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 | 493.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.493 |
Dual form | 1050.2.bc.d.607.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | −0.258819 | + | 0.965926i | −0.0747146 | + | 0.278839i | ||||
\(13\) | −1.60368 | + | 1.60368i | −0.444781 | + | 0.444781i | −0.893615 | − | 0.448834i | \(-0.851840\pi\) |
0.448834 | + | 0.893615i | \(0.351840\pi\) | |||||||
\(14\) | −2.59808 | − | 0.500000i | −0.694365 | − | 0.133631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −0.517638 | + | 0.138701i | −0.125546 | + | 0.0336399i | −0.321045 | − | 0.947064i | \(-0.604034\pi\) |
0.195499 | + | 0.980704i | \(0.437367\pi\) | |||||||
\(18\) | −0.965926 | + | 0.258819i | −0.227671 | + | 0.0610042i | ||||
\(19\) | 2.86603 | + | 4.96410i | 0.657511 | + | 1.13884i | 0.981258 | + | 0.192699i | \(0.0617242\pi\) |
−0.323747 | + | 0.946144i | \(0.604943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.866025 | − | 2.50000i | −0.188982 | − | 0.545545i | ||||
\(22\) | −0.707107 | + | 0.707107i | −0.150756 | + | 0.150756i | ||||
\(23\) | −2.05197 | + | 7.65806i | −0.427865 | + | 1.59682i | 0.329720 | + | 0.944079i | \(0.393046\pi\) |
−0.757585 | + | 0.652736i | \(0.773621\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.96410 | + | 1.13397i | −0.385192 | + | 0.222391i | ||||
\(27\) | −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 | ||||||||
\(31\) | −0.464102 | − | 0.267949i | −0.0833551 | − | 0.0481251i | 0.457743 | − | 0.889085i | \(-0.348658\pi\) |
−0.541098 | + | 0.840959i | \(0.681991\pi\) | |||||||
\(32\) | 0.258819 | + | 0.965926i | 0.0457532 | + | 0.170753i | ||||
\(33\) | −0.965926 | − | 0.258819i | −0.168146 | − | 0.0450546i | ||||
\(34\) | −0.535898 | −0.0919058 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −9.58991 | − | 2.56961i | −1.57657 | − | 0.422441i | −0.638709 | − | 0.769449i | \(-0.720531\pi\) |
−0.937862 | + | 0.347008i | \(0.887198\pi\) | |||||||
\(38\) | 1.48356 | + | 5.53674i | 0.240666 | + | 0.898177i | ||||
\(39\) | −1.96410 | − | 1.13397i | −0.314508 | − | 0.181581i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.73205i | − | 0.895196i | −0.894235 | − | 0.447598i | \(-0.852280\pi\) | ||
0.894235 | − | 0.447598i | \(-0.147720\pi\) | |||||||
\(42\) | −0.189469 | − | 2.63896i | −0.0292357 | − | 0.407200i | ||||
\(43\) | 3.48477 | + | 3.48477i | 0.531422 | + | 0.531422i | 0.920995 | − | 0.389574i | \(-0.127378\pi\) |
−0.389574 | + | 0.920995i | \(0.627378\pi\) | |||||||
\(44\) | −0.866025 | + | 0.500000i | −0.130558 | + | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.96410 | + | 6.86603i | −0.584475 | + | 1.01234i | ||||
\(47\) | 2.38014 | − | 8.88280i | 0.347179 | − | 1.29569i | −0.542867 | − | 0.839819i | \(-0.682661\pi\) |
0.890046 | − | 0.455871i | \(-0.150672\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 6.92820 | − | 1.00000i | 0.989743 | − | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.267949 | − | 0.464102i | −0.0375204 | − | 0.0649872i | ||||
\(52\) | −2.19067 | + | 0.586988i | −0.303791 | + | 0.0814007i | ||||
\(53\) | 0.965926 | − | 0.258819i | 0.132680 | − | 0.0355515i | −0.191868 | − | 0.981421i | \(-0.561454\pi\) |
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | − | 1.73205i | −0.267261 | − | 0.231455i | ||||
\(57\) | −4.05317 | + | 4.05317i | −0.536856 | + | 0.536856i | ||||
\(58\) | −1.79315 | + | 6.69213i | −0.235452 | + | 0.878720i | ||||
\(59\) | 2.26795 | − | 3.92820i | 0.295262 | − | 0.511409i | −0.679784 | − | 0.733412i | \(-0.737926\pi\) |
0.975046 | + | 0.222004i | \(0.0712598\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.92820 | − | 2.26795i | 0.502955 | − | 0.290381i | −0.226978 | − | 0.973900i | \(-0.572885\pi\) |
0.729933 | + | 0.683519i | \(0.239551\pi\) | |||||||
\(62\) | −0.378937 | − | 0.378937i | −0.0481251 | − | 0.0481251i | ||||
\(63\) | 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 | 0.990310 | − | 0.138874i | \(-0.0443482\pi\) |
−0.927071 | + | 0.374887i | \(0.877682\pi\) | |||||||
\(68\) | −0.517638 | − | 0.138701i | −0.0627728 | − | 0.0168199i | ||||
\(69\) | −7.92820 | −0.954444 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.92820 | 0.584870 | 0.292435 | − | 0.956285i | \(-0.405534\pi\) | ||||
0.292435 | + | 0.956285i | \(0.405534\pi\) | |||||||
\(72\) | −0.965926 | − | 0.258819i | −0.113835 | − | 0.0305021i | ||||
\(73\) | 1.03528 | + | 3.86370i | 0.121170 | + | 0.452212i | 0.999674 | − | 0.0255221i | \(-0.00812481\pi\) |
−0.878504 | + | 0.477734i | \(0.841458\pi\) | |||||||
\(74\) | −8.59808 | − | 4.96410i | −0.999506 | − | 0.577065i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.73205i | 0.657511i | ||||||||
\(77\) | 1.15539 | − | 2.38014i | 0.131669 | − | 0.271242i | ||||
\(78\) | −1.60368 | − | 1.60368i | −0.181581 | − | 0.181581i | ||||
\(79\) | 14.6603 | − | 8.46410i | 1.64941 | − | 0.952286i | 0.672100 | − | 0.740460i | \(-0.265393\pi\) |
0.977308 | − | 0.211825i | \(-0.0679408\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.48356 | − | 5.53674i | 0.163832 | − | 0.611430i | ||||
\(83\) | −7.34847 | + | 7.34847i | −0.806599 | + | 0.806599i | −0.984118 | − | 0.177518i | \(-0.943193\pi\) |
0.177518 | + | 0.984118i | \(0.443193\pi\) | |||||||
\(84\) | 0.500000 | − | 2.59808i | 0.0545545 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.46410 | + | 4.26795i | 0.265711 | + | 0.460225i | ||||
\(87\) | −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 | 0.621932 | − | 0.783072i | \(-0.286348\pi\) |
−0.989126 | + | 0.147073i | \(0.953015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.92820 | − | 4.53590i | 0.411788 | − | 0.475491i | ||||
\(92\) | −5.60609 | + | 5.60609i | −0.584475 | + | 0.584475i | ||||
\(93\) | 0.138701 | − | 0.517638i | 0.0143826 | − | 0.0536766i | ||||
\(94\) | 4.59808 | − | 7.96410i | 0.474255 | − | 0.821434i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.866025 | + | 0.500000i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | 7.72741 | + | 7.72741i | 0.784599 | + | 0.784599i | 0.980603 | − | 0.196004i | \(-0.0627965\pi\) |
−0.196004 | + | 0.980603i | \(0.562797\pi\) | |||||||
\(98\) | 6.95095 | + | 0.827225i | 0.702152 | + | 0.0835624i | ||||
\(99\) | − | 1.00000i | − | 0.100504i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.9282 | − | 7.46410i | −1.28640 | − | 0.742706i | −0.308393 | − | 0.951259i | \(-0.599791\pi\) |
−0.978011 | + | 0.208553i | \(0.933125\pi\) | |||||||
\(102\) | −0.138701 | − | 0.517638i | −0.0137334 | − | 0.0512538i | ||||
\(103\) | 2.31079 | + | 0.619174i | 0.227689 | + | 0.0610090i | 0.370860 | − | 0.928689i | \(-0.379063\pi\) |
−0.143171 | + | 0.989698i | \(0.545730\pi\) | |||||||
\(104\) | −2.26795 | −0.222391 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | 1.03528 | + | 0.277401i | 0.100084 | + | 0.0268174i | 0.308513 | − | 0.951220i | \(-0.400169\pi\) |
−0.208430 | + | 0.978037i | \(0.566835\pi\) | |||||||
\(108\) | −0.258819 | − | 0.965926i | −0.0249049 | − | 0.0929463i | ||||
\(109\) | 2.66025 | + | 1.53590i | 0.254806 | + | 0.147112i | 0.621963 | − | 0.783047i | \(-0.286335\pi\) |
−0.367157 | + | 0.930159i | \(0.619669\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 9.92820i | − | 0.942343i | ||||||
\(112\) | −1.48356 | − | 2.19067i | −0.140184 | − | 0.206999i | ||||
\(113\) | 0.656339 | + | 0.656339i | 0.0617432 | + | 0.0617432i | 0.737304 | − | 0.675561i | \(-0.236098\pi\) |
−0.675561 | + | 0.737304i | \(0.736098\pi\) | |||||||
\(114\) | −4.96410 | + | 2.86603i | −0.464931 | + | 0.268428i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.46410 | + | 6.00000i | −0.321634 | + | 0.557086i | ||||
\(117\) | 0.586988 | − | 2.19067i | 0.0542671 | − | 0.202528i | ||||
\(118\) | 3.20736 | − | 3.20736i | 0.295262 | − | 0.295262i | ||||
\(119\) | 1.33975 | − | 0.464102i | 0.122814 | − | 0.0425441i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 4.38134 | − | 1.17398i | 0.396668 | − | 0.106287i | ||||
\(123\) | 5.53674 | − | 1.48356i | 0.499231 | − | 0.133768i | ||||
\(124\) | −0.267949 | − | 0.464102i | −0.0240625 | − | 0.0416776i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.50000 | − | 0.866025i | 0.222718 | − | 0.0771517i | ||||
\(127\) | −3.53553 | + | 3.53553i | −0.313728 | + | 0.313728i | −0.846352 | − | 0.532624i | \(-0.821206\pi\) |
0.532624 | + | 0.846352i | \(0.321206\pi\) | |||||||
\(128\) | −0.258819 | + | 0.965926i | −0.0228766 | + | 0.0853766i | ||||
\(129\) | −2.46410 | + | 4.26795i | −0.216952 | + | 0.375772i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4282 | − | 10.0622i | 1.52271 | − | 0.879137i | 0.523070 | − | 0.852290i | \(-0.324787\pi\) |
0.999640 | − | 0.0268466i | \(-0.00854657\pi\) | |||||||
\(132\) | −0.707107 | − | 0.707107i | −0.0615457 | − | 0.0615457i | ||||
\(133\) | −8.50386 | − | 12.5570i | −0.737379 | − | 1.08883i | ||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.464102 | − | 0.267949i | −0.0397964 | − | 0.0229765i | ||||
