Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(51,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.51");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 51.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.51 |
Dual form | 350.2.e.k.151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.00000 | + | 1.73205i | 0.577350 | + | 1.00000i | 0.995782 | + | 0.0917517i | \(0.0292466\pi\) |
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 1.00000 | − | 1.73205i | 0.288675 | − | 0.500000i | ||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −4.00000 | + | 6.92820i | −0.917663 | + | 1.58944i | −0.114708 | + | 0.993399i | \(0.536593\pi\) |
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | + | 3.46410i | 0.872872 | + | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.50000 | − | 7.79423i | 0.938315 | − | 1.62521i | 0.169701 | − | 0.985496i | \(-0.445720\pi\) |
0.768613 | − | 0.639713i | \(-0.220947\pi\) | |||||||
\(24\) | −1.00000 | − | 1.73205i | −0.204124 | − | 0.353553i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.00000 | + | 6.92820i | −0.657596 | + | 1.13899i | 0.323640 | + | 0.946180i | \(0.395093\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | 4.00000 | + | 6.92820i | 0.648886 | + | 1.12390i | ||||
\(39\) | 2.00000 | + | 3.46410i | 0.320256 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 5.00000 | − | 1.73205i | 0.771517 | − | 0.267261i | ||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.50000 | − | 7.79423i | −0.663489 | − | 1.14920i | ||||
\(47\) | 1.50000 | − | 2.59808i | 0.218797 | − | 0.378968i | −0.735643 | − | 0.677369i | \(-0.763120\pi\) |
0.954441 | + | 0.298401i | \(0.0964533\pi\) | |||||||
\(48\) | −2.00000 | −0.288675 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | + | 5.19615i | −0.420084 | + | 0.727607i | ||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 2.00000 | − | 3.46410i | 0.272166 | − | 0.471405i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.50000 | + | 0.866025i | −0.334077 | + | 0.115728i | ||||
\(57\) | −16.0000 | −2.11925 | ||||||||
\(58\) | −3.00000 | + | 5.19615i | −0.393919 | + | 0.682288i | ||||
\(59\) | −6.00000 | − | 10.3923i | −0.781133 | − | 1.35296i | −0.931282 | − | 0.364299i | \(-0.881308\pi\) |
0.150148 | − | 0.988663i | \(-0.452025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | − | 3.46410i | 0.256074 | − | 0.443533i | −0.709113 | − | 0.705095i | \(-0.750904\pi\) |
0.965187 | + | 0.261562i | \(0.0842377\pi\) | |||||||
\(62\) | −5.00000 | −0.635001 | ||||||||
\(63\) | −0.500000 | + | 2.59808i | −0.0629941 | + | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 18.0000 | 2.16695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | −1.06810 | −0.534052 | − | 0.845452i | \(-0.679331\pi\) | ||||
−0.534052 | + | 0.845452i | \(0.679331\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 5.00000 | + | 8.66025i | 0.585206 | + | 1.01361i | 0.994850 | + | 0.101361i | \(0.0323196\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 4.00000 | + | 6.92820i | 0.464991 | + | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.00000 | 0.917663 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | −2.50000 | + | 4.33013i | −0.281272 | + | 0.487177i | −0.971698 | − | 0.236225i | \(-0.924090\pi\) |
0.690426 | + | 0.723403i | \(0.257423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | −1.50000 | + | 2.59808i | −0.165647 | + | 0.286910i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 1.00000 | − | 5.19615i | 0.109109 | − | 0.566947i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.00000 | + | 8.66025i | −0.539164 | + | 0.933859i | ||||
\(87\) | −6.00000 | − | 10.3923i | −0.643268 | − | 1.11417i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | + | 2.59808i | −0.159000 | + | 0.275396i | −0.934508 | − | 0.355942i | \(-0.884160\pi\) |
