Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(37,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.m (of order \(4\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.6 | ||
Root | \(1.53190 - 1.53190i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.37 |
Dual form | 570.2.m.a.493.6 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.23502 | + | 0.0685835i | −0.999530 | + | 0.0306715i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.16643 | − | 2.16643i | −0.818835 | − | 0.818835i | 0.167105 | − | 0.985939i | \(-0.446558\pi\) |
−0.985939 | + | 0.167105i | \(0.946558\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −1.53190 | + | 1.62889i | −0.484429 | + | 0.515100i | ||||
\(11\) | −5.68402 | −1.71380 | −0.856899 | − | 0.515485i | \(-0.827612\pi\) | ||||
−0.856899 | + | 0.515485i | \(0.827612\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | −3.92222 | − | 3.92222i | −1.08783 | − | 1.08783i | −0.995752 | − | 0.0920758i | \(-0.970650\pi\) |
−0.0920758 | − | 0.995752i | \(-0.529350\pi\) | |||||||
\(14\) | −3.06380 | −0.818835 | ||||||||
\(15\) | −1.62889 | − | 1.53190i | −0.420578 | − | 0.395535i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.99059 | + | 4.99059i | 1.21040 | + | 1.21040i | 0.970896 | + | 0.239500i | \(0.0769836\pi\) |
0.239500 | + | 0.970896i | \(0.423016\pi\) | |||||||
\(18\) | 0.707107 | + | 0.707107i | 0.166667 | + | 0.166667i | ||||
\(19\) | −4.01921 | − | 1.68699i | −0.922070 | − | 0.387023i | ||||
\(20\) | 0.0685835 | + | 2.23502i | 0.0153357 | + | 0.499765i | ||||
\(21\) | − | 3.06380i | − | 0.668576i | ||||||
\(22\) | −4.01921 | + | 4.01921i | −0.856899 | + | 0.856899i | ||||
\(23\) | 4.30360 | − | 4.30360i | 0.897363 | − | 0.897363i | −0.0978397 | − | 0.995202i | \(-0.531193\pi\) |
0.995202 | + | 0.0978397i | \(0.0311932\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | 4.99059 | − | 0.306570i | 0.998119 | − | 0.0613141i | ||||
\(26\) | −5.54686 | −1.08783 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −2.16643 | + | 2.16643i | −0.409417 | + | 0.409417i | ||||
\(29\) | 4.04446 | 0.751037 | 0.375518 | − | 0.926815i | \(-0.377465\pi\) | ||||
0.375518 | + | 0.926815i | \(0.377465\pi\) | |||||||
\(30\) | −2.23502 | + | 0.0685835i | −0.408056 | + | 0.0125216i | ||||
\(31\) | − | 4.04446i | − | 0.726406i | −0.931710 | − | 0.363203i | \(-0.881683\pi\) | ||
0.931710 | − | 0.363203i | \(-0.118317\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −4.01921 | − | 4.01921i | −0.699655 | − | 0.699655i | ||||
\(34\) | 7.05776 | 1.21040 | ||||||||
\(35\) | 4.99059 | + | 4.69343i | 0.843564 | + | 0.793334i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.19934 | + | 6.19934i | −1.01917 | + | 1.01917i | −0.0193530 | + | 0.999813i | \(0.506161\pi\) |
−0.999813 | + | 0.0193530i | \(0.993839\pi\) | |||||||
\(38\) | −4.03490 | + | 1.64913i | −0.654546 | + | 0.267524i | ||||
\(39\) | − | 5.54686i | − | 0.888208i | ||||||
\(40\) | 1.62889 | + | 1.53190i | 0.257550 | + | 0.242215i | ||||
\(41\) | − | 6.38884i | − | 0.997769i | −0.866669 | − | 0.498884i | \(-0.833743\pi\) | ||
0.866669 | − | 0.498884i | \(-0.166257\pi\) | |||||||
\(42\) | −2.16643 | − | 2.16643i | −0.334288 | − | 0.334288i | ||||
\(43\) | −4.15703 | + | 4.15703i | −0.633940 | + | 0.633940i | −0.949054 | − | 0.315114i | \(-0.897957\pi\) |
0.315114 | + | 0.949054i | \(0.397957\pi\) | |||||||
\(44\) | 5.68402i | 0.856899i | ||||||||
\(45\) | −0.0685835 | − | 2.23502i | −0.0102238 | − | 0.333177i | ||||
\(46\) | − | 6.08621i | − | 0.897363i | ||||||
\(47\) | 3.24326 | + | 3.24326i | 0.473077 | + | 0.473077i | 0.902909 | − | 0.429832i | \(-0.141427\pi\) |
−0.429832 | + | 0.902909i | \(0.641427\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | 2.38686i | 0.340980i | ||||||||
\(50\) | 3.31210 | − | 3.74566i | 0.468402 | − | 0.529716i | ||||
\(51\) | 7.05776i | 0.988285i | ||||||||
\(52\) | −3.92222 | + | 3.92222i | −0.543914 | + | 0.543914i | ||||
\(53\) | −5.40818 | − | 5.40818i | −0.742871 | − | 0.742871i | 0.230259 | − | 0.973129i | \(-0.426043\pi\) |
−0.973129 | + | 0.230259i | \(0.926043\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 12.7039 | − | 0.389830i | 1.71299 | − | 0.0525647i | ||||
\(56\) | 3.06380i | 0.409417i | ||||||||
\(57\) | −1.64913 | − | 4.03490i | −0.218432 | − | 0.534435i | ||||
\(58\) | 2.85986 | − | 2.85986i | 0.375518 | − | 0.375518i | ||||
\(59\) | 2.39487 | 0.311786 | 0.155893 | − | 0.987774i | \(-0.450175\pi\) | ||||
0.155893 | + | 0.987774i | \(0.450175\pi\) | |||||||
\(60\) | −1.53190 | + | 1.62889i | −0.197767 | + | 0.210289i | ||||
\(61\) | −2.33286 | −0.298693 | −0.149346 | − | 0.988785i | \(-0.547717\pi\) | ||||
−0.149346 | + | 0.988785i | \(0.547717\pi\) | |||||||
\(62\) | −2.85986 | − | 2.85986i | −0.363203 | − | 0.363203i | ||||
\(63\) | 2.16643 | − | 2.16643i | 0.272945 | − | 0.272945i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 9.03522 | + | 8.49722i | 1.12068 | + | 1.05395i | ||||
\(66\) | −5.68402 | −0.699655 | ||||||||
\(67\) | 6.12760 | − | 6.12760i | 0.748605 | − | 0.748605i | −0.225612 | − | 0.974217i | \(-0.572438\pi\) |
0.974217 | + | 0.225612i | \(0.0724382\pi\) | |||||||
\(68\) | 4.99059 | − | 4.99059i | 0.605198 | − | 0.605198i | ||||
\(69\) | 6.08621 | 0.732693 | ||||||||
\(70\) | 6.84764 | − | 0.210126i | 0.818449 | − | 0.0251149i | ||||
\(71\) | − | 6.51556i | − | 0.773255i | −0.922236 | − | 0.386628i | \(-0.873640\pi\) | ||
0.922236 | − | 0.386628i | \(-0.126360\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −2.07682 | + | 2.07682i | −0.243074 | + | 0.243074i | −0.818121 | − | 0.575047i | \(-0.804984\pi\) |
0.575047 | + | 0.818121i | \(0.304984\pi\) | |||||||
\(74\) | 8.76719i | 1.01917i | ||||||||
\(75\) | 3.74566 | + | 3.31210i | 0.432512 | + | 0.382449i | ||||
\(76\) | −1.68699 | + | 4.01921i | −0.193511 | + | 0.461035i | ||||
\(77\) | 12.3141 | + | 12.3141i | 1.40332 | + | 1.40332i | ||||
\(78\) | −3.92222 | − | 3.92222i | −0.444104 | − | 0.444104i | ||||
\(79\) | −4.23844 | −0.476862 | −0.238431 | − | 0.971159i | \(-0.576633\pi\) | ||||
−0.238431 | + | 0.971159i | \(0.576633\pi\) | |||||||
\(80\) | 2.23502 | − | 0.0685835i | 0.249882 | − | 0.00766787i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −4.51759 | − | 4.51759i | −0.498884 | − | 0.498884i | ||||
\(83\) | −5.30657 | + | 5.30657i | −0.582472 | + | 0.582472i | −0.935582 | − | 0.353110i | \(-0.885124\pi\) |
0.353110 | + | 0.935582i | \(0.385124\pi\) | |||||||
\(84\) | −3.06380 | −0.334288 | ||||||||
\(85\) | −11.4963 | − | 10.8118i | −1.24695 | − | 1.17270i | ||||
\(86\) | 5.87892i | 0.633940i | ||||||||
\(87\) | 2.85986 | + | 2.85986i | 0.306609 | + | 0.306609i | ||||
\(88\) | 4.01921 | + | 4.01921i | 0.428449 | + | 0.428449i | ||||
\(89\) | 2.50829 | 0.265879 | 0.132939 | − | 0.991124i | \(-0.457558\pi\) | ||||
0.132939 | + | 0.991124i | \(0.457558\pi\) | |||||||
\(90\) | −1.62889 | − | 1.53190i | −0.171700 | − | 0.161476i | ||||
\(91\) | 16.9944i | 1.78150i | ||||||||
\(92\) | −4.30360 | − | 4.30360i | −0.448681 | − | 0.448681i | ||||
\(93\) | 2.85986 | − | 2.85986i | 0.296554 | − | 0.296554i | ||||
\(94\) | 4.58666 | 0.473077 | ||||||||
\(95\) | 9.09870 | + | 3.49481i | 0.933507 | + | 0.358559i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.22010 | + | 6.22010i | −0.631555 | + | 0.631555i | −0.948458 | − | 0.316903i | \(-0.897357\pi\) |
0.316903 | + | 0.948458i | \(0.397357\pi\) | |||||||
\(98\) | 1.68776 | + | 1.68776i | 0.170490 | + | 0.170490i | ||||
\(99\) | − | 5.68402i | − | 0.571266i | ||||||
\(100\) | −0.306570 | − | 4.99059i | −0.0306570 | − | 0.499059i | ||||
\(101\) | 3.42891 | 0.341189 | 0.170595 | − | 0.985341i | \(-0.445431\pi\) | ||||
0.170595 | + | 0.985341i | \(0.445431\pi\) | |||||||
\(102\) | 4.99059 | + | 4.99059i | 0.494142 | + | 0.494142i | ||||
\(103\) | −13.0842 | − | 13.0842i | −1.28922 | − | 1.28922i | −0.935260 | − | 0.353961i | \(-0.884835\pi\) |
−0.353961 | − | 0.935260i | \(-0.615165\pi\) | |||||||
\(104\) | 5.54686i | 0.543914i | ||||||||
\(105\) | 0.210126 | + | 6.84764i | 0.0205062 | + | 0.668261i | ||||
\(106\) | −7.64832 | −0.742871 | ||||||||
\(107\) | −5.02931 | + | 5.02931i | −0.486202 | + | 0.486202i | −0.907106 | − | 0.420903i | \(-0.861713\pi\) |
0.420903 | + | 0.907106i | \(0.361713\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 5.95528 | 0.570412 | 0.285206 | − | 0.958466i | \(-0.407938\pi\) | ||||
0.285206 | + | 0.958466i | \(0.407938\pi\) | |||||||
\(110\) | 8.70735 | − | 9.25865i | 0.830213 | − | 0.882778i | ||||
\(111\) | −8.76719 | −0.832145 | ||||||||
\(112\) | 2.16643 | + | 2.16643i | 0.204709 | + | 0.204709i | ||||
\(113\) | 0.0413876 | + | 0.0413876i | 0.00389342 | + | 0.00389342i | 0.709051 | − | 0.705157i | \(-0.249124\pi\) |
−0.705157 | + | 0.709051i | \(0.749124\pi\) | |||||||
\(114\) | −4.01921 | − | 1.68699i | −0.376434 | − | 0.158001i | ||||
\(115\) | −9.32346 | + | 9.91377i | −0.869417 | + | 0.924464i | ||||
\(116\) | − | 4.04446i | − | 0.375518i | ||||||
\(117\) | 3.92222 | − | 3.92222i | 0.362609 | − | 0.362609i | ||||
\(118\) | 1.69343 | − | 1.69343i | 0.155893 | − | 0.155893i | ||||
\(119\) | − | 21.6236i | − | 1.98223i | ||||||
\(120\) | 0.0685835 | + | 2.23502i | 0.00626079 | + | 0.204028i | ||||
\(121\) | 21.3081 | 1.93710 | ||||||||
\(122\) | −1.64958 | + | 1.64958i | −0.149346 | + | 0.149346i | ||||