\(137\) | −1.31268 | − | 4.89898i | −0.112150 | − | 0.418548i | 0.886908 | − | 0.461946i | \(-0.152848\pi\) |
−0.999058 | + | 0.0433975i | \(0.986182\pi\) | |||||||
\(138\) | −7.65806 | − | 2.05197i | −0.651897 | − | 0.174675i | ||||
\(139\) | 10.3923 | 0.881464 | 0.440732 | − | 0.897639i | \(-0.354719\pi\) | ||||
0.440732 | + | 0.897639i | \(0.354719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.19615 | 0.774456 | ||||||||
\(142\) | 4.76028 | + | 1.27551i | 0.399474 | + | 0.107039i | ||||
\(143\) | −0.586988 | − | 2.19067i | −0.0490864 | − | 0.183193i | ||||
\(144\) | −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 | ||||
\(148\) | −7.02030 | − | 7.02030i | −0.577065 | − | 0.577065i | ||||
\(149\) | −11.1962 | + | 6.46410i | −0.917225 | + | 0.529560i | −0.882749 | − | 0.469846i | \(-0.844310\pi\) |
−0.0344760 | + | 0.999406i | \(0.510976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9282 | + | 20.6603i | −0.970703 | + | 1.68131i | −0.277262 | + | 0.960794i | \(0.589427\pi\) |
−0.693441 | + | 0.720513i | \(0.743906\pi\) | |||||||
\(152\) | −1.48356 | + | 5.53674i | −0.120333 | + | 0.449089i | ||||
\(153\) | 0.378937 | − | 0.378937i | 0.0306353 | − | 0.0306353i | ||||
\(154\) | 1.73205 | − | 2.00000i | 0.139573 | − | 0.161165i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.13397 | − | 1.96410i | −0.0907906 | − | 0.157254i | ||||
\(157\) | 12.2289 | − | 3.27671i | 0.975970 | − | 0.261510i | 0.264623 | − | 0.964352i | \(-0.414752\pi\) |
0.711346 | + | 0.702842i | \(0.248086\pi\) | |||||||
\(158\) | 16.3514 | − | 4.38134i | 1.30085 | − | 0.348561i | ||||
\(159\) | 0.500000 | + | 0.866025i | 0.0396526 | + | 0.0686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.96410 | − | 20.5981i | 0.312415 | − | 1.62336i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −3.10583 | + | 11.5911i | −0.243267 | + | 0.907886i | 0.730979 | + | 0.682400i | \(0.239064\pi\) |
−0.974246 | + | 0.225486i | \(0.927603\pi\) | |||||||
\(164\) | 2.86603 | − | 4.96410i | 0.223799 | − | 0.387631i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.00000 | + | 5.19615i | −0.698535 | + | 0.403300i | ||||
\(167\) | 12.1595 | + | 12.1595i | 0.940932 | + | 0.940932i | 0.998350 | − | 0.0574186i | \(-0.0182870\pi\) |
−0.0574186 | + | 0.998350i | \(0.518287\pi\) | |||||||
\(168\) | 1.15539 | − | 2.38014i | 0.0891406 | − | 0.183632i | ||||
\(169\) | 7.85641i | 0.604339i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.96410 | − | 2.86603i | −0.379614 | − | 0.219170i | ||||
\(172\) | 1.27551 | + | 4.76028i | 0.0972569 | + | 0.362968i | ||||
\(173\) | −22.7847 | − | 6.10514i | −1.73229 | − | 0.464165i | −0.751580 | − | 0.659642i | \(-0.770708\pi\) |
−0.980708 | + | 0.195476i | \(0.937375\pi\) | |||||||
\(174\) | −6.92820 | −0.525226 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 4.38134 | + | 1.17398i | 0.329322 | + | 0.0882415i | ||||
\(178\) | −1.79315 | − | 6.69213i | −0.134402 | − | 0.501596i | ||||
\(179\) | −7.79423 | − | 4.50000i | −0.582568 | − | 0.336346i | 0.179585 | − | 0.983742i | \(-0.442524\pi\) |
−0.762153 | + | 0.647397i | \(0.775858\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.39230i | 0.475136i | 0.971371 | + | 0.237568i | \(0.0763503\pi\) | ||||
−0.971371 | + | 0.237568i | \(0.923650\pi\) | |||||||
\(182\) | 4.96833 | − | 3.36465i | 0.368277 | − | 0.249404i | ||||
\(183\) | 3.20736 | + | 3.20736i | 0.237095 | + | 0.237095i | ||||
\(184\) | −6.86603 | + | 3.96410i | −0.506170 | + | 0.292237i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.267949 | − | 0.464102i | 0.0196470 | − | 0.0340296i | ||||
\(187\) | 0.138701 | − | 0.517638i | 0.0101428 | − | 0.0378534i | ||||
\(188\) | 6.50266 | − | 6.50266i | 0.474255 | − | 0.474255i | ||||
\(189\) | 2.00000 | + | 1.73205i | 0.145479 | + | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.46410 | + | 9.46410i | 0.395369 | + | 0.684798i | 0.993148 | − | 0.116862i | \(-0.0372836\pi\) |
−0.597780 | + | 0.801660i | \(0.703950\pi\) | |||||||
\(192\) | −0.965926 | + | 0.258819i | −0.0697097 | + | 0.0186787i | ||||
\(193\) | 18.1445 | − | 4.86181i | 1.30607 | − | 0.349961i | 0.462329 | − | 0.886708i | \(-0.347014\pi\) |
0.843743 | + | 0.536747i | \(0.180347\pi\) | |||||||
\(194\) | 5.46410 | + | 9.46410i | 0.392300 | + | 0.679483i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.50000 | + | 2.59808i | 0.464286 | + | 0.185577i | ||||
\(197\) | 7.67664 | − | 7.67664i | 0.546938 | − | 0.546938i | −0.378616 | − | 0.925554i | \(-0.623600\pi\) |
0.925554 | + | 0.378616i | \(0.123600\pi\) | |||||||
\(198\) | 0.258819 | − | 0.965926i | 0.0183935 | − | 0.0686454i | ||||
\(199\) | 9.73205 | − | 16.8564i | 0.689887 | − | 1.19492i | −0.281987 | − | 0.959418i | \(-0.590994\pi\) |
0.971874 | − | 0.235501i | \(-0.0756730\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.73205 | + | 1.00000i | −0.122169 | + | 0.0705346i | ||||
\(202\) | −10.5558 | − | 10.5558i | −0.742706 | − | 0.742706i | ||||
\(203\) | −1.31268 | − | 18.2832i | −0.0921319 | − | 1.28323i | ||||
\(204\) | − | 0.535898i | − | 0.0375204i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.07180 | + | 1.19615i | 0.144349 | + | 0.0833399i | ||||
\(207\) | −2.05197 | − | 7.65806i | −0.142622 | − | 0.532272i | ||||
\(208\) | −2.19067 | − | 0.586988i | −0.151896 | − | 0.0407003i | ||||
\(209\) | −5.73205 | −0.396494 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.7846 | 1.49971 | 0.749857 | − | 0.661600i | \(-0.230122\pi\) | ||||
0.749857 | + | 0.661600i | \(0.230122\pi\) | |||||||
\(212\) | 0.965926 | + | 0.258819i | 0.0663401 | + | 0.0177758i | ||||
\(213\) | 1.27551 | + | 4.76028i | 0.0873967 | + | 0.326169i | ||||
\(214\) | 0.928203 | + | 0.535898i | 0.0634507 | + | 0.0366333i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 1.27551 | + | 0.619174i | 0.0865875 | + | 0.0420323i | ||||
\(218\) | 2.17209 | + | 2.17209i | 0.147112 | + | 0.147112i | ||||
\(219\) | −3.46410 | + | 2.00000i | −0.234082 | + | 0.135147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.607695 | − | 1.05256i | 0.0408780 | − | 0.0708028i | ||||
\(222\) | 2.56961 | − | 9.58991i | 0.172461 | − | 0.643632i | ||||
\(223\) | 17.9043 | − | 17.9043i | 1.19896 | − | 1.19896i | 0.224483 | − | 0.974478i | \(-0.427931\pi\) |
0.974478 | − | 0.224483i | \(-0.0720692\pi\) | |||||||
\(224\) | −0.866025 | − | 2.50000i | −0.0578638 | − | 0.167038i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.464102 | + | 0.803848i | 0.0308716 | + | 0.0534711i | ||||
\(227\) | −3.34607 | + | 0.896575i | −0.222086 | + | 0.0595078i | −0.368146 | − | 0.929768i | \(-0.620007\pi\) |
0.146060 | + | 0.989276i | \(0.453341\pi\) | |||||||
\(228\) | −5.53674 | + | 1.48356i | −0.366679 | + | 0.0982514i | ||||
\(229\) | 5.46410 | + | 9.46410i | 0.361078 | + | 0.625405i | 0.988139 | − | 0.153565i | \(-0.0490755\pi\) |
−0.627061 | + | 0.778971i | \(0.715742\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.59808 | + | 0.500000i | 0.170941 | + | 0.0328976i | ||||
\(232\) | −4.89898 | + | 4.89898i | −0.321634 | + | 0.321634i | ||||
\(233\) | 6.69213 | − | 24.9754i | 0.438416 | − | 1.63619i | −0.294341 | − | 0.955700i | \(-0.595100\pi\) |
0.732757 | − | 0.680490i | \(-0.238233\pi\) | |||||||
\(234\) | 1.13397 | − | 1.96410i | 0.0741302 | − | 0.128397i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.92820 | − | 2.26795i | 0.255704 | − | 0.147631i | ||||
\(237\) | 11.9700 | + | 11.9700i | 0.777538 | + | 0.777538i | ||||
\(238\) | 1.41421 | − | 0.101536i | 0.0916698 | − | 0.00658160i | ||||
\(239\) | 24.0000i | 1.55243i | 0.630468 | + | 0.776215i | \(0.282863\pi\) | ||||
−0.630468 | + | 0.776215i | \(0.717137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.2846 | − | 12.8660i | −1.43548 | − | 0.828774i | −0.437947 | − | 0.899001i | \(-0.644294\pi\) |
−0.997531 | + | 0.0702273i | \(0.977628\pi\) | |||||||
\(242\) | 2.58819 | + | 9.65926i | 0.166375 | + | 0.620921i | ||||
\(243\) | 0.965926 | + | 0.258819i | 0.0619642 | + | 0.0166032i | ||||
\(244\) | 4.53590 | 0.290381 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.73205 | 0.365462 | ||||||||
\(247\) | −12.5570 | − | 3.36465i | −0.798985 | − | 0.214087i | ||||
\(248\) | −0.138701 | − | 0.517638i | −0.00880750 | − | 0.0328701i | ||||
\(249\) | −9.00000 | − | 5.19615i | −0.570352 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.6603i | 1.55654i | 0.627929 | + | 0.778271i | \(0.283903\pi\) | ||||
−0.627929 | + | 0.778271i | \(0.716097\pi\) | |||||||
\(252\) | 2.63896 | − | 0.189469i | 0.166239 | − | 0.0119354i | ||||
\(253\) | −5.60609 | − | 5.60609i | −0.352452 | − | 0.352452i | ||||
\(254\) | −4.33013 | + | 2.50000i | −0.271696 | + | 0.156864i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 4.76028 | − | 17.7656i | 0.296938 | − | 1.10819i | −0.642728 | − | 0.766094i | \(-0.722197\pi\) |
0.939666 | − | 0.342093i | \(-0.111136\pi\) | |||||||
\(258\) | −3.48477 | + | 3.48477i | −0.216952 | + | 0.216952i | ||||
