Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(157,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.bc (of order \(12\), degree \(4\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 607.2 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.607 |
Dual form | 1050.2.bc.a.493.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | − | 0.258819i | 0.683013 | − | 0.183013i | ||||
\(3\) | −0.258819 | + | 0.965926i | −0.149429 | + | 0.557678i | ||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | −2.63896 | − | 0.189469i | −0.997433 | − | 0.0716124i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | 0.780750 | − | 0.624844i | \(-0.214837\pi\) |
−0.931505 | + | 0.363727i | \(0.881504\pi\) | |||||||
\(12\) | 0.258819 | + | 0.965926i | 0.0747146 | + | 0.278839i | ||||
\(13\) | 4.05317 | + | 4.05317i | 1.12415 | + | 1.12415i | 0.991111 | + | 0.133037i | \(0.0424728\pi\) |
0.133037 | + | 0.991111i | \(0.457527\pi\) | |||||||
\(14\) | −2.59808 | + | 0.500000i | −0.694365 | + | 0.133631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 7.20977 | + | 1.93185i | 1.74863 | + | 0.468543i | 0.984332 | − | 0.176325i | \(-0.0564211\pi\) |
0.764294 | + | 0.644868i | \(0.223088\pi\) | |||||||
\(18\) | −0.965926 | − | 0.258819i | −0.227671 | − | 0.0610042i | ||||
\(19\) | −1.13397 | + | 1.96410i | −0.260152 | + | 0.450596i | −0.966282 | − | 0.257486i | \(-0.917106\pi\) |
0.706130 | + | 0.708082i | \(0.250439\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.866025 | − | 2.50000i | 0.188982 | − | 0.545545i | ||||
\(22\) | −0.707107 | − | 0.707107i | −0.150756 | − | 0.150756i | ||||
\(23\) | 1.53433 | + | 5.72620i | 0.319930 | + | 1.19400i | 0.919311 | + | 0.393532i | \(0.128747\pi\) |
−0.599381 | + | 0.800464i | \(0.704586\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.96410 | + | 2.86603i | 0.973540 | + | 0.562074i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −2.38014 | + | 1.15539i | −0.449804 | + | 0.218349i | ||||
\(29\) | 6.92820i | 1.28654i | 0.765641 | + | 0.643268i | \(0.222422\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.46410 | − | 3.73205i | 1.16099 | − | 0.670296i | 0.209447 | − | 0.977820i | \(-0.432834\pi\) |
0.951540 | + | 0.307524i | \(0.0995004\pi\) | |||||||
\(32\) | 0.258819 | − | 0.965926i | 0.0457532 | − | 0.170753i | ||||
\(33\) | 0.965926 | − | 0.258819i | 0.168146 | − | 0.0450546i | ||||
\(34\) | 7.46410 | 1.28008 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 3.79435 | − | 1.01669i | 0.623788 | − | 0.167143i | 0.0669387 | − | 0.997757i | \(-0.478677\pi\) |
0.556849 | + | 0.830614i | \(0.312010\pi\) | |||||||
\(38\) | −0.586988 | + | 2.19067i | −0.0952221 | + | 0.355374i | ||||
\(39\) | −4.96410 | + | 2.86603i | −0.794892 | + | 0.458931i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.26795i | − | 0.354194i | −0.984193 | − | 0.177097i | \(-0.943329\pi\) | ||
0.984193 | − | 0.177097i | \(-0.0566707\pi\) | |||||||
\(42\) | 0.189469 | − | 2.63896i | 0.0292357 | − | 0.407200i | ||||
\(43\) | −6.31319 | + | 6.31319i | −0.962753 | + | 0.962753i | −0.999331 | − | 0.0365779i | \(-0.988354\pi\) |
0.0365779 | + | 0.999331i | \(0.488354\pi\) | |||||||
\(44\) | −0.866025 | − | 0.500000i | −0.130558 | − | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.96410 | + | 5.13397i | 0.437033 | + | 0.756963i | ||||
\(47\) | 0.309587 | + | 1.15539i | 0.0451579 | + | 0.168532i | 0.984822 | − | 0.173566i | \(-0.0555292\pi\) |
−0.939664 | + | 0.342098i | \(0.888862\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | 6.92820 | + | 1.00000i | 0.989743 | + | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.73205 | + | 6.46410i | −0.522592 | + | 0.905155i | ||||
\(52\) | 5.53674 | + | 1.48356i | 0.767807 | + | 0.205733i | ||||
\(53\) | 0.965926 | + | 0.258819i | 0.132680 | + | 0.0355515i | 0.324548 | − | 0.945869i | \(-0.394788\pi\) |
−0.191868 | + | 0.981421i | \(0.561454\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | + | 1.73205i | −0.267261 | + | 0.231455i | ||||
\(57\) | −1.60368 | − | 1.60368i | −0.212413 | − | 0.212413i | ||||
\(58\) | 1.79315 | + | 6.69213i | 0.235452 | + | 0.878720i | ||||
\(59\) | −5.73205 | − | 9.92820i | −0.746249 | − | 1.29254i | −0.949609 | − | 0.313438i | \(-0.898519\pi\) |
0.203359 | − | 0.979104i | \(-0.434814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.92820 | − | 5.73205i | −1.27118 | − | 0.733914i | −0.295967 | − | 0.955198i | \(-0.595642\pi\) |
−0.975209 | + | 0.221284i | \(0.928975\pi\) | |||||||
\(62\) | 5.27792 | − | 5.27792i | 0.670296 | − | 0.670296i | ||||
\(63\) | 2.19067 | + | 1.48356i | 0.275999 | + | 0.186911i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.866025 | − | 0.500000i | 0.106600 | − | 0.0615457i | ||||
\(67\) | 0.517638 | − | 1.93185i | 0.0632396 | − | 0.236013i | −0.927071 | − | 0.374887i | \(-0.877682\pi\) |
0.990310 | + | 0.138874i | \(0.0443482\pi\) | |||||||
\(68\) | 7.20977 | − | 1.93185i | 0.874313 | − | 0.234271i | ||||
\(69\) | −5.92820 | −0.713672 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.92820 | −1.05958 | −0.529791 | − | 0.848128i | \(-0.677730\pi\) | ||||
−0.529791 | + | 0.848128i | \(0.677730\pi\) | |||||||
\(72\) | −0.965926 | + | 0.258819i | −0.113835 | + | 0.0305021i | ||||
\(73\) | −1.03528 | + | 3.86370i | −0.121170 | + | 0.452212i | −0.999674 | − | 0.0255221i | \(-0.991875\pi\) |
0.878504 | + | 0.477734i | \(0.158542\pi\) | |||||||
\(74\) | 3.40192 | − | 1.96410i | 0.395466 | − | 0.228322i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.26795i | 0.260152i | ||||||||
\(77\) | 1.15539 | + | 2.38014i | 0.131669 | + | 0.271242i | ||||
\(78\) | −4.05317 | + | 4.05317i | −0.458931 | + | 0.458931i | ||||
\(79\) | 2.66025 | + | 1.53590i | 0.299302 | + | 0.172802i | 0.642129 | − | 0.766596i | \(-0.278051\pi\) |
−0.342827 | + | 0.939398i | \(0.611385\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.586988 | − | 2.19067i | −0.0648220 | − | 0.241919i | ||||
\(83\) | −7.34847 | − | 7.34847i | −0.806599 | − | 0.806599i | 0.177518 | − | 0.984118i | \(-0.443193\pi\) |
−0.984118 | + | 0.177518i | \(0.943193\pi\) | |||||||
\(84\) | −0.500000 | − | 2.59808i | −0.0545545 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.46410 | + | 7.73205i | −0.481376 | + | 0.833768i | ||||
\(87\) | −6.69213 | − | 1.79315i | −0.717472 | − | 0.192246i | ||||
\(88\) | −0.965926 | − | 0.258819i | −0.102968 | − | 0.0275902i | ||||
\(89\) | −3.46410 | + | 6.00000i | −0.367194 | + | 0.635999i | −0.989126 | − | 0.147073i | \(-0.953015\pi\) |
0.621932 | + | 0.783072i | \(0.286348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.92820 | − | 11.4641i | −1.04076 | − | 1.20176i | ||||
\(92\) | 4.19187 | + | 4.19187i | 0.437033 | + | 0.437033i | ||||
\(93\) | 1.93185 | + | 7.20977i | 0.200324 | + | 0.747618i | ||||
\(94\) | 0.598076 | + | 1.03590i | 0.0616869 | + | 0.106845i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 2.07055 | − | 2.07055i | 0.210233 | − | 0.210233i | −0.594134 | − | 0.804366i | \(-0.702505\pi\) |
0.804366 | + | 0.594134i | \(0.202505\pi\) | |||||||
\(98\) | 6.95095 | − | 0.827225i | 0.702152 | − | 0.0835624i | ||||
\(99\) | 1.00000i | 0.100504i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.928203 | − | 0.535898i | 0.0923597 | − | 0.0533239i | −0.453109 | − | 0.891455i | \(-0.649685\pi\) |
0.545468 | + | 0.838131i | \(0.316352\pi\) | |||||||
\(102\) | −1.93185 | + | 7.20977i | −0.191282 | + | 0.713873i | ||||
\(103\) | 17.7656 | − | 4.76028i | 1.75050 | − | 0.469044i | 0.765765 | − | 0.643121i | \(-0.222361\pi\) |
0.984732 | + | 0.174077i | \(0.0556941\pi\) | |||||||
\(104\) | 5.73205 | 0.562074 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | 14.4195 | − | 3.86370i | 1.39399 | − | 0.373518i | 0.517807 | − | 0.855498i | \(-0.326749\pi\) |
0.876183 | + | 0.481979i | \(0.160082\pi\) | |||||||
\(108\) | 0.258819 | − | 0.965926i | 0.0249049 | − | 0.0929463i | ||||
\(109\) | 14.6603 | − | 8.46410i | 1.40420 | − | 0.810714i | 0.409378 | − | 0.912365i | \(-0.365746\pi\) |
0.994820 | + | 0.101651i | \(0.0324126\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.92820i | 0.372849i | ||||||||
\(112\) | −1.48356 | + | 2.19067i | −0.140184 | + | 0.206999i | ||||
\(113\) | −9.14162 | + | 9.14162i | −0.859971 | + | 0.859971i | −0.991334 | − | 0.131363i | \(-0.958065\pi\) |
0.131363 | + | 0.991334i | \(0.458065\pi\) | |||||||
\(114\) | −1.96410 | − | 1.13397i | −0.183955 | − | 0.106206i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.46410 | + | 6.00000i | 0.321634 | + | 0.557086i | ||||
\(117\) | −1.48356 | − | 5.53674i | −0.137156 | − | 0.511871i | ||||
\(118\) | −8.10634 | − | 8.10634i | −0.746249 | − | 0.746249i | ||||
\(119\) | −18.6603 | − | 6.46410i | −1.71058 | − | 0.592563i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | −11.0735 | − | 2.96713i | −1.00255 | − | 0.268631i | ||||
\(123\) | 2.19067 | + | 0.586988i | 0.197526 | + | 0.0529270i | ||||
\(124\) | 3.73205 | − | 6.46410i | 0.335148 | − | 0.580493i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.50000 | + | 0.866025i | 0.222718 | + | 0.0771517i | ||||
\(127\) | −3.53553 | − | 3.53553i | −0.313728 | − | 0.313728i | 0.532624 | − | 0.846352i | \(-0.321206\pi\) |