\(123\) | 4.51759 | − | 4.51759i | 0.407337 | − | 0.407337i | ||||
\(124\) | −4.04446 | −0.363203 | ||||||||
\(125\) | −11.1330 | + | 1.02746i | −0.995768 | + | 0.0918990i | ||||
\(126\) | − | 3.06380i | − | 0.272945i | ||||||
\(127\) | 10.0379 | − | 10.0379i | 0.890717 | − | 0.890717i | −0.103873 | − | 0.994591i | \(-0.533124\pi\) |
0.994591 | + | 0.103873i | \(0.0331236\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −5.87892 | −0.517610 | ||||||||
\(130\) | 12.3973 | − | 0.380423i | 1.08732 | − | 0.0333653i | ||||
\(131\) | 4.64290 | 0.405652 | 0.202826 | − | 0.979215i | \(-0.434987\pi\) | ||||
0.202826 | + | 0.979215i | \(0.434987\pi\) | |||||||
\(132\) | −4.01921 | + | 4.01921i | −0.349827 | + | 0.349827i | ||||
\(133\) | 5.05259 | + | 12.3621i | 0.438115 | + | 1.07193i | ||||
\(134\) | − | 8.66573i | − | 0.748605i | ||||||
\(135\) | 1.53190 | − | 1.62889i | 0.131845 | − | 0.140193i | ||||
\(136\) | − | 7.05776i | − | 0.605198i | ||||||
\(137\) | −2.26545 | − | 2.26545i | −0.193550 | − | 0.193550i | 0.603678 | − | 0.797228i | \(-0.293701\pi\) |
−0.797228 | + | 0.603678i | \(0.793701\pi\) | |||||||
\(138\) | 4.30360 | − | 4.30360i | 0.366347 | − | 0.366347i | ||||
\(139\) | − | 17.4266i | − | 1.47810i | −0.673649 | − | 0.739051i | \(-0.735274\pi\) | ||
0.673649 | − | 0.739051i | \(-0.264726\pi\) | |||||||
\(140\) | 4.69343 | − | 4.99059i | 0.396667 | − | 0.421782i | ||||
\(141\) | 4.58666i | 0.386266i | ||||||||
\(142\) | −4.60720 | − | 4.60720i | −0.386628 | − | 0.386628i | ||||
\(143\) | 22.2940 | + | 22.2940i | 1.86432 | + | 1.86432i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −9.03942 | + | 0.277383i | −0.750683 | + | 0.0230354i | ||||
\(146\) | 2.93707i | 0.243074i | ||||||||
\(147\) | −1.68776 | + | 1.68776i | −0.139204 | + | 0.139204i | ||||
\(148\) | 6.19934 | + | 6.19934i | 0.509583 | + | 0.509583i | ||||
\(149\) | − | 1.79836i | − | 0.147327i | −0.997283 | − | 0.0736637i | \(-0.976531\pi\) | ||
0.997283 | − | 0.0736637i | \(-0.0234691\pi\) | |||||||
\(150\) | 4.99059 | − | 0.306570i | 0.407480 | − | 0.0250314i | ||||
\(151\) | − | 8.62201i | − | 0.701649i | −0.936441 | − | 0.350825i | \(-0.885901\pi\) | ||
0.936441 | − | 0.350825i | \(-0.114099\pi\) | |||||||
\(152\) | 1.64913 | + | 4.03490i | 0.133762 | + | 0.327273i | ||||
\(153\) | −4.99059 | + | 4.99059i | −0.403465 | + | 0.403465i | ||||
\(154\) | 17.4147 | 1.40332 | ||||||||
\(155\) | 0.277383 | + | 9.03942i | 0.0222799 | + | 0.726064i | ||||
\(156\) | −5.54686 | −0.444104 | ||||||||
\(157\) | 7.79308 | + | 7.79308i | 0.621956 | + | 0.621956i | 0.946031 | − | 0.324076i | \(-0.105053\pi\) |
−0.324076 | + | 0.946031i | \(0.605053\pi\) | |||||||
\(158\) | −2.99703 | + | 2.99703i | −0.238431 | + | 0.238431i | ||||
\(159\) | − | 7.64832i | − | 0.606551i | ||||||
\(160\) | 1.53190 | − | 1.62889i | 0.121107 | − | 0.128775i | ||||
\(161\) | −18.6469 | −1.46958 | ||||||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 7.85986 | − | 7.85986i | 0.615632 | − | 0.615632i | −0.328776 | − | 0.944408i | \(-0.606636\pi\) |
0.944408 | + | 0.328776i | \(0.106636\pi\) | |||||||
\(164\) | −6.38884 | −0.498884 | ||||||||
\(165\) | 9.25865 | + | 8.70735i | 0.720785 | + | 0.677866i | ||||
\(166\) | 7.50462i | 0.582472i | ||||||||
\(167\) | −17.5764 | + | 17.5764i | −1.36010 | + | 1.36010i | −0.486323 | + | 0.873779i | \(0.661662\pi\) |
−0.873779 | + | 0.486323i | \(0.838338\pi\) | |||||||
\(168\) | −2.16643 | + | 2.16643i | −0.167144 | + | 0.167144i | ||||
\(169\) | 17.7676i | 1.36674i | ||||||||
\(170\) | −15.7742 | + | 0.484046i | −1.20983 | + | 0.0371246i | ||||
\(171\) | 1.68699 | − | 4.01921i | 0.129008 | − | 0.307357i | ||||
\(172\) | 4.15703 | + | 4.15703i | 0.316970 | + | 0.316970i | ||||
\(173\) | 0.108645 | + | 0.108645i | 0.00826009 | + | 0.00826009i | 0.711225 | − | 0.702965i | \(-0.248141\pi\) |
−0.702965 | + | 0.711225i | \(0.748141\pi\) | |||||||
\(174\) | 4.04446 | 0.306609 | ||||||||
\(175\) | −11.4759 | − | 10.1476i | −0.867500 | − | 0.767088i | ||||
\(176\) | 5.68402 | 0.428449 | ||||||||
\(177\) | 1.69343 | + | 1.69343i | 0.127286 | + | 0.127286i | ||||
\(178\) | 1.77363 | − | 1.77363i | 0.132939 | − | 0.132939i | ||||
\(179\) | −9.54798 | −0.713649 | −0.356825 | − | 0.934171i | \(-0.616141\pi\) | ||||
−0.356825 | + | 0.934171i | \(0.616141\pi\) | |||||||
\(180\) | −2.23502 | + | 0.0685835i | −0.166588 | + | 0.00511191i | ||||
\(181\) | − | 19.4384i | − | 1.44484i | −0.691453 | − | 0.722421i | \(-0.743029\pi\) | ||
0.691453 | − | 0.722421i | \(-0.256971\pi\) | |||||||
\(182\) | 12.0169 | + | 12.0169i | 0.890751 | + | 0.890751i | ||||
\(183\) | −1.64958 | − | 1.64958i | −0.121941 | − | 0.121941i | ||||
\(184\) | −6.08621 | −0.448681 | ||||||||
\(185\) | 13.4305 | − | 14.2808i | 0.987427 | − | 1.04995i | ||||
\(186\) | − | 4.04446i | − | 0.296554i | ||||||
\(187\) | −28.3666 | − | 28.3666i | −2.07437 | − | 2.07437i | ||||
\(188\) | 3.24326 | − | 3.24326i | 0.236539 | − | 0.236539i | ||||
\(189\) | 3.06380 | 0.222859 | ||||||||
\(190\) | 8.90495 | − | 3.96255i | 0.646033 | − | 0.287474i | ||||
\(191\) | 25.1526 | 1.81998 | 0.909991 | − | 0.414628i | \(-0.136088\pi\) | ||||
0.909991 | + | 0.414628i | \(0.136088\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 1.23637 | + | 1.23637i | 0.0889961 | + | 0.0889961i | 0.750203 | − | 0.661207i | \(-0.229956\pi\) |
−0.661207 | + | 0.750203i | \(0.729956\pi\) | |||||||
\(194\) | 8.79655i | 0.631555i | ||||||||
\(195\) | 0.380423 | + | 12.3973i | 0.0272426 | + | 0.887790i | ||||
\(196\) | 2.38686 | 0.170490 | ||||||||
\(197\) | 5.67759 | + | 5.67759i | 0.404511 | + | 0.404511i | 0.879819 | − | 0.475308i | \(-0.157663\pi\) |
−0.475308 | + | 0.879819i | \(0.657663\pi\) | |||||||
\(198\) | −4.01921 | − | 4.01921i | −0.285633 | − | 0.285633i | ||||
\(199\) | − | 3.89894i | − | 0.276389i | −0.990405 | − | 0.138194i | \(-0.955870\pi\) | ||
0.990405 | − | 0.138194i | \(-0.0441299\pi\) | |||||||
\(200\) | −3.74566 | − | 3.31210i | −0.264858 | − | 0.234201i | ||||
\(201\) | 8.66573 | 0.611233 | ||||||||
\(202\) | 2.42461 | − | 2.42461i | 0.170595 | − | 0.170595i | ||||
\(203\) | −8.76204 | − | 8.76204i | −0.614975 | − | 0.614975i | ||||
\(204\) | 7.05776 | 0.494142 | ||||||||
\(205\) | 0.438169 | + | 14.2792i | 0.0306030 | + | 0.997299i | ||||
\(206\) | −18.5038 | −1.28922 | ||||||||
\(207\) | 4.30360 | + | 4.30360i | 0.299121 | + | 0.299121i | ||||
\(208\) | 3.92222 | + | 3.92222i | 0.271957 | + | 0.271957i | ||||
\(209\) | 22.8453 | + | 9.58891i | 1.58024 | + | 0.663279i | ||||
\(210\) | 4.99059 | + | 4.69343i | 0.344384 | + | 0.323877i | ||||
\(211\) | − | 18.9376i | − | 1.30372i | −0.758341 | − | 0.651858i | \(-0.773990\pi\) | ||
0.758341 | − | 0.651858i | \(-0.226010\pi\) | |||||||
\(212\) | −5.40818 | + | 5.40818i | −0.371435 | + | 0.371435i | ||||
\(213\) | 4.60720 | − | 4.60720i | 0.315680 | − | 0.315680i | ||||
\(214\) | 7.11253i | 0.486202i | ||||||||
\(215\) | 9.00591 | − | 9.57612i | 0.614198 | − | 0.653086i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −8.76204 | + | 8.76204i | −0.594806 | + | 0.594806i | ||||
\(218\) | 4.21102 | − | 4.21102i | 0.285206 | − | 0.285206i | ||||
\(219\) | −2.93707 | −0.198469 | ||||||||
\(220\) | −0.389830 | − | 12.7039i | −0.0262823 | − | 0.856495i | ||||
\(221\) | − | 39.1484i | − | 2.63341i | ||||||
\(222\) | −6.19934 | + | 6.19934i | −0.416073 | + | 0.416073i | ||||
\(223\) | −9.26030 | − | 9.26030i | −0.620116 | − | 0.620116i | 0.325445 | − | 0.945561i | \(-0.394486\pi\) |
−0.945561 | + | 0.325445i | \(0.894486\pi\) | |||||||
\(224\) | 3.06380 | 0.204709 | ||||||||
\(225\) | 0.306570 | + | 4.99059i | 0.0204380 | + | 0.332706i | ||||
\(226\) | 0.0585309 | 0.00389342 | ||||||||
\(227\) | −2.63934 | + | 2.63934i | −0.175179 | + | 0.175179i | −0.789251 | − | 0.614071i | \(-0.789531\pi\) |
0.614071 | + | 0.789251i | \(0.289531\pi\) | |||||||
\(228\) | −4.03490 | + | 1.64913i | −0.267217 | + | 0.109216i | ||||
\(229\) | − | 4.94601i | − | 0.326841i | −0.986556 | − | 0.163421i | \(-0.947747\pi\) | ||
0.986556 | − | 0.163421i | \(-0.0522528\pi\) | |||||||
\(230\) | 0.417413 | + | 13.6028i | 0.0275234 | + | 0.896940i | ||||
\(231\) | 17.4147i | 1.14580i | ||||||||
\(232\) | −2.85986 | − | 2.85986i | −0.187759 | − | 0.187759i | ||||
\(233\) | −18.1200 | + | 18.1200i | −1.18708 | + | 1.18708i | −0.209210 | + | 0.977871i | \(0.567089\pi\) |
−0.977871 | + | 0.209210i | \(0.932911\pi\) | |||||||
\(234\) | − | 5.54686i | − | 0.362609i | ||||||
\(235\) | −7.47116 | − | 7.02629i | −0.487365 | − | 0.458345i | ||||
\(236\) | − | 2.39487i | − | 0.155893i | ||||||
\(237\) | −2.99703 | − | 2.99703i | −0.194678 | − | 0.194678i | ||||
\(238\) | −15.2902 | − | 15.2902i | −0.991114 | − | 0.991114i | ||||
\(239\) | 6.98300i | 0.451693i | 0.974163 | + | 0.225846i | \(0.0725147\pi\) | ||||
−0.974163 | + | 0.225846i | \(0.927485\pi\) | |||||||
\(240\) | 1.62889 | + | 1.53190i | 0.105144 | + | 0.0988837i | ||||
\(241\) | − | 7.54947i | − | 0.486304i | −0.969988 | − | 0.243152i | \(-0.921819\pi\) | ||
0.969988 | − | 0.243152i | \(-0.0781814\pi\) | |||||||
\(242\) | 15.0671 | − | 15.0671i | 0.968550 | − | 0.968550i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 2.33286i | 0.149346i | ||||||||
\(245\) | −0.163699 | − | 5.33467i | −0.0104584 | − | 0.340819i | ||||
