.4 | 8 | 201.29 | odd | 6 |