−0.846352 | + | 0.532624i | \(0.821206\pi\) | |||||||
\(128\) | −0.258819 | − | 0.965926i | −0.0228766 | − | 0.0853766i | ||||
\(129\) | −4.46410 | − | 7.73205i | −0.393042 | − | 0.680769i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.57180 | + | 2.06218i | 0.312069 | + | 0.180173i | 0.647852 | − | 0.761766i | \(-0.275667\pi\) |
−0.335783 | + | 0.941939i | \(0.609001\pi\) | |||||||
\(132\) | 0.707107 | − | 0.707107i | 0.0615457 | − | 0.0615457i | ||||
\(133\) | 3.36465 | − | 4.96833i | 0.291752 | − | 0.430809i | ||||
\(134\) | − | 2.00000i | − | 0.172774i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.46410 | − | 3.73205i | 0.554292 | − | 0.320021i | ||||
\(137\) | −4.89898 | + | 18.2832i | −0.418548 | + | 1.56204i | 0.359073 | + | 0.933309i | \(0.383093\pi\) |
−0.777621 | + | 0.628733i | \(0.783574\pi\) | |||||||
\(138\) | −5.72620 | + | 1.53433i | −0.487447 | + | 0.130611i | ||||
\(139\) | 10.3923 | 0.881464 | 0.440732 | − | 0.897639i | \(-0.354719\pi\) | ||||
0.440732 | + | 0.897639i | \(0.354719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.19615 | −0.100734 | ||||||||
\(142\) | −8.62398 | + | 2.31079i | −0.723708 | + | 0.193917i | ||||
\(143\) | 1.48356 | − | 5.53674i | 0.124062 | − | 0.463005i | ||||
\(144\) | −0.866025 | + | 0.500000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.00000i | 0.331042i | ||||||||
\(147\) | −2.75908 | + | 6.43331i | −0.227565 | + | 0.530611i | ||||
\(148\) | 2.77766 | − | 2.77766i | 0.228322 | − | 0.228322i | ||||
\(149\) | 0.803848 | + | 0.464102i | 0.0658538 | + | 0.0380207i | 0.532565 | − | 0.846389i | \(-0.321228\pi\) |
−0.466712 | + | 0.884410i | \(0.654561\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.92820 | + | 3.33975i | 0.156915 | + | 0.271785i | 0.933755 | − | 0.357914i | \(-0.116512\pi\) |
−0.776840 | + | 0.629698i | \(0.783178\pi\) | |||||||
\(152\) | 0.586988 | + | 2.19067i | 0.0476110 | + | 0.177687i | ||||
\(153\) | −5.27792 | − | 5.27792i | −0.426694 | − | 0.426694i | ||||
\(154\) | 1.73205 | + | 2.00000i | 0.139573 | + | 0.161165i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.86603 | + | 4.96410i | −0.229466 | + | 0.397446i | ||||
\(157\) | 4.50146 | + | 1.20616i | 0.359256 | + | 0.0962622i | 0.433932 | − | 0.900946i | \(-0.357126\pi\) |
−0.0746765 | + | 0.997208i | \(0.523792\pi\) | |||||||
\(158\) | 2.96713 | + | 0.795040i | 0.236052 | + | 0.0632499i | ||||
\(159\) | −0.500000 | + | 0.866025i | −0.0396526 | + | 0.0686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.96410 | − | 15.4019i | −0.233604 | − | 1.21384i | ||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −3.10583 | − | 11.5911i | −0.243267 | − | 0.907886i | −0.974246 | − | 0.225486i | \(-0.927603\pi\) |
0.730979 | − | 0.682400i | \(-0.239064\pi\) | |||||||
\(164\) | −1.13397 | − | 1.96410i | −0.0885485 | − | 0.153371i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.00000 | − | 5.19615i | −0.698535 | − | 0.403300i | ||||
\(167\) | −4.81105 | + | 4.81105i | −0.372290 | + | 0.372290i | −0.868311 | − | 0.496021i | \(-0.834794\pi\) |
0.496021 | + | 0.868311i | \(0.334794\pi\) | |||||||
\(168\) | −1.15539 | − | 2.38014i | −0.0891406 | − | 0.183632i | ||||
\(169\) | 19.8564i | 1.52742i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.96410 | − | 1.13397i | 0.150199 | − | 0.0867172i | ||||
\(172\) | −2.31079 | + | 8.62398i | −0.176196 | + | 0.657572i | ||||
\(173\) | −7.32989 | + | 1.96404i | −0.557281 | + | 0.149323i | −0.526457 | − | 0.850202i | \(-0.676480\pi\) |
−0.0308241 | + | 0.999525i | \(0.509813\pi\) | |||||||
\(174\) | −6.92820 | −0.525226 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 11.0735 | − | 2.96713i | 0.832333 | − | 0.223023i | ||||
\(178\) | −1.79315 | + | 6.69213i | −0.134402 | + | 0.501596i | ||||
\(179\) | −7.79423 | + | 4.50000i | −0.582568 | + | 0.336346i | −0.762153 | − | 0.647397i | \(-0.775858\pi\) |
0.179585 | + | 0.983742i | \(0.442524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.3923i | − | 1.06977i | −0.844924 | − | 0.534886i | \(-0.820355\pi\) | ||
0.844924 | − | 0.534886i | \(-0.179645\pi\) | |||||||
\(182\) | −12.5570 | − | 8.50386i | −0.930789 | − | 0.630348i | ||||
\(183\) | 8.10634 | − | 8.10634i | 0.599238 | − | 0.599238i | ||||
\(184\) | 5.13397 | + | 2.96410i | 0.378482 | + | 0.218516i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.73205 | + | 6.46410i | 0.273647 | + | 0.473971i | ||||
\(187\) | −1.93185 | − | 7.20977i | −0.141271 | − | 0.527230i | ||||
\(188\) | 0.845807 | + | 0.845807i | 0.0616869 | + | 0.0616869i | ||||
\(189\) | −2.00000 | + | 1.73205i | −0.145479 | + | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.46410 | + | 2.53590i | −0.105939 | + | 0.183491i | −0.914121 | − | 0.405441i | \(-0.867118\pi\) |
0.808183 | + | 0.588932i | \(0.200451\pi\) | |||||||
\(192\) | 0.965926 | + | 0.258819i | 0.0697097 | + | 0.0186787i | ||||
\(193\) | −22.0082 | − | 5.89709i | −1.58419 | − | 0.424482i | −0.643969 | − | 0.765052i | \(-0.722713\pi\) |
−0.940219 | + | 0.340570i | \(0.889380\pi\) | |||||||
\(194\) | 1.46410 | − | 2.53590i | 0.105116 | − | 0.182067i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.50000 | − | 2.59808i | 0.464286 | − | 0.185577i | ||||
\(197\) | −11.9193 | − | 11.9193i | −0.849213 | − | 0.849213i | 0.140822 | − | 0.990035i | \(-0.455026\pi\) |
−0.990035 | + | 0.140822i | \(0.955026\pi\) | |||||||
\(198\) | 0.258819 | + | 0.965926i | 0.0183935 | + | 0.0686454i | ||||
\(199\) | −6.26795 | − | 10.8564i | −0.444323 | − | 0.769590i | 0.553682 | − | 0.832728i | \(-0.313222\pi\) |
−0.998005 | + | 0.0631382i | \(0.979889\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.73205 | + | 1.00000i | 0.122169 | + | 0.0705346i | ||||
\(202\) | 0.757875 | − | 0.757875i | 0.0533239 | − | 0.0533239i | ||||
\(203\) | 1.31268 | − | 18.2832i | 0.0921319 | − | 1.28323i | ||||
\(204\) | 7.46410i | 0.522592i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.9282 | − | 9.19615i | 1.10977 | − | 0.640726i | ||||
\(207\) | 1.53433 | − | 5.72620i | 0.106643 | − | 0.397999i | ||||
\(208\) | 5.53674 | − | 1.48356i | 0.383904 | − | 0.102867i | ||||
\(209\) | 2.26795 | 0.156877 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.7846 | −1.36203 | −0.681014 | − | 0.732270i | \(-0.738461\pi\) | ||||
−0.681014 | + | 0.732270i | \(0.738461\pi\) | |||||||
\(212\) | 0.965926 | − | 0.258819i | 0.0663401 | − | 0.0177758i | ||||
\(213\) | 2.31079 | − | 8.62398i | 0.158333 | − | 0.590906i | ||||
\(214\) | 12.9282 | − | 7.46410i | 0.883754 | − | 0.510235i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −17.7656 | + | 8.62398i | −1.20601 | + | 0.585434i | ||||
\(218\) | 11.9700 | − | 11.9700i | 0.810714 | − | 0.810714i | ||||
\(219\) | −3.46410 | − | 2.00000i | −0.234082 | − | 0.135147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.3923 | + | 37.0526i | 1.43900 | + | 2.49242i | ||||
\(222\) | 1.01669 | + | 3.79435i | 0.0682360 | + | 0.254660i | ||||
\(223\) | 6.59059 | + | 6.59059i | 0.441339 | + | 0.441339i | 0.892462 | − | 0.451123i | \(-0.148976\pi\) |
−0.451123 | + | 0.892462i | \(0.648976\pi\) | |||||||
\(224\) | −0.866025 | + | 2.50000i | −0.0578638 | + | 0.167038i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.46410 | + | 11.1962i | −0.429986 | + | 0.744757i | ||||
\(227\) | −3.34607 | − | 0.896575i | −0.222086 | − | 0.0595078i | 0.146060 | − | 0.989276i | \(-0.453341\pi\) |
−0.368146 | + | 0.929768i | \(0.620007\pi\) | |||||||
\(228\) | −2.19067 | − | 0.586988i | −0.145081 | − | 0.0388743i | ||||
\(229\) | 1.46410 | − | 2.53590i | 0.0967506 | − | 0.167577i | −0.813587 | − | 0.581443i | \(-0.802488\pi\) |
0.910338 | + | 0.413866i | \(0.135822\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.59808 | + | 0.500000i | −0.170941 | + | 0.0328976i | ||||
\(232\) | 4.89898 | + | 4.89898i | 0.321634 | + | 0.321634i | ||||
\(233\) | −0.480473 | − | 1.79315i | −0.0314769 | − | 0.117473i | 0.948400 | − | 0.317077i | \(-0.102701\pi\) |
−0.979877 | + | 0.199603i | \(0.936035\pi\) | |||||||
\(234\) | −2.86603 | − | 4.96410i | −0.187358 | − | 0.324513i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.92820 | − | 5.73205i | −0.646271 | − | 0.373125i | ||||
\(237\) | −2.17209 | + | 2.17209i | −0.141092 | + | 0.141092i | ||||
\(238\) | −19.6975 | − | 1.41421i | −1.27680 | − | 0.0916698i | ||||
\(239\) | − | 24.0000i | − | 1.55243i | −0.630468 | − | 0.776215i | \(-0.717137\pi\) | ||
0.630468 | − | 0.776215i | \(-0.282863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.2846 | − | 11.1340i | 1.24223 | − | 0.717202i | 0.272683 | − | 0.962104i | \(-0.412089\pi\) |
0.969548 | + | 0.244902i | \(0.0787557\pi\) | |||||||
\(242\) | 2.58819 | − | 9.65926i | 0.166375 | − | 0.620921i | ||||
\(243\) | −0.965926 | + | 0.258819i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | −11.4641 | −0.733914 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.26795 | 0.144599 | ||||||||
\(247\) | −12.5570 | + | 3.36465i | −0.798985 | + | 0.214087i | ||||
\(248\) | 1.93185 | − | 7.20977i | 0.122673 | − | 0.457821i | ||||