\(246\) | − | 6.38884i | − | 0.407337i | ||||||
\(247\) | 9.14747 | + | 22.3810i | 0.582039 | + | 1.42407i | ||||
\(248\) | −2.85986 | + | 2.85986i | −0.181601 | + | 0.181601i | ||||
\(249\) | −7.50462 | −0.475586 | ||||||||
\(250\) | −7.14571 | + | 8.59877i | −0.451935 | + | 0.543834i | ||||
\(251\) | −20.0566 | −1.26596 | −0.632981 | − | 0.774168i | \(-0.718169\pi\) | ||||
−0.632981 | + | 0.774168i | \(0.718169\pi\) | |||||||
\(252\) | −2.16643 | − | 2.16643i | −0.136472 | − | 0.136472i | ||||
\(253\) | −24.4618 | + | 24.4618i | −1.53790 | + | 1.53790i | ||||
\(254\) | − | 14.1957i | − | 0.890717i | ||||||
\(255\) | −0.484046 | − | 15.7742i | −0.0303121 | − | 0.987820i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.66176 | + | 8.66176i | −0.540306 | + | 0.540306i | −0.923619 | − | 0.383313i | \(-0.874783\pi\) |
0.383313 | + | 0.923619i | \(0.374783\pi\) | |||||||
\(258\) | −4.15703 | + | 4.15703i | −0.258805 | + | 0.258805i | ||||
\(259\) | 26.8609 | 1.66906 | ||||||||
\(260\) | 8.49722 | − | 9.03522i | 0.526975 | − | 0.560341i | ||||
\(261\) | 4.04446i | 0.250346i | ||||||||
\(262\) | 3.28303 | − | 3.28303i | 0.202826 | − | 0.202826i | ||||
\(263\) | 7.51759 | − | 7.51759i | 0.463554 | − | 0.463554i | −0.436264 | − | 0.899819i | \(-0.643699\pi\) |
0.899819 | + | 0.436264i | \(0.143699\pi\) | |||||||
\(264\) | 5.68402i | 0.349827i | ||||||||
\(265\) | 12.4583 | + | 11.7165i | 0.765306 | + | 0.719736i | ||||
\(266\) | 12.3141 | + | 5.16861i | 0.755023 | + | 0.316908i | ||||
\(267\) | 1.77363 | + | 1.77363i | 0.108544 | + | 0.108544i | ||||
\(268\) | −6.12760 | − | 6.12760i | −0.374303 | − | 0.374303i | ||||
\(269\) | −20.3832 | −1.24278 | −0.621391 | − | 0.783500i | \(-0.713432\pi\) | ||||
−0.621391 | + | 0.783500i | \(0.713432\pi\) | |||||||
\(270\) | −0.0685835 | − | 2.23502i | −0.00417386 | − | 0.136019i | ||||
\(271\) | −20.5647 | −1.24921 | −0.624607 | − | 0.780939i | \(-0.714741\pi\) | ||||
−0.624607 | + | 0.780939i | \(0.714741\pi\) | |||||||
\(272\) | −4.99059 | − | 4.99059i | −0.302599 | − | 0.302599i | ||||
\(273\) | −12.0169 | + | 12.0169i | −0.727295 | + | 0.727295i | ||||
\(274\) | −3.20383 | −0.193550 | ||||||||
\(275\) | −28.3666 | + | 1.74255i | −1.71057 | + | 0.105080i | ||||
\(276\) | − | 6.08621i | − | 0.366347i | ||||||
\(277\) | 16.5022 | + | 16.5022i | 0.991518 | + | 0.991518i | 0.999964 | − | 0.00844603i | \(-0.00268849\pi\) |
−0.00844603 | + | 0.999964i | \(0.502688\pi\) | |||||||
\(278\) | −12.3224 | − | 12.3224i | −0.739051 | − | 0.739051i | ||||
\(279\) | 4.04446 | 0.242135 | ||||||||
\(280\) | −0.210126 | − | 6.84764i | −0.0125574 | − | 0.409225i | ||||
\(281\) | 16.7009i | 0.996293i | 0.867093 | + | 0.498147i | \(0.165986\pi\) | ||||
−0.867093 | + | 0.498147i | \(0.834014\pi\) | |||||||
\(282\) | 3.24326 | + | 3.24326i | 0.193133 | + | 0.193133i | ||||
\(283\) | −9.16938 | + | 9.16938i | −0.545063 | + | 0.545063i | −0.925009 | − | 0.379946i | \(-0.875943\pi\) |
0.379946 | + | 0.925009i | \(0.375943\pi\) | |||||||
\(284\) | −6.51556 | −0.386628 | ||||||||
\(285\) | 3.96255 | + | 8.90495i | 0.234721 | + | 0.527484i | ||||
\(286\) | 31.5284 | 1.86432 | ||||||||
\(287\) | −13.8410 | + | 13.8410i | −0.817007 | + | 0.817007i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | 32.8120i | 1.93012i | ||||||||
\(290\) | −6.19570 | + | 6.58798i | −0.363824 | + | 0.386859i | ||||
\(291\) | −8.79655 | −0.515663 | ||||||||
\(292\) | 2.07682 | + | 2.07682i | 0.121537 | + | 0.121537i | ||||
\(293\) | 11.7298 | + | 11.7298i | 0.685260 | + | 0.685260i | 0.961180 | − | 0.275921i | \(-0.0889827\pi\) |
−0.275921 | + | 0.961180i | \(0.588983\pi\) | |||||||
\(294\) | 2.38686i | 0.139204i | ||||||||
\(295\) | −5.35258 | + | 0.164249i | −0.311639 | + | 0.00956293i | ||||
\(296\) | 8.76719 | 0.509583 | ||||||||
\(297\) | 4.01921 | − | 4.01921i | 0.233218 | − | 0.233218i | ||||
\(298\) | −1.27163 | − | 1.27163i | −0.0736637 | − | 0.0736637i | ||||
\(299\) | −33.7593 | −1.95235 | ||||||||
\(300\) | 3.31210 | − | 3.74566i | 0.191224 | − | 0.216256i | ||||
\(301\) | 18.0118 | 1.03818 | ||||||||
\(302\) | −6.09668 | − | 6.09668i | −0.350825 | − | 0.350825i | ||||
\(303\) | 2.42461 | + | 2.42461i | 0.139290 | + | 0.139290i | ||||
\(304\) | 4.01921 | + | 1.68699i | 0.230518 | + | 0.0967557i | ||||
\(305\) | 5.21399 | − | 0.159996i | 0.298552 | − | 0.00916135i | ||||
\(306\) | 7.05776i | 0.403465i | ||||||||
\(307\) | 7.51719 | − | 7.51719i | 0.429029 | − | 0.429029i | −0.459269 | − | 0.888297i | \(-0.651889\pi\) |
0.888297 | + | 0.459269i | \(0.151889\pi\) | |||||||
\(308\) | 12.3141 | − | 12.3141i | 0.701658 | − | 0.701658i | ||||
\(309\) | − | 18.5038i | − | 1.05264i | ||||||
\(310\) | 6.58798 | + | 6.19570i | 0.374172 | + | 0.351892i | ||||
\(311\) | −17.0941 | −0.969318 | −0.484659 | − | 0.874703i | \(-0.661056\pi\) | ||||
−0.484659 | + | 0.874703i | \(0.661056\pi\) | |||||||
\(312\) | −3.92222 | + | 3.92222i | −0.222052 | + | 0.222052i | ||||
\(313\) | −4.46822 | + | 4.46822i | −0.252559 | + | 0.252559i | −0.822019 | − | 0.569460i | \(-0.807152\pi\) |
0.569460 | + | 0.822019i | \(0.307152\pi\) | |||||||
\(314\) | 11.0211 | 0.621956 | ||||||||
\(315\) | −4.69343 | + | 4.99059i | −0.264445 | + | 0.281188i | ||||
\(316\) | 4.23844i | 0.238431i | ||||||||
\(317\) | 20.3285 | − | 20.3285i | 1.14176 | − | 1.14176i | 0.153632 | − | 0.988128i | \(-0.450903\pi\) |
0.988128 | − | 0.153632i | \(-0.0490971\pi\) | |||||||
\(318\) | −5.40818 | − | 5.40818i | −0.303276 | − | 0.303276i | ||||
\(319\) | −22.9888 | −1.28712 | ||||||||
\(320\) | −0.0685835 | − | 2.23502i | −0.00383393 | − | 0.124941i | ||||
\(321\) | −7.11253 | −0.396982 | ||||||||
\(322\) | −13.1854 | + | 13.1854i | −0.734791 | + | 0.734791i | ||||
\(323\) | −11.6391 | − | 28.4773i | −0.647619 | − | 1.58452i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −20.7766 | − | 18.3718i | −1.15248 | − | 1.01908i | ||||
\(326\) | − | 11.1155i | − | 0.615632i | ||||||
\(327\) | 4.21102 | + | 4.21102i | 0.232870 | + | 0.232870i | ||||
\(328\) | −4.51759 | + | 4.51759i | −0.249442 | + | 0.249442i | ||||
\(329\) | − | 14.0526i | − | 0.774744i | ||||||
\(330\) | 12.7039 | − | 0.389830i | 0.699326 | − | 0.0214594i | ||||
\(331\) | − | 21.9956i | − | 1.20898i | −0.796611 | − | 0.604492i | \(-0.793376\pi\) | ||
0.796611 | − | 0.604492i | \(-0.206624\pi\) | |||||||
\(332\) | 5.30657 | + | 5.30657i | 0.291236 | + | 0.291236i | ||||
\(333\) | −6.19934 | − | 6.19934i | −0.339722 | − | 0.339722i | ||||
\(334\) | 24.8568i | 1.36010i | ||||||||
\(335\) | −13.2750 | + | 14.1155i | −0.725292 | + | 0.771214i | ||||
\(336\) | 3.06380i | 0.167144i | ||||||||
\(337\) | −4.20829 | + | 4.20829i | −0.229240 | + | 0.229240i | −0.812375 | − | 0.583135i | \(-0.801826\pi\) |
0.583135 | + | 0.812375i | \(0.301826\pi\) | |||||||
\(338\) | 12.5636 | + | 12.5636i | 0.683369 | + | 0.683369i | ||||
\(339\) | 0.0585309i | 0.00317896i | ||||||||
\(340\) | −10.8118 | + | 11.4963i | −0.586351 | + | 0.623476i | ||||
\(341\) | 22.9888i | 1.24491i | ||||||||
\(342\) | −1.64913 | − | 4.03490i | −0.0891746 | − | 0.218182i | ||||
\(343\) | −9.99406 | + | 9.99406i | −0.539628 | + | 0.539628i | ||||
\(344\) | 5.87892 | 0.316970 | ||||||||
\(345\) | −13.6028 | + | 0.417413i | −0.732349 | + | 0.0224728i | ||||
\(346\) | 0.153647 | 0.00826009 | ||||||||
\(347\) | −18.8707 | − | 18.8707i | −1.01303 | − | 1.01303i | −0.999914 | − | 0.0131194i | \(-0.995824\pi\) |
−0.0131194 | − | 0.999914i | \(-0.504176\pi\) | |||||||
\(348\) | 2.85986 | − | 2.85986i | 0.153305 | − | 0.153305i | ||||
\(349\) | 3.34923i | 0.179280i | 0.995974 | + | 0.0896401i | \(0.0285717\pi\) | ||||
−0.995974 | + | 0.0896401i | \(0.971428\pi\) | |||||||
\(350\) | −15.2902 | + | 0.939270i | −0.817294 | + | 0.0502061i | ||||
\(351\) | 5.54686 | 0.296069 | ||||||||
\(352\) | 4.01921 | − | 4.01921i | 0.214225 | − | 0.214225i | ||||
\(353\) | 21.8457 | − | 21.8457i | 1.16273 | − | 1.16273i | 0.178852 | − | 0.983876i | \(-0.442762\pi\) |
0.983876 | − | 0.178852i | \(-0.0572382\pi\) | |||||||
\(354\) | 2.39487 | 0.127286 | ||||||||
\(355\) | 0.446860 | + | 14.5624i | 0.0237169 | + | 0.772891i | ||||
\(356\) | − | 2.50829i | − | 0.132939i | ||||||
\(357\) | 15.2902 | − | 15.2902i | 0.809242 | − | 0.809242i | ||||
\(358\) | −6.75144 | + | 6.75144i | −0.356825 | + | 0.356825i | ||||
\(359\) | 5.22092i | 0.275550i | 0.990464 | + | 0.137775i | \(0.0439950\pi\) | ||||
−0.990464 | + | 0.137775i | \(0.956005\pi\) | |||||||
\(360\) | −1.53190 | + | 1.62889i | −0.0807382 | + | 0.0858501i | ||||
\(361\) | 13.3081 | + | 13.5608i | 0.700427 | + | 0.713724i | ||||
\(362\) | −13.7450 | − | 13.7450i | −0.722421 | − | 0.722421i | ||||
\(363\) | 15.0671 | + | 15.0671i | 0.790818 | + | 0.790818i | ||||
\(364\) | 16.9944 | 0.890751 | ||||||||
\(365\) | 4.49930 | − | 4.78417i | 0.235504 | − | 0.250415i | ||||
\(366\) | −2.33286 | −0.121941 | ||||||||
\(367\) | 3.73845 | + | 3.73845i | 0.195146 | + | 0.195146i | 0.797915 | − | 0.602770i | \(-0.205936\pi\) |
−0.602770 | + | 0.797915i | \(0.705936\pi\) | |||||||
\(368\) | −4.30360 | + | 4.30360i | −0.224341 | + | 0.224341i | ||||
\(369\) | 6.38884 | 0.332590 | ||||||||
\(370\) | −0.601285 | − | 19.5948i | −0.0312593 | − | 1.01869i | ||||
\(371\) | 23.4329i | 1.21658i | ||||||||
\(372\) | −2.85986 | − | 2.85986i | −0.148277 | − | 0.148277i | ||||