\(259\) | 25.7942 | + | 4.96410i | 1.60278 | + | 0.308454i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.46410 | − | 6.00000i | −0.214423 | − | 0.371391i | ||||
\(262\) | 19.4386 | − | 5.20857i | 1.20092 | − | 0.321786i | ||||
\(263\) | −2.07055 | + | 0.554803i | −0.127676 | + | 0.0342106i | −0.322091 | − | 0.946709i | \(-0.604386\pi\) |
0.194415 | + | 0.980919i | \(0.437719\pi\) | |||||||
\(264\) | −0.500000 | − | 0.866025i | −0.0307729 | − | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.96410 | − | 14.3301i | −0.304369 | − | 0.878636i | ||||
\(267\) | 4.89898 | − | 4.89898i | 0.299813 | − | 0.299813i | ||||
\(268\) | −0.517638 | + | 1.93185i | −0.0316198 | + | 0.118007i | ||||
\(269\) | 4.66025 | − | 8.07180i | 0.284141 | − | 0.492146i | −0.688260 | − | 0.725464i | \(-0.741625\pi\) |
0.972400 | + | 0.233318i | \(0.0749584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.92820 | + | 4.00000i | −0.420858 | + | 0.242983i | −0.695444 | − | 0.718580i | \(-0.744792\pi\) |
0.274586 | + | 0.961563i | \(0.411459\pi\) | |||||||
\(272\) | −0.378937 | − | 0.378937i | −0.0229765 | − | 0.0229765i | ||||
\(273\) | 5.39804 | + | 2.62038i | 0.326704 | + | 0.158592i | ||||
\(274\) | − | 5.07180i | − | 0.306398i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.86603 | − | 3.96410i | −0.413286 | − | 0.238611i | ||||
\(277\) | 5.69402 | + | 21.2504i | 0.342120 | + | 1.27681i | 0.895940 | + | 0.444174i | \(0.146503\pi\) |
−0.553820 | + | 0.832636i | \(0.686830\pi\) | |||||||
\(278\) | 10.0382 | + | 2.68973i | 0.602051 | + | 0.161319i | ||||
\(279\) | 0.535898 | 0.0320834 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0718 | −0.839453 | −0.419727 | − | 0.907651i | \(-0.637874\pi\) | ||||
−0.419727 | + | 0.907651i | \(0.637874\pi\) | |||||||
\(282\) | 8.88280 | + | 2.38014i | 0.528963 | + | 0.141735i | ||||
\(283\) | −5.03768 | − | 18.8009i | −0.299459 | − | 1.11760i | −0.937611 | − | 0.347686i | \(-0.886968\pi\) |
0.638152 | − | 0.769910i | \(-0.279699\pi\) | |||||||
\(284\) | 4.26795 | + | 2.46410i | 0.253256 | + | 0.146218i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.26795i | − | 0.134107i | ||||||
\(287\) | 1.08604 | + | 15.1266i | 0.0641072 | + | 0.892898i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | −14.4737 | + | 8.35641i | −0.851395 | + | 0.491553i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.46410 | + | 9.46410i | −0.320311 | + | 0.554795i | ||||
\(292\) | −1.03528 | + | 3.86370i | −0.0605850 | + | 0.226106i | ||||
\(293\) | −1.22474 | + | 1.22474i | −0.0715504 | + | 0.0715504i | −0.741976 | − | 0.670426i | \(-0.766111\pi\) |
0.670426 | + | 0.741976i | \(0.266111\pi\) | |||||||
\(294\) | 1.00000 | + | 6.92820i | 0.0583212 | + | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.96410 | − | 8.59808i | −0.288533 | − | 0.499753i | ||||
\(297\) | 0.965926 | − | 0.258819i | 0.0560487 | − | 0.0150182i | ||||
\(298\) | −12.4877 | + | 3.34607i | −0.723392 | + | 0.193832i | ||||
\(299\) | −8.99038 | − | 15.5718i | −0.519927 | − | 0.900540i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.85641 | − | 8.53590i | −0.568114 | − | 0.492001i | ||||
\(302\) | −16.8690 | + | 16.8690i | −0.970703 | + | 0.970703i | ||||
\(303\) | 3.86370 | − | 14.4195i | 0.221964 | − | 0.828381i | ||||
\(304\) | −2.86603 | + | 4.96410i | −0.164378 | + | 0.284711i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.464102 | − | 0.267949i | 0.0265309 | − | 0.0153176i | ||||
\(307\) | 1.13681 | + | 1.13681i | 0.0648813 | + | 0.0648813i | 0.738803 | − | 0.673922i | \(-0.235391\pi\) |
−0.673922 | + | 0.738803i | \(0.735391\pi\) | |||||||
\(308\) | 2.19067 | − | 1.48356i | 0.124825 | − | 0.0845339i | ||||
\(309\) | 2.39230i | 0.136093i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.7846 | − | 13.7321i | −1.34870 | − | 0.778673i | −0.360636 | − | 0.932707i | \(-0.617440\pi\) |
−0.988066 | + | 0.154034i | \(0.950774\pi\) | |||||||
\(312\) | −0.586988 | − | 2.19067i | −0.0332317 | − | 0.124022i | ||||
\(313\) | 30.1146 | + | 8.06918i | 1.70218 | + | 0.456097i | 0.973486 | − | 0.228746i | \(-0.0734624\pi\) |
0.728691 | + | 0.684843i | \(0.240129\pi\) | |||||||
\(314\) | 12.6603 | 0.714459 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.9282 | 0.952286 | ||||||||
\(317\) | −13.5230 | − | 3.62347i | −0.759525 | − | 0.203514i | −0.141786 | − | 0.989897i | \(-0.545285\pi\) |
−0.617739 | + | 0.786383i | \(0.711951\pi\) | |||||||
\(318\) | 0.258819 | + | 0.965926i | 0.0145139 | + | 0.0541664i | ||||
\(319\) | −6.00000 | − | 3.46410i | −0.335936 | − | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.07180i | 0.0598219i | ||||||||
\(322\) | 9.16020 | − | 18.8702i | 0.510478 | − | 1.05160i | ||||
\(323\) | −2.17209 | − | 2.17209i | −0.120858 | − | 0.120858i | ||||
\(324\) | 0.866025 | − | 0.500000i | 0.0481125 | − | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.00000 | + | 10.3923i | −0.332309 | + | 0.575577i | ||||
\(327\) | −0.795040 | + | 2.96713i | −0.0439658 | + | 0.164083i | ||||
\(328\) | 4.05317 | − | 4.05317i | 0.223799 | − | 0.223799i | ||||
\(329\) | −4.59808 | + | 23.8923i | −0.253500 | + | 1.31723i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.89230 | + | 13.6699i | 0.433800 | + | 0.751364i | 0.997197 | − | 0.0748224i | \(-0.0238390\pi\) |
−0.563397 | + | 0.826187i | \(0.690506\pi\) | |||||||
\(332\) | −10.0382 | + | 2.68973i | −0.550918 | + | 0.147618i | ||||
\(333\) | 9.58991 | − | 2.56961i | 0.525524 | − | 0.140814i | ||||
\(334\) | 8.59808 | + | 14.8923i | 0.470466 | + | 0.814871i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.73205 | − | 2.00000i | 0.0944911 | − | 0.109109i | ||||
\(337\) | 17.6269 | − | 17.6269i | 0.960199 | − | 0.960199i | −0.0390392 | − | 0.999238i | \(-0.512430\pi\) |
0.999238 | + | 0.0390392i | \(0.0124297\pi\) | |||||||
\(338\) | −2.03339 | + | 7.58871i | −0.110602 | + | 0.412771i | ||||
\(339\) | −0.464102 | + | 0.803848i | −0.0252065 | + | 0.0436590i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.464102 | − | 0.267949i | 0.0251325 | − | 0.0145103i | ||||
\(342\) | −4.05317 | − | 4.05317i | −0.219170 | − | 0.219170i | ||||
\(343\) | −18.0938 | + | 3.95164i | −0.976972 | + | 0.213368i | ||||
\(344\) | 4.92820i | 0.265711i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.4282 | − | 11.7942i | −1.09823 | − | 0.634062i | ||||
\(347\) | −2.82843 | − | 10.5558i | −0.151838 | − | 0.566667i | −0.999355 | − | 0.0358994i | \(-0.988570\pi\) |
0.847517 | − | 0.530767i | \(-0.178096\pi\) | |||||||
\(348\) | −6.69213 | − | 1.79315i | −0.358736 | − | 0.0961230i | ||||
\(349\) | −25.8564 | −1.38406 | −0.692031 | − | 0.721868i | \(-0.743284\pi\) | ||||
−0.692031 | + | 0.721868i | \(0.743284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.26795 | 0.121054 | ||||||||
\(352\) | −0.965926 | − | 0.258819i | −0.0514840 | − | 0.0137951i | ||||
\(353\) | −1.79315 | − | 6.69213i | −0.0954398 | − | 0.356186i | 0.901646 | − | 0.432475i | \(-0.142360\pi\) |
−0.997086 | + | 0.0762887i | \(0.975693\pi\) | |||||||
\(354\) | 3.92820 | + | 2.26795i | 0.208782 | + | 0.120540i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.92820i | − | 0.367194i | ||||||
\(357\) | 0.795040 | + | 1.17398i | 0.0420780 | + | 0.0621334i | ||||
\(358\) | −6.36396 | − | 6.36396i | −0.336346 | − | 0.336346i | ||||
\(359\) | 16.3923 | − | 9.46410i | 0.865153 | − | 0.499496i | −0.000581665 | − | 1.00000i | \(-0.500185\pi\) |
0.865734 | + | 0.500504i | \(0.166852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.92820 | + | 12.0000i | −0.364642 | + | 0.631579i | ||||
\(362\) | −1.65445 | + | 6.17449i | −0.0869560 | + | 0.324524i | ||||
\(363\) | −7.07107 | + | 7.07107i | −0.371135 | + | 0.371135i | ||||
\(364\) | 5.66987 | − | 1.96410i | 0.297182 | − | 0.102947i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.26795 | + | 3.92820i | 0.118548 | + | 0.205330i | ||||
\(367\) | 14.0220 | − | 3.75719i | 0.731943 | − | 0.196124i | 0.126449 | − | 0.991973i | \(-0.459642\pi\) |
0.605494 | + | 0.795849i | \(0.292975\pi\) | |||||||
\(368\) | −7.65806 | + | 2.05197i | −0.399204 | + | 0.106966i | ||||
\(369\) | 2.86603 | + | 4.96410i | 0.149199 | + | 0.258421i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.50000 | + | 0.866025i | −0.129794 | + | 0.0449618i | ||||
\(372\) | 0.378937 | − | 0.378937i | 0.0196470 | − | 0.0196470i | ||||
\(373\) | −6.72930 | + | 25.1141i | −0.348430 | + | 1.30036i | 0.540124 | + | 0.841585i | \(0.318377\pi\) |
−0.888554 | + | 0.458772i | \(0.848289\pi\) | |||||||
\(374\) | 0.267949 | − | 0.464102i | 0.0138553 | − | 0.0239981i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.96410 | − | 4.59808i | 0.410717 | − | 0.237128i | ||||
\(377\) | −11.1106 | − | 11.1106i | −0.572227 | − | 0.572227i | ||||
\(378\) | 1.48356 | + | 2.19067i | 0.0763063 | + | 0.112676i | ||||
\(379\) | − | 9.92820i | − | 0.509978i | −0.966944 | − | 0.254989i | \(-0.917928\pi\) | ||
0.966944 | − | 0.254989i | \(-0.0820718\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.33013 | − | 2.50000i | −0.221839 | − | 0.128079i | ||||