0.775509 | + | 0.631337i | \(0.217494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000 | − | 1.73205i | 0.524142 | − | 0.181568i | ||||
\(92\) | −9.00000 | −0.938315 | ||||||||
\(93\) | 5.00000 | − | 8.66025i | 0.518476 | − | 0.898027i | ||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | + | 1.73205i | −0.102062 | + | 0.176777i | ||||
\(97\) | 5.00000 | 0.507673 | 0.253837 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 3.00000 | + | 5.19615i | 0.297044 | + | 0.514496i | ||||
\(103\) | −5.50000 | + | 9.52628i | −0.541931 | + | 0.938652i | 0.456862 | + | 0.889538i | \(0.348973\pi\) |
−0.998793 | + | 0.0491146i | \(0.984360\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | −2.00000 | − | 3.46410i | −0.192450 | − | 0.333333i | ||||
\(109\) | 5.00000 | + | 8.66025i | 0.478913 | + | 0.829502i | 0.999708 | − | 0.0241802i | \(-0.00769755\pi\) |
−0.520794 | + | 0.853682i | \(0.674364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.0000 | −1.51865 | ||||||||
\(112\) | −0.500000 | + | 2.59808i | −0.0472456 | + | 0.245495i | ||||
\(113\) | 15.0000 | 1.41108 | 0.705541 | − | 0.708669i | \(-0.250704\pi\) | ||||
0.705541 | + | 0.708669i | \(0.250704\pi\) | |||||||
\(114\) | −8.00000 | + | 13.8564i | −0.749269 | + | 1.29777i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | −1.00000 | + | 1.73205i | −0.0924500 | + | 0.160128i | ||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 6.00000 | + | 5.19615i | 0.550019 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | −2.00000 | − | 3.46410i | −0.181071 | − | 0.313625i | ||||
\(123\) | −3.00000 | − | 5.19615i | −0.270501 | − | 0.468521i | ||||
\(124\) | −2.50000 | + | 4.33013i | −0.224507 | + | 0.388857i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | + | 1.73205i | 0.178174 | + | 0.154303i | ||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −10.0000 | − | 17.3205i | −0.880451 | − | 1.52499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 20.7846i | −0.346844 | + | 1.80225i | ||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50000 | − | 2.59808i | −0.128624 | − | 0.222783i | ||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 9.00000 | − | 15.5885i | 0.766131 | − | 1.32698i | ||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | −4.50000 | + | 7.79423i | −0.377632 | + | 0.654077i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 13.0000 | + | 5.19615i | 1.07222 | + | 0.428571i | ||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | + | 3.46410i | 0.162758 | + | 0.281905i | 0.935857 | − | 0.352381i | \(-0.114628\pi\) |
−0.773099 | + | 0.634285i | \(0.781294\pi\) | |||||||
\(152\) | 4.00000 | − | 6.92820i | 0.324443 | − | 0.561951i | ||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 3.46410i | 0.160128 | − | 0.277350i | ||||
\(157\) | −1.00000 | − | 1.73205i | −0.0798087 | − | 0.138233i | 0.823359 | − | 0.567521i | \(-0.192098\pi\) |
−0.903167 | + | 0.429289i | \(0.858764\pi\) | |||||||
\(158\) | 2.50000 | + | 4.33013i | 0.198889 | + | 0.344486i | ||||
\(159\) | 6.00000 | − | 10.3923i | 0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.50000 | − | 23.3827i | 0.354650 | − | 1.84281i | ||||
\(162\) | 11.0000 | 0.864242 | ||||||||
\(163\) | −4.00000 | + | 6.92820i | −0.313304 | + | 0.542659i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | 1.50000 | + | 2.59808i | 0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | 24.0000 | 1.85718 | 0.928588 | − | 0.371113i | \(-0.121024\pi\) | ||||
0.928588 | + | 0.371113i | \(0.121024\pi\) | |||||||
\(168\) | −4.00000 | − | 3.46410i | −0.308607 | − | 0.267261i | ||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | − | 6.92820i | −0.305888 | − | 0.529813i | ||||
\(172\) | 5.00000 | + | 8.66025i | 0.381246 | + | 0.660338i | ||||
\(173\) | 6.00000 | − | 10.3923i | 0.456172 | − | 0.790112i | −0.542583 | − | 0.840002i | \(-0.682554\pi\) |