\(373\) | 16.6782 | + | 16.6782i | 0.863566 | + | 0.863566i | 0.991750 | − | 0.128185i | \(-0.0409150\pi\) |
−0.128185 | + | 0.991750i | \(0.540915\pi\) | |||||||
\(374\) | −40.1165 | −2.07437 | ||||||||
\(375\) | −8.59877 | − | 7.14571i | −0.444038 | − | 0.369003i | ||||
\(376\) | − | 4.58666i | − | 0.236539i | ||||||
\(377\) | −15.8632 | − | 15.8632i | −0.816998 | − | 0.816998i | ||||
\(378\) | 2.16643 | − | 2.16643i | 0.111429 | − | 0.111429i | ||||
\(379\) | 20.7405 | 1.06537 | 0.532683 | − | 0.846315i | \(-0.321184\pi\) | ||||
0.532683 | + | 0.846315i | \(0.321184\pi\) | |||||||
\(380\) | 3.49481 | − | 9.09870i | 0.179280 | − | 0.466753i | ||||
\(381\) | 14.1957 | 0.727268 | ||||||||
\(382\) | 17.7856 | − | 17.7856i | 0.909991 | − | 0.909991i | ||||
\(383\) | −0.963152 | − | 0.963152i | −0.0492148 | − | 0.0492148i | 0.682071 | − | 0.731286i | \(-0.261079\pi\) |
−0.731286 | + | 0.682071i | \(0.761079\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −28.3666 | − | 26.6776i | −1.44570 | − | 1.35961i | ||||
\(386\) | 1.74850 | 0.0889961 | ||||||||
\(387\) | −4.15703 | − | 4.15703i | −0.211313 | − | 0.211313i | ||||
\(388\) | 6.22010 | + | 6.22010i | 0.315778 | + | 0.315778i | ||||
\(389\) | − | 37.2714i | − | 1.88974i | −0.327452 | − | 0.944868i | \(-0.606190\pi\) | ||
0.327452 | − | 0.944868i | \(-0.393810\pi\) | |||||||
\(390\) | 9.03522 | + | 8.49722i | 0.457516 | + | 0.430274i | ||||
\(391\) | 42.9550 | 2.17233 | ||||||||
\(392\) | 1.68776 | − | 1.68776i | 0.0852450 | − | 0.0852450i | ||||
\(393\) | 3.28303 | + | 3.28303i | 0.165607 | + | 0.165607i | ||||
\(394\) | 8.02932 | 0.404511 | ||||||||
\(395\) | 9.47298 | − | 0.290687i | 0.476637 | − | 0.0146260i | ||||
\(396\) | −5.68402 | −0.285633 | ||||||||
\(397\) | 10.2595 | + | 10.2595i | 0.514910 | + | 0.514910i | 0.916027 | − | 0.401117i | \(-0.131378\pi\) |
−0.401117 | + | 0.916027i | \(0.631378\pi\) | |||||||
\(398\) | −2.75697 | − | 2.75697i | −0.138194 | − | 0.138194i | ||||
\(399\) | −5.16861 | + | 12.3141i | −0.258754 | + | 0.616474i | ||||
\(400\) | −4.99059 | + | 0.306570i | −0.249530 | + | 0.0153285i | ||||
\(401\) | − | 7.24755i | − | 0.361925i | −0.983490 | − | 0.180963i | \(-0.942079\pi\) | ||
0.983490 | − | 0.180963i | \(-0.0579213\pi\) | |||||||
\(402\) | 6.12760 | − | 6.12760i | 0.305617 | − | 0.305617i | ||||
\(403\) | −15.8632 | + | 15.8632i | −0.790204 | + | 0.790204i | ||||
\(404\) | − | 3.42891i | − | 0.170595i | ||||||
\(405\) | 2.23502 | − | 0.0685835i | 0.111059 | − | 0.00340794i | ||||
\(406\) | −12.3914 | −0.614975 | ||||||||
\(407\) | 35.2372 | − | 35.2372i | 1.74664 | − | 1.74664i | ||||
\(408\) | 4.99059 | − | 4.99059i | 0.247071 | − | 0.247071i | ||||
\(409\) | 4.10739 | 0.203097 | 0.101549 | − | 0.994831i | \(-0.467620\pi\) | ||||
0.101549 | + | 0.994831i | \(0.467620\pi\) | |||||||
\(410\) | 10.4067 | + | 9.78705i | 0.513951 | + | 0.483348i | ||||
\(411\) | − | 3.20383i | − | 0.158033i | ||||||
\(412\) | −13.0842 | + | 13.0842i | −0.644611 | + | 0.644611i | ||||
\(413\) | −5.18833 | − | 5.18833i | −0.255301 | − | 0.255301i | ||||
\(414\) | 6.08621 | 0.299121 | ||||||||
\(415\) | 11.4963 | − | 12.2242i | 0.564332 | − | 0.600063i | ||||
\(416\) | 5.54686 | 0.271957 | ||||||||
\(417\) | 12.3224 | − | 12.3224i | 0.603433 | − | 0.603433i | ||||
\(418\) | 22.9344 | − | 9.37367i | 1.12176 | − | 0.458481i | ||||
\(419\) | − | 11.2890i | − | 0.551504i | −0.961229 | − | 0.275752i | \(-0.911073\pi\) | ||
0.961229 | − | 0.275752i | \(-0.0889268\pi\) | |||||||
\(420\) | 6.84764 | − | 0.210126i | 0.334131 | − | 0.0102531i | ||||
\(421\) | 4.87088i | 0.237392i | 0.992931 | + | 0.118696i | \(0.0378714\pi\) | ||||
−0.992931 | + | 0.118696i | \(0.962129\pi\) | |||||||
\(422\) | −13.3909 | − | 13.3909i | −0.651858 | − | 0.651858i | ||||
\(423\) | −3.24326 | + | 3.24326i | −0.157692 | + | 0.157692i | ||||
\(424\) | 7.64832i | 0.371435i | ||||||||
\(425\) | 26.4360 | + | 23.3760i | 1.28233 | + | 1.13390i | ||||
\(426\) | − | 6.51556i | − | 0.315680i | ||||||
\(427\) | 5.05399 | + | 5.05399i | 0.244580 | + | 0.244580i | ||||
\(428\) | 5.02931 | + | 5.02931i | 0.243101 | + | 0.243101i | ||||
\(429\) | 31.5284i | 1.52221i | ||||||||
\(430\) | −0.403197 | − | 13.1395i | −0.0194439 | − | 0.633642i | ||||
\(431\) | − | 7.08729i | − | 0.341383i | −0.985325 | − | 0.170691i | \(-0.945400\pi\) | ||
0.985325 | − | 0.170691i | \(-0.0546001\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −21.2804 | − | 21.2804i | −1.02267 | − | 1.02267i | −0.999737 | − | 0.0229344i | \(-0.992699\pi\) |
−0.0229344 | − | 0.999737i | \(-0.507301\pi\) | |||||||
\(434\) | 12.3914i | 0.594806i | ||||||||
\(435\) | −6.58798 | − | 6.19570i | −0.315869 | − | 0.297061i | ||||
\(436\) | − | 5.95528i | − | 0.285206i | ||||||
\(437\) | −24.5572 | + | 10.0369i | −1.17473 | + | 0.480131i | ||||
\(438\) | −2.07682 | + | 2.07682i | −0.0992345 | + | 0.0992345i | ||||
\(439\) | −27.9747 | −1.33516 | −0.667580 | − | 0.744538i | \(-0.732670\pi\) | ||||
−0.667580 | + | 0.744538i | \(0.732670\pi\) | |||||||
\(440\) | −9.25865 | − | 8.70735i | −0.441389 | − | 0.415107i | ||||
\(441\) | −2.38686 | −0.113660 | ||||||||
\(442\) | −27.6821 | − | 27.6821i | −1.31670 | − | 1.31670i | ||||
\(443\) | −11.9554 | + | 11.9554i | −0.568019 | + | 0.568019i | −0.931573 | − | 0.363554i | \(-0.881563\pi\) |
0.363554 | + | 0.931573i | \(0.381563\pi\) | |||||||
\(444\) | 8.76719i | 0.416073i | ||||||||
\(445\) | −5.60608 | + | 0.172028i | −0.265753 | + | 0.00815489i | ||||
\(446\) | −13.0960 | −0.620116 | ||||||||
\(447\) | 1.27163 | − | 1.27163i | 0.0601462 | − | 0.0601462i | ||||
\(448\) | 2.16643 | − | 2.16643i | 0.102354 | − | 0.102354i | ||||
\(449\) | 0.799279 | 0.0377203 | 0.0188602 | − | 0.999822i | \(-0.493996\pi\) | ||||
0.0188602 | + | 0.999822i | \(0.493996\pi\) | |||||||
\(450\) | 3.74566 | + | 3.31210i | 0.176572 | + | 0.156134i | ||||
\(451\) | 36.3143i | 1.70997i | ||||||||
\(452\) | 0.0413876 | − | 0.0413876i | 0.00194671 | − | 0.00194671i | ||||
\(453\) | 6.09668 | − | 6.09668i | 0.286447 | − | 0.286447i | ||||
\(454\) | 3.73260i | 0.175179i | ||||||||
\(455\) | −1.16554 | − | 37.9829i | −0.0546413 | − | 1.78066i | ||||
\(456\) | −1.68699 | + | 4.01921i | −0.0790007 | + | 0.188217i | ||||
\(457\) | −19.9638 | − | 19.9638i | −0.933866 | − | 0.933866i | 0.0640788 | − | 0.997945i | \(-0.479589\pi\) |
−0.997945 | + | 0.0640788i | \(0.979589\pi\) | |||||||
\(458\) | −3.49735 | − | 3.49735i | −0.163421 | − | 0.163421i | ||||
\(459\) | −7.05776 | −0.329428 | ||||||||
\(460\) | 9.91377 | + | 9.32346i | 0.462232 | + | 0.434708i | ||||
\(461\) | −16.7900 | −0.781989 | −0.390995 | − | 0.920393i | \(-0.627869\pi\) | ||||
−0.390995 | + | 0.920393i | \(0.627869\pi\) | |||||||
\(462\) | 12.3141 | + | 12.3141i | 0.572901 | + | 0.572901i | ||||
\(463\) | 13.2413 | − | 13.2413i | 0.615377 | − | 0.615377i | −0.328965 | − | 0.944342i | \(-0.606700\pi\) |
0.944342 | + | 0.328965i | \(0.106700\pi\) | |||||||
\(464\) | −4.04446 | −0.187759 | ||||||||
\(465\) | −6.19570 | + | 6.58798i | −0.287319 | + | 0.305510i | ||||
\(466\) | 25.6256i | 1.18708i | ||||||||
\(467\) | 18.9064 | + | 18.9064i | 0.874885 | + | 0.874885i | 0.993000 | − | 0.118115i | \(-0.0376852\pi\) |
−0.118115 | + | 0.993000i | \(0.537685\pi\) | |||||||
\(468\) | −3.92222 | − | 3.92222i | −0.181305 | − | 0.181305i | ||||
\(469\) | −26.5500 | −1.22597 | ||||||||
\(470\) | −10.2512 | + | 0.314569i | −0.472855 | + | 0.0145100i | ||||
\(471\) | 11.0211i | 0.507825i | ||||||||
\(472\) | −1.69343 | − | 1.69343i | −0.0779464 | − | 0.0779464i | ||||
\(473\) | 23.6286 | − | 23.6286i | 1.08645 | − | 1.08645i | ||||
\(474\) | −4.23844 | −0.194678 | ||||||||
\(475\) | −20.5754 | − | 7.18692i | −0.944065 | − | 0.329759i | ||||
\(476\) | −21.6236 | −0.991114 | ||||||||
\(477\) | 5.40818 | − | 5.40818i | 0.247624 | − | 0.247624i | ||||
\(478\) | 4.93773 | + | 4.93773i | 0.225846 | + | 0.225846i | ||||
\(479\) | − | 6.59491i | − | 0.301329i | −0.988585 | − | 0.150665i | \(-0.951859\pi\) | ||
0.988585 | − | 0.150665i | \(-0.0481413\pi\) | |||||||
\(480\) | 2.23502 | − | 0.0685835i | 0.102014 | − | 0.00313039i | ||||
\(481\) | 48.6304 | 2.21735 | ||||||||
\(482\) | −5.33828 | − | 5.33828i | −0.243152 | − | 0.243152i | ||||
\(483\) | −13.1854 | − | 13.1854i | −0.599955 | − | 0.599955i | ||||
\(484\) | − | 21.3081i | − | 0.968550i | ||||||
\(485\) | 13.4754 | − | 14.3286i | 0.611887 | − | 0.650629i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 3.62733 | − | 3.62733i | 0.164370 | − | 0.164370i | −0.620129 | − | 0.784499i | \(-0.712920\pi\) |
0.784499 | + | 0.620129i | \(0.212920\pi\) | |||||||
\(488\) | 1.64958 | + | 1.64958i | 0.0746732 | + | 0.0746732i | ||||
\(489\) | 11.1155 | 0.502661 | ||||||||
\(490\) | −3.88793 | − | 3.65643i | −0.175639 | − | 0.165181i | ||||
\(491\) | 3.35710 | 0.151504 | 0.0757519 | − | 0.997127i | \(-0.475864\pi\) | ||||
0.0757519 | + | 0.997127i | \(0.475864\pi\) | |||||||
\(492\) | −4.51759 | − | 4.51759i | −0.203669 | − | 0.203669i | ||||
\(493\) | 20.1842 | + | 20.1842i | 0.909052 | + | 0.909052i | ||||
\(494\) | 22.2940 | + | 9.35751i | 1.00305 | + | 0.421014i | ||||
\(495\) | 0.389830 | + | 12.7039i | 0.0175216 | + | 0.570997i | ||||
\(496\) | 4.04446i | 0.181601i | ||||||||
\(497\) | −14.1155 | + | 14.1155i | −0.633168 | + | 0.633168i | ||||