\(382\) | 2.82843 | + | 10.5558i | 0.144715 | + | 0.540083i | ||||
\(383\) | −28.9592 | − | 7.75959i | −1.47975 | − | 0.396497i | −0.573485 | − | 0.819216i | \(-0.694409\pi\) |
−0.906261 | + | 0.422719i | \(0.861076\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.7846 | 0.956111 | ||||||||
\(387\) | −4.76028 | − | 1.27551i | −0.241979 | − | 0.0648380i | ||||
\(388\) | 2.82843 | + | 10.5558i | 0.143592 | + | 0.535891i | ||||
\(389\) | −28.2679 | − | 16.3205i | −1.43324 | − | 0.827483i | −0.435875 | − | 0.900007i | \(-0.643561\pi\) |
−0.997367 | + | 0.0725245i | \(0.976894\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.24871i | − | 0.214867i | ||||||
\(392\) | 5.60609 | + | 4.19187i | 0.283150 | + | 0.211722i | ||||
\(393\) | 14.2301 | + | 14.2301i | 0.717812 | + | 0.717812i | ||||
\(394\) | 9.40192 | − | 5.42820i | 0.473662 | − | 0.273469i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.500000 | − | 0.866025i | 0.0251259 | − | 0.0435194i | ||||
\(397\) | −3.30890 | + | 12.3490i | −0.166069 | + | 0.619778i | 0.831832 | + | 0.555027i | \(0.187292\pi\) |
−0.997901 | + | 0.0647510i | \(0.979375\pi\) | |||||||
\(398\) | 13.7632 | − | 13.7632i | 0.689887 | − | 0.689887i | ||||
\(399\) | 9.92820 | − | 11.4641i | 0.497032 | − | 0.573923i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.96410 | + | 10.3301i | 0.297833 | + | 0.515862i | 0.975640 | − | 0.219378i | \(-0.0704028\pi\) |
−0.677807 | + | 0.735240i | \(0.737069\pi\) | |||||||
\(402\) | −1.93185 | + | 0.517638i | −0.0963520 | + | 0.0258174i | ||||
\(403\) | 1.17398 | − | 0.314566i | 0.0584800 | − | 0.0156697i | ||||
\(404\) | −7.46410 | − | 12.9282i | −0.371353 | − | 0.643202i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.46410 | − | 18.0000i | 0.171920 | − | 0.893325i | ||||
\(407\) | 7.02030 | − | 7.02030i | 0.347983 | − | 0.347983i | ||||
\(408\) | 0.138701 | − | 0.517638i | 0.00686671 | − | 0.0256269i | ||||
\(409\) | −6.39230 | + | 11.0718i | −0.316079 | + | 0.547465i | −0.979666 | − | 0.200634i | \(-0.935700\pi\) |
0.663587 | + | 0.748099i | \(0.269033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.39230 | − | 2.53590i | 0.216656 | − | 0.125087i | ||||
\(412\) | 1.69161 | + | 1.69161i | 0.0833399 | + | 0.0833399i | ||||
\(413\) | −5.24075 | + | 10.7961i | −0.257881 | + | 0.531240i | ||||
\(414\) | − | 7.92820i | − | 0.389650i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.96410 | − | 1.13397i | −0.0962980 | − | 0.0555977i | ||||
\(417\) | 2.68973 | + | 10.0382i | 0.131716 | + | 0.491573i | ||||
\(418\) | −5.53674 | − | 1.48356i | −0.270811 | − | 0.0725635i | ||||
\(419\) | 27.0526 | 1.32160 | 0.660802 | − | 0.750560i | \(-0.270216\pi\) | ||||
0.660802 | + | 0.750560i | \(0.270216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8564 | 0.675320 | 0.337660 | − | 0.941268i | \(-0.390365\pi\) | ||||
0.337660 | + | 0.941268i | \(0.390365\pi\) | |||||||
\(422\) | 21.0423 | + | 5.63827i | 1.02432 | + | 0.274467i | ||||
\(423\) | 2.38014 | + | 8.88280i | 0.115726 | + | 0.431897i | ||||
\(424\) | 0.866025 | + | 0.500000i | 0.0420579 | + | 0.0242821i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.92820i | 0.238772i | ||||||||
\(427\) | −9.93666 | + | 6.72930i | −0.480869 | + | 0.325653i | ||||
\(428\) | 0.757875 | + | 0.757875i | 0.0366333 | + | 0.0366333i | ||||
\(429\) | 1.96410 | − | 1.13397i | 0.0948277 | − | 0.0547488i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.8564 | + | 18.8038i | −0.522935 | + | 0.905749i | 0.476709 | + | 0.879061i | \(0.341830\pi\) |
−0.999644 | + | 0.0266884i | \(0.991504\pi\) | |||||||
\(432\) | 0.258819 | − | 0.965926i | 0.0124524 | − | 0.0464731i | ||||
\(433\) | −11.3137 | + | 11.3137i | −0.543702 | + | 0.543702i | −0.924612 | − | 0.380910i | \(-0.875611\pi\) |
0.380910 | + | 0.924612i | \(0.375611\pi\) | |||||||
\(434\) | 1.07180 | + | 0.928203i | 0.0514479 | + | 0.0445552i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.53590 | + | 2.66025i | 0.0735562 | + | 0.127403i | ||||
\(437\) | −43.8964 | + | 11.7620i | −2.09985 | + | 0.562653i | ||||
\(438\) | −3.86370 | + | 1.03528i | −0.184615 | + | 0.0494674i | ||||
\(439\) | −10.0000 | − | 17.3205i | −0.477274 | − | 0.826663i | 0.522387 | − | 0.852709i | \(-0.325042\pi\) |
−0.999661 | + | 0.0260459i | \(0.991708\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.50000 | + | 4.33013i | −0.261905 | + | 0.206197i | ||||
\(442\) | 0.859411 | − | 0.859411i | 0.0408780 | − | 0.0408780i | ||||
\(443\) | 0.0371647 | − | 0.138701i | 0.00176575 | − | 0.00658987i | −0.965037 | − | 0.262112i | \(-0.915581\pi\) |
0.966803 | + | 0.255523i | \(0.0822475\pi\) | |||||||
\(444\) | 4.96410 | − | 8.59808i | 0.235586 | − | 0.408047i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.9282 | − | 12.6603i | 1.03833 | − | 0.599480i | ||||
\(447\) | −9.14162 | − | 9.14162i | −0.432384 | − | 0.432384i | ||||
\(448\) | −0.189469 | − | 2.63896i | −0.00895155 | − | 0.124679i | ||||
\(449\) | 0.0717968i | 0.00338830i | 0.999999 | + | 0.00169415i | \(0.000539265\pi\) | ||||
−0.999999 | + | 0.00169415i | \(0.999461\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.96410 | + | 2.86603i | 0.233750 | + | 0.134956i | ||||
\(452\) | 0.240237 | + | 0.896575i | 0.0112998 | + | 0.0421714i | ||||
\(453\) | −23.0435 | − | 6.17449i | −1.08268 | − | 0.290103i | ||||
\(454\) | −3.46410 | −0.162578 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.73205 | −0.268428 | ||||||||
\(457\) | −11.4524 | − | 3.06866i | −0.535721 | − | 0.143546i | −0.0191922 | − | 0.999816i | \(-0.506109\pi\) |
−0.516529 | + | 0.856270i | \(0.672776\pi\) | |||||||
\(458\) | 2.82843 | + | 10.5558i | 0.132164 | + | 0.493242i | ||||
\(459\) | 0.464102 | + | 0.267949i | 0.0216624 | + | 0.0125068i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.6410i | 1.42709i | 0.700607 | + | 0.713547i | \(0.252913\pi\) | ||||
−0.700607 | + | 0.713547i | \(0.747087\pi\) | |||||||
\(462\) | 2.38014 | + | 1.15539i | 0.110734 | + | 0.0537538i | ||||
\(463\) | 23.1315 | + | 23.1315i | 1.07501 | + | 1.07501i | 0.996949 | + | 0.0780612i | \(0.0248729\pi\) |
0.0780612 | + | 0.996949i | \(0.475127\pi\) | |||||||
\(464\) | −6.00000 | + | 3.46410i | −0.278543 | + | 0.160817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.9282 | − | 22.3923i | 0.598887 | − | 1.03730i | ||||
\(467\) | −3.72500 | + | 13.9019i | −0.172373 | + | 0.643303i | 0.824612 | + | 0.565699i | \(0.191394\pi\) |
−0.996984 | + | 0.0776040i | \(0.975273\pi\) | |||||||
\(468\) | 1.60368 | − | 1.60368i | 0.0741302 | − | 0.0741302i | ||||
\(469\) | −1.73205 | − | 5.00000i | −0.0799787 | − | 0.230879i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.33013 | + | 10.9641i | 0.291677 | + | 0.505199i | ||||
\(472\) | 4.38134 | − | 1.17398i | 0.201668 | − | 0.0540367i | ||||
\(473\) | −4.76028 | + | 1.27551i | −0.218878 | + | 0.0586481i | ||||
\(474\) | 8.46410 | + | 14.6603i | 0.388769 | + | 0.673368i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.39230 | + | 0.267949i | 0.0638162 | + | 0.0122814i | ||||
\(477\) | −0.707107 | + | 0.707107i | −0.0323762 | + | 0.0323762i | ||||
\(478\) | −6.21166 | + | 23.1822i | −0.284115 | + | 1.06033i | ||||
\(479\) | 21.4641 | − | 37.1769i | 0.980720 | − | 1.69866i | 0.321122 | − | 0.947038i | \(-0.395940\pi\) |
0.659598 | − | 0.751619i | \(-0.270727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.5000 | − | 11.2583i | 0.889123 | − | 0.513336i | ||||
\(482\) | −18.1953 | − | 18.1953i | −0.828774 | − | 0.828774i | ||||
\(483\) | 20.9222 | − | 1.50215i | 0.951993 | − | 0.0683500i | ||||
\(484\) | 10.0000i | 0.454545i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.866025 | + | 0.500000i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | −5.65685 | − | 21.1117i | −0.256337 | − | 0.956661i | −0.967342 | − | 0.253475i | \(-0.918427\pi\) |
0.711006 | − | 0.703186i | \(-0.248240\pi\) | |||||||
\(488\) | 4.38134 | + | 1.17398i | 0.198334 | + | 0.0531434i | ||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.7128 | 1.97273 | 0.986366 | − | 0.164568i | \(-0.0526229\pi\) | ||||
0.986366 | + | 0.164568i | \(0.0526229\pi\) | |||||||
\(492\) | 5.53674 | + | 1.48356i | 0.249615 | + | 0.0668842i | ||||
\(493\) | −0.960947 | − | 3.58630i | −0.0432789 | − | 0.161519i | ||||
\(494\) | −11.2583 | − | 6.50000i | −0.506536 | − | 0.292449i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.535898i | − | 0.0240625i | ||||||
\(497\) | −13.0053 | + | 0.933740i | −0.583368 | + | 0.0418840i | ||||
\(498\) | −7.34847 | − | 7.34847i | −0.329293 | − | 0.329293i | ||||
\(499\) | −24.2487 | + | 14.0000i | −1.08552 | + | 0.626726i | −0.932381 | − | 0.361478i | \(-0.882272\pi\) |
−0.153141 | + | 0.988204i | \(0.548939\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.59808 | + | 14.8923i | −0.384134 | + | 0.665339i | ||||
\(502\) | −6.38254 | + | 23.8200i | −0.284867 | + | 1.06314i | ||||
\(503\) | −24.3190 | + | 24.3190i | −1.08433 | + | 1.08433i | −0.0882321 | + | 0.996100i | \(0.528122\pi\) |