0.998755 | + | 0.0498898i | \(0.0158870\pi\) | |||||||
\(174\) | −12.0000 | −0.909718 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | − | 20.7846i | 0.901975 | − | 1.56227i | ||||
\(178\) | 1.50000 | + | 2.59808i | 0.112430 | + | 0.194734i | ||||
\(179\) | −12.0000 | − | 20.7846i | −0.896922 | − | 1.55351i | −0.831408 | − | 0.555663i | \(-0.812464\pi\) |
−0.0655145 | − | 0.997852i | \(-0.520869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 1.00000 | − | 5.19615i | 0.0741249 | − | 0.385164i | ||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | −4.50000 | + | 7.79423i | −0.331744 | + | 0.574598i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.00000 | − | 8.66025i | −0.366618 | − | 0.635001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.00000 | −0.218797 | ||||||||
\(189\) | 10.0000 | − | 3.46410i | 0.727393 | − | 0.251976i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.50000 | + | 12.9904i | −0.542681 | + | 0.939951i | 0.456068 | + | 0.889945i | \(0.349257\pi\) |
−0.998749 | + | 0.0500060i | \(0.984076\pi\) | |||||||
\(192\) | 1.00000 | + | 1.73205i | 0.0721688 | + | 0.125000i | ||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | 2.50000 | − | 4.33013i | 0.179490 | − | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.50000 | − | 14.7224i | −0.602549 | − | 1.04365i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) |
0.389885 | − | 0.920864i | \(-0.372515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | − | 3.46410i | 0.141069 | − | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.0000 | + | 5.19615i | −1.05279 | + | 0.364698i | ||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.50000 | + | 9.52628i | 0.383203 | + | 0.663727i | ||||
\(207\) | 4.50000 | + | 7.79423i | 0.312772 | + | 0.541736i | ||||
\(208\) | −1.00000 | + | 1.73205i | −0.0693375 | + | 0.120096i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | −9.00000 | − | 15.5885i | −0.616670 | − | 1.06810i | ||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | −10.0000 | − | 8.66025i | −0.678844 | − | 0.587896i | ||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | −10.0000 | + | 17.3205i | −0.675737 | + | 1.17041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | −8.00000 | + | 13.8564i | −0.536925 | + | 0.929981i | ||||
\(223\) | 23.0000 | 1.54019 | 0.770097 | − | 0.637927i | \(-0.220208\pi\) | ||||
0.770097 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(224\) | 2.00000 | + | 1.73205i | 0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.50000 | − | 12.9904i | 0.498893 | − | 0.864107i | ||||
\(227\) | −9.00000 | − | 15.5885i | −0.597351 | − | 1.03464i | −0.993210 | − | 0.116331i | \(-0.962887\pi\) |
0.395860 | − | 0.918311i | \(-0.370447\pi\) | |||||||
\(228\) | 8.00000 | + | 13.8564i | 0.529813 | + | 0.917663i | ||||
\(229\) | −10.0000 | + | 17.3205i | −0.660819 | + | 1.14457i | 0.319582 | + | 0.947559i | \(0.396457\pi\) |
−0.980401 | + | 0.197013i | \(0.936876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | 3.00000 | − | 5.19615i | 0.196537 | − | 0.340411i | −0.750867 | − | 0.660454i | \(-0.770364\pi\) |
0.947403 | + | 0.320043i | \(0.103697\pi\) | |||||||
\(234\) | 1.00000 | + | 1.73205i | 0.0653720 | + | 0.113228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | −10.0000 | −0.649570 | ||||||||
\(238\) | 7.50000 | − | 2.59808i | 0.486153 | − | 0.168408i | ||||
\(239\) | 15.0000 | 0.970269 | 0.485135 | − | 0.874439i | \(-0.338771\pi\) | ||||
0.485135 | + | 0.874439i | \(0.338771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | + | 19.0526i | 0.708572 | + | 1.22728i | 0.965387 | + | 0.260822i | \(0.0839937\pi\) |
−0.256814 | + | 0.966461i | \(0.582673\pi\) | |||||||
\(242\) | −5.50000 | − | 9.52628i | −0.353553 | − | 0.612372i | ||||