\(249\) | 9.00000 | − | 5.19615i | 0.570352 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.33975i | 0.463281i | 0.972801 | + | 0.231640i | \(0.0744092\pi\) | ||||
−0.972801 | + | 0.231640i | \(0.925591\pi\) | |||||||
\(252\) | 2.63896 | + | 0.189469i | 0.166239 | + | 0.0119354i | ||||
\(253\) | 4.19187 | − | 4.19187i | 0.263541 | − | 0.263541i | ||||
\(254\) | −4.33013 | − | 2.50000i | −0.271696 | − | 0.156864i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.619174 | + | 2.31079i | 0.0386230 | + | 0.144143i | 0.982545 | − | 0.186026i | \(-0.0595609\pi\) |
−0.943922 | + | 0.330169i | \(0.892894\pi\) | |||||||
\(258\) | −6.31319 | − | 6.31319i | −0.393042 | − | 0.393042i | ||||
\(259\) | −10.2058 | + | 1.96410i | −0.634156 | + | 0.122043i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.46410 | − | 6.00000i | 0.214423 | − | 0.371391i | ||||
\(262\) | 3.98382 | + | 1.06746i | 0.246121 | + | 0.0659480i | ||||
\(263\) | −28.8391 | − | 7.72741i | −1.77829 | − | 0.476492i | −0.788023 | − | 0.615646i | \(-0.788895\pi\) |
−0.990271 | + | 0.139154i | \(0.955562\pi\) | |||||||
\(264\) | 0.500000 | − | 0.866025i | 0.0307729 | − | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.96410 | − | 5.66987i | 0.120427 | − | 0.347642i | ||||
\(267\) | −4.89898 | − | 4.89898i | −0.299813 | − | 0.299813i | ||||
\(268\) | −0.517638 | − | 1.93185i | −0.0316198 | − | 0.118007i | ||||
\(269\) | 12.6603 | + | 21.9282i | 0.771909 | + | 1.33699i | 0.936515 | + | 0.350627i | \(0.114031\pi\) |
−0.164606 | + | 0.986359i | \(0.552635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.92820 | + | 4.00000i | 0.420858 | + | 0.242983i | 0.695444 | − | 0.718580i | \(-0.255208\pi\) |
−0.274586 | + | 0.961563i | \(0.588541\pi\) | |||||||
\(272\) | 5.27792 | − | 5.27792i | 0.320021 | − | 0.320021i | ||||
\(273\) | 13.6431 | − | 6.62278i | 0.825717 | − | 0.400829i | ||||
\(274\) | 18.9282i | 1.14349i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.13397 | + | 2.96410i | −0.309029 | + | 0.178418i | ||||
\(277\) | 5.69402 | − | 21.2504i | 0.342120 | − | 1.27681i | −0.553820 | − | 0.832636i | \(-0.686830\pi\) |
0.895940 | − | 0.444174i | \(-0.146503\pi\) | |||||||
\(278\) | 10.0382 | − | 2.68973i | 0.602051 | − | 0.161319i | ||||
\(279\) | −7.46410 | −0.446864 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.9282 | −1.66606 | −0.833028 | − | 0.553230i | \(-0.813395\pi\) | ||||
−0.833028 | + | 0.553230i | \(0.813395\pi\) | |||||||
\(282\) | −1.15539 | + | 0.309587i | −0.0688027 | + | 0.0184356i | ||||
\(283\) | 3.24453 | − | 12.1087i | 0.192867 | − | 0.719790i | −0.799941 | − | 0.600078i | \(-0.795136\pi\) |
0.992809 | − | 0.119712i | \(-0.0381972\pi\) | |||||||
\(284\) | −7.73205 | + | 4.46410i | −0.458813 | + | 0.264896i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 5.73205i | − | 0.338943i | ||||||
\(287\) | −0.429705 | + | 5.98502i | −0.0253647 | + | 0.353285i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 33.5263 | + | 19.3564i | 1.97213 | + | 1.13861i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.46410 | + | 2.53590i | 0.0858272 | + | 0.148657i | ||||
\(292\) | 1.03528 | + | 3.86370i | 0.0605850 | + | 0.226106i | ||||
\(293\) | −1.22474 | − | 1.22474i | −0.0715504 | − | 0.0715504i | 0.670426 | − | 0.741976i | \(-0.266111\pi\) |
−0.741976 | + | 0.670426i | \(0.766111\pi\) | |||||||
\(294\) | −1.00000 | + | 6.92820i | −0.0583212 | + | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.96410 | − | 3.40192i | 0.114161 | − | 0.197733i | ||||
\(297\) | −0.965926 | − | 0.258819i | −0.0560487 | − | 0.0150182i | ||||
\(298\) | 0.896575 | + | 0.240237i | 0.0519372 | + | 0.0139165i | ||||
\(299\) | −16.9904 | + | 29.4282i | −0.982579 | + | 1.70188i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.8564 | − | 15.4641i | 1.02923 | − | 0.891336i | ||||
\(302\) | 2.72689 | + | 2.72689i | 0.156915 | + | 0.156915i | ||||
\(303\) | 0.277401 | + | 1.03528i | 0.0159363 | + | 0.0594751i | ||||
\(304\) | 1.13397 | + | 1.96410i | 0.0650379 | + | 0.112649i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.46410 | − | 3.73205i | −0.369528 | − | 0.213347i | ||||
\(307\) | −15.8338 | + | 15.8338i | −0.903680 | + | 0.903680i | −0.995752 | − | 0.0920724i | \(-0.970651\pi\) |
0.0920724 | + | 0.995752i | \(0.470651\pi\) | |||||||
\(308\) | 2.19067 | + | 1.48356i | 0.124825 | + | 0.0845339i | ||||
\(309\) | 18.3923i | 1.04630i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7846 | − | 10.2679i | 1.00847 | − | 0.582242i | 0.0977286 | − | 0.995213i | \(-0.468842\pi\) |
0.910744 | + | 0.412971i | \(0.135509\pi\) | |||||||
\(312\) | −1.48356 | + | 5.53674i | −0.0839903 | + | 0.313456i | ||||
\(313\) | 30.1146 | − | 8.06918i | 1.70218 | − | 0.456097i | 0.728691 | − | 0.684843i | \(-0.240129\pi\) |
0.973486 | + | 0.228746i | \(0.0734624\pi\) | |||||||
\(314\) | 4.66025 | 0.262993 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.07180 | 0.172802 | ||||||||
\(317\) | −13.5230 | + | 3.62347i | −0.759525 | + | 0.203514i | −0.617739 | − | 0.786383i | \(-0.711951\pi\) |
−0.141786 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(318\) | −0.258819 | + | 0.965926i | −0.0145139 | + | 0.0541664i | ||||
\(319\) | 6.00000 | − | 3.46410i | 0.335936 | − | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.9282i | 0.833211i | ||||||||
\(322\) | −6.84941 | − | 14.1100i | −0.381703 | − | 0.786317i | ||||
\(323\) | −11.9700 | + | 11.9700i | −0.666031 | + | 0.666031i | ||||
\(324\) | 0.866025 | + | 0.500000i | 0.0481125 | + | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.00000 | − | 10.3923i | −0.332309 | − | 0.575577i | ||||
\(327\) | 4.38134 | + | 16.3514i | 0.242289 | + | 0.904234i | ||||
\(328\) | −1.60368 | − | 1.60368i | −0.0885485 | − | 0.0885485i | ||||
\(329\) | −0.598076 | − | 3.10770i | −0.0329730 | − | 0.171333i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8923 | + | 22.3301i | −0.708625 | + | 1.22737i | 0.256742 | + | 0.966480i | \(0.417351\pi\) |
−0.965367 | + | 0.260895i | \(0.915982\pi\) | |||||||
\(332\) | −10.0382 | − | 2.68973i | −0.550918 | − | 0.147618i | ||||
\(333\) | −3.79435 | − | 1.01669i | −0.207929 | − | 0.0557145i | ||||
\(334\) | −3.40192 | + | 5.89230i | −0.186145 | + | 0.322413i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.73205 | − | 2.00000i | −0.0944911 | − | 0.109109i | ||||
\(337\) | 7.82894 | + | 7.82894i | 0.426470 | + | 0.426470i | 0.887424 | − | 0.460954i | \(-0.152493\pi\) |
−0.460954 | + | 0.887424i | \(0.652493\pi\) | |||||||
\(338\) | 5.13922 | + | 19.1798i | 0.279537 | + | 1.04324i | ||||
\(339\) | −6.46410 | − | 11.1962i | −0.351082 | − | 0.608092i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.46410 | − | 3.73205i | −0.350051 | − | 0.202102i | ||||
\(342\) | 1.60368 | − | 1.60368i | 0.0867172 | − | 0.0867172i | ||||
\(343\) | −18.0938 | − | 3.95164i | −0.976972 | − | 0.213368i | ||||
\(344\) | 8.92820i | 0.481376i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.57180 | + | 3.79423i | −0.353302 | + | 0.203979i | ||||
\(347\) | 0.757875 | − | 2.82843i | 0.0406848 | − | 0.151838i | −0.942595 | − | 0.333937i | \(-0.891623\pi\) |
0.983280 | + | 0.182099i | \(0.0582893\pi\) | |||||||
\(348\) | −6.69213 | + | 1.79315i | −0.358736 | + | 0.0961230i | ||||
\(349\) | −1.85641 | −0.0993712 | −0.0496856 | − | 0.998765i | \(-0.515822\pi\) | ||||
−0.0496856 | + | 0.998765i | \(0.515822\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.73205 | 0.305954 | ||||||||
\(352\) | −0.965926 | + | 0.258819i | −0.0514840 | + | 0.0137951i | ||||
\(353\) | −1.79315 | + | 6.69213i | −0.0954398 | + | 0.356186i | −0.997086 | − | 0.0762887i | \(-0.975693\pi\) |
0.901646 | + | 0.432475i | \(0.142360\pi\) | |||||||
\(354\) | 9.92820 | − | 5.73205i | 0.527678 | − | 0.304655i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.92820i | 0.367194i | ||||||||
\(357\) | 11.0735 | − | 16.3514i | 0.586070 | − | 0.865407i | ||||
\(358\) | −6.36396 | + | 6.36396i | −0.336346 | + | 0.336346i | ||||
\(359\) | 4.39230 | + | 2.53590i | 0.231817 | + | 0.133840i | 0.611410 | − | 0.791314i | \(-0.290603\pi\) |
−0.379593 | + | 0.925154i | \(0.623936\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.92820 | + | 12.0000i | 0.364642 | + | 0.631579i | ||||
\(362\) | −3.72500 | − | 13.9019i | −0.195782 | − | 0.730668i | ||||
\(363\) | 7.07107 | + | 7.07107i | 0.371135 | + | 0.371135i | ||||
\(364\) | −14.3301 | − | 4.96410i | −0.751103 | − | 0.260190i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.73205 | − | 9.92820i | 0.299619 | − | 0.518955i | ||||
\(367\) | 29.4768 | + | 7.89829i | 1.53868 | + | 0.412288i | 0.925838 | − | 0.377920i | \(-0.123360\pi\) |
0.612840 | + | 0.790207i | \(0.290027\pi\) | |||||||
\(368\) | 5.72620 | + | 1.53433i | 0.298499 | + | 0.0799826i | ||||
\(369\) | −1.13397 | + | 1.96410i | −0.0590324 | + | 0.102247i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.50000 | − | 0.866025i | −0.129794 | − | 0.0449618i | ||||
\(372\) | 5.27792 | + | 5.27792i | 0.273647 | + | 0.273647i | ||||
\(373\) | −6.72930 | − | 25.1141i | −0.348430 | − | 1.30036i | −0.888554 | − | 0.458772i | \(-0.848289\pi\) |
0.540124 | − | 0.841585i | \(-0.318377\pi\) | |||||||