−0.996100 | + | 0.0882321i | \(0.971878\pi\) | |||||||
\(504\) | 2.59808 | + | 0.500000i | 0.115728 | + | 0.0222718i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.96410 | − | 6.86603i | −0.176226 | − | 0.305232i | ||||
\(507\) | −7.58871 | + | 2.03339i | −0.337026 | + | 0.0903059i | ||||
\(508\) | −4.82963 | + | 1.29410i | −0.214280 | + | 0.0574162i | ||||
\(509\) | 5.19615 | + | 9.00000i | 0.230315 | + | 0.398918i | 0.957901 | − | 0.287099i | \(-0.0926909\pi\) |
−0.727586 | + | 0.686017i | \(0.759358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.46410 | − | 10.0000i | −0.153243 | − | 0.442374i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 1.48356 | − | 5.53674i | 0.0655009 | − | 0.244453i | ||||
\(514\) | 9.19615 | − | 15.9282i | 0.405625 | − | 0.702563i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.26795 | + | 2.46410i | −0.187886 | + | 0.108476i | ||||
\(517\) | 6.50266 | + | 6.50266i | 0.285987 | + | 0.285987i | ||||
\(518\) | 23.6305 | + | 11.4710i | 1.03826 | + | 0.504006i | ||||
\(519\) | − | 23.5885i | − | 1.03542i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.82051 | − | 3.93782i | −0.298812 | − | 0.172519i | 0.343097 | − | 0.939300i | \(-0.388524\pi\) |
−0.641909 | + | 0.766781i | \(0.721857\pi\) | |||||||
\(522\) | −1.79315 | − | 6.69213i | −0.0784841 | − | 0.292907i | ||||
\(523\) | 32.7028 | + | 8.76268i | 1.42999 | + | 0.383165i | 0.889017 | − | 0.457873i | \(-0.151389\pi\) |
0.540975 | + | 0.841039i | \(0.318055\pi\) | |||||||
\(524\) | 20.1244 | 0.879137 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.14359 | −0.0934651 | ||||||||
\(527\) | 0.277401 | + | 0.0743295i | 0.0120838 | + | 0.00323784i | ||||
\(528\) | −0.258819 | − | 0.965926i | −0.0112637 | − | 0.0420365i | ||||
\(529\) | −34.5167 | − | 19.9282i | −1.50072 | − | 0.866444i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.53590i | 0.196841i | ||||||||
\(532\) | −1.08604 | − | 15.1266i | −0.0470860 | − | 0.655823i | ||||
\(533\) | 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 | ||||
\(538\) | 6.59059 | − | 6.59059i | 0.284141 | − | 0.284141i | ||||
\(539\) | −2.59808 | + | 6.50000i | −0.111907 | + | 0.279975i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.53590 | − | 14.7846i | −0.366987 | − | 0.635640i | 0.622106 | − | 0.782933i | \(-0.286277\pi\) |
−0.989093 | + | 0.147293i | \(0.952944\pi\) | |||||||
\(542\) | −7.72741 | + | 2.07055i | −0.331921 | + | 0.0889378i | ||||
\(543\) | −6.17449 | + | 1.65445i | −0.264973 | + | 0.0709993i | ||||
\(544\) | −0.267949 | − | 0.464102i | −0.0114882 | − | 0.0198982i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.53590 | + | 3.92820i | 0.194119 | + | 0.168112i | ||||
\(547\) | 21.0101 | − | 21.0101i | 0.898328 | − | 0.898328i | −0.0969599 | − | 0.995288i | \(-0.530912\pi\) |
0.995288 | + | 0.0969599i | \(0.0309119\pi\) | |||||||
\(548\) | 1.31268 | − | 4.89898i | 0.0560748 | − | 0.209274i | ||||
\(549\) | −2.26795 | + | 3.92820i | −0.0967937 | + | 0.167652i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.3923 | + | 19.8564i | −1.46516 | + | 0.845911i | ||||
\(552\) | −5.60609 | − | 5.60609i | −0.238611 | − | 0.238611i | ||||
\(553\) | −37.0841 | + | 25.1141i | −1.57698 | + | 1.06796i | ||||
\(554\) | 22.0000i | 0.934690i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.00000 | + | 5.19615i | 0.381685 | + | 0.220366i | ||||
\(557\) | −5.91567 | − | 22.0776i | −0.250655 | − | 0.935458i | −0.970456 | − | 0.241277i | \(-0.922434\pi\) |
0.719801 | − | 0.694180i | \(-0.244233\pi\) | |||||||
\(558\) | 0.517638 | + | 0.138701i | 0.0219134 | + | 0.00587167i | ||||
\(559\) | −11.1769 | −0.472733 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.535898 | 0.0226256 | ||||||||
\(562\) | −13.5923 | − | 3.64205i | −0.573357 | − | 0.153631i | ||||
\(563\) | 4.76028 | + | 17.7656i | 0.200622 | + | 0.748731i | 0.990740 | + | 0.135776i | \(0.0433527\pi\) |
−0.790118 | + | 0.612955i | \(0.789981\pi\) | |||||||
\(564\) | 7.96410 | + | 4.59808i | 0.335349 | + | 0.193614i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 19.4641i | − | 0.818137i | ||||||
\(567\) | −1.15539 | + | 2.38014i | −0.0485220 | + | 0.0999565i | ||||
\(568\) | 3.48477 | + | 3.48477i | 0.146218 | + | 0.146218i | ||||
\(569\) | −8.47372 | + | 4.89230i | −0.355237 | + | 0.205096i | −0.666989 | − | 0.745067i | \(-0.732417\pi\) |
0.311752 | + | 0.950163i | \(0.399084\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.92820 | + | 12.0000i | −0.289936 | + | 0.502184i | −0.973794 | − | 0.227431i | \(-0.926967\pi\) |
0.683858 | + | 0.729615i | \(0.260301\pi\) | |||||||
\(572\) | 0.586988 | − | 2.19067i | 0.0245432 | − | 0.0915965i | ||||
\(573\) | −7.72741 | + | 7.72741i | −0.322817 | + | 0.322817i | ||||
\(574\) | −2.86603 | + | 14.8923i | −0.119626 | + | 0.621593i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −33.7381 | + | 9.04008i | −1.40453 | + | 0.376344i | −0.879971 | − | 0.475028i | \(-0.842438\pi\) |
−0.524563 | + | 0.851372i | \(0.675771\pi\) | |||||||
\(578\) | −16.1433 | + | 4.32559i | −0.671474 | + | 0.179921i | ||||
\(579\) | 9.39230 | + | 16.2679i | 0.390331 | + | 0.676073i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.0000 | − | 20.7846i | 0.746766 | − | 0.862291i | ||||
\(582\) | −7.72741 | + | 7.72741i | −0.320311 | + | 0.320311i | ||||
\(583\) | −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 | ||||
\(587\) | 9.41902 | + | 9.41902i | 0.388765 | + | 0.388765i | 0.874247 | − | 0.485482i | \(-0.161356\pi\) |
−0.485482 | + | 0.874247i | \(0.661356\pi\) | |||||||
\(588\) | −0.827225 | + | 6.95095i | −0.0341142 | + | 0.286652i | ||||
\(589\) | − | 3.07180i | − | 0.126571i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.40192 | + | 5.42820i | 0.386743 | + | 0.223286i | ||||
\(592\) | −2.56961 | − | 9.58991i | −0.105610 | − | 0.394143i | ||||
\(593\) | 20.8714 | + | 5.59248i | 0.857087 | + | 0.229656i | 0.660496 | − | 0.750830i | \(-0.270346\pi\) |
0.196591 | + | 0.980486i | \(0.437013\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.9282 | −0.529560 | ||||||||
\(597\) | 18.8009 | + | 5.03768i | 0.769469 | + | 0.206179i | ||||
\(598\) | −4.65376 | − | 17.3681i | −0.190307 | − | 0.710234i | ||||
\(599\) | 12.2487 | + | 7.07180i | 0.500469 | + | 0.288946i | 0.728907 | − | 0.684613i | \(-0.240029\pi\) |
−0.228438 | + | 0.973558i | \(0.573362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.7846i | − | 0.521495i | −0.965407 | − | 0.260748i | \(-0.916031\pi\) | ||
0.965407 | − | 0.260748i | \(-0.0839690\pi\) | |||||||
\(602\) | −7.31130 | − | 10.7961i | −0.297987 | − | 0.440015i | ||||
\(603\) | −1.41421 | − | 1.41421i | −0.0575912 | − | 0.0575912i | ||||
\(604\) | −20.6603 | + | 11.9282i | −0.840654 | + | 0.485352i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.46410 | − | 12.9282i | 0.303208 | − | 0.525172i | ||||
\(607\) | −4.93117 | + | 18.4034i | −0.200150 | + | 0.746969i | 0.790724 | + | 0.612173i | \(0.209705\pi\) |
−0.990873 | + | 0.134796i | \(0.956962\pi\) | |||||||
\(608\) | −4.05317 | + | 4.05317i | −0.164378 | + | 0.164378i | ||||
\(609\) | 17.3205 | − | 6.00000i | 0.701862 | − | 0.243132i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4282 | + | 18.0622i | 0.421880 | + | 0.730718i | ||||
\(612\) | 0.517638 | − | 0.138701i | 0.0209243 | − | 0.00560664i | ||||
\(613\) | −3.93305 | + | 1.05386i | −0.158855 | + | 0.0425649i | −0.337370 | − | 0.941372i | \(-0.609537\pi\) |
0.178515 | + | 0.983937i | \(0.442871\pi\) | |||||||
\(614\) | 0.803848 | + | 1.39230i | 0.0324406 | + | 0.0561889i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.50000 | − | 0.866025i | 0.100728 | − | 0.0348932i | ||||
\(617\) | 11.9700 | − | 11.9700i | 0.481896 | − | 0.481896i | −0.423841 | − | 0.905737i | \(-0.639318\pi\) |
0.905737 | + | 0.423841i | \(0.139318\pi\) | |||||||
\(618\) | −0.619174 | + | 2.31079i | −0.0249068 | + | 0.0929536i | ||||
\(619\) | −9.79423 | + | 16.9641i | −0.393663 | + | 0.681845i | −0.992930 | − | 0.118705i | \(-0.962126\pi\) |
0.599266 | + | 0.800550i | \(0.295459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.86603 | − | 3.96410i | 0.275524 | − | 0.159074i | ||||
\(622\) | −19.4201 | − | 19.4201i | −0.778673 | − | 0.778673i | ||||
\(623\) | 10.2784 | + | 15.1774i | 0.411797 | + | 0.608070i | ||||
\(624\) | − | 2.26795i | − | 0.0907906i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.0000 | + | 15.5885i | 1.07914 | + | 0.623040i | ||||
\(627\) | −1.48356 | − | 5.53674i | −0.0592478 | − | 0.221116i | ||||
\(628\) | 12.2289 | + | 3.27671i | 0.487985 | + | 0.130755i | ||||
\(629\) | 5.32051 | 0.212143 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.21539 | 0.0483839 | 0.0241920 | − | 0.999707i | \(-0.492299\pi\) | ||||
0.0241920 | + | 0.999707i | \(0.492299\pi\) | |||||||
\(632\) | 16.3514 | + | 4.38134i | 0.650423 | + | 0.174280i | ||||
\(633\) | 5.63827 | + | 21.0423i | 0.224101 | + | 0.836357i | ||||