\(498\) | −5.30657 | + | 5.30657i | −0.237793 | + | 0.237793i | ||||
\(499\) | 13.9250i | 0.623367i | 0.950186 | + | 0.311684i | \(0.100893\pi\) | ||||
−0.950186 | + | 0.311684i | \(0.899107\pi\) | |||||||
\(500\) | 1.02746 | + | 11.1330i | 0.0459495 | + | 0.497884i | ||||
\(501\) | −24.8568 | −1.11052 | ||||||||
\(502\) | −14.1822 | + | 14.1822i | −0.632981 | + | 0.632981i | ||||
\(503\) | 18.2263 | − | 18.2263i | 0.812668 | − | 0.812668i | −0.172365 | − | 0.985033i | \(-0.555141\pi\) |
0.985033 | + | 0.172365i | \(0.0551408\pi\) | |||||||
\(504\) | −3.06380 | −0.136472 | ||||||||
\(505\) | −7.66367 | + | 0.235167i | −0.341029 | + | 0.0104648i | ||||
\(506\) | 34.5941i | 1.53790i | ||||||||
\(507\) | −12.5636 | + | 12.5636i | −0.557969 | + | 0.557969i | ||||
\(508\) | −10.0379 | − | 10.0379i | −0.445359 | − | 0.445359i | ||||
\(509\) | 31.4996 | 1.39619 | 0.698097 | − | 0.716003i | \(-0.254030\pi\) | ||||
0.698097 | + | 0.716003i | \(0.254030\pi\) | |||||||
\(510\) | −11.4963 | − | 10.8118i | −0.509066 | − | 0.478754i | ||||
\(511\) | 8.99859 | 0.398074 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 4.03490 | − | 1.64913i | 0.178145 | − | 0.0728107i | ||||
\(514\) | 12.2496i | 0.540306i | ||||||||
\(515\) | 30.1407 | + | 28.3460i | 1.32816 | + | 1.24907i | ||||
\(516\) | 5.87892i | 0.258805i | ||||||||
\(517\) | −18.4347 | − | 18.4347i | −0.810759 | − | 0.810759i | ||||
\(518\) | 18.9935 | − | 18.9935i | 0.834528 | − | 0.834528i | ||||
\(519\) | 0.153647i | 0.00674434i | ||||||||
\(520\) | −0.380423 | − | 12.3973i | −0.0166826 | − | 0.543658i | ||||
\(521\) | 32.9541i | 1.44375i | 0.692026 | + | 0.721873i | \(0.256719\pi\) | ||||
−0.692026 | + | 0.721873i | \(0.743281\pi\) | |||||||
\(522\) | 2.85986 | + | 2.85986i | 0.125173 | + | 0.125173i | ||||
\(523\) | 30.6631 | + | 30.6631i | 1.34080 | + | 1.34080i | 0.895260 | + | 0.445544i | \(0.146990\pi\) |
0.445544 | + | 0.895260i | \(0.353010\pi\) | |||||||
\(524\) | − | 4.64290i | − | 0.202826i | ||||||
\(525\) | −0.939270 | − | 15.2902i | −0.0409931 | − | 0.667318i | ||||
\(526\) | − | 10.6315i | − | 0.463554i | ||||||
\(527\) | 20.1842 | − | 20.1842i | 0.879239 | − | 0.879239i | ||||
\(528\) | 4.01921 | + | 4.01921i | 0.174914 | + | 0.174914i | ||||
\(529\) | − | 14.0419i | − | 0.610519i | ||||||
\(530\) | 17.0941 | − | 0.524549i | 0.742521 | − | 0.0227849i | ||||
\(531\) | 2.39487i | 0.103929i | ||||||||
\(532\) | 12.3621 | − | 5.05259i | 0.535965 | − | 0.219058i | ||||
\(533\) | −25.0584 | + | 25.0584i | −1.08540 | + | 1.08540i | ||||
\(534\) | 2.50829 | 0.108544 | ||||||||
\(535\) | 10.8957 | − | 11.5855i | 0.471061 | − | 0.500886i | ||||
\(536\) | −8.66573 | −0.374303 | ||||||||
\(537\) | −6.75144 | − | 6.75144i | −0.291346 | − | 0.291346i | ||||
\(538\) | −14.4131 | + | 14.4131i | −0.621391 | + | 0.621391i | ||||
\(539\) | − | 13.5670i | − | 0.584370i | ||||||
\(540\) | −1.62889 | − | 1.53190i | −0.0700963 | − | 0.0659224i | ||||
\(541\) | −5.86517 | −0.252163 | −0.126082 | − | 0.992020i | \(-0.540240\pi\) | ||||
−0.126082 | + | 0.992020i | \(0.540240\pi\) | |||||||
\(542\) | −14.5414 | + | 14.5414i | −0.624607 | + | 0.624607i | ||||
\(543\) | 13.7450 | − | 13.7450i | 0.589854 | − | 0.589854i | ||||
\(544\) | −7.05776 | −0.302599 | ||||||||
\(545\) | −13.3101 | + | 0.408434i | −0.570144 | + | 0.0174954i | ||||
\(546\) | 16.9944i | 0.727295i | ||||||||
\(547\) | 27.3401 | − | 27.3401i | 1.16898 | − | 1.16898i | 0.186527 | − | 0.982450i | \(-0.440277\pi\) |
0.982450 | − | 0.186527i | \(-0.0597231\pi\) | |||||||
\(548\) | −2.26545 | + | 2.26545i | −0.0967752 | + | 0.0967752i | ||||
\(549\) | − | 2.33286i | − | 0.0995642i | ||||||
\(550\) | −18.8261 | + | 21.2904i | −0.802746 | + | 0.907826i | ||||
\(551\) | −16.2555 | − | 6.82297i | −0.692508 | − | 0.290668i | ||||
\(552\) | −4.30360 | − | 4.30360i | −0.183173 | − | 0.183173i | ||||
\(553\) | 9.18229 | + | 9.18229i | 0.390471 | + | 0.390471i | ||||
\(554\) | 23.3376 | 0.991518 | ||||||||
\(555\) | 19.5948 | − | 0.601285i | 0.831754 | − | 0.0255231i | ||||
\(556\) | −17.4266 | −0.739051 | ||||||||
\(557\) | 30.4617 | + | 30.4617i | 1.29070 | + | 1.29070i | 0.934353 | + | 0.356350i | \(0.115979\pi\) |
0.356350 | + | 0.934353i | \(0.384021\pi\) | |||||||
\(558\) | 2.85986 | − | 2.85986i | 0.121068 | − | 0.121068i | ||||
\(559\) | 32.6095 | 1.37924 | ||||||||
\(560\) | −4.99059 | − | 4.69343i | −0.210891 | − | 0.198334i | ||||
\(561\) | − | 40.1165i | − | 1.69372i | ||||||
\(562\) | 11.8093 | + | 11.8093i | 0.498147 | + | 0.498147i | ||||
\(563\) | 9.62507 | + | 9.62507i | 0.405648 | + | 0.405648i | 0.880218 | − | 0.474570i | \(-0.157396\pi\) |
−0.474570 | + | 0.880218i | \(0.657396\pi\) | |||||||
\(564\) | 4.58666 | 0.193133 | ||||||||
\(565\) | −0.0953405 | − | 0.0896635i | −0.00401100 | − | 0.00377217i | ||||
\(566\) | 12.9675i | 0.545063i | ||||||||
\(567\) | 2.16643 | + | 2.16643i | 0.0909816 | + | 0.0909816i | ||||
\(568\) | −4.60720 | + | 4.60720i | −0.193314 | + | 0.193314i | ||||
\(569\) | 12.8721 | 0.539627 | 0.269814 | − | 0.962913i | \(-0.413038\pi\) | ||||
0.269814 | + | 0.962913i | \(0.413038\pi\) | |||||||
\(570\) | 9.09870 | + | 3.49481i | 0.381103 | + | 0.146381i | ||||
\(571\) | 6.13588 | 0.256778 | 0.128389 | − | 0.991724i | \(-0.459019\pi\) | ||||
0.128389 | + | 0.991724i | \(0.459019\pi\) | |||||||
\(572\) | 22.2940 | − | 22.2940i | 0.932158 | − | 0.932158i | ||||
\(573\) | 17.7856 | + | 17.7856i | 0.743004 | + | 0.743004i | ||||
\(574\) | 19.5741i | 0.817007i | ||||||||
\(575\) | 20.1582 | − | 22.7969i | 0.840653 | − | 0.950695i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −18.5088 | − | 18.5088i | −0.770532 | − | 0.770532i | 0.207667 | − | 0.978200i | \(-0.433413\pi\) |
−0.978200 | + | 0.207667i | \(0.933413\pi\) | |||||||
\(578\) | 23.2016 | + | 23.2016i | 0.965060 | + | 0.965060i | ||||
\(579\) | 1.74850i | 0.0726650i | ||||||||
\(580\) | 0.277383 | + | 9.03942i | 0.0115177 | + | 0.375342i | ||||
\(581\) | 22.9927 | 0.953896 | ||||||||
\(582\) | −6.22010 | + | 6.22010i | −0.257831 | + | 0.257831i | ||||
\(583\) | 30.7402 | + | 30.7402i | 1.27313 | + | 1.27313i | ||||
\(584\) | 2.93707 | 0.121537 | ||||||||
\(585\) | −8.49722 | + | 9.03522i | −0.351317 | + | 0.373560i | ||||
\(586\) | 16.5884 | 0.685260 | ||||||||
\(587\) | 25.9416 | + | 25.9416i | 1.07072 | + | 1.07072i | 0.997301 | + | 0.0734236i | \(0.0233925\pi\) |
0.0734236 | + | 0.997301i | \(0.476607\pi\) | |||||||
\(588\) | 1.68776 | + | 1.68776i | 0.0696022 | + | 0.0696022i | ||||
\(589\) | −6.82297 | + | 16.2555i | −0.281136 | + | 0.669797i | ||||
\(590\) | −3.66870 | + | 3.90098i | −0.151038 | + | 0.160601i | ||||
\(591\) | 8.02932i | 0.330282i | ||||||||
\(592\) | 6.19934 | − | 6.19934i | 0.254791 | − | 0.254791i | ||||
\(593\) | 5.30063 | − | 5.30063i | 0.217671 | − | 0.217671i | −0.589845 | − | 0.807516i | \(-0.700811\pi\) |
0.807516 | + | 0.589845i | \(0.200811\pi\) | |||||||
\(594\) | − | 5.68402i | − | 0.233218i | ||||||
\(595\) | 1.48302 | + | 48.3290i | 0.0607979 | + | 1.98130i | ||||
\(596\) | −1.79836 | −0.0736637 | ||||||||
\(597\) | 2.75697 | − | 2.75697i | 0.112835 | − | 0.112835i | ||||
\(598\) | −23.8714 | + | 23.8714i | −0.976176 | + | 0.976176i | ||||
\(599\) | −8.38430 | −0.342573 | −0.171287 | − | 0.985221i | \(-0.554792\pi\) | ||||
−0.171287 | + | 0.985221i | \(0.554792\pi\) | |||||||
\(600\) | −0.306570 | − | 4.99059i | −0.0125157 | − | 0.203740i | ||||
\(601\) | 11.8588i | 0.483731i | 0.970310 | + | 0.241866i | \(0.0777594\pi\) | ||||
−0.970310 | + | 0.241866i | \(0.922241\pi\) | |||||||
\(602\) | 12.7363 | − | 12.7363i | 0.519092 | − | 0.519092i | ||||
\(603\) | 6.12760 | + | 6.12760i | 0.249535 | + | 0.249535i | ||||
\(604\) | −8.62201 | −0.350825 | ||||||||
\(605\) | −47.6240 | + | 1.46138i | −1.93619 | + | 0.0594137i | ||||
\(606\) | 3.42891 | 0.139290 | ||||||||
\(607\) | −11.1795 | + | 11.1795i | −0.453763 | + | 0.453763i | −0.896601 | − | 0.442838i | \(-0.853972\pi\) |
0.442838 | + | 0.896601i | \(0.353972\pi\) | |||||||
\(608\) | 4.03490 | − | 1.64913i | 0.163637 | − | 0.0668809i | ||||
\(609\) | − | 12.3914i | − | 0.502125i | ||||||
\(610\) | 3.57371 | − | 3.79998i | 0.144695 | − | 0.153857i | ||||
\(611\) | − | 25.4415i | − | 1.02925i | ||||||
\(612\) | 4.99059 | + | 4.99059i | 0.201733 | + | 0.201733i | ||||
\(613\) | 27.8634 | − | 27.8634i | 1.12539 | − | 1.12539i | 0.134477 | − | 0.990917i | \(-0.457065\pi\) |
0.990917 | − | 0.134477i | \(-0.0429355\pi\) | |||||||
\(614\) | − | 10.6309i | − | 0.429029i | ||||||
\(615\) | −9.78705 | + | 10.4067i | −0.394652 | + | 0.419639i | ||||
\(616\) | − | 17.4147i | − | 0.701658i | ||||||
\(617\) | −9.90590 | − | 9.90590i | −0.398797 | − | 0.398797i | 0.479012 | − | 0.877808i | \(-0.340995\pi\) |
−0.877808 | + | 0.479012i | \(0.840995\pi\) | |||||||
\(618\) | −13.0842 | − | 13.0842i | −0.526322 | − | 0.526322i | ||||
\(619\) | − | 13.1404i | − | 0.528156i | −0.964501 | − | 0.264078i | \(-0.914932\pi\) | ||
0.964501 | − | 0.264078i | \(-0.0850676\pi\) | |||||||
\(620\) | 9.03942 | − | 0.277383i | 0.363032 | − | 0.0111400i | ||||
\(621\) | 6.08621i | 0.244231i | ||||||||
\(622\) | −12.0874 | + | 12.0874i | −0.484659 | + | 0.484659i | ||||
\(623\) | −5.43405 | − | 5.43405i | −0.217711 | − | 0.217711i | ||||
\(624\) | 5.54686i | 0.222052i | ||||||||
\(625\) | 24.8120 | − | 3.05994i | 0.992481 | − | 0.122397i | ||||