\(374\) | −3.73205 | − | 6.46410i | −0.192980 | − | 0.334251i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.03590 | + | 0.598076i | 0.0534224 | + | 0.0308434i | ||||
\(377\) | −28.0812 | + | 28.0812i | −1.44626 | + | 1.44626i | ||||
\(378\) | −1.48356 | + | 2.19067i | −0.0763063 | + | 0.112676i | ||||
\(379\) | − | 3.92820i | − | 0.201778i | −0.994898 | − | 0.100889i | \(-0.967831\pi\) | ||
0.994898 | − | 0.100889i | \(-0.0321687\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.33013 | − | 2.50000i | 0.221839 | − | 0.128079i | ||||
\(382\) | −0.757875 | + | 2.82843i | −0.0387762 | + | 0.144715i | ||||
\(383\) | −21.2318 | + | 5.68904i | −1.08489 | + | 0.290696i | −0.756599 | − | 0.653879i | \(-0.773141\pi\) |
−0.328294 | + | 0.944575i | \(0.606474\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.7846 | −1.15971 | ||||||||
\(387\) | 8.62398 | − | 2.31079i | 0.438382 | − | 0.117464i | ||||
\(388\) | 0.757875 | − | 2.82843i | 0.0384753 | − | 0.143592i | ||||
\(389\) | 31.7321 | − | 18.3205i | 1.60888 | − | 0.928887i | 0.619257 | − | 0.785188i | \(-0.287434\pi\) |
0.989622 | − | 0.143699i | \(-0.0458996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.2487i | 2.23775i | ||||||||
\(392\) | 5.60609 | − | 4.19187i | 0.283150 | − | 0.211722i | ||||
\(393\) | −2.91636 | + | 2.91636i | −0.147111 | + | 0.147111i | ||||
\(394\) | −14.5981 | − | 8.42820i | −0.735440 | − | 0.424607i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.500000 | + | 0.866025i | 0.0251259 | + | 0.0435194i | ||||
\(397\) | −7.45001 | − | 27.8038i | −0.373905 | − | 1.39543i | −0.854938 | − | 0.518730i | \(-0.826405\pi\) |
0.481033 | − | 0.876702i | \(-0.340262\pi\) | |||||||
\(398\) | −8.86422 | − | 8.86422i | −0.444323 | − | 0.444323i | ||||
\(399\) | 3.92820 | + | 4.53590i | 0.196656 | + | 0.227079i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.964102 | + | 1.66987i | −0.0481449 | + | 0.0833895i | −0.889094 | − | 0.457725i | \(-0.848664\pi\) |
0.840949 | + | 0.541115i | \(0.181998\pi\) | |||||||
\(402\) | 1.93185 | + | 0.517638i | 0.0963520 | + | 0.0258174i | ||||
\(403\) | 41.3268 | + | 11.0735i | 2.05863 | + | 0.551609i | ||||
\(404\) | 0.535898 | − | 0.928203i | 0.0266619 | − | 0.0461798i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.46410 | − | 18.0000i | −0.171920 | − | 0.893325i | ||||
\(407\) | −2.77766 | − | 2.77766i | −0.137683 | − | 0.137683i | ||||
\(408\) | 1.93185 | + | 7.20977i | 0.0956409 | + | 0.356937i | ||||
\(409\) | −14.3923 | − | 24.9282i | −0.711654 | − | 1.23262i | −0.964236 | − | 0.265045i | \(-0.914613\pi\) |
0.252582 | − | 0.967575i | \(-0.418720\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.3923 | − | 9.46410i | −0.808573 | − | 0.466830i | ||||
\(412\) | 13.0053 | − | 13.0053i | 0.640726 | − | 0.640726i | ||||
\(413\) | 13.2456 | + | 27.2862i | 0.651771 | + | 1.34266i | ||||
\(414\) | − | 5.92820i | − | 0.291355i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.96410 | − | 2.86603i | 0.243385 | − | 0.140518i | ||||
\(417\) | −2.68973 | + | 10.0382i | −0.131716 | + | 0.491573i | ||||
\(418\) | 2.19067 | − | 0.586988i | 0.107149 | − | 0.0287105i | ||||
\(419\) | 11.0526 | 0.539953 | 0.269976 | − | 0.962867i | \(-0.412984\pi\) | ||||
0.269976 | + | 0.962867i | \(0.412984\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8564 | −0.675320 | −0.337660 | − | 0.941268i | \(-0.609635\pi\) | ||||
−0.337660 | + | 0.941268i | \(0.609635\pi\) | |||||||
\(422\) | −19.1105 | + | 5.12063i | −0.930283 | + | 0.249269i | ||||
\(423\) | 0.309587 | − | 1.15539i | 0.0150526 | − | 0.0561772i | ||||
\(424\) | 0.866025 | − | 0.500000i | 0.0420579 | − | 0.0242821i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 8.92820i | − | 0.432573i | ||||||
\(427\) | 25.1141 | + | 17.0077i | 1.21536 | + | 0.823062i | ||||
\(428\) | 10.5558 | − | 10.5558i | 0.510235 | − | 0.510235i | ||||
\(429\) | 4.96410 | + | 2.86603i | 0.239669 | + | 0.138373i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.8564 | + | 29.1962i | 0.811945 | + | 1.40633i | 0.911501 | + | 0.411297i | \(0.134924\pi\) |
−0.0995567 | + | 0.995032i | \(0.531742\pi\) | |||||||
\(432\) | −0.258819 | − | 0.965926i | −0.0124524 | − | 0.0464731i | ||||
\(433\) | 11.3137 | + | 11.3137i | 0.543702 | + | 0.543702i | 0.924612 | − | 0.380910i | \(-0.124389\pi\) |
−0.380910 | + | 0.924612i | \(0.624389\pi\) | |||||||
\(434\) | −14.9282 | + | 12.9282i | −0.716577 | + | 0.620574i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.46410 | − | 14.6603i | 0.405357 | − | 0.702099i | ||||
\(437\) | −12.9867 | − | 3.47979i | −0.621240 | − | 0.166461i | ||||
\(438\) | −3.86370 | − | 1.03528i | −0.184615 | − | 0.0494674i | ||||
\(439\) | 10.0000 | − | 17.3205i | 0.477274 | − | 0.826663i | −0.522387 | − | 0.852709i | \(-0.674958\pi\) |
0.999661 | + | 0.0260459i | \(0.00829161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.50000 | − | 4.33013i | −0.261905 | − | 0.206197i | ||||
\(442\) | 30.2533 | + | 30.2533i | 1.43900 | + | 1.43900i | ||||
\(443\) | 7.20977 | + | 26.9072i | 0.342546 | + | 1.27840i | 0.895452 | + | 0.445157i | \(0.146852\pi\) |
−0.552906 | + | 0.833244i | \(0.686481\pi\) | |||||||
\(444\) | 1.96410 | + | 3.40192i | 0.0932121 | + | 0.161448i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.07180 | + | 4.66025i | 0.382211 | + | 0.220669i | ||||
\(447\) | −0.656339 | + | 0.656339i | −0.0310438 | + | 0.0310438i | ||||
\(448\) | −0.189469 | + | 2.63896i | −0.00895155 | + | 0.124679i | ||||
\(449\) | − | 13.9282i | − | 0.657313i | −0.944450 | − | 0.328656i | \(-0.893404\pi\) | ||
0.944450 | − | 0.328656i | \(-0.106596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.96410 | + | 1.13397i | −0.0924859 | + | 0.0533968i | ||||
\(452\) | −3.34607 | + | 12.4877i | −0.157386 | + | 0.587371i | ||||
\(453\) | −3.72500 | + | 0.998111i | −0.175016 | + | 0.0468954i | ||||
\(454\) | −3.46410 | −0.162578 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.26795 | −0.106206 | ||||||||
\(457\) | 15.3161 | − | 4.10394i | 0.716458 | − | 0.191974i | 0.117867 | − | 0.993029i | \(-0.462394\pi\) |
0.598591 | + | 0.801055i | \(0.295728\pi\) | |||||||
\(458\) | 0.757875 | − | 2.82843i | 0.0354132 | − | 0.132164i | ||||
\(459\) | 6.46410 | − | 3.73205i | 0.301718 | − | 0.174197i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 38.6410i | − | 1.79969i | −0.436208 | − | 0.899846i | \(-0.643679\pi\) | ||
0.436208 | − | 0.899846i | \(-0.356321\pi\) | |||||||
\(462\) | −2.38014 | + | 1.15539i | −0.110734 | + | 0.0537538i | ||||
\(463\) | −16.0604 | + | 16.0604i | −0.746389 | + | 0.746389i | −0.973799 | − | 0.227410i | \(-0.926974\pi\) |
0.227410 | + | 0.973799i | \(0.426974\pi\) | |||||||
\(464\) | 6.00000 | + | 3.46410i | 0.278543 | + | 0.160817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.928203 | − | 1.60770i | −0.0429982 | − | 0.0744750i | ||||
\(467\) | −1.65445 | − | 6.17449i | −0.0765588 | − | 0.285721i | 0.917023 | − | 0.398833i | \(-0.130585\pi\) |
−0.993582 | + | 0.113112i | \(0.963918\pi\) | |||||||
\(468\) | −4.05317 | − | 4.05317i | −0.187358 | − | 0.187358i | ||||
\(469\) | −1.73205 | + | 5.00000i | −0.0799787 | + | 0.230879i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.33013 | + | 4.03590i | −0.107367 | + | 0.185964i | ||||
\(472\) | −11.0735 | − | 2.96713i | −0.509698 | − | 0.136573i | ||||
\(473\) | 8.62398 | + | 2.31079i | 0.396531 | + | 0.106250i | ||||
\(474\) | −1.53590 | + | 2.66025i | −0.0705461 | + | 0.122190i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −19.3923 | + | 3.73205i | −0.888845 | + | 0.171058i | ||||
\(477\) | −0.707107 | − | 0.707107i | −0.0323762 | − | 0.0323762i | ||||
\(478\) | −6.21166 | − | 23.1822i | −0.284115 | − | 1.06033i | ||||
\(479\) | −14.5359 | − | 25.1769i | −0.664162 | − | 1.15036i | −0.979512 | − | 0.201387i | \(-0.935455\pi\) |
0.315350 | − | 0.948976i | \(-0.397878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.5000 | + | 11.2583i | 0.889123 | + | 0.513336i | ||||
\(482\) | 15.7458 | − | 15.7458i | 0.717202 | − | 0.717202i | ||||
\(483\) | 15.6443 | + | 1.12321i | 0.711839 | + | 0.0511078i | ||||
\(484\) | − | 10.0000i | − | 0.454545i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 1.51575 | − | 5.65685i | 0.0686852 | − | 0.256337i | −0.923042 | − | 0.384699i | \(-0.874305\pi\) |
0.991727 | + | 0.128362i | \(0.0409720\pi\) | |||||||
\(488\) | −11.0735 | + | 2.96713i | −0.501273 | + | 0.134316i | ||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.7128 | −0.528592 | −0.264296 | − | 0.964442i | \(-0.585140\pi\) | ||||
−0.264296 | + | 0.964442i | \(0.585140\pi\) | |||||||
\(492\) | 2.19067 | − | 0.586988i | 0.0987631 | − | 0.0264635i | ||||
\(493\) | −13.3843 | + | 49.9507i | −0.602797 | + | 2.24967i | ||||
\(494\) | −11.2583 | + | 6.50000i | −0.506536 | + | 0.292449i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 7.46410i | − | 0.335148i | ||||||
\(497\) | 23.5612 | + | 1.69161i | 1.05686 | + | 0.0758793i | ||||
\(498\) | 7.34847 | − | 7.34847i | 0.329293 | − | 0.329293i | ||||
\(499\) | −24.2487 | − | 14.0000i | −1.08552 | − | 0.626726i | −0.153141 | − | 0.988204i | \(-0.548939\pi\) |