\(634\) | −12.1244 | − | 7.00000i | −0.481520 | − | 0.278006i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.00000i | 0.0396526i | ||||||||
\(637\) | −9.50695 | + | 12.7143i | −0.376679 | + | 0.503760i | ||||
\(638\) | −4.89898 | − | 4.89898i | −0.193952 | − | 0.193952i | ||||
\(639\) | −4.26795 | + | 2.46410i | −0.168837 | + | 0.0974784i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.03590 | + | 15.6506i | −0.356897 | + | 0.618163i | −0.987441 | − | 0.157991i | \(-0.949498\pi\) |
0.630544 | + | 0.776153i | \(0.282832\pi\) | |||||||
\(642\) | −0.277401 | + | 1.03528i | −0.0109482 | + | 0.0408591i | ||||
\(643\) | −4.72311 | + | 4.72311i | −0.186261 | + | 0.186261i | −0.794078 | − | 0.607816i | \(-0.792046\pi\) |
0.607816 | + | 0.794078i | \(0.292046\pi\) | |||||||
\(644\) | 13.7321 | − | 15.8564i | 0.541119 | − | 0.624830i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.53590 | − | 2.66025i | −0.0604291 | − | 0.104666i | ||||
\(647\) | 34.3758 | − | 9.21097i | 1.35145 | − | 0.362121i | 0.490782 | − | 0.871283i | \(-0.336711\pi\) |
0.860671 | + | 0.509162i | \(0.170045\pi\) | |||||||
\(648\) | 0.965926 | − | 0.258819i | 0.0379452 | − | 0.0101674i | ||||
\(649\) | 2.26795 | + | 3.92820i | 0.0890248 | + | 0.154195i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.267949 | + | 1.39230i | −0.0105018 | + | 0.0545687i | ||||
\(652\) | −8.48528 | + | 8.48528i | −0.332309 | + | 0.332309i | ||||
\(653\) | 7.94906 | − | 29.6663i | 0.311071 | − | 1.16093i | −0.616522 | − | 0.787338i | \(-0.711459\pi\) |
0.927592 | − | 0.373594i | \(-0.121875\pi\) | |||||||
\(654\) | −1.53590 | + | 2.66025i | −0.0600584 | + | 0.104024i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.96410 | − | 2.86603i | 0.193816 | − | 0.111899i | ||||
\(657\) | −2.82843 | − | 2.82843i | −0.110347 | − | 0.110347i | ||||
\(658\) | −10.6252 | + | 21.8881i | −0.414213 | + | 0.853288i | ||||
\(659\) | 15.7128i | 0.612084i | 0.952018 | + | 0.306042i | \(0.0990048\pi\) | ||||
−0.952018 | + | 0.306042i | \(0.900995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.8564 | − | 11.4641i | −0.772325 | − | 0.445902i | 0.0613786 | − | 0.998115i | \(-0.480450\pi\) |
−0.833703 | + | 0.552213i | \(0.813784\pi\) | |||||||
\(662\) | 4.08536 | + | 15.2468i | 0.158782 | + | 0.592582i | ||||
\(663\) | 1.17398 | + | 0.314566i | 0.0455935 | + | 0.0122167i | ||||
\(664\) | −10.3923 | −0.403300 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.92820 | 0.384710 | ||||||||
\(667\) | −53.0566 | − | 14.2165i | −2.05436 | − | 0.550464i | ||||
\(668\) | 4.45069 | + | 16.6102i | 0.172202 | + | 0.642668i | ||||
\(669\) | 21.9282 | + | 12.6603i | 0.847793 | + | 0.489474i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.53590i | 0.175106i | ||||||||
\(672\) | 2.19067 | − | 1.48356i | 0.0845070 | − | 0.0572297i | ||||
\(673\) | −11.8685 | − | 11.8685i | −0.457497 | − | 0.457497i | 0.440336 | − | 0.897833i | \(-0.354859\pi\) |
−0.897833 | + | 0.440336i | \(0.854859\pi\) | |||||||
\(674\) | 21.5885 | − | 12.4641i | 0.831556 | − | 0.480099i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.92820 | + | 6.80385i | −0.151085 | + | 0.261686i | ||||
\(677\) | 0.512659 | − | 1.91327i | 0.0197031 | − | 0.0735329i | −0.955374 | − | 0.295398i | \(-0.904548\pi\) |
0.975077 | + | 0.221865i | \(0.0712144\pi\) | |||||||
\(678\) | −0.656339 | + | 0.656339i | −0.0252065 | + | 0.0252065i | ||||
\(679\) | −21.8564 | − | 18.9282i | −0.838772 | − | 0.726398i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.73205 | − | 3.00000i | −0.0663723 | − | 0.114960i | ||||
\(682\) | 0.517638 | − | 0.138701i | 0.0198214 | − | 0.00531112i | ||||
\(683\) | −40.4302 | + | 10.8332i | −1.54702 | + | 0.414522i | −0.928526 | − | 0.371269i | \(-0.878923\pi\) |
−0.618492 | + | 0.785791i | \(0.712256\pi\) | |||||||
\(684\) | −2.86603 | − | 4.96410i | −0.109585 | − | 0.189807i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.5000 | − | 0.866025i | −0.706333 | − | 0.0330650i | ||||
\(687\) | −7.72741 | + | 7.72741i | −0.294819 | + | 0.294819i | ||||
\(688\) | −1.27551 | + | 4.76028i | −0.0486285 | + | 0.181484i | ||||
\(689\) | −1.13397 | + | 1.96410i | −0.0432010 | + | 0.0748263i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.14359 | + | 4.12436i | −0.271755 | + | 0.156898i | −0.629685 | − | 0.776851i | \(-0.716816\pi\) |
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(692\) | −16.6796 | − | 16.6796i | −0.634062 | − | 0.634062i | ||||
\(693\) | 0.189469 | + | 2.63896i | 0.00719732 | + | 0.100246i | ||||
\(694\) | − | 10.9282i | − | 0.414829i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.00000 | − | 3.46410i | −0.227429 | − | 0.131306i | ||||
\(697\) | 0.795040 | + | 2.96713i | 0.0301143 | + | 0.112388i | ||||
\(698\) | −24.9754 | − | 6.69213i | −0.945332 | − | 0.253301i | ||||
\(699\) | 25.8564 | 0.977979 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.8564 | −1.20320 | −0.601600 | − | 0.798798i | \(-0.705470\pi\) | ||||
−0.601600 | + | 0.798798i | \(0.705470\pi\) | |||||||
\(702\) | 2.19067 | + | 0.586988i | 0.0826815 | + | 0.0221545i | ||||
\(703\) | −14.7291 | − | 54.9698i | −0.555519 | − | 2.07323i | ||||
\(704\) | −0.866025 | − | 0.500000i | −0.0326396 | − | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 6.92820i | − | 0.260746i | ||||||
\(707\) | 35.5312 | + | 17.2480i | 1.33629 | + | 0.648676i | ||||
\(708\) | 3.20736 | + | 3.20736i | 0.120540 | + | 0.120540i | ||||
\(709\) | −11.3205 | + | 6.53590i | −0.425151 | + | 0.245461i | −0.697279 | − | 0.716800i | \(-0.745606\pi\) |
0.272128 | + | 0.962261i | \(0.412273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.46410 | + | 14.6603i | −0.317429 | + | 0.549802i | ||||
\(712\) | 1.79315 | − | 6.69213i | 0.0672012 | − | 0.250798i | ||||
\(713\) | 3.00429 | − | 3.00429i | 0.112512 | − | 0.112512i | ||||
\(714\) | 0.464102 | + | 1.33975i | 0.0173686 | + | 0.0501387i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.50000 | − | 7.79423i | −0.168173 | − | 0.291284i | ||||
\(717\) | −23.1822 | + | 6.21166i | −0.865756 | + | 0.231979i | ||||
\(718\) | 18.2832 | − | 4.89898i | 0.682324 | − | 0.182828i | ||||
\(719\) | −7.19615 | − | 12.4641i | −0.268371 | − | 0.464833i | 0.700070 | − | 0.714074i | \(-0.253152\pi\) |
−0.968441 | + | 0.249242i | \(0.919819\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.21539 | − | 1.19615i | −0.231473 | − | 0.0445470i | ||||
\(722\) | −9.79796 | + | 9.79796i | −0.364642 | + | 0.364642i | ||||
\(723\) | 6.65994 | − | 24.8553i | 0.247686 | − | 0.924377i | ||||
\(724\) | −3.19615 | + | 5.53590i | −0.118784 | + | 0.205740i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.66025 | + | 5.00000i | −0.321412 | + | 0.185567i | ||||
\(727\) | 23.0943 | + | 23.0943i | 0.856520 | + | 0.856520i | 0.990926 | − | 0.134407i | \(-0.0429128\pi\) |
−0.134407 | + | 0.990926i | \(0.542913\pi\) | |||||||
\(728\) | 5.98502 | − | 0.429705i | 0.221820 | − | 0.0159259i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.28719 | − | 1.32051i | −0.0845947 | − | 0.0488408i | ||||
\(732\) | 1.17398 | + | 4.38134i | 0.0433914 | + | 0.161939i | ||||
\(733\) | 22.2671 | + | 5.96644i | 0.822453 | + | 0.220376i | 0.645418 | − | 0.763829i | \(-0.276683\pi\) |
0.177034 | + | 0.984205i | \(0.443350\pi\) | |||||||
\(734\) | 14.5167 | 0.535820 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.92820 | −0.292237 | ||||||||
\(737\) | −1.93185 | − | 0.517638i | −0.0711607 | − | 0.0190674i | ||||
\(738\) | 1.48356 | + | 5.53674i | 0.0546107 | + | 0.203810i | ||||
\(739\) | −5.25833 | − | 3.03590i | −0.193431 | − | 0.111677i | 0.400157 | − | 0.916447i | \(-0.368956\pi\) |
−0.593588 | + | 0.804769i | \(0.702289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 13.0000i | − | 0.477567i | ||||||
\(742\) | −2.63896 | + | 0.189469i | −0.0968792 | + | 0.00695561i | ||||
\(743\) | 23.8893 | + | 23.8893i | 0.876414 | + | 0.876414i | 0.993162 | − | 0.116747i | \(-0.0372467\pi\) |
−0.116747 | + | 0.993162i | \(0.537247\pi\) | |||||||
\(744\) | 0.464102 | − | 0.267949i | 0.0170148 | − | 0.00982349i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.0000 | + | 22.5167i | −0.475964 | + | 0.824394i | ||||
\(747\) | 2.68973 | − | 10.0382i | 0.0984119 | − | 0.367278i | ||||
\(748\) | 0.378937 | − | 0.378937i | 0.0138553 | − | 0.0138553i | ||||
\(749\) | −2.78461 | − | 0.535898i | −0.101747 | − | 0.0195813i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.92820 | − | 12.0000i | −0.252814 | − | 0.437886i | 0.711486 | − | 0.702701i | \(-0.248023\pi\) |
−0.964299 | + | 0.264814i | \(0.914689\pi\) | |||||||
\(752\) | 8.88280 | − | 2.38014i | 0.323922 | − | 0.0867948i | ||||
\(753\) | −23.8200 | + | 6.38254i | −0.868048 | + | 0.232593i | ||||
\(754\) | −7.85641 | − | 13.6077i | −0.286113 | − | 0.495563i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.866025 | + | 2.50000i | 0.0314970 | + | 0.0909241i | ||||
\(757\) | 12.5249 | − | 12.5249i | 0.455223 | − | 0.455223i | −0.441860 | − | 0.897084i | \(-0.645681\pi\) |