\(626\) | 6.31902i | 0.252559i | ||||||||
\(627\) | 9.37367 | + | 22.9344i | 0.374348 | + | 0.915913i | ||||
\(628\) | 7.79308 | − | 7.79308i | 0.310978 | − | 0.310978i | ||||
\(629\) | −61.8768 | −2.46719 | ||||||||
\(630\) | 0.210126 | + | 6.84764i | 0.00837162 | + | 0.272816i | ||||
\(631\) | −1.22727 | −0.0488569 | −0.0244284 | − | 0.999702i | \(-0.507777\pi\) | ||||
−0.0244284 | + | 0.999702i | \(0.507777\pi\) | |||||||
\(632\) | 2.99703 | + | 2.99703i | 0.119215 | + | 0.119215i | ||||
\(633\) | 13.3909 | − | 13.3909i | 0.532239 | − | 0.532239i | ||||
\(634\) | − | 28.7488i | − | 1.14176i | ||||||
\(635\) | −21.7464 | + | 23.1232i | −0.862979 | + | 0.917618i | ||||
\(636\) | −7.64832 | −0.303276 | ||||||||
\(637\) | 9.36178 | − | 9.36178i | 0.370927 | − | 0.370927i | ||||
\(638\) | −16.2555 | + | 16.2555i | −0.643562 | + | 0.643562i | ||||
\(639\) | 6.51556 | 0.257752 | ||||||||
\(640\) | −1.62889 | − | 1.53190i | −0.0643876 | − | 0.0605536i | ||||
\(641\) | − | 36.0180i | − | 1.42263i | −0.702875 | − | 0.711313i | \(-0.748101\pi\) | ||
0.702875 | − | 0.711313i | \(-0.251899\pi\) | |||||||
\(642\) | −5.02931 | + | 5.02931i | −0.198491 | + | 0.198491i | ||||
\(643\) | −2.37113 | + | 2.37113i | −0.0935082 | + | 0.0935082i | −0.752314 | − | 0.658805i | \(-0.771062\pi\) |
0.658805 | + | 0.752314i | \(0.271062\pi\) | |||||||
\(644\) | 18.6469i | 0.734791i | ||||||||
\(645\) | 13.1395 | − | 0.403197i | 0.517367 | − | 0.0158759i | ||||
\(646\) | −28.3666 | − | 11.9064i | −1.11607 | − | 0.468451i | ||||
\(647\) | −1.07039 | − | 1.07039i | −0.0420812 | − | 0.0420812i | 0.685753 | − | 0.727834i | \(-0.259473\pi\) |
−0.727834 | + | 0.685753i | \(0.759473\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | −13.6125 | −0.534337 | ||||||||
\(650\) | −27.6821 | + | 1.70050i | −1.08578 | + | 0.0666992i | ||||
\(651\) | −12.3914 | −0.485657 | ||||||||
\(652\) | −7.85986 | − | 7.85986i | −0.307816 | − | 0.307816i | ||||
\(653\) | −17.2204 | + | 17.2204i | −0.673887 | + | 0.673887i | −0.958610 | − | 0.284723i | \(-0.908099\pi\) |
0.284723 | + | 0.958610i | \(0.408099\pi\) | |||||||
\(654\) | 5.95528 | 0.232870 | ||||||||
\(655\) | −10.3770 | + | 0.318426i | −0.405461 | + | 0.0124419i | ||||
\(656\) | 6.38884i | 0.249442i | ||||||||
\(657\) | −2.07682 | − | 2.07682i | −0.0810246 | − | 0.0810246i | ||||
\(658\) | −9.93668 | − | 9.93668i | −0.387372 | − | 0.387372i | ||||
\(659\) | 33.5146 | 1.30555 | 0.652773 | − | 0.757554i | \(-0.273606\pi\) | ||||
0.652773 | + | 0.757554i | \(0.273606\pi\) | |||||||
\(660\) | 8.70735 | − | 9.25865i | 0.338933 | − | 0.360393i | ||||
\(661\) | − | 38.1923i | − | 1.48551i | −0.669564 | − | 0.742754i | \(-0.733519\pi\) | ||
0.669564 | − | 0.742754i | \(-0.266481\pi\) | |||||||
\(662\) | −15.5532 | − | 15.5532i | −0.604492 | − | 0.604492i | ||||
\(663\) | 27.6821 | − | 27.6821i | 1.07508 | − | 1.07508i | ||||
\(664\) | 7.50462 | 0.291236 | ||||||||
\(665\) | −12.1405 | − | 27.2830i | −0.470787 | − | 1.05799i | ||||
\(666\) | −8.76719 | −0.339722 | ||||||||
\(667\) | 17.4057 | − | 17.4057i | 0.673952 | − | 0.673952i | ||||
\(668\) | 17.5764 | + | 17.5764i | 0.680051 | + | 0.680051i | ||||
\(669\) | − | 13.0960i | − | 0.506322i | ||||||
\(670\) | 0.594326 | + | 19.3680i | 0.0229608 | + | 0.748253i | ||||
\(671\) | 13.2601 | 0.511899 | ||||||||
\(672\) | 2.16643 | + | 2.16643i | 0.0835719 | + | 0.0835719i | ||||
\(673\) | 12.1639 | + | 12.1639i | 0.468885 | + | 0.468885i | 0.901553 | − | 0.432668i | \(-0.142428\pi\) |
−0.432668 | + | 0.901553i | \(0.642428\pi\) | |||||||
\(674\) | 5.95143i | 0.229240i | ||||||||
\(675\) | −3.31210 | + | 3.74566i | −0.127483 | + | 0.144171i | ||||
\(676\) | 17.7676 | 0.683369 | ||||||||
\(677\) | −27.8121 | + | 27.8121i | −1.06891 | + | 1.06891i | −0.0714633 | + | 0.997443i | \(0.522767\pi\) |
−0.997443 | + | 0.0714633i | \(0.977233\pi\) | |||||||
\(678\) | 0.0413876 | + | 0.0413876i | 0.00158948 | + | 0.00158948i | ||||
\(679\) | 26.9508 | 1.03428 | ||||||||
\(680\) | 0.484046 | + | 15.7742i | 0.0185623 | + | 0.604914i | ||||
\(681\) | −3.73260 | −0.143033 | ||||||||
\(682\) | 16.2555 | + | 16.2555i | 0.622456 | + | 0.622456i | ||||
\(683\) | −17.1745 | − | 17.1745i | −0.657166 | − | 0.657166i | 0.297543 | − | 0.954709i | \(-0.403833\pi\) |
−0.954709 | + | 0.297543i | \(0.903833\pi\) | |||||||
\(684\) | −4.01921 | − | 1.68699i | −0.153678 | − | 0.0645038i | ||||
\(685\) | 5.21869 | + | 4.90794i | 0.199396 | + | 0.187523i | ||||
\(686\) | 14.1337i | 0.539628i | ||||||||
\(687\) | 3.49735 | − | 3.49735i | 0.133432 | − | 0.133432i | ||||
\(688\) | 4.15703 | − | 4.15703i | 0.158485 | − | 0.158485i | ||||
\(689\) | 42.4241i | 1.61623i | ||||||||
\(690\) | −9.32346 | + | 9.91377i | −0.354938 | + | 0.377411i | ||||
\(691\) | −9.98119 | −0.379702 | −0.189851 | − | 0.981813i | \(-0.560801\pi\) | ||||
−0.189851 | + | 0.981813i | \(0.560801\pi\) | |||||||
\(692\) | 0.108645 | − | 0.108645i | 0.00413005 | − | 0.00413005i | ||||
\(693\) | −12.3141 | + | 12.3141i | −0.467772 | + | 0.467772i | ||||
\(694\) | −26.6872 | −1.01303 | ||||||||
\(695\) | 1.19518 | + | 38.9487i | 0.0453356 | + | 1.47741i | ||||
\(696\) | − | 4.04446i | − | 0.153305i | ||||||
\(697\) | 31.8841 | − | 31.8841i | 1.20770 | − | 1.20770i | ||||
\(698\) | 2.36826 | + | 2.36826i | 0.0896401 | + | 0.0896401i | ||||
\(699\) | −25.6256 | −0.969248 | ||||||||
\(700\) | −10.1476 | + | 11.4759i | −0.383544 | + | 0.433750i | ||||
\(701\) | 8.14987 | 0.307816 | 0.153908 | − | 0.988085i | \(-0.450814\pi\) | ||||
0.153908 | + | 0.988085i | \(0.450814\pi\) | |||||||
\(702\) | 3.92222 | − | 3.92222i | 0.148035 | − | 0.148035i | ||||
\(703\) | 35.3747 | − | 14.4582i | 1.33418 | − | 0.545302i | ||||
\(704\) | − | 5.68402i | − | 0.214225i | ||||||
\(705\) | −0.314569 | − | 10.2512i | −0.0118474 | − | 0.386084i | ||||
\(706\) | − | 30.8944i | − | 1.16273i | ||||||
\(707\) | −7.42850 | − | 7.42850i | −0.279378 | − | 0.279378i | ||||
\(708\) | 1.69343 | − | 1.69343i | 0.0636430 | − | 0.0636430i | ||||
\(709\) | − | 24.1408i | − | 0.906626i | −0.891351 | − | 0.453313i | \(-0.850242\pi\) | ||
0.891351 | − | 0.453313i | \(-0.149758\pi\) | |||||||
\(710\) | 10.6131 | + | 9.98119i | 0.398304 | + | 0.374587i | ||||
\(711\) | − | 4.23844i | − | 0.158954i | ||||||
\(712\) | −1.77363 | − | 1.77363i | −0.0664696 | − | 0.0664696i | ||||
\(713\) | −17.4057 | − | 17.4057i | −0.651849 | − | 0.651849i | ||||
\(714\) | − | 21.6236i | − | 0.809242i | ||||||
\(715\) | −51.3564 | − | 48.2984i | −1.92062 | − | 1.80626i | ||||
\(716\) | 9.54798i | 0.356825i | ||||||||
\(717\) | −4.93773 | + | 4.93773i | −0.184403 | + | 0.184403i | ||||
\(718\) | 3.69175 | + | 3.69175i | 0.137775 | + | 0.137775i | ||||
\(719\) | 12.6723i | 0.472595i | 0.971681 | + | 0.236298i | \(0.0759340\pi\) | ||||
−0.971681 | + | 0.236298i | \(0.924066\pi\) | |||||||
\(720\) | 0.0685835 | + | 2.23502i | 0.00255596 | + | 0.0832941i | ||||
\(721\) | 56.6919i | 2.11132i | ||||||||
\(722\) | 18.9992 | + | 0.178653i | 0.707076 | + | 0.00664878i | ||||
\(723\) | 5.33828 | − | 5.33828i | 0.198533 | − | 0.198533i | ||||
\(724\) | −19.4384 | −0.722421 | ||||||||
\(725\) | 20.1842 | − | 1.23991i | 0.749624 | − | 0.0460491i | ||||
\(726\) | 21.3081 | 0.790818 | ||||||||
\(727\) | 12.3201 | + | 12.3201i | 0.456926 | + | 0.456926i | 0.897645 | − | 0.440719i | \(-0.145276\pi\) |
−0.440719 | + | 0.897645i | \(0.645276\pi\) | |||||||
\(728\) | 12.0169 | − | 12.0169i | 0.445375 | − | 0.445375i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −0.201435 | − | 6.56440i | −0.00745543 | − | 0.242959i | ||||
\(731\) | −41.4920 | −1.53464 | ||||||||
\(732\) | −1.64958 | + | 1.64958i | −0.0609704 | + | 0.0609704i | ||||
\(733\) | −1.44833 | + | 1.44833i | −0.0534954 | + | 0.0534954i | −0.733348 | − | 0.679853i | \(-0.762044\pi\) |
0.679853 | + | 0.733348i | \(0.262044\pi\) | |||||||
\(734\) | 5.28697 | 0.195146 | ||||||||
\(735\) | 3.65643 | − | 3.88793i | 0.134869 | − | 0.143409i | ||||
\(736\) | 6.08621i | 0.224341i | ||||||||
\(737\) | −34.8294 | + | 34.8294i | −1.28296 | + | 1.28296i | ||||
\(738\) | 4.51759 | − | 4.51759i | 0.166295 | − | 0.166295i | ||||
\(739\) | − | 8.64709i | − | 0.318088i | −0.987271 | − | 0.159044i | \(-0.949159\pi\) | ||
0.987271 | − | 0.159044i | \(-0.0508412\pi\) | |||||||
\(740\) | −14.2808 | − | 13.4305i | −0.524973 | − | 0.493713i | ||||
\(741\) | −9.35751 | + | 22.2940i | −0.343757 | + | 0.818990i | ||||
\(742\) | 16.5696 | + | 16.5696i | 0.608288 | + | 0.608288i | ||||
\(743\) | −18.4885 | − | 18.4885i | −0.678277 | − | 0.678277i | 0.281333 | − | 0.959610i | \(-0.409223\pi\) |
−0.959610 | + | 0.281333i | \(0.909223\pi\) | |||||||
\(744\) | −4.04446 | −0.148277 | ||||||||
\(745\) | 0.123338 | + | 4.01936i | 0.00451875 | + | 0.147258i | ||||
\(746\) | 23.5866 | 0.863566 | ||||||||
\(747\) | −5.30657 | − | 5.30657i | −0.194157 | − | 0.194157i | ||||
\(748\) | −28.3666 | + | 28.3666i | −1.03719 | + | 1.03719i | ||||
\(749\) | 21.7913 | 0.796238 | ||||||||
\(750\) | −11.1330 | + | 1.02746i | −0.406521 | + | 0.0375176i | ||||
\(751\) | − | 7.72319i | − | 0.281823i | −0.990022 | − | 0.140912i | \(-0.954997\pi\) | ||
0.990022 | − | 0.140912i | \(-0.0450033\pi\) | |||||||
\(752\) | −3.24326 | − | 3.24326i | −0.118269 | − | 0.118269i | ||||
\(753\) | −14.1822 | − | 14.1822i | −0.516827 | − | 0.516827i | ||||