−0.932381 | + | 0.361478i | \(0.882272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.40192 | − | 5.89230i | −0.151987 | − | 0.263249i | ||||
\(502\) | 1.89967 | + | 7.08965i | 0.0847862 | + | 0.316427i | ||||
\(503\) | 9.62209 | + | 9.62209i | 0.429028 | + | 0.429028i | 0.888297 | − | 0.459269i | \(-0.151889\pi\) |
−0.459269 | + | 0.888297i | \(0.651889\pi\) | |||||||
\(504\) | 2.59808 | − | 0.500000i | 0.115728 | − | 0.0222718i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.96410 | − | 5.13397i | 0.131770 | − | 0.228233i | ||||
\(507\) | −19.1798 | − | 5.13922i | −0.851806 | − | 0.228241i | ||||
\(508\) | −4.82963 | − | 1.29410i | −0.214280 | − | 0.0574162i | ||||
\(509\) | 5.19615 | − | 9.00000i | 0.230315 | − | 0.398918i | −0.727586 | − | 0.686017i | \(-0.759358\pi\) |
0.957901 | + | 0.287099i | \(0.0926909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.46410 | − | 10.0000i | 0.153243 | − | 0.442374i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0.586988 | + | 2.19067i | 0.0259162 | + | 0.0967205i | ||||
\(514\) | 1.19615 | + | 2.07180i | 0.0527600 | + | 0.0913830i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.73205 | − | 4.46410i | −0.340385 | − | 0.196521i | ||||
\(517\) | 0.845807 | − | 0.845807i | 0.0371986 | − | 0.0371986i | ||||
\(518\) | −9.34967 | + | 4.53862i | −0.410801 | + | 0.199416i | ||||
\(519\) | − | 7.58846i | − | 0.333096i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.8205 | − | 16.0622i | 1.21884 | − | 0.703697i | 0.254169 | − | 0.967160i | \(-0.418198\pi\) |
0.964669 | + | 0.263463i | \(0.0848647\pi\) | |||||||
\(522\) | 1.79315 | − | 6.69213i | 0.0784841 | − | 0.292907i | ||||
\(523\) | −5.93426 | + | 1.59008i | −0.259487 | + | 0.0695293i | −0.386217 | − | 0.922408i | \(-0.626218\pi\) |
0.126730 | + | 0.991937i | \(0.459552\pi\) | |||||||
\(524\) | 4.12436 | 0.180173 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.8564 | −1.30180 | ||||||||
\(527\) | 53.8144 | − | 14.4195i | 2.34419 | − | 0.628125i | ||||
\(528\) | 0.258819 | − | 0.965926i | 0.0112637 | − | 0.0420365i | ||||
\(529\) | −10.5167 | + | 6.07180i | −0.457246 | + | 0.263991i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.4641i | 0.497500i | ||||||||
\(532\) | 0.429705 | − | 5.98502i | 0.0186301 | − | 0.259484i | ||||
\(533\) | 9.19239 | − | 9.19239i | 0.398167 | − | 0.398167i | ||||
\(534\) | −6.00000 | − | 3.46410i | −0.259645 | − | 0.149906i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.00000 | − | 1.73205i | −0.0431934 | − | 0.0748132i | ||||
\(537\) | −2.32937 | − | 8.69333i | −0.100520 | − | 0.375145i | ||||
\(538\) | 17.9043 | + | 17.9043i | 0.771909 | + | 0.771909i | ||||
\(539\) | −2.59808 | − | 6.50000i | −0.111907 | − | 0.279975i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.4641 | + | 26.7846i | −0.664854 | + | 1.15156i | 0.314471 | + | 0.949267i | \(0.398173\pi\) |
−0.979325 | + | 0.202293i | \(0.935161\pi\) | |||||||
\(542\) | 7.72741 | + | 2.07055i | 0.331921 | + | 0.0889378i | ||||
\(543\) | 13.9019 | + | 3.72500i | 0.596588 | + | 0.159855i | ||||
\(544\) | 3.73205 | − | 6.46410i | 0.160010 | − | 0.277146i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.4641 | − | 9.92820i | 0.490618 | − | 0.424888i | ||||
\(547\) | −18.1817 | − | 18.1817i | −0.777394 | − | 0.777394i | 0.201993 | − | 0.979387i | \(-0.435258\pi\) |
−0.979387 | + | 0.201993i | \(0.935258\pi\) | |||||||
\(548\) | 4.89898 | + | 18.2832i | 0.209274 | + | 0.781021i | ||||
\(549\) | 5.73205 | + | 9.92820i | 0.244638 | + | 0.423725i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.6077 | − | 7.85641i | −0.579707 | − | 0.334694i | ||||
\(552\) | −4.19187 | + | 4.19187i | −0.178418 | + | 0.178418i | ||||
\(553\) | −6.72930 | − | 4.55721i | −0.286159 | − | 0.193792i | ||||
\(554\) | − | 22.0000i | − | 0.934690i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.00000 | − | 5.19615i | 0.381685 | − | 0.220366i | ||||
\(557\) | 1.25693 | − | 4.69093i | 0.0532579 | − | 0.198761i | −0.934171 | − | 0.356826i | \(-0.883859\pi\) |
0.987429 | + | 0.158065i | \(0.0505256\pi\) | |||||||
\(558\) | −7.20977 | + | 1.93185i | −0.305214 | + | 0.0817818i | ||||
\(559\) | −51.1769 | −2.16455 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.46410 | 0.315135 | ||||||||
\(562\) | −26.9766 | + | 7.22835i | −1.13794 | + | 0.304910i | ||||
\(563\) | 0.619174 | − | 2.31079i | 0.0260951 | − | 0.0973881i | −0.951650 | − | 0.307184i | \(-0.900613\pi\) |
0.977745 | + | 0.209796i | \(0.0672800\pi\) | |||||||
\(564\) | −1.03590 | + | 0.598076i | −0.0436192 | + | 0.0251836i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 12.5359i | − | 0.526923i | ||||||
\(567\) | −1.15539 | − | 2.38014i | −0.0485220 | − | 0.0999565i | ||||
\(568\) | −6.31319 | + | 6.31319i | −0.264896 | + | 0.264896i | ||||
\(569\) | 27.5263 | + | 15.8923i | 1.15396 | + | 0.666240i | 0.949849 | − | 0.312707i | \(-0.101236\pi\) |
0.204112 | + | 0.978948i | \(0.434569\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.92820 | + | 12.0000i | 0.289936 | + | 0.502184i | 0.973794 | − | 0.227431i | \(-0.0730325\pi\) |
−0.683858 | + | 0.729615i | \(0.739699\pi\) | |||||||
\(572\) | −1.48356 | − | 5.53674i | −0.0620309 | − | 0.231503i | ||||
\(573\) | −2.07055 | − | 2.07055i | −0.0864986 | − | 0.0864986i | ||||
\(574\) | 1.13397 | + | 5.89230i | 0.0473312 | + | 0.245940i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 20.3538 | + | 5.45378i | 0.847339 | + | 0.227044i | 0.656264 | − | 0.754531i | \(-0.272136\pi\) |
0.191076 | + | 0.981575i | \(0.438802\pi\) | |||||||
\(578\) | 37.3937 | + | 10.0196i | 1.55537 | + | 0.416761i | ||||
\(579\) | 11.3923 | − | 19.7321i | 0.473448 | − | 0.820036i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.0000 | + | 20.7846i | 0.746766 | + | 0.862291i | ||||
\(582\) | 2.07055 | + | 2.07055i | 0.0858272 | + | 0.0858272i | ||||
\(583\) | −0.258819 | − | 0.965926i | −0.0107192 | − | 0.0400046i | ||||
\(584\) | 2.00000 | + | 3.46410i | 0.0827606 | + | 0.143346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.50000 | − | 0.866025i | −0.0619644 | − | 0.0357752i | ||||
\(587\) | 15.0759 | − | 15.0759i | 0.622248 | − | 0.622248i | −0.323858 | − | 0.946106i | \(-0.604980\pi\) |
0.946106 | + | 0.323858i | \(0.104980\pi\) | |||||||
\(588\) | 0.827225 | + | 6.95095i | 0.0341142 | + | 0.286652i | ||||
\(589\) | 16.9282i | 0.697514i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.5981 | − | 8.42820i | 0.600485 | − | 0.346690i | ||||
\(592\) | 1.01669 | − | 3.79435i | 0.0417859 | − | 0.155947i | ||||
\(593\) | −40.9478 | + | 10.9719i | −1.68153 | + | 0.450563i | −0.968181 | − | 0.250250i | \(-0.919487\pi\) |
−0.713344 | + | 0.700814i | \(0.752820\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.928203 | 0.0380207 | ||||||||
\(597\) | 12.1087 | − | 3.24453i | 0.495578 | − | 0.132790i | ||||
\(598\) | −8.79487 | + | 32.8229i | −0.359649 | + | 1.34223i | ||||
\(599\) | 36.2487 | − | 20.9282i | 1.48108 | − | 0.855103i | 0.481312 | − | 0.876549i | \(-0.340160\pi\) |
0.999770 | + | 0.0214460i | \(0.00682701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.7846i | 1.17415i | 0.809533 | + | 0.587074i | \(0.199720\pi\) | ||||
−0.809533 | + | 0.587074i | \(0.800280\pi\) | |||||||
\(602\) | 13.2456 | − | 19.5588i | 0.539849 | − | 0.797155i | ||||
\(603\) | −1.41421 | + | 1.41421i | −0.0575912 | + | 0.0575912i | ||||
\(604\) | 3.33975 | + | 1.92820i | 0.135892 | + | 0.0784575i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.535898 | + | 0.928203i | 0.0217694 | + | 0.0377057i | ||||
\(607\) | −4.93117 | − | 18.4034i | −0.200150 | − | 0.746969i | −0.990873 | − | 0.134796i | \(-0.956962\pi\) |
0.790724 | − | 0.612173i | \(-0.209705\pi\) | |||||||
\(608\) | 1.60368 | + | 1.60368i | 0.0650379 | + | 0.0650379i | ||||
\(609\) | 17.3205 | + | 6.00000i | 0.701862 | + | 0.243132i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.42820 | + | 5.93782i | −0.138690 | + | 0.240219i | ||||
\(612\) | −7.20977 | − | 1.93185i | −0.291438 | − | 0.0780905i | ||||
\(613\) | −17.3173 | − | 4.64016i | −0.699440 | − | 0.187414i | −0.108460 | − | 0.994101i | \(-0.534592\pi\) |
−0.590980 | + | 0.806686i | \(0.701259\pi\) | |||||||
\(614\) | −11.1962 | + | 19.3923i | −0.451840 | + | 0.782610i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.50000 | + | 0.866025i | 0.100728 | + | 0.0348932i | ||||
\(617\) | 2.17209 | + | 2.17209i | 0.0874450 | + | 0.0874450i | 0.749476 | − | 0.662031i | \(-0.230305\pi\) |
−0.662031 | + | 0.749476i | \(0.730305\pi\) | |||||||
\(618\) | 4.76028 | + | 17.7656i | 0.191486 | + | 0.714637i | ||||
\(619\) | −5.79423 | − | 10.0359i | −0.232890 | − | 0.403377i | 0.725768 | − | 0.687940i | \(-0.241485\pi\) |
−0.958657 | + | 0.284563i | \(0.908151\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.13397 | + | 2.96410i | 0.206019 | + | 0.118945i | ||||
\(622\) | 14.5211 | − | 14.5211i | 0.582242 | − | 0.582242i | ||||
\(623\) | 10.2784 | − | 15.1774i | 0.411797 | − | 0.608070i | ||||
\(624\) | 5.73205i | 0.229466i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.0000 | − | 15.5885i | 1.07914 | − | 0.623040i | ||||
\(627\) | −0.586988 | + | 2.19067i | −0.0234421 | + | 0.0874870i | ||||