0.897084 | + | 0.441860i | \(0.145681\pi\) | |||||||
\(758\) | 2.56961 | − | 9.58991i | 0.0933324 | − | 0.348321i | ||||
\(759\) | 3.96410 | − | 6.86603i | 0.143888 | − | 0.249221i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.1077 | − | 12.1865i | 0.765153 | − | 0.441761i | −0.0659896 | − | 0.997820i | \(-0.521020\pi\) |
0.831143 | + | 0.556059i | \(0.187687\pi\) | |||||||
\(762\) | −3.53553 | − | 3.53553i | −0.128079 | − | 0.128079i | ||||
\(763\) | −7.31130 | − | 3.54914i | −0.264687 | − | 0.128487i | ||||
\(764\) | 10.9282i | 0.395369i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.9641 | − | 14.9904i | −0.938121 | − | 0.541624i | ||||
\(767\) | 2.66252 | + | 9.93666i | 0.0961380 | + | 0.358792i | ||||
\(768\) | −0.965926 | − | 0.258819i | −0.0348548 | − | 0.00933933i | ||||
\(769\) | −21.1962 | −0.764353 | −0.382176 | − | 0.924089i | \(-0.624825\pi\) | ||||
−0.382176 | + | 0.924089i | \(0.624825\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.3923 | 0.662383 | ||||||||
\(772\) | 18.1445 | + | 4.86181i | 0.653036 | + | 0.174981i | ||||
\(773\) | 9.41404 | + | 35.1337i | 0.338600 | + | 1.26367i | 0.899914 | + | 0.436068i | \(0.143629\pi\) |
−0.561314 | + | 0.827603i | \(0.689704\pi\) | |||||||
\(774\) | −4.26795 | − | 2.46410i | −0.153408 | − | 0.0885703i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.9282i | 0.392300i | ||||||||
\(777\) | 1.88108 | + | 26.2001i | 0.0674835 | + | 0.939924i | ||||
\(778\) | −23.0807 | − | 23.0807i | −0.827483 | − | 0.827483i | ||||
\(779\) | 28.4545 | − | 16.4282i | 1.01949 | − | 0.588601i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.46410 | + | 4.26795i | −0.0881725 | + | 0.152719i | ||||
\(782\) | 1.09965 | − | 4.10394i | 0.0393233 | − | 0.146757i | ||||
\(783\) | 4.89898 | − | 4.89898i | 0.175075 | − | 0.175075i | ||||
\(784\) | 4.33013 | + | 5.50000i | 0.154647 | + | 0.196429i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10.0622 | + | 17.4282i | 0.358906 | + | 0.621643i | ||||
\(787\) | 17.7656 | − | 4.76028i | 0.633275 | − | 0.169686i | 0.0721198 | − | 0.997396i | \(-0.477024\pi\) |
0.561156 | + | 0.827710i | \(0.310357\pi\) | |||||||
\(788\) | 10.4865 | − | 2.80984i | 0.373566 | − | 0.100097i | ||||
\(789\) | −1.07180 | − | 1.85641i | −0.0381570 | − | 0.0660898i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.85641 | − | 1.60770i | −0.0660062 | − | 0.0571631i | ||||
\(792\) | 0.707107 | − | 0.707107i | 0.0251259 | − | 0.0251259i | ||||
\(793\) | −2.66252 | + | 9.93666i | −0.0945489 | + | 0.352861i | ||||
\(794\) | −6.39230 | + | 11.0718i | −0.226854 | + | 0.392923i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.8564 | − | 9.73205i | 0.597459 | − | 0.344943i | ||||
\(797\) | 1.51575 | + | 1.51575i | 0.0536906 | + | 0.0536906i | 0.733442 | − | 0.679752i | \(-0.237912\pi\) |
−0.679752 | + | 0.733442i | \(0.737912\pi\) | |||||||
\(798\) | 12.5570 | − | 8.50386i | 0.444514 | − | 0.301034i | ||||
\(799\) | 4.92820i | 0.174347i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | + | 3.46410i | 0.212000 | + | 0.122398i | ||||
\(802\) | 3.08725 | + | 11.5218i | 0.109014 | + | 0.406847i | ||||
\(803\) | −3.86370 | − | 1.03528i | −0.136347 | − | 0.0365341i | ||||
\(804\) | −2.00000 | −0.0705346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.21539 | 0.0428103 | ||||||||
\(807\) | 9.00292 | + | 2.41233i | 0.316918 | + | 0.0849179i | ||||
\(808\) | −3.86370 | − | 14.4195i | −0.135925 | − | 0.507278i | ||||
\(809\) | 37.7942 | + | 21.8205i | 1.32877 | + | 0.767168i | 0.985110 | − | 0.171924i | \(-0.0549985\pi\) |
0.343664 | + | 0.939093i | \(0.388332\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 42.5167i | − | 1.49296i | −0.665407 | − | 0.746481i | \(-0.731742\pi\) | ||
0.665407 | − | 0.746481i | \(-0.268258\pi\) | |||||||
\(812\) | 8.00481 | − | 16.4901i | 0.280914 | − | 0.578689i | ||||
\(813\) | −5.65685 | − | 5.65685i | −0.198395 | − | 0.198395i | ||||
\(814\) | 8.59808 | − | 4.96410i | 0.301362 | − | 0.173992i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.267949 | − | 0.464102i | 0.00938010 | − | 0.0162468i | ||||
\(817\) | −7.31130 | + | 27.2862i | −0.255790 | + | 0.954622i | ||||
\(818\) | −9.04008 | + | 9.04008i | −0.316079 | + | 0.316079i | ||||
\(819\) | −1.13397 | + | 5.89230i | −0.0396243 | + | 0.205894i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.92820 | − | 3.33975i | −0.0672948 | − | 0.116558i | 0.830415 | − | 0.557146i | \(-0.188103\pi\) |
−0.897710 | + | 0.440588i | \(0.854770\pi\) | |||||||
\(822\) | 4.89898 | − | 1.31268i | 0.170872 | − | 0.0457849i | ||||
\(823\) | −19.0411 | + | 5.10205i | −0.663732 | + | 0.177846i | −0.574929 | − | 0.818203i | \(-0.694971\pi\) |
−0.0888021 | + | 0.996049i | \(0.528304\pi\) | |||||||
\(824\) | 1.19615 | + | 2.07180i | 0.0416699 | + | 0.0721745i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.85641 | + | 9.07180i | −0.273359 | + | 0.315648i | ||||
\(827\) | 11.4152 | − | 11.4152i | 0.396947 | − | 0.396947i | −0.480208 | − | 0.877155i | \(-0.659439\pi\) |
0.877155 | + | 0.480208i | \(0.159439\pi\) | |||||||
\(828\) | 2.05197 | − | 7.65806i | 0.0713109 | − | 0.266136i | ||||
\(829\) | −11.7321 | + | 20.3205i | −0.407471 | + | 0.705760i | −0.994606 | − | 0.103729i | \(-0.966923\pi\) |
0.587135 | + | 0.809489i | \(0.300256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.0526 | + | 11.0000i | −0.660926 | + | 0.381586i | ||||
\(832\) | −1.60368 | − | 1.60368i | −0.0555977 | − | 0.0555977i | ||||
\(833\) | −3.44760 | + | 1.47858i | −0.119452 | + | 0.0512299i | ||||
\(834\) | 10.3923i | 0.359856i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.96410 | − | 2.86603i | −0.171687 | − | 0.0991236i | ||||
\(837\) | 0.138701 | + | 0.517638i | 0.00479420 | + | 0.0178922i | ||||
\(838\) | 26.1308 | + | 7.00172i | 0.902672 | + | 0.241870i | ||||
\(839\) | −15.4641 | −0.533880 | −0.266940 | − | 0.963713i | \(-0.586013\pi\) | ||||
−0.266940 | + | 0.963713i | \(0.586013\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 13.3843 | + | 3.58630i | 0.461252 | + | 0.123592i | ||||
\(843\) | −3.64205 | − | 13.5923i | −0.125439 | − | 0.468144i | ||||
\(844\) | 18.8660 | + | 10.8923i | 0.649395 | + | 0.374929i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.19615i | 0.316170i | ||||||||
\(847\) | −14.8356 | − | 21.9067i | −0.509759 | − | 0.752723i | ||||
\(848\) | 0.707107 | + | 0.707107i | 0.0242821 | + | 0.0242821i | ||||
\(849\) | 16.8564 | − | 9.73205i | 0.578510 | − | 0.334003i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.3564 | − | 68.1673i | 1.34912 | − | 2.33674i | ||||
\(852\) | −1.27551 | + | 4.76028i | −0.0436984 | + | 0.163084i | ||||
\(853\) | 22.7153 | − | 22.7153i | 0.777759 | − | 0.777759i | −0.201691 | − | 0.979449i | \(-0.564644\pi\) |
0.979449 | + | 0.201691i | \(0.0646435\pi\) | |||||||
\(854\) | −11.3397 | + | 3.92820i | −0.388038 | + | 0.134420i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.535898 | + | 0.928203i | 0.0183166 | + | 0.0317253i | ||||
\(857\) | 15.4548 | − | 4.14110i | 0.527926 | − | 0.141457i | 0.0149958 | − | 0.999888i | \(-0.495227\pi\) |
0.512931 | + | 0.858430i | \(0.328560\pi\) | |||||||
\(858\) | 2.19067 | − | 0.586988i | 0.0747883 | − | 0.0200395i | ||||
\(859\) | 17.1962 | + | 29.7846i | 0.586725 | + | 1.01624i | 0.994658 | + | 0.103226i | \(0.0329164\pi\) |
−0.407933 | + | 0.913012i | \(0.633750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.3301 | + | 4.96410i | −0.488369 | + | 0.169176i | ||||
\(862\) | −15.3533 | + | 15.3533i | −0.522935 | + | 0.522935i | ||||
\(863\) | 7.67166 | − | 28.6310i | 0.261146 | − | 0.974611i | −0.703421 | − | 0.710774i | \(-0.748345\pi\) |
0.964567 | − | 0.263838i | \(-0.0849883\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.8564 | + | 8.00000i | −0.470860 | + | 0.271851i | ||||
\(867\) | −11.8177 | − | 11.8177i | −0.401352 | − | 0.401352i | ||||
\(868\) | 0.795040 | + | 1.17398i | 0.0269854 | + | 0.0398474i | ||||
\(869\) | 16.9282i | 0.574250i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.92820 | − | 2.26795i | −0.133102 | − | 0.0768465i | ||||
\(872\) | 0.795040 | + | 2.96713i | 0.0269234 | + | 0.100480i | ||||
\(873\) | −10.5558 | − | 2.82843i | −0.357261 | − | 0.0957278i | ||||
\(874\) | −45.4449 | −1.53720 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | 9.58991 | + | 2.56961i | 0.323828 | + | 0.0867695i | 0.417071 | − | 0.908874i | \(-0.363057\pi\) |
−0.0932428 | + | 0.995643i | \(0.529723\pi\) | |||||||
\(878\) | −5.17638 | − | 19.3185i | −0.174694 | − | 0.651968i | ||||
\(879\) | −1.50000 | − | 0.866025i | −0.0505937 | − | 0.0292103i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.9090i | 0.973968i | 0.873411 | + | 0.486984i | \(0.161903\pi\) | ||||
−0.873411 | + | 0.486984i | \(0.838097\pi\) | |||||||
\(882\) | −6.43331 | + | 2.75908i | −0.216621 | + | 0.0929029i | ||||
\(883\) | −14.9000 | − | 14.9000i | −0.501425 | − | 0.501425i | 0.410455 | − | 0.911881i | \(-0.365370\pi\) |