\(754\) | −22.4340 | −0.816998 | ||||||||
\(755\) | 0.591328 | + | 19.2703i | 0.0215206 | + | 0.701319i | ||||
\(756\) | − | 3.06380i | − | 0.111429i | ||||||
\(757\) | −16.2864 | − | 16.2864i | −0.591937 | − | 0.591937i | 0.346217 | − | 0.938154i | \(-0.387466\pi\) |
−0.938154 | + | 0.346217i | \(0.887466\pi\) | |||||||
\(758\) | 14.6657 | − | 14.6657i | 0.532683 | − | 0.532683i | ||||
\(759\) | −34.5941 | −1.25569 | ||||||||
\(760\) | −3.96255 | − | 8.90495i | −0.143737 | − | 0.323017i | ||||
\(761\) | 0.887475 | 0.0321709 | 0.0160855 | − | 0.999871i | \(-0.494880\pi\) | ||||
0.0160855 | + | 0.999871i | \(0.494880\pi\) | |||||||
\(762\) | 10.0379 | − | 10.0379i | 0.363634 | − | 0.363634i | ||||
\(763\) | −12.9017 | − | 12.9017i | −0.467073 | − | 0.467073i | ||||
\(764\) | − | 25.1526i | − | 0.909991i | ||||||
\(765\) | 10.8118 | − | 11.4963i | 0.390901 | − | 0.415651i | ||||
\(766\) | −1.36210 | −0.0492148 | ||||||||
\(767\) | −9.39321 | − | 9.39321i | −0.339169 | − | 0.339169i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | 1.13134i | 0.0407972i | 0.999792 | + | 0.0203986i | \(0.00649352\pi\) | ||||
−0.999792 | + | 0.0203986i | \(0.993506\pi\) | |||||||
\(770\) | −38.9221 | + | 1.19436i | −1.40266 | + | 0.0430418i | ||||
\(771\) | −12.2496 | −0.441158 | ||||||||
\(772\) | 1.23637 | − | 1.23637i | 0.0444980 | − | 0.0444980i | ||||
\(773\) | −6.34620 | − | 6.34620i | −0.228257 | − | 0.228257i | 0.583707 | − | 0.811964i | \(-0.301602\pi\) |
−0.811964 | + | 0.583707i | \(0.801602\pi\) | |||||||
\(774\) | −5.87892 | −0.211313 | ||||||||
\(775\) | −1.23991 | − | 20.1842i | −0.0445389 | − | 0.725039i | ||||
\(776\) | 8.79655 | 0.315778 | ||||||||
\(777\) | 18.9935 | + | 18.9935i | 0.681389 | + | 0.681389i | ||||
\(778\) | −26.3549 | − | 26.3549i | −0.944868 | − | 0.944868i | ||||
\(779\) | −10.7779 | + | 25.6781i | −0.386159 | + | 0.920013i | ||||
\(780\) | 12.3973 | − | 0.380423i | 0.443895 | − | 0.0136213i | ||||
\(781\) | 37.0346i | 1.32520i | ||||||||
\(782\) | 30.3738 | − | 30.3738i | 1.08616 | − | 1.08616i | ||||
\(783\) | −2.85986 | + | 2.85986i | −0.102203 | + | 0.102203i | ||||
\(784\) | − | 2.38686i | − | 0.0852450i | ||||||
\(785\) | −17.9521 | − | 16.8832i | −0.640739 | − | 0.602587i | ||||
\(786\) | 4.64290 | 0.165607 | ||||||||
\(787\) | 2.61114 | − | 2.61114i | 0.0930770 | − | 0.0930770i | −0.659035 | − | 0.752112i | \(-0.729035\pi\) |
0.752112 | + | 0.659035i | \(0.229035\pi\) | |||||||
\(788\) | 5.67759 | − | 5.67759i | 0.202256 | − | 0.202256i | ||||
\(789\) | 10.6315 | 0.378491 | ||||||||
\(790\) | 6.49286 | − | 6.90395i | 0.231006 | − | 0.245632i | ||||
\(791\) | − | 0.179327i | − | 0.00637613i | ||||||
\(792\) | −4.01921 | + | 4.01921i | −0.142816 | + | 0.142816i | ||||
\(793\) | 9.15001 | + | 9.15001i | 0.324926 | + | 0.324926i | ||||
\(794\) | 14.5091 | 0.514910 | ||||||||
\(795\) | 0.524549 | + | 17.0941i | 0.0186038 | + | 0.606266i | ||||
\(796\) | −3.89894 | −0.138194 | ||||||||
\(797\) | 37.6179 | − | 37.6179i | 1.33249 | − | 1.33249i | 0.429360 | − | 0.903133i | \(-0.358739\pi\) |
0.903133 | − | 0.429360i | \(-0.141261\pi\) | |||||||
\(798\) | 5.05259 | + | 12.3621i | 0.178860 | + | 0.437614i | ||||
\(799\) | 32.3715i | 1.14522i | ||||||||
\(800\) | −3.31210 | + | 3.74566i | −0.117101 | + | 0.132429i | ||||
\(801\) | 2.50829i | 0.0886262i | ||||||||
\(802\) | −5.12479 | − | 5.12479i | −0.180963 | − | 0.180963i | ||||
\(803\) | 11.8047 | − | 11.8047i | 0.416579 | − | 0.416579i | ||||
\(804\) | − | 8.66573i | − | 0.305617i | ||||||
\(805\) | 41.6762 | − | 1.27887i | 1.46889 | − | 0.0450743i | ||||
\(806\) | 22.4340i | 0.790204i | ||||||||
\(807\) | −14.4131 | − | 14.4131i | −0.507364 | − | 0.507364i | ||||
\(808\) | −2.42461 | − | 2.42461i | −0.0852973 | − | 0.0852973i | ||||
\(809\) | 36.3150i | 1.27677i | 0.769718 | + | 0.638384i | \(0.220397\pi\) | ||||
−0.769718 | + | 0.638384i | \(0.779603\pi\) | |||||||
\(810\) | 1.53190 | − | 1.62889i | 0.0538254 | − | 0.0572334i | ||||
\(811\) | 33.7689i | 1.18579i | 0.805281 | + | 0.592893i | \(0.202014\pi\) | ||||
−0.805281 | + | 0.592893i | \(0.797986\pi\) | |||||||
\(812\) | −8.76204 | + | 8.76204i | −0.307487 | + | 0.307487i | ||||
\(813\) | −14.5414 | − | 14.5414i | −0.509990 | − | 0.509990i | ||||
\(814\) | − | 49.8329i | − | 1.74664i | ||||||
\(815\) | −17.0279 | + | 18.1060i | −0.596460 | + | 0.634225i | ||||
\(816\) | − | 7.05776i | − | 0.247071i | ||||||
\(817\) | 23.7208 | − | 9.69509i | 0.829887 | − | 0.339188i | ||||
\(818\) | 2.90436 | − | 2.90436i | 0.101549 | − | 0.101549i | ||||
\(819\) | −16.9944 | −0.593834 | ||||||||
\(820\) | 14.2792 | − | 0.438169i | 0.498650 | − | 0.0153015i | ||||
\(821\) | 35.2486 | 1.23019 | 0.615093 | − | 0.788454i | \(-0.289118\pi\) | ||||
0.615093 | + | 0.788454i | \(0.289118\pi\) | |||||||
\(822\) | −2.26545 | − | 2.26545i | −0.0790166 | − | 0.0790166i | ||||
\(823\) | −1.01419 | + | 1.01419i | −0.0353525 | + | 0.0353525i | −0.724562 | − | 0.689210i | \(-0.757958\pi\) |
0.689210 | + | 0.724562i | \(0.257958\pi\) | |||||||
\(824\) | 18.5038i | 0.644611i | ||||||||
\(825\) | −21.2904 | − | 18.8261i | −0.741237 | − | 0.655440i | ||||
\(826\) | −7.33740 | −0.255301 | ||||||||
\(827\) | 26.2979 | − | 26.2979i | 0.914469 | − | 0.914469i | −0.0821507 | − | 0.996620i | \(-0.526179\pi\) |
0.996620 | + | 0.0821507i | \(0.0261789\pi\) | |||||||
\(828\) | 4.30360 | − | 4.30360i | 0.149560 | − | 0.149560i | ||||
\(829\) | −24.6910 | −0.857555 | −0.428777 | − | 0.903410i | \(-0.641056\pi\) | ||||
−0.428777 | + | 0.903410i | \(0.641056\pi\) | |||||||
\(830\) | −0.514693 | − | 16.7730i | −0.0178653 | − | 0.582198i | ||||
\(831\) | 23.3376i | 0.809571i | ||||||||
\(832\) | 3.92222 | − | 3.92222i | 0.135978 | − | 0.135978i | ||||
\(833\) | −11.9118 | + | 11.9118i | −0.412721 | + | 0.412721i | ||||
\(834\) | − | 17.4266i | − | 0.603433i | ||||||
\(835\) | 38.0781 | − | 40.4890i | 1.31775 | − | 1.40118i | ||||
\(836\) | 9.58891 | − | 22.8453i | 0.331639 | − | 0.790121i | ||||
\(837\) | 2.85986 | + | 2.85986i | 0.0988513 | + | 0.0988513i | ||||
\(838\) | −7.98253 | − | 7.98253i | −0.275752 | − | 0.275752i | ||||
\(839\) | −27.5645 | −0.951632 | −0.475816 | − | 0.879545i | \(-0.657847\pi\) | ||||
−0.475816 | + | 0.879545i | \(0.657847\pi\) | |||||||
\(840\) | 4.69343 | − | 4.99059i | 0.161939 | − | 0.172192i | ||||
\(841\) | −12.6424 | −0.435944 | ||||||||
\(842\) | 3.44423 | + | 3.44423i | 0.118696 | + | 0.118696i | ||||
\(843\) | −11.8093 | + | 11.8093i | −0.406735 | + | 0.406735i | ||||
\(844\) | −18.9376 | −0.651858 | ||||||||
\(845\) | −1.21856 | − | 39.7109i | −0.0419199 | − | 1.36610i | ||||
\(846\) | 4.58666i | 0.157692i | ||||||||
\(847\) | −46.1626 | − | 46.1626i | −1.58616 | − | 1.58616i | ||||
\(848\) | 5.40818 | + | 5.40818i | 0.185718 | + | 0.185718i | ||||
\(849\) | −12.9675 | −0.445042 | ||||||||
\(850\) | 35.2224 | − | 2.16370i | 1.20812 | − | 0.0742144i | ||||
\(851\) | 53.3590i | 1.82912i | ||||||||
\(852\) | −4.60720 | − | 4.60720i | −0.157840 | − | 0.157840i | ||||
\(853\) | −24.5359 | + | 24.5359i | −0.840094 | + | 0.840094i | −0.988871 | − | 0.148777i | \(-0.952466\pi\) |
0.148777 | + | 0.988871i | \(0.452466\pi\) | |||||||
\(854\) | 7.14743 | 0.244580 | ||||||||
\(855\) | −3.49481 | + | 9.09870i | −0.119520 | + | 0.311169i | ||||
\(856\) | 7.11253 | 0.243101 | ||||||||
\(857\) | 21.4801 | − | 21.4801i | 0.733747 | − | 0.733747i | −0.237613 | − | 0.971360i | \(-0.576365\pi\) |
0.971360 | + | 0.237613i | \(0.0763650\pi\) | |||||||
\(858\) | 22.2940 | + | 22.2940i | 0.761104 | + | 0.761104i | ||||
\(859\) | − | 28.6835i | − | 0.978668i | −0.872096 | − | 0.489334i | \(-0.837240\pi\) | ||
0.872096 | − | 0.489334i | \(-0.162760\pi\) | |||||||
\(860\) | −9.57612 | − | 9.00591i | −0.326543 | − | 0.307099i | ||||
\(861\) | −19.5741 | −0.667084 | ||||||||
\(862\) | −5.01147 | − | 5.01147i | −0.170691 | − | 0.170691i | ||||
\(863\) | 10.4760 | + | 10.4760i | 0.356607 | + | 0.356607i | 0.862561 | − | 0.505954i | \(-0.168859\pi\) |
−0.505954 | + | 0.862561i | \(0.668859\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | −0.250273 | − | 0.235371i | −0.00850955 | − | 0.00800286i | ||||
\(866\) | −30.0950 | −1.02267 | ||||||||
\(867\) | −23.2016 | + | 23.2016i | −0.787968 | + | 0.787968i | ||||
\(868\) | 8.76204 | + | 8.76204i | 0.297403 | + | 0.297403i | ||||
\(869\) | 24.0914 | 0.817244 | ||||||||
\(870\) | −9.03942 | + | 0.277383i | −0.306465 | + | 0.00940416i | ||||
\(871\) | −48.0675 | −1.62871 | ||||||||
\(872\) | −4.21102 | − | 4.21102i | −0.142603 | − | 0.142603i | ||||
\(873\) | −6.22010 | − | 6.22010i | −0.210518 | − | 0.210518i | ||||
\(874\) | −10.2674 | + | 24.4618i | −0.347300 | + | 0.827431i | ||||
\(875\) | 26.3449 | + | 21.8930i | 0.890620 | + | 0.740119i | ||||
\(876\) | 2.93707i | 0.0992345i | ||||||||
\(877\) | −41.3628 | + | 41.3628i | −1.39672 | + | 1.39672i | −0.587488 | + | 0.809233i | \(0.699883\pi\) |
−0.809233 | + | 0.587488i | \(0.800117\pi\) | |||||||
\(878\) | −19.7811 | + | 19.7811i | −0.667580 | + | 0.667580i | ||||
\(879\) | 16.5884i | 0.559512i | ||||||||
\(880\) | −12.7039 | + | 0.389830i | −0.428248 | + | 0.0131412i | ||||
\(881\) | 24.8371 | 0.836785 | 0.418392 | − | 0.908266i | \(-0.362594\pi\) | ||||
0.418392 | + | 0.908266i | \(0.362594\pi\) | |||||||