\(628\) | 4.50146 | − | 1.20616i | 0.179628 | − | 0.0481311i | ||||
\(629\) | 29.3205 | 1.16909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.7846 | 1.70323 | 0.851614 | − | 0.524169i | \(-0.175624\pi\) | ||||
0.851614 | + | 0.524169i | \(0.175624\pi\) | |||||||
\(632\) | 2.96713 | − | 0.795040i | 0.118026 | − | 0.0316250i | ||||
\(633\) | 5.12063 | − | 19.1105i | 0.203527 | − | 0.759573i | ||||
\(634\) | −12.1244 | + | 7.00000i | −0.481520 | + | 0.278006i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.00000i | 0.0396526i | ||||||||
\(637\) | 24.0280 | + | 32.1344i | 0.952025 | + | 1.27321i | ||||
\(638\) | 4.89898 | − | 4.89898i | 0.193952 | − | 0.193952i | ||||
\(639\) | 7.73205 | + | 4.46410i | 0.305875 | + | 0.176597i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.9641 | − | 27.6506i | −0.630544 | − | 1.09213i | −0.987441 | − | 0.157991i | \(-0.949498\pi\) |
0.356897 | − | 0.934144i | \(-0.383835\pi\) | |||||||
\(642\) | 3.86370 | + | 14.4195i | 0.152488 | + | 0.569094i | ||||
\(643\) | 29.2180 | + | 29.2180i | 1.15225 | + | 1.15225i | 0.986101 | + | 0.166144i | \(0.0531318\pi\) |
0.166144 | + | 0.986101i | \(0.446868\pi\) | |||||||
\(644\) | −10.2679 | − | 11.8564i | −0.404614 | − | 0.467208i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.46410 | + | 14.6603i | −0.333016 | + | 0.576800i | ||||
\(647\) | −4.26122 | − | 1.14179i | −0.167526 | − | 0.0448884i | 0.174081 | − | 0.984731i | \(-0.444305\pi\) |
−0.341607 | + | 0.939843i | \(0.610971\pi\) | |||||||
\(648\) | 0.965926 | + | 0.258819i | 0.0379452 | + | 0.0101674i | ||||
\(649\) | −5.73205 | + | 9.92820i | −0.225003 | + | 0.389716i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.73205 | − | 19.3923i | −0.146271 | − | 0.760044i | ||||
\(652\) | −8.48528 | − | 8.48528i | −0.332309 | − | 0.332309i | ||||
\(653\) | −6.39615 | − | 23.8707i | −0.250301 | − | 0.934134i | −0.970645 | − | 0.240518i | \(-0.922683\pi\) |
0.720344 | − | 0.693617i | \(-0.243984\pi\) | |||||||
\(654\) | 8.46410 | + | 14.6603i | 0.330973 | + | 0.573261i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.96410 | − | 1.13397i | −0.0766853 | − | 0.0442743i | ||||
\(657\) | 2.82843 | − | 2.82843i | 0.110347 | − | 0.110347i | ||||
\(658\) | −1.38203 | − | 2.84701i | −0.0538771 | − | 0.110988i | ||||
\(659\) | 39.7128i | 1.54699i | 0.633801 | + | 0.773496i | \(0.281494\pi\) | ||||
−0.633801 | + | 0.773496i | \(0.718506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.85641 | − | 4.53590i | 0.305579 | − | 0.176426i | −0.339368 | − | 0.940654i | \(-0.610213\pi\) |
0.644946 | + | 0.764228i | \(0.276880\pi\) | |||||||
\(662\) | −6.67355 | + | 24.9060i | −0.259375 | + | 0.968000i | ||||
\(663\) | −41.3268 | + | 11.0735i | −1.60500 | + | 0.430058i | ||||
\(664\) | −10.3923 | −0.403300 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.92820 | −0.152215 | ||||||||
\(667\) | −39.6723 | + | 10.6302i | −1.53612 | + | 0.411602i | ||||
\(668\) | −1.76097 | + | 6.57201i | −0.0681338 | + | 0.254279i | ||||
\(669\) | −8.07180 | + | 4.66025i | −0.312074 | + | 0.180176i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4641i | 0.442567i | ||||||||
\(672\) | −2.19067 | − | 1.48356i | −0.0845070 | − | 0.0572297i | ||||
\(673\) | 17.5254 | − | 17.5254i | 0.675553 | − | 0.675553i | −0.283438 | − | 0.958991i | \(-0.591475\pi\) |
0.958991 | + | 0.283438i | \(0.0914749\pi\) | |||||||
\(674\) | 9.58846 | + | 5.53590i | 0.369334 | + | 0.213235i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.92820 | + | 17.1962i | 0.381854 | + | 0.661390i | ||||
\(677\) | 12.9360 | + | 48.2777i | 0.497170 | + | 1.85546i | 0.517522 | + | 0.855670i | \(0.326855\pi\) |
−0.0203517 | + | 0.999793i | \(0.506479\pi\) | |||||||
\(678\) | −9.14162 | − | 9.14162i | −0.351082 | − | 0.351082i | ||||
\(679\) | −5.85641 | + | 5.07180i | −0.224748 | + | 0.194638i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.73205 | − | 3.00000i | 0.0663723 | − | 0.114960i | ||||
\(682\) | −7.20977 | − | 1.93185i | −0.276076 | − | 0.0739744i | ||||
\(683\) | −13.6617 | − | 3.66063i | −0.522749 | − | 0.140070i | −0.0122111 | − | 0.999925i | \(-0.503887\pi\) |
−0.510538 | + | 0.859855i | \(0.670554\pi\) | |||||||
\(684\) | 1.13397 | − | 1.96410i | 0.0433586 | − | 0.0750993i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.5000 | + | 0.866025i | −0.706333 | + | 0.0330650i | ||||
\(687\) | 2.07055 | + | 2.07055i | 0.0789965 | + | 0.0789965i | ||||
\(688\) | 2.31079 | + | 8.62398i | 0.0880980 | + | 0.328786i | ||||
\(689\) | 2.86603 | + | 4.96410i | 0.109187 | + | 0.189117i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.8564 | − | 20.1244i | −1.32600 | − | 0.765567i | −0.341322 | − | 0.939947i | \(-0.610875\pi\) |
−0.984678 | + | 0.174380i | \(0.944208\pi\) | |||||||
\(692\) | −5.36585 | + | 5.36585i | −0.203979 | + | 0.203979i | ||||
\(693\) | 0.189469 | − | 2.63896i | 0.00719732 | − | 0.100246i | ||||
\(694\) | − | 2.92820i | − | 0.111153i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.00000 | + | 3.46410i | −0.227429 | + | 0.131306i | ||||
\(697\) | 4.38134 | − | 16.3514i | 0.165955 | − | 0.619353i | ||||
\(698\) | −1.79315 | + | 0.480473i | −0.0678718 | + | 0.0181862i | ||||
\(699\) | 1.85641 | 0.0702157 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.14359 | −0.156501 | −0.0782507 | − | 0.996934i | \(-0.524933\pi\) | ||||
−0.0782507 | + | 0.996934i | \(0.524933\pi\) | |||||||
\(702\) | 5.53674 | − | 1.48356i | 0.208971 | − | 0.0559935i | ||||
\(703\) | −2.30581 | + | 8.60540i | −0.0869653 | + | 0.324559i | ||||
\(704\) | −0.866025 | + | 0.500000i | −0.0326396 | + | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.92820i | 0.260746i | ||||||||
\(707\) | −2.55103 | + | 1.23835i | −0.0959412 | + | 0.0465729i | ||||
\(708\) | 8.10634 | − | 8.10634i | 0.304655 | − | 0.304655i | ||||
\(709\) | −23.3205 | − | 13.4641i | −0.875820 | − | 0.505655i | −0.00654213 | − | 0.999979i | \(-0.502082\pi\) |
−0.869278 | + | 0.494324i | \(0.835416\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.53590 | − | 2.66025i | −0.0576007 | − | 0.0997673i | ||||
\(712\) | 1.79315 | + | 6.69213i | 0.0672012 | + | 0.250798i | ||||
\(713\) | 31.2886 | + | 31.2886i | 1.17177 | + | 1.17177i | ||||
\(714\) | 6.46410 | − | 18.6603i | 0.241913 | − | 0.698342i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.50000 | + | 7.79423i | −0.168173 | + | 0.291284i | ||||
\(717\) | 23.1822 | + | 6.21166i | 0.865756 | + | 0.231979i | ||||
\(718\) | 4.89898 | + | 1.31268i | 0.182828 | + | 0.0489887i | ||||
\(719\) | −3.19615 | + | 5.53590i | −0.119196 | + | 0.206454i | −0.919449 | − | 0.393208i | \(-0.871365\pi\) |
0.800253 | + | 0.599662i | \(0.204698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.7846 | + | 9.19615i | −1.77959 | + | 0.342483i | ||||
\(722\) | 9.79796 | + | 9.79796i | 0.364642 | + | 0.364642i | ||||
\(723\) | 5.76337 | + | 21.5092i | 0.214342 | + | 0.799935i | ||||
\(724\) | −7.19615 | − | 12.4641i | −0.267443 | − | 0.463225i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.66025 | + | 5.00000i | 0.321412 | + | 0.185567i | ||||
\(727\) | −10.8468 | + | 10.8468i | −0.402287 | + | 0.402287i | −0.879038 | − | 0.476751i | \(-0.841814\pi\) |
0.476751 | + | 0.879038i | \(0.341814\pi\) | |||||||
\(728\) | −15.1266 | − | 1.08604i | −0.560631 | − | 0.0402515i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −57.7128 | + | 33.3205i | −2.13459 | + | 1.23240i | ||||
\(732\) | 2.96713 | − | 11.0735i | 0.109668 | − | 0.409287i | ||||
\(733\) | 14.5397 | − | 3.89589i | 0.537034 | − | 0.143898i | 0.0198997 | − | 0.999802i | \(-0.493665\pi\) |
0.517135 | + | 0.855904i | \(0.326999\pi\) | |||||||
\(734\) | 30.5167 | 1.12639 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.92820 | 0.218516 | ||||||||
\(737\) | −1.93185 | + | 0.517638i | −0.0711607 | + | 0.0190674i | ||||
\(738\) | −0.586988 | + | 2.19067i | −0.0216073 | + | 0.0806397i | ||||
\(739\) | −17.2583 | + | 9.96410i | −0.634858 | + | 0.366535i | −0.782631 | − | 0.622486i | \(-0.786123\pi\) |
0.147773 | + | 0.989021i | \(0.452789\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 13.0000i | − | 0.477567i | ||||||
\(742\) | −2.63896 | − | 0.189469i | −0.0968792 | − | 0.00695561i | ||||
\(743\) | −5.50455 | + | 5.50455i | −0.201942 | + | 0.201942i | −0.800832 | − | 0.598889i | \(-0.795609\pi\) |
0.598889 | + | 0.800832i | \(0.295609\pi\) | |||||||
\(744\) | 6.46410 | + | 3.73205i | 0.236985 | + | 0.136824i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.0000 | − | 22.5167i | −0.475964 | − | 0.824394i | ||||
\(747\) | 2.68973 | + | 10.0382i | 0.0984119 | + | 0.367278i | ||||
\(748\) | −5.27792 | − | 5.27792i | −0.192980 | − | 0.192980i | ||||
\(749\) | −38.7846 | + | 7.46410i | −1.41716 | + | 0.272732i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.92820 | − | 12.0000i | 0.252814 | − | 0.437886i | −0.711486 | − | 0.702701i | \(-0.751977\pi\) |
0.964299 | + | 0.264814i | \(0.0853107\pi\) | |||||||
\(752\) | 1.15539 | + | 0.309587i | 0.0421329 | + | 0.0112895i | ||||
\(753\) | −7.08965 | − | 1.89967i | −0.258361 | − | 0.0692277i | ||||