−0.911881 | + | 0.410455i | \(0.865370\pi\) | |||||||
\(884\) | 1.05256 | − | 0.607695i | 0.0354014 | − | 0.0204390i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.0717968 | − | 0.124356i | 0.00241206 | − | 0.00417781i | ||||
\(887\) | −0.896575 | + | 3.34607i | −0.0301041 | + | 0.112350i | −0.979343 | − | 0.202206i | \(-0.935189\pi\) |
0.949239 | + | 0.314556i | \(0.101856\pi\) | |||||||
\(888\) | 7.02030 | − | 7.02030i | 0.235586 | − | 0.235586i | ||||
\(889\) | 8.66025 | − | 10.0000i | 0.290456 | − | 0.335389i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | 24.4577 | − | 6.55343i | 0.818905 | − | 0.219425i | ||||
\(893\) | 50.9167 | − | 13.6431i | 1.70386 | − | 0.456548i | ||||
\(894\) | −6.46410 | − | 11.1962i | −0.216192 | − | 0.374455i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | − | 2.59808i | 0.0167038 | − | 0.0867956i | ||||
\(897\) | 12.7143 | − | 12.7143i | 0.424519 | − | 0.424519i | ||||
\(898\) | −0.0185824 | + | 0.0693504i | −0.000620102 | + | 0.00231425i | ||||
\(899\) | 1.85641 | − | 3.21539i | 0.0619146 | − | 0.107239i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.464102 | + | 0.267949i | −0.0154615 | + | 0.00892668i | ||||
\(902\) | 4.05317 | + | 4.05317i | 0.134956 | + | 0.134956i | ||||
\(903\) | 5.69402 | − | 11.7298i | 0.189485 | − | 0.390344i | ||||
\(904\) | 0.928203i | 0.0308716i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −20.6603 | − | 11.9282i | −0.686391 | − | 0.396288i | ||||
\(907\) | −7.72741 | − | 28.8391i | −0.256584 | − | 0.957586i | −0.967202 | − | 0.254008i | \(-0.918251\pi\) |
0.710618 | − | 0.703578i | \(-0.248415\pi\) | |||||||
\(908\) | −3.34607 | − | 0.896575i | −0.111043 | − | 0.0297539i | ||||
\(909\) | 14.9282 | 0.495137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.7128 | −1.91211 | −0.956055 | − | 0.293186i | \(-0.905284\pi\) | ||||
−0.956055 | + | 0.293186i | \(0.905284\pi\) | |||||||
\(912\) | −5.53674 | − | 1.48356i | −0.183340 | − | 0.0491257i | ||||
\(913\) | −2.68973 | − | 10.0382i | −0.0890170 | − | 0.332216i | ||||
\(914\) | −10.2679 | − | 5.92820i | −0.339634 | − | 0.196088i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.9282i | 0.361078i | ||||||||
\(917\) | −44.0858 | + | 29.8558i | −1.45584 | + | 0.985924i | ||||
\(918\) | 0.378937 | + | 0.378937i | 0.0125068 | + | 0.0125068i | ||||
\(919\) | −2.78461 | + | 1.60770i | −0.0918558 | + | 0.0530330i | −0.545224 | − | 0.838290i | \(-0.683556\pi\) |
0.453368 | + | 0.891323i | \(0.350222\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.803848 | + | 1.39230i | −0.0264877 | + | 0.0458780i | ||||
\(922\) | −7.93048 | + | 29.5969i | −0.261176 | + | 0.974724i | ||||
\(923\) | −7.90327 | + | 7.90327i | −0.260139 | + | 0.260139i | ||||
\(924\) | 2.00000 | + | 1.73205i | 0.0657952 | + | 0.0569803i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.3564 | + | 28.3301i | 0.537505 | + | 0.930986i | ||||
\(927\) | −2.31079 | + | 0.619174i | −0.0758963 | + | 0.0203363i | ||||
\(928\) | −6.69213 | + | 1.79315i | −0.219680 | + | 0.0588631i | ||||
\(929\) | −4.06218 | − | 7.03590i | −0.133276 | − | 0.230840i | 0.791662 | − | 0.610960i | \(-0.209216\pi\) |
−0.924937 | + | 0.380119i | \(0.875883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.8205 | + | 31.5263i | 0.813459 | + | 1.03323i | ||||
\(932\) | 18.2832 | − | 18.2832i | 0.598887 | − | 0.598887i | ||||
\(933\) | 7.10823 | − | 26.5283i | 0.232713 | − | 0.868497i | ||||
\(934\) | −7.19615 | + | 12.4641i | −0.235465 | + | 0.407838i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.96410 | − | 1.13397i | 0.0641987 | − | 0.0370651i | ||||
\(937\) | 21.4906 | + | 21.4906i | 0.702067 | + | 0.702067i | 0.964854 | − | 0.262787i | \(-0.0846415\pi\) |
−0.262787 | + | 0.964854i | \(0.584641\pi\) | |||||||
\(938\) | −0.378937 | − | 5.27792i | −0.0123727 | − | 0.172330i | ||||
\(939\) | 31.1769i | 1.01742i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.3205 | + | 23.8564i | 1.34701 | + | 0.777697i | 0.987825 | − | 0.155570i | \(-0.0497213\pi\) |
0.359185 | + | 0.933266i | \(0.383055\pi\) | |||||||
\(942\) | 3.27671 | + | 12.2289i | 0.106761 | + | 0.398438i | ||||
\(943\) | 43.8964 | + | 11.7620i | 1.42946 | + | 0.383023i | ||||
\(944\) | 4.53590 | 0.147631 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.92820 | −0.160230 | ||||||||
\(947\) | 44.2939 | + | 11.8685i | 1.43936 | + | 0.385675i | 0.892309 | − | 0.451426i | \(-0.149084\pi\) |
0.547049 | + | 0.837100i | \(0.315751\pi\) | |||||||
\(948\) | 4.38134 | + | 16.3514i | 0.142299 | + | 0.531068i | ||||
\(949\) | −7.85641 | − | 4.53590i | −0.255030 | − | 0.147241i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 14.0000i | − | 0.453981i | ||||||
\(952\) | 1.27551 | + | 0.619174i | 0.0413396 | + | 0.0200675i | ||||
\(953\) | −26.5654 | − | 26.5654i | −0.860539 | − | 0.860539i | 0.130861 | − | 0.991401i | \(-0.458226\pi\) |
−0.991401 | + | 0.130861i | \(0.958226\pi\) | |||||||
\(954\) | −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 | ||||
\(958\) | 30.3548 | − | 30.3548i | 0.980720 | − | 0.980720i | ||||
\(959\) | 4.39230 | + | 12.6795i | 0.141835 | + | 0.409442i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3564 | − | 26.5981i | −0.495368 | − | 0.858002i | ||||
\(962\) | 21.7494 | − | 5.82774i | 0.701230 | − | 0.187894i | ||||
\(963\) | −1.03528 | + | 0.277401i | −0.0333613 | + | 0.00893914i | ||||
\(964\) | −12.8660 | − | 22.2846i | −0.414387 | − | 0.717739i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 20.5981 | + | 3.96410i | 0.662732 | + | 0.127543i | ||||
\(967\) | 1.51575 | − | 1.51575i | 0.0487432 | − | 0.0487432i | −0.682315 | − | 0.731058i | \(-0.739027\pi\) |
0.731058 | + | 0.682315i | \(0.239027\pi\) | |||||||
\(968\) | −2.58819 | + | 9.65926i | −0.0831876 | + | 0.310460i | ||||
\(969\) | 1.53590 | − | 2.66025i | 0.0493402 | − | 0.0854597i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.2128 | − | 9.93782i | 0.552385 | − | 0.318920i | −0.197698 | − | 0.980263i | \(-0.563347\pi\) |
0.750084 | + | 0.661343i | \(0.230013\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −27.4249 | + | 1.96902i | −0.879201 | + | 0.0631238i | ||||
\(974\) | − | 21.8564i | − | 0.700324i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.92820 | + | 2.26795i | 0.125739 | + | 0.0725953i | ||||
\(977\) | −7.76457 | − | 28.9778i | −0.248411 | − | 0.927081i | −0.971638 | − | 0.236472i | \(-0.924009\pi\) |
0.723228 | − | 0.690610i | \(-0.242658\pi\) | |||||||
\(978\) | −11.5911 | − | 3.10583i | −0.370643 | − | 0.0993134i | ||||
\(979\) | 6.92820 | 0.221426 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.07180 | −0.0980749 | ||||||||
\(982\) | 42.2233 | + | 11.3137i | 1.34740 | + | 0.361035i | ||||
\(983\) | −8.25002 | − | 30.7895i | −0.263135 | − | 0.982033i | −0.963382 | − | 0.268132i | \(-0.913594\pi\) |
0.700247 | − | 0.713900i | \(-0.253073\pi\) | |||||||
\(984\) | 4.96410 | + | 2.86603i | 0.158250 | + | 0.0913656i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 3.71281i | − | 0.118240i | ||||||
\(987\) | −24.2683 | + | 1.74238i | −0.772467 | + | 0.0554607i | ||||
\(988\) | −9.19239 | − | 9.19239i | −0.292449 | − | 0.292449i | ||||
\(989\) | −33.8372 | + | 19.5359i | −1.07596 | + | 0.621205i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.39230 | − | 14.5359i | 0.266590 | − | 0.461748i | −0.701389 | − | 0.712779i | \(-0.747436\pi\) |
0.967979 | + | 0.251031i | \(0.0807696\pi\) | |||||||
\(992\) | 0.138701 | − | 0.517638i | 0.00440375 | − | 0.0164350i | ||||
\(993\) | −11.1614 | + | 11.1614i | −0.354196 | + | 0.354196i | ||||
\(994\) | −12.8038 | − | 2.46410i | −0.406113 | − | 0.0781566i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.19615 | − | 9.00000i | −0.164646 | − | 0.285176i | ||||
\(997\) | 49.9507 | − | 13.3843i | 1.58196 | − | 0.423884i | 0.642425 | − | 0.766348i | \(-0.277928\pi\) |
0.939531 | + | 0.342465i | \(0.111262\pi\) | |||||||
\(998\) | −27.0459 | + | 7.24693i | −0.856124 | + | 0.229398i | ||||
\(999\) | 4.96410 | + | 8.59808i | 0.157057 | + | 0.272031i |
(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.d.493.2 | yes | 8 | |
5.2 | odd | 4 | 1050.2.bc.a.157.1 | ✓ | 8 | ||
5.3 | odd | 4 | 1050.2.bc.a.157.2 | yes | 8 | ||
5.4 | even | 2 | inner | 1050.2.bc.d.493.1 | yes | 8 | |
7.5 | odd | 6 | 1050.2.bc.a.943.1 | yes | 8 | ||
35.12 | even | 12 | inner | 1050.2.bc.d.607.2 | yes | 8 | |
35.19 | odd | 6 | 1050.2.bc.a.943.2 | yes | 8 | ||
35.33 | even | 12 | inner | 1050.2.bc.d.607.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.bc.a.157.1 | ✓ | 8 | 5.2 | odd | 4 | ||
1050.2.bc.a.157.2 | yes | 8 | 5.3 | odd | 4 | ||
1050.2.bc.a.943.1 | yes | 8 | 7.5 | odd | 6 | ||
1050.2.bc.a.943.2 | yes | 8 | 35.19 | odd | 6 | ||
1050.2.bc.d.493.1 | yes | 8 | 5.4 | even | 2 | inner | |
1050.2.bc.d.493.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1050.2.bc.d.607.1 | yes | 8 | 35.33 | even | 12 | inner | |
1050.2.bc.d.607.2 | yes | 8 | 35.12 | even | 12 | inner |