\(882\) | −1.68776 | + | 1.68776i | −0.0568300 | + | 0.0568300i | ||||
\(883\) | 39.3033 | − | 39.3033i | 1.32266 | − | 1.32266i | 0.411049 | − | 0.911613i | \(-0.365163\pi\) |
0.911613 | − | 0.411049i | \(-0.134837\pi\) | |||||||
\(884\) | −39.1484 | −1.31670 | ||||||||
\(885\) | −3.90098 | − | 3.66870i | −0.131130 | − | 0.123322i | ||||
\(886\) | 16.9075i | 0.568019i | ||||||||
\(887\) | −0.809857 | + | 0.809857i | −0.0271923 | + | 0.0271923i | −0.720572 | − | 0.693380i | \(-0.756121\pi\) |
0.693380 | + | 0.720572i | \(0.256121\pi\) | |||||||
\(888\) | 6.19934 | + | 6.19934i | 0.208036 | + | 0.208036i | ||||
\(889\) | −43.4928 | −1.45870 | ||||||||
\(890\) | −3.84245 | + | 4.08574i | −0.128799 | + | 0.136954i | ||||
\(891\) | 5.68402 | 0.190422 | ||||||||
\(892\) | −9.26030 | + | 9.26030i | −0.310058 | + | 0.310058i | ||||
\(893\) | −7.56398 | − | 18.5067i | −0.253119 | − | 0.619302i | ||||
\(894\) | − | 1.79836i | − | 0.0601462i | ||||||
\(895\) | 21.3399 | − | 0.654834i | 0.713313 | − | 0.0218887i | ||||
\(896\) | − | 3.06380i | − | 0.102354i | ||||||
\(897\) | −23.8714 | − | 23.8714i | −0.797044 | − | 0.797044i | ||||
\(898\) | 0.565176 | − | 0.565176i | 0.0188602 | − | 0.0188602i | ||||
\(899\) | − | 16.3576i | − | 0.545557i | ||||||
\(900\) | 4.99059 | − | 0.306570i | 0.166353 | − | 0.0102190i | ||||
\(901\) | − | 53.9800i | − | 1.79834i | ||||||
\(902\) | 25.6781 | + | 25.6781i | 0.854987 | + | 0.854987i | ||||
\(903\) | 12.7363 | + | 12.7363i | 0.423837 | + | 0.423837i | ||||
\(904\) | − | 0.0585309i | − | 0.00194671i | ||||||
\(905\) | 1.33315 | + | 43.4451i | 0.0443154 | + | 1.44416i | ||||
\(906\) | − | 8.62201i | − | 0.286447i | ||||||
\(907\) | −11.4153 | + | 11.4153i | −0.379038 | + | 0.379038i | −0.870755 | − | 0.491717i | \(-0.836369\pi\) |
0.491717 | + | 0.870755i | \(0.336369\pi\) | |||||||
\(908\) | 2.63934 | + | 2.63934i | 0.0875897 | + | 0.0875897i | ||||
\(909\) | 3.42891i | 0.113730i | ||||||||
\(910\) | −27.6821 | − | 26.0338i | −0.917652 | − | 0.863011i | ||||
\(911\) | 23.8379i | 0.789786i | 0.918727 | + | 0.394893i | \(0.129218\pi\) | ||||
−0.918727 | + | 0.394893i | \(0.870782\pi\) | |||||||
\(912\) | 1.64913 | + | 4.03490i | 0.0546080 | + | 0.133609i | ||||
\(913\) | 30.1627 | − | 30.1627i | 0.998238 | − | 0.998238i | ||||
\(914\) | −28.2330 | −0.933866 | ||||||||
\(915\) | 3.79998 | + | 3.57371i | 0.125624 | + | 0.118143i | ||||
\(916\) | −4.94601 | −0.163421 | ||||||||
\(917\) | −10.0585 | − | 10.0585i | −0.332162 | − | 0.332162i | ||||
\(918\) | −4.99059 | + | 4.99059i | −0.164714 | + | 0.164714i | ||||
\(919\) | 10.0575i | 0.331766i | 0.986145 | + | 0.165883i | \(0.0530474\pi\) | ||||
−0.986145 | + | 0.165883i | \(0.946953\pi\) | |||||||
\(920\) | 13.6028 | − | 0.417413i | 0.448470 | − | 0.0137617i | ||||
\(921\) | 10.6309 | 0.350300 | ||||||||
\(922\) | −11.8723 | + | 11.8723i | −0.390995 | + | 0.390995i | ||||
\(923\) | −25.5555 | + | 25.5555i | −0.841168 | + | 0.841168i | ||||
\(924\) | 17.4147 | 0.572901 | ||||||||
\(925\) | −29.0379 | + | 32.8389i | −0.954759 | + | 1.07974i | ||||
\(926\) | − | 18.7261i | − | 0.615377i | ||||||
\(927\) | 13.0842 | − | 13.0842i | 0.429740 | − | 0.429740i | ||||
\(928\) | −2.85986 | + | 2.85986i | −0.0938796 | + | 0.0938796i | ||||
\(929\) | − | 25.9657i | − | 0.851906i | −0.904745 | − | 0.425953i | \(-0.859939\pi\) | ||
0.904745 | − | 0.425953i | \(-0.140061\pi\) | |||||||
\(930\) | 0.277383 | + | 9.03942i | 0.00909574 | + | 0.296414i | ||||
\(931\) | 4.02662 | − | 9.59329i | 0.131967 | − | 0.314407i | ||||
\(932\) | 18.1200 | + | 18.1200i | 0.593540 | + | 0.593540i | ||||
\(933\) | −12.0874 | − | 12.0874i | −0.395723 | − | 0.395723i | ||||
\(934\) | 26.7377 | 0.874885 | ||||||||
\(935\) | 65.3454 | + | 61.4544i | 2.13702 | + | 2.00977i | ||||
\(936\) | −5.54686 | −0.181305 | ||||||||
\(937\) | −15.1765 | − | 15.1765i | −0.495794 | − | 0.495794i | 0.414332 | − | 0.910126i | \(-0.364015\pi\) |
−0.910126 | + | 0.414332i | \(0.864015\pi\) | |||||||
\(938\) | −18.7737 | + | 18.7737i | −0.612984 | + | 0.612984i | ||||
\(939\) | −6.31902 | −0.206213 | ||||||||
\(940\) | −7.02629 | + | 7.47116i | −0.229172 | + | 0.243682i | ||||
\(941\) | − | 3.32842i | − | 0.108503i | −0.998527 | − | 0.0542517i | \(-0.982723\pi\) | ||
0.998527 | − | 0.0542517i | \(-0.0172773\pi\) | |||||||
\(942\) | 7.79308 | + | 7.79308i | 0.253912 | + | 0.253912i | ||||
\(943\) | −27.4950 | − | 27.4950i | −0.895360 | − | 0.895360i | ||||
\(944\) | −2.39487 | −0.0779464 | ||||||||
\(945\) | −6.84764 | + | 0.210126i | −0.222754 | + | 0.00683540i | ||||
\(946\) | − | 33.4159i | − | 1.08645i | ||||||
\(947\) | 17.1510 | + | 17.1510i | 0.557332 | + | 0.557332i | 0.928547 | − | 0.371215i | \(-0.121059\pi\) |
−0.371215 | + | 0.928547i | \(0.621059\pi\) | |||||||
\(948\) | −2.99703 | + | 2.99703i | −0.0973390 | + | 0.0973390i | ||||
\(949\) | 16.2915 | 0.528845 | ||||||||
\(950\) | −19.6309 | + | 9.46710i | −0.636912 | + | 0.307153i | ||||
\(951\) | 28.7488 | 0.932243 | ||||||||
\(952\) | −15.2902 | + | 15.2902i | −0.495557 | + | 0.495557i | ||||
\(953\) | −17.4495 | − | 17.4495i | −0.565246 | − | 0.565246i | 0.365547 | − | 0.930793i | \(-0.380882\pi\) |
−0.930793 | + | 0.365547i | \(0.880882\pi\) | |||||||
\(954\) | − | 7.64832i | − | 0.247624i | ||||||
\(955\) | −56.2166 | + | 1.72506i | −1.81913 | + | 0.0558215i | ||||
\(956\) | 6.98300 | 0.225846 | ||||||||
\(957\) | −16.2555 | − | 16.2555i | −0.525466 | − | 0.525466i | ||||
\(958\) | −4.66330 | − | 4.66330i | −0.150665 | − | 0.150665i | ||||
\(959\) | 9.81588i | 0.316971i | ||||||||
\(960\) | 1.53190 | − | 1.62889i | 0.0494418 | − | 0.0525722i | ||||
\(961\) | 14.6424 | 0.472335 | ||||||||
\(962\) | 34.3869 | − | 34.3869i | 1.10868 | − | 1.10868i | ||||
\(963\) | −5.02931 | − | 5.02931i | −0.162067 | − | 0.162067i | ||||
\(964\) | −7.54947 | −0.243152 | ||||||||
\(965\) | −2.84811 | − | 2.67852i | −0.0916838 | − | 0.0862245i | ||||
\(966\) | −18.6469 | −0.599955 | ||||||||
\(967\) | 12.3387 | + | 12.3387i | 0.396786 | + | 0.396786i | 0.877098 | − | 0.480311i | \(-0.159476\pi\) |
−0.480311 | + | 0.877098i | \(0.659476\pi\) | |||||||
\(968\) | −15.0671 | − | 15.0671i | −0.484275 | − | 0.484275i | ||||
\(969\) | 11.9064 | − | 28.3666i | 0.382489 | − | 0.911268i | ||||
\(970\) | −0.603298 | − | 19.6604i | −0.0193707 | − | 0.631258i | ||||
\(971\) | 34.0584i | 1.09298i | 0.837464 | + | 0.546492i | \(0.184037\pi\) | ||||
−0.837464 | + | 0.546492i | \(0.815963\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −37.7535 | + | 37.7535i | −1.21032 | + | 1.21032i | ||||
\(974\) | − | 5.12982i | − | 0.164370i | ||||||
\(975\) | −1.70050 | − | 27.6821i | −0.0544596 | − | 0.886537i | ||||
\(976\) | 2.33286 | 0.0746732 | ||||||||
\(977\) | −28.7226 | + | 28.7226i | −0.918916 | + | 0.918916i | −0.996951 | − | 0.0780344i | \(-0.975136\pi\) |
0.0780344 | + | 0.996951i | \(0.475136\pi\) | |||||||
\(978\) | 7.85986 | − | 7.85986i | 0.251331 | − | 0.251331i | ||||
\(979\) | −14.2572 | −0.455662 | ||||||||
\(980\) | −5.33467 | + | 0.163699i | −0.170410 | + | 0.00522918i | ||||
\(981\) | 5.95528i | 0.190137i | ||||||||
\(982\) | 2.37383 | − | 2.37383i | 0.0757519 | − | 0.0757519i | ||||
\(983\) | −22.6513 | − | 22.6513i | −0.722464 | − | 0.722464i | 0.246642 | − | 0.969107i | \(-0.420673\pi\) |
−0.969107 | + | 0.246642i | \(0.920673\pi\) | |||||||
\(984\) | −6.38884 | −0.203669 | ||||||||
\(985\) | −13.0789 | − | 12.3001i | −0.416728 | − | 0.391914i | ||||
\(986\) | 28.5448 | 0.909052 | ||||||||
\(987\) | 9.93668 | − | 9.93668i | 0.316288 | − | 0.316288i | ||||
\(988\) | 22.3810 | − | 9.14747i | 0.712034 | − | 0.291020i | ||||
\(989\) | 35.7803i | 1.13775i | ||||||||
\(990\) | 9.25865 | + | 8.70735i | 0.294259 | + | 0.276738i | ||||
\(991\) | − | 33.5419i | − | 1.06549i | −0.846275 | − | 0.532746i | \(-0.821160\pi\) | ||
0.846275 | − | 0.532746i | \(-0.178840\pi\) | |||||||
\(992\) | 2.85986 | + | 2.85986i | 0.0908007 | + | 0.0908007i | ||||
\(993\) | 15.5532 | − | 15.5532i | 0.493566 | − | 0.493566i | ||||
\(994\) | 19.9624i | 0.633168i | ||||||||
\(995\) | 0.267403 | + | 8.71420i | 0.00847725 | + | 0.276259i | ||||
\(996\) | 7.50462i | 0.237793i | ||||||||
\(997\) | −5.19281 | − | 5.19281i | −0.164458 | − | 0.164458i | 0.620080 | − | 0.784538i | \(-0.287100\pi\) |
−0.784538 | + | 0.620080i | \(0.787100\pi\) | |||||||
\(998\) | 9.84644 | + | 9.84644i | 0.311684 | + | 0.311684i | ||||
\(999\) | − | 8.76719i | − | 0.277382i |
(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 | 570.2.m.a.37.6 | yes | 20 | |
3.2 | odd | 2 | 1710.2.p.d.37.5 | 20 | |||
5.3 | odd | 4 | inner | 570.2.m.a.493.1 | yes | 20 | |
15.8 | even | 4 | 1710.2.p.d.1063.10 | 20 | |||
19.18 | odd | 2 | inner | 570.2.m.a.37.1 | ✓ | 20 | |
57.56 | even | 2 | 1710.2.p.d.37.10 | 20 | |||
95.18 | even | 4 | inner | 570.2.m.a.493.6 | yes | 20 | |
285.113 | odd | 4 | 1710.2.p.d.1063.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.m.a.37.1 | ✓ | 20 | 19.18 | odd | 2 | inner | |
570.2.m.a.37.6 | yes | 20 | 1.1 | even | 1 | trivial | |
570.2.m.a.493.1 | yes | 20 | 5.3 | odd | 4 | inner | |
570.2.m.a.493.6 | yes | 20 | 95.18 | even | 4 | inner | |
1710.2.p.d.37.5 | 20 | 3.2 | odd | 2 | |||
1710.2.p.d.37.10 | 20 | 57.56 | even | 2 | |||
1710.2.p.d.1063.5 | 20 | 285.113 | odd | 4 | |||
1710.2.p.d.1063.10 | 20 | 15.8 | even | 4 |