\(754\) | −19.8564 | + | 34.3923i | −0.723128 | + | 1.25249i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.866025 | + | 2.50000i | −0.0314970 | + | 0.0909241i | ||||
\(757\) | −26.6670 | − | 26.6670i | −0.969228 | − | 0.969228i | 0.0303124 | − | 0.999540i | \(-0.490350\pi\) |
−0.999540 | + | 0.0303124i | \(0.990350\pi\) | |||||||
\(758\) | −1.01669 | − | 3.79435i | −0.0369280 | − | 0.137817i | ||||
\(759\) | 2.96410 | + | 5.13397i | 0.107590 | + | 0.186351i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.8923 | + | 24.1865i | 1.51859 | + | 0.876761i | 0.999760 | + | 0.0218864i | \(0.00696721\pi\) |
0.518834 | + | 0.854875i | \(0.326366\pi\) | |||||||
\(762\) | 3.53553 | − | 3.53553i | 0.128079 | − | 0.128079i | ||||
\(763\) | −40.2915 | + | 19.5588i | −1.45865 | + | 0.708074i | ||||
\(764\) | 2.92820i | 0.105939i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.0359 | + | 10.9904i | −0.687795 | + | 0.397099i | ||||
\(767\) | 17.0077 | − | 63.4737i | 0.614113 | − | 2.29190i | ||||
\(768\) | 0.965926 | − | 0.258819i | 0.0348548 | − | 0.00933933i | ||||
\(769\) | 10.8038 | 0.389597 | 0.194798 | − | 0.980843i | \(-0.437595\pi\) | ||||
0.194798 | + | 0.980843i | \(0.437595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.39230 | −0.0861568 | ||||||||
\(772\) | −22.0082 | + | 5.89709i | −0.792094 | + | 0.212241i | ||||
\(773\) | 9.41404 | − | 35.1337i | 0.338600 | − | 1.26367i | −0.561314 | − | 0.827603i | \(-0.689704\pi\) |
0.899914 | − | 0.436068i | \(-0.143629\pi\) | |||||||
\(774\) | 7.73205 | − | 4.46410i | 0.277923 | − | 0.160459i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 2.92820i | − | 0.105116i | ||||||
\(777\) | 0.744272 | − | 10.3664i | 0.0267006 | − | 0.371891i | ||||
\(778\) | 25.9091 | − | 25.9091i | 0.928887 | − | 0.928887i | ||||
\(779\) | 4.45448 | + | 2.57180i | 0.159598 | + | 0.0921442i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.46410 | + | 7.73205i | 0.159738 | + | 0.276675i | ||||
\(782\) | 11.4524 | + | 42.7410i | 0.409537 | + | 1.52841i | ||||
\(783\) | 4.89898 | + | 4.89898i | 0.175075 | + | 0.175075i | ||||
\(784\) | 4.33013 | − | 5.50000i | 0.154647 | − | 0.196429i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.06218 | + | 3.57180i | −0.0735554 | + | 0.127402i | ||||
\(787\) | 2.31079 | + | 0.619174i | 0.0823707 | + | 0.0220712i | 0.299769 | − | 0.954012i | \(-0.403090\pi\) |
−0.217398 | + | 0.976083i | \(0.569757\pi\) | |||||||
\(788\) | −16.2820 | − | 4.36276i | −0.580024 | − | 0.155417i | ||||
\(789\) | 14.9282 | − | 25.8564i | 0.531458 | − | 0.920512i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.8564 | − | 22.3923i | 0.919348 | − | 0.796179i | ||||
\(792\) | 0.707107 | + | 0.707107i | 0.0251259 | + | 0.0251259i | ||||
\(793\) | −17.0077 | − | 63.4737i | −0.603962 | − | 2.25402i | ||||
\(794\) | −14.3923 | − | 24.9282i | −0.510764 | − | 0.884669i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.8564 | − | 6.26795i | −0.384795 | − | 0.222162i | ||||
\(797\) | −21.1117 | + | 21.1117i | −0.747814 | + | 0.747814i | −0.974068 | − | 0.226255i | \(-0.927352\pi\) |
0.226255 | + | 0.974068i | \(0.427352\pi\) | |||||||
\(798\) | 4.96833 | + | 3.36465i | 0.175877 | + | 0.119107i | ||||
\(799\) | 8.92820i | 0.315857i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | − | 3.46410i | 0.212000 | − | 0.122398i | ||||
\(802\) | −0.499056 | + | 1.86250i | −0.0176223 | + | 0.0657672i | ||||
\(803\) | 3.86370 | − | 1.03528i | 0.136347 | − | 0.0365341i | ||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 42.7846 | 1.50702 | ||||||||
\(807\) | −24.4577 | + | 6.55343i | −0.860953 | + | 0.230692i | ||||
\(808\) | 0.277401 | − | 1.03528i | 0.00975895 | − | 0.0364209i | ||||
\(809\) | −22.2058 | + | 12.8205i | −0.780713 | + | 0.450745i | −0.836683 | − | 0.547687i | \(-0.815508\pi\) |
0.0559697 | + | 0.998432i | \(0.482175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.51666i | 0.0883719i | 0.999023 | + | 0.0441860i | \(0.0140694\pi\) | ||||
−0.999023 | + | 0.0441860i | \(0.985931\pi\) | |||||||
\(812\) | −8.00481 | − | 16.4901i | −0.280914 | − | 0.578689i | ||||
\(813\) | −5.65685 | + | 5.65685i | −0.198395 | + | 0.198395i | ||||
\(814\) | −3.40192 | − | 1.96410i | −0.119237 | − | 0.0688417i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.73205 | + | 6.46410i | 0.130648 | + | 0.226289i | ||||
\(817\) | −5.24075 | − | 19.5588i | −0.183351 | − | 0.684274i | ||||
\(818\) | −20.3538 | − | 20.3538i | −0.711654 | − | 0.711654i | ||||
\(819\) | 2.86603 | + | 14.8923i | 0.100147 | + | 0.520379i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.9282 | − | 20.6603i | 0.416297 | − | 0.721048i | −0.579266 | − | 0.815138i | \(-0.696661\pi\) |
0.995564 | + | 0.0940904i | \(0.0299943\pi\) | |||||||
\(822\) | −18.2832 | − | 4.89898i | −0.637701 | − | 0.170872i | ||||
\(823\) | 34.4959 | + | 9.24316i | 1.20245 | + | 0.322196i | 0.803796 | − | 0.594904i | \(-0.202810\pi\) |
0.398656 | + | 0.917101i | \(0.369477\pi\) | |||||||
\(824\) | 9.19615 | − | 15.9282i | 0.320363 | − | 0.554885i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.8564 | + | 22.9282i | 0.690893 | + | 0.797774i | ||||
\(827\) | 31.0112 | + | 31.0112i | 1.07836 | + | 1.07836i | 0.996656 | + | 0.0817074i | \(0.0260373\pi\) |
0.0817074 | + | 0.996656i | \(0.473963\pi\) | |||||||
\(828\) | −1.53433 | − | 5.72620i | −0.0533217 | − | 0.198999i | ||||
\(829\) | 8.26795 | + | 14.3205i | 0.287158 | + | 0.497372i | 0.973130 | − | 0.230256i | \(-0.0739563\pi\) |
−0.685972 | + | 0.727628i | \(0.740623\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.0526 | + | 11.0000i | 0.660926 | + | 0.381586i | ||||
\(832\) | 4.05317 | − | 4.05317i | 0.140518 | − | 0.140518i | ||||
\(833\) | 48.0189 | + | 20.5940i | 1.66376 | + | 0.713541i | ||||
\(834\) | 10.3923i | 0.359856i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.96410 | − | 1.13397i | 0.0679299 | − | 0.0392193i | ||||
\(837\) | 1.93185 | − | 7.20977i | 0.0667746 | − | 0.249206i | ||||
\(838\) | 10.6760 | − | 2.86061i | 0.368795 | − | 0.0988182i | ||||
\(839\) | 8.53590 | 0.294692 | 0.147346 | − | 0.989085i | \(-0.452927\pi\) | ||||
0.147346 | + | 0.989085i | \(0.452927\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | −13.3843 | + | 3.58630i | −0.461252 | + | 0.123592i | ||||
\(843\) | 7.22835 | − | 26.9766i | 0.248958 | − | 0.929123i | ||||
\(844\) | −17.1340 | + | 9.89230i | −0.589776 | + | 0.340507i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 1.19615i | − | 0.0411246i | ||||||
\(847\) | −14.8356 | + | 21.9067i | −0.509759 | + | 0.752723i | ||||
\(848\) | 0.707107 | − | 0.707107i | 0.0242821 | − | 0.0242821i | ||||
\(849\) | 10.8564 | + | 6.26795i | 0.372591 | + | 0.215115i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.6436 | + | 20.1673i | 0.399137 | + | 0.691326i | ||||
\(852\) | −2.31079 | − | 8.62398i | −0.0791663 | − | 0.295453i | ||||
\(853\) | −5.56892 | − | 5.56892i | −0.190676 | − | 0.190676i | 0.605312 | − | 0.795988i | \(-0.293048\pi\) |
−0.795988 | + | 0.605312i | \(0.793048\pi\) | |||||||
\(854\) | 28.6603 | + | 9.92820i | 0.980734 | + | 0.339736i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.46410 | − | 12.9282i | 0.255118 | − | 0.441877i | ||||
\(857\) | −15.4548 | − | 4.14110i | −0.527926 | − | 0.141457i | −0.0149958 | − | 0.999888i | \(-0.504773\pi\) |
−0.512931 | + | 0.858430i | \(0.671440\pi\) | |||||||
\(858\) | 5.53674 | + | 1.48356i | 0.189021 | + | 0.0506480i | ||||
\(859\) | −6.80385 | + | 11.7846i | −0.232144 | + | 0.402086i | −0.958439 | − | 0.285298i | \(-0.907907\pi\) |
0.726295 | + | 0.687384i | \(0.241241\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.66987 | − | 1.96410i | −0.193229 | − | 0.0669364i | ||||
\(862\) | 23.8386 | + | 23.8386i | 0.811945 | + | 0.811945i | ||||
\(863\) | −10.2598 | − | 38.2903i | −0.349249 | − | 1.30342i | −0.887569 | − | 0.460675i | \(-0.847607\pi\) |
0.538319 | − | 0.842741i | \(-0.319059\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.8564 | + | 8.00000i | 0.470860 | + | 0.271851i | ||||
\(867\) | −27.3741 | + | 27.3741i | −0.929673 | + | 0.929673i | ||||
\(868\) | −11.0735 | + | 16.3514i | −0.375858 | + | 0.555002i | ||||
\(869\) | − | 3.07180i | − | 0.104204i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.92820 | − | 5.73205i | 0.336404 | − | 0.194223i | ||||
\(872\) | 4.38134 | − | 16.3514i | 0.148371 | − | 0.553728i | ||||
\(873\) | −2.82843 | + | 0.757875i | −0.0957278 | + | 0.0256502i | ||||
\(874\) | −13.4449 | −0.454779 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | −3.79435 | + | 1.01669i | −0.128126 | + | 0.0343313i | −0.322312 | − | 0.946633i | \(-0.604460\pi\) |
0.194186 | + | 0.980965i | \(0.437793\pi\) | |||||||
\(878\) | 5.17638 | − | 19.3185i | 0.174694 | − | 0.651968i | ||||
\(879\) | 1.50000 | − | 0.866025i | 0.0505937 | − | 0.0292103i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 36.9090i | − | 1.24349i | −0.783218 | − | 0.621747i | \(-0.786423\pi\) | ||
0.783218 | − | 0.621747i | \(-0.213577\pi\) | |||||||
\(882\) | −6.43331 | − | 2.75908i | −0.216621 | − | 0.0929029i | ||||
\(883\) | −24.6980 | + | 24.6980i | −0.831153 | + | 0.831153i | −0.987675 | − | 0.156522i | \(-0.949972\pi\) |