\(243\) | −5.00000 | + | 8.66025i | −0.320750 | + | 0.555556i | ||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | −8.00000 | + | 13.8564i | −0.509028 | + | 0.881662i | ||||
\(248\) | 2.50000 | + | 4.33013i | 0.158750 | + | 0.274963i | ||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 2.50000 | − | 0.866025i | 0.157485 | − | 0.0545545i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.00000 | − | 6.92820i | 0.250982 | − | 0.434714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | −20.0000 | −1.24515 | ||||||||
\(259\) | −4.00000 | + | 20.7846i | −0.248548 | + | 1.29149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.50000 | − | 7.79423i | −0.277482 | − | 0.480613i | 0.693276 | − | 0.720672i | \(-0.256167\pi\) |
−0.970758 | + | 0.240059i | \(0.922833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 16.0000 | + | 13.8564i | 0.981023 | + | 0.849591i | ||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | −1.00000 | + | 1.73205i | −0.0610847 | + | 0.105802i | ||||
\(269\) | 15.0000 | + | 25.9808i | 0.914566 | + | 1.58408i | 0.807535 | + | 0.589819i | \(0.200801\pi\) |
0.107031 | + | 0.994256i | \(0.465866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.50000 | + | 9.52628i | −0.334101 | + | 0.578680i | −0.983312 | − | 0.181928i | \(-0.941766\pi\) |
0.649211 | + | 0.760609i | \(0.275099\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 8.00000 | + | 6.92820i | 0.484182 | + | 0.419314i | ||||
\(274\) | −9.00000 | −0.543710 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.00000 | − | 15.5885i | −0.541736 | − | 0.938315i | ||||
\(277\) | 2.00000 | + | 3.46410i | 0.120168 | + | 0.208138i | 0.919834 | − | 0.392308i | \(-0.128323\pi\) |
−0.799666 | + | 0.600446i | \(0.794990\pi\) | |||||||
\(278\) | 1.00000 | − | 1.73205i | 0.0599760 | − | 0.103882i | ||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 3.00000 | − | 5.19615i | 0.178647 | − | 0.309426i | ||||
\(283\) | −1.00000 | − | 1.73205i | −0.0594438 | − | 0.102960i | 0.834772 | − | 0.550596i | \(-0.185599\pi\) |
−0.894216 | + | 0.447636i | \(0.852266\pi\) | |||||||
\(284\) | 4.50000 | + | 7.79423i | 0.267026 | + | 0.462502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.50000 | + | 2.59808i | −0.442711 | + | 0.153360i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | + | 8.66025i | 0.293105 | + | 0.507673i | ||||
\(292\) | 5.00000 | − | 8.66025i | 0.292603 | − | 0.506803i | ||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 11.0000 | − | 8.66025i | 0.641533 | − | 0.505076i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | − | 6.92820i | 0.232495 | − | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.00000 | − | 15.5885i | 0.520483 | − | 0.901504i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.0000 | + | 8.66025i | −1.44098 | + | 0.499169i | ||||
\(302\) | 4.00000 | 0.230174 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | − | 6.92820i | −0.229416 | − | 0.397360i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.50000 | + | 2.59808i | −0.0857493 | + | 0.148522i | ||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.0000 | −1.25154 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5000 | − | 18.1865i | −0.595400 | − | 1.03126i | −0.993490 | − | 0.113917i | \(-0.963660\pi\) |
0.398090 | − | 0.917346i | \(-0.369673\pi\) | |||||||
\(312\) | −2.00000 | − | 3.46410i | −0.113228 | − | 0.196116i | ||||
\(313\) | −8.50000 | + | 14.7224i | −0.480448 | + | 0.832161i | −0.999748 | − | 0.0224310i | \(-0.992859\pi\) |
0.519300 | + | 0.854592i | \(0.326193\pi\) | |||||||
\(314\) | −2.00000 | −0.112867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | 0.281272 | ||||||||
\(317\) | 6.00000 | − | 10.3923i | 0.336994 | − | 0.583690i | −0.646872 | − | 0.762598i | \(-0.723923\pi\) |
0.983866 | + | 0.178908i | \(0.0572566\pi\) | |||||||
\(318\) | −6.00000 | − | 10.3923i | −0.336463 | − | 0.582772i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | −18.0000 | − | 15.5885i | −1.00310 | − | 0.868711i | ||||