0.156522 | + | 0.987675i | \(0.449972\pi\) | |||||||
\(884\) | 37.0526 | + | 21.3923i | 1.24621 | + | 0.719501i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.9282 | + | 24.1244i | 0.467927 | + | 0.810474i | ||||
\(887\) | −0.896575 | − | 3.34607i | −0.0301041 | − | 0.112350i | 0.949239 | − | 0.314556i | \(-0.101856\pi\) |
−0.979343 | + | 0.202206i | \(0.935189\pi\) | |||||||
\(888\) | 2.77766 | + | 2.77766i | 0.0932121 | + | 0.0932121i | ||||
\(889\) | 8.66025 | + | 10.0000i | 0.290456 | + | 0.335389i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | 9.00292 | + | 2.41233i | 0.301440 | + | 0.0807706i | ||||
\(893\) | −2.62038 | − | 0.702128i | −0.0876875 | − | 0.0234958i | ||||
\(894\) | −0.464102 | + | 0.803848i | −0.0155219 | + | 0.0268847i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | + | 2.59808i | 0.0167038 | + | 0.0867956i | ||||
\(897\) | −24.0280 | − | 24.0280i | −0.802272 | − | 0.802272i | ||||
\(898\) | −3.60488 | − | 13.4536i | −0.120297 | − | 0.448953i | ||||
\(899\) | 25.8564 | + | 44.7846i | 0.862359 | + | 1.49365i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.46410 | + | 3.73205i | 0.215350 | + | 0.124333i | ||||
\(902\) | −1.60368 | + | 1.60368i | −0.0533968 | + | 0.0533968i | ||||
\(903\) | 10.3156 | + | 21.2504i | 0.343282 | + | 0.707168i | ||||
\(904\) | 12.9282i | 0.429986i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.33975 | + | 1.92820i | −0.110956 | + | 0.0640603i | ||||
\(907\) | −0.554803 | + | 2.07055i | −0.0184219 | + | 0.0687516i | −0.974525 | − | 0.224279i | \(-0.927997\pi\) |
0.956103 | + | 0.293031i | \(0.0946639\pi\) | |||||||
\(908\) | −3.34607 | + | 0.896575i | −0.111043 | + | 0.0297539i | ||||
\(909\) | −1.07180 | −0.0355493 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.28719 | −0.0757779 | −0.0378889 | − | 0.999282i | \(-0.512063\pi\) | ||||
−0.0378889 | + | 0.999282i | \(0.512063\pi\) | |||||||
\(912\) | −2.19067 | + | 0.586988i | −0.0725404 | + | 0.0194371i | ||||
\(913\) | −2.68973 | + | 10.0382i | −0.0890170 | + | 0.332216i | ||||
\(914\) | 13.7321 | − | 7.92820i | 0.454216 | − | 0.262242i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 2.92820i | − | 0.0967506i | ||||||
\(917\) | −9.03511 | − | 6.11875i | −0.298365 | − | 0.202059i | ||||
\(918\) | 5.27792 | − | 5.27792i | 0.174197 | − | 0.174197i | ||||
\(919\) | −38.7846 | − | 22.3923i | −1.27939 | − | 0.738654i | −0.302651 | − | 0.953102i | \(-0.597872\pi\) |
−0.976736 | + | 0.214448i | \(0.931205\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.1962 | − | 19.3923i | −0.368926 | − | 0.638998i | ||||
\(922\) | −10.0010 | − | 37.3244i | −0.329366 | − | 1.22921i | ||||
\(923\) | −36.1875 | − | 36.1875i | −1.19113 | − | 1.19113i | ||||
\(924\) | −2.00000 | + | 1.73205i | −0.0657952 | + | 0.0569803i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.3564 | + | 19.6699i | −0.373195 | + | 0.646392i | ||||
\(927\) | −17.7656 | − | 4.76028i | −0.583499 | − | 0.156348i | ||||
\(928\) | 6.69213 | + | 1.79315i | 0.219680 | + | 0.0588631i | ||||
\(929\) | −8.06218 | + | 13.9641i | −0.264511 | + | 0.458147i | −0.967436 | − | 0.253118i | \(-0.918544\pi\) |
0.702924 | + | 0.711265i | \(0.251877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.82051 | + | 12.4737i | −0.321854 | + | 0.408810i | ||||
\(932\) | −1.31268 | − | 1.31268i | −0.0429982 | − | 0.0429982i | ||||
\(933\) | 5.31508 | + | 19.8362i | 0.174008 | + | 0.649407i | ||||
\(934\) | −3.19615 | − | 5.53590i | −0.104581 | − | 0.181140i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.96410 | − | 2.86603i | −0.162257 | − | 0.0936790i | ||||
\(937\) | −6.79367 | + | 6.79367i | −0.221939 | + | 0.221939i | −0.809315 | − | 0.587375i | \(-0.800161\pi\) |
0.587375 | + | 0.809315i | \(0.300161\pi\) | |||||||
\(938\) | −0.378937 | + | 5.27792i | −0.0123727 | + | 0.172330i | ||||
\(939\) | 31.1769i | 1.01742i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.67949 | − | 3.85641i | 0.217745 | − | 0.125715i | −0.387161 | − | 0.922012i | \(-0.626544\pi\) |
0.604906 | + | 0.796297i | \(0.293211\pi\) | |||||||
\(942\) | −1.20616 | + | 4.50146i | −0.0392989 | + | 0.146665i | ||||
\(943\) | 12.9867 | − | 3.47979i | 0.422906 | − | 0.113317i | ||||
\(944\) | −11.4641 | −0.373125 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.92820 | 0.290281 | ||||||||
\(947\) | 17.5254 | − | 4.69591i | 0.569498 | − | 0.152596i | 0.0374316 | − | 0.999299i | \(-0.488082\pi\) |
0.532066 | + | 0.846703i | \(0.321416\pi\) | |||||||
\(948\) | −0.795040 | + | 2.96713i | −0.0258217 | + | 0.0963678i | ||||
\(949\) | −19.8564 | + | 11.4641i | −0.644566 | + | 0.372140i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 14.0000i | − | 0.453981i | ||||||
\(952\) | −17.7656 | + | 8.62398i | −0.575786 | + | 0.279505i | ||||
\(953\) | 32.2223 | − | 32.2223i | 1.04378 | − | 1.04378i | 0.0447862 | − | 0.998997i | \(-0.485739\pi\) |
0.998997 | − | 0.0447862i | \(-0.0142607\pi\) | |||||||
\(954\) | −0.866025 | − | 0.500000i | −0.0280386 | − | 0.0161881i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.0000 | − | 20.7846i | −0.388108 | − | 0.672222i | ||||
\(957\) | 1.79315 | + | 6.69213i | 0.0579643 | + | 0.216326i | ||||
\(958\) | −20.5569 | − | 20.5569i | −0.664162 | − | 0.664162i | ||||
\(959\) | 16.3923 | − | 47.3205i | 0.529335 | − | 1.52806i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3564 | − | 21.4019i | 0.398594 | − | 0.690385i | ||||
\(962\) | 21.7494 | + | 5.82774i | 0.701230 | + | 0.187894i | ||||
\(963\) | −14.4195 | − | 3.86370i | −0.464663 | − | 0.124506i | ||||
\(964\) | 11.1340 | − | 19.2846i | 0.358601 | − | 0.621115i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.4019 | − | 2.96410i | 0.495549 | − | 0.0953684i | ||||
\(967\) | 21.1117 | + | 21.1117i | 0.678905 | + | 0.678905i | 0.959753 | − | 0.280847i | \(-0.0906154\pi\) |
−0.280847 | + | 0.959753i | \(0.590615\pi\) | |||||||
\(968\) | −2.58819 | − | 9.65926i | −0.0831876 | − | 0.310460i | ||||
\(969\) | −8.46410 | − | 14.6603i | −0.271906 | − | 0.470955i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.2128 | − | 22.0622i | −1.22631 | − | 0.708009i | −0.260052 | − | 0.965595i | \(-0.583740\pi\) |
−0.966255 | + | 0.257586i | \(0.917073\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −27.4249 | − | 1.96902i | −0.879201 | − | 0.0631238i | ||||
\(974\) | − | 5.85641i | − | 0.187651i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.92820 | + | 5.73205i | −0.317794 | + | 0.183478i | ||||
\(977\) | −7.76457 | + | 28.9778i | −0.248411 | + | 0.927081i | 0.723228 | + | 0.690610i | \(0.242658\pi\) |
−0.971638 | + | 0.236472i | \(0.924009\pi\) | |||||||
\(978\) | 11.5911 | − | 3.10583i | 0.370643 | − | 0.0993134i | ||||
\(979\) | 6.92820 | 0.221426 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.9282 | −0.540476 | ||||||||
\(982\) | −11.3137 | + | 3.03150i | −0.361035 | + | 0.0967390i | ||||
\(983\) | 14.5261 | − | 54.2120i | 0.463309 | − | 1.72909i | −0.199126 | − | 0.979974i | \(-0.563810\pi\) |
0.662435 | − | 0.749119i | \(-0.269523\pi\) | |||||||
\(984\) | 1.96410 | − | 1.13397i | 0.0626133 | − | 0.0361498i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 51.7128i | 1.64687i | ||||||||
\(987\) | 3.15660 | + | 0.226633i | 0.100476 | + | 0.00721382i | ||||
\(988\) | −9.19239 | + | 9.19239i | −0.292449 | + | 0.292449i | ||||
\(989\) | −45.8372 | − | 26.4641i | −1.45754 | − | 0.841509i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.3923 | − | 21.4641i | −0.393655 | − | 0.681830i | 0.599274 | − | 0.800544i | \(-0.295456\pi\) |
−0.992928 | + | 0.118714i | \(0.962123\pi\) | |||||||
\(992\) | −1.93185 | − | 7.20977i | −0.0613364 | − | 0.228910i | ||||
\(993\) | −18.2325 | − | 18.2325i | −0.578590 | − | 0.578590i | ||||
\(994\) | 23.1962 | − | 4.46410i | 0.735737 | − | 0.141593i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.19615 | − | 9.00000i | 0.164646 | − | 0.285176i | ||||
\(997\) | 3.58630 | + | 0.960947i | 0.113579 | + | 0.0304335i | 0.315161 | − | 0.949038i | \(-0.397941\pi\) |
−0.201582 | + | 0.979472i | \(0.564608\pi\) | |||||||
\(998\) | −27.0459 | − | 7.24693i | −0.856124 | − | 0.229398i | ||||
\(999\) | 1.96410 | − | 3.40192i | 0.0621414 | − | 0.107632i |
(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 | 1050.2.bc.a.607.2 | yes | 8 | |
5.2 | odd | 4 | 1050.2.bc.d.943.2 | yes | 8 | ||
5.3 | odd | 4 | 1050.2.bc.d.943.1 | yes | 8 | ||
5.4 | even | 2 | inner | 1050.2.bc.a.607.1 | yes | 8 | |
7.3 | odd | 6 | 1050.2.bc.d.157.1 | yes | 8 | ||
35.3 | even | 12 | inner | 1050.2.bc.a.493.2 | yes | 8 | |
35.17 | even | 12 | inner | 1050.2.bc.a.493.1 | ✓ | 8 | |
35.24 | odd | 6 | 1050.2.bc.d.157.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.bc.a.493.1 | ✓ | 8 | 35.17 | even | 12 | inner | |
1050.2.bc.a.493.2 | yes | 8 | 35.3 | even | 12 | inner | |
1050.2.bc.a.607.1 | yes | 8 | 5.4 | even | 2 | inner | |
1050.2.bc.a.607.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1050.2.bc.d.157.1 | yes | 8 | 7.3 | odd | 6 | ||
1050.2.bc.d.157.2 | yes | 8 | 35.24 | odd | 6 | ||
1050.2.bc.d.943.1 | yes | 8 | 5.3 | odd | 4 | ||
1050.2.bc.d.943.2 | yes | 8 | 5.2 | odd | 4 |