\(323\) | −24.0000 | −1.33540 | ||||||||
\(324\) | 5.50000 | − | 9.52628i | 0.305556 | − | 0.529238i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.00000 | + | 6.92820i | 0.221540 | + | 0.383718i | ||||
\(327\) | −10.0000 | + | 17.3205i | −0.553001 | + | 0.957826i | ||||
\(328\) | 3.00000 | 0.165647 | ||||||||
\(329\) | 1.50000 | − | 7.79423i | 0.0826977 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00000 | + | 12.1244i | −0.384755 | + | 0.666415i | −0.991735 | − | 0.128302i | \(-0.959047\pi\) |
0.606980 | + | 0.794717i | \(0.292381\pi\) | |||||||
\(332\) | 3.00000 | + | 5.19615i | 0.164646 | + | 0.285176i | ||||
\(333\) | −4.00000 | − | 6.92820i | −0.219199 | − | 0.379663i | ||||
\(334\) | 12.0000 | − | 20.7846i | 0.656611 | − | 1.13728i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.00000 | + | 1.73205i | −0.272772 | + | 0.0944911i | ||||
\(337\) | −13.0000 | −0.708155 | −0.354078 | − | 0.935216i | \(-0.615205\pi\) | ||||
−0.354078 | + | 0.935216i | \(0.615205\pi\) | |||||||
\(338\) | −4.50000 | + | 7.79423i | −0.244768 | + | 0.423950i | ||||
\(339\) | 15.0000 | + | 25.9808i | 0.814688 | + | 1.41108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −8.00000 | −0.432590 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 10.0000 | 0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.00000 | − | 10.3923i | −0.322562 | − | 0.558694i | ||||
\(347\) | 3.00000 | + | 5.19615i | 0.161048 | + | 0.278944i | 0.935245 | − | 0.354001i | \(-0.115179\pi\) |
−0.774197 | + | 0.632945i | \(0.781846\pi\) | |||||||
\(348\) | −6.00000 | + | 10.3923i | −0.321634 | + | 0.557086i | ||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.00000 | 0.427008 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.50000 | + | 7.79423i | 0.239511 | + | 0.414845i | 0.960574 | − | 0.278024i | \(-0.0896796\pi\) |
−0.721063 | + | 0.692869i | \(0.756346\pi\) | |||||||
\(354\) | −12.0000 | − | 20.7846i | −0.637793 | − | 1.10469i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.00000 | 0.159000 | ||||||||
\(357\) | −3.00000 | + | 15.5885i | −0.158777 | + | 0.825029i | ||||
\(358\) | −24.0000 | −1.26844 | ||||||||
\(359\) | 12.0000 | − | 20.7846i | 0.633336 | − | 1.09697i | −0.353529 | − | 0.935423i | \(-0.615019\pi\) |
0.986865 | − | 0.161546i | \(-0.0516481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.5000 | − | 38.9711i | −1.18421 | − | 2.05111i | ||||
\(362\) | 10.0000 | − | 17.3205i | 0.525588 | − | 0.910346i | ||||
\(363\) | 22.0000 | 1.15470 | ||||||||
\(364\) | −4.00000 | − | 3.46410i | −0.209657 | − | 0.181568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.00000 | − | 6.92820i | 0.209083 | − | 0.362143i | ||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | 4.50000 | + | 7.79423i | 0.234579 | + | 0.406302i | ||||
\(369\) | 1.50000 | − | 2.59808i | 0.0780869 | − | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | − | 10.3923i | −0.623009 | − | 0.539542i | ||||
\(372\) | −10.0000 | −0.518476 | ||||||||
\(373\) | −1.00000 | + | 1.73205i | −0.0517780 | + | 0.0896822i | −0.890753 | − | 0.454488i | \(-0.849822\pi\) |
0.838975 | + | 0.544170i | \(0.183156\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.50000 | + | 2.59808i | −0.0773566 | + | 0.133986i | ||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 2.00000 | − | 10.3923i | 0.102869 | − | 0.534522i | ||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | + | 13.8564i | 0.409852 | + | 0.709885i | ||||
\(382\) | 7.50000 | + | 12.9904i | 0.383733 | + | 0.664646i | ||||
\(383\) | −4.50000 | + | 7.79423i | −0.229939 | + | 0.398266i | −0.957790 | − | 0.287469i | \(-0.907186\pi\) |
0.727851 | + | 0.685736i | \(0.240519\pi\) | |||||||
\(384\) | 2.00000 | 0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | 5.00000 | − | 8.66025i | 0.254164 | − | 0.440225i | ||||
\(388\) | −2.50000 | − | 4.33013i | −0.126918 | − | 0.219829i | ||||
\(389\) | 9.00000 | + | 15.5885i | 0.456318 | + | 0.790366i | 0.998763 | − | 0.0497253i | \(-0.0158346\pi\) |
−0.542445 | + | 0.840091i | \(0.682501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.0000 | 1.36545 | ||||||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.00000 | − | 15.5885i | 0.453413 | − | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00000 | + | 1.73205i | −0.0501886 | + | 0.0869291i | −0.890028 | − | 0.455905i | \(-0.849316\pi\) |
0.839840 | + | 0.542834i | \(0.182649\pi\) | |||||||
\(398\) | −17.0000 | −0.852133 | ||||||||
\(399\) | −40.0000 | + | 13.8564i | −2.00250 | + | 0.693688i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.00000 | + | 15.5885i | −0.449439 | + | 0.778450i | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | −2.00000 | − | 3.46410i | −0.0997509 | − | 0.172774i | ||||
\(403\) | −5.00000 | − | 8.66025i | −0.249068 | − | 0.431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00000 | + | 15.5885i | −0.148888 | + | 0.773642i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.00000 | − | 5.19615i | 0.148522 | − | 0.257248i | ||||
\(409\) | 3.50000 | + | 6.06218i | 0.173064 | + | 0.299755i | 0.939490 | − | 0.342578i | \(-0.111300\pi\) |
−0.766426 | + | 0.642333i | \(0.777967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.00000 | − | 15.5885i | 0.443937 | − | 0.768922i | ||||
\(412\) | 11.0000 | 0.541931 | ||||||||
\(413\) | −24.0000 | − | 20.7846i | −1.18096 | − | 1.02274i | ||||
\(414\) | 9.00000 | 0.442326 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | + | 1.73205i | 0.0490290 | + | 0.0849208i | ||||
\(417\) | 2.00000 | + | 3.46410i | 0.0979404 | + | 0.169638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0000 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | 1.00000 | − | 1.73205i | 0.0486792 | − | 0.0843149i | ||||
\(423\) | 1.50000 | + | 2.59808i | 0.0729325 | + | 0.126323i | ||||
\(424\) | 3.00000 | + | 5.19615i | 0.145693 | + | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −18.0000 | −0.872103 | ||||||||
\(427\) | 2.00000 | − | 10.3923i | 0.0967868 | − | 0.502919i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.50000 | + | 2.59808i | 0.0722525 | + | 0.125145i | 0.899888 | − | 0.436121i | \(-0.143648\pi\) |
−0.827636 | + | 0.561266i | \(0.810315\pi\) | |||||||
\(432\) | −2.00000 | + | 3.46410i | −0.0962250 | + | 0.166667i | ||||
\(433\) | 29.0000 | 1.39365 | 0.696826 | − | 0.717241i | \(-0.254595\pi\) | ||||
0.696826 | + | 0.717241i | \(0.254595\pi\) | |||||||
\(434\) | −12.5000 | + | 4.33013i | −0.600019 | + | 0.207853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | 36.0000 | + | 62.3538i | 1.72211 | + | 2.98279i | ||||
\(438\) | 10.0000 | + | 17.3205i | 0.477818 | + | 0.827606i | ||||
\(439\) | −11.5000 | + | 19.9186i | −0.548865 | + | 0.950662i | 0.449488 | + | 0.893287i | \(0.351607\pi\) |
−0.998353 | + | 0.0573756i | \(0.981727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 6.00000 | 0.285391 | ||||||||
\(443\) | 6.00000 | − | 10.3923i | 0.285069 | − | 0.493753i | −0.687557 | − | 0.726130i | \(-0.741317\pi\) |
0.972626 | + | 0.232377i | \(0.0746503\pi\) | |||||||
\(444\) | 8.00000 | + | 13.8564i | 0.379663 | + | 0.657596i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.5000 | − | 19.9186i | 0.544541 | − | 0.943172i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | −27.0000 | −1.27421 | −0.637104 | − | 0.770778i | \(-0.719868\pi\) | ||||
−0.637104 | + | 0.770778i | \(0.719868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.50000 | − | 12.9904i | −0.352770 | − | 0.611016i | ||||
\(453\) | −4.00000 | + | 6.92820i | −0.187936 | + | 0.325515i | ||||
\(454\) | −18.0000 | −0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.0000 | 0.749269 | ||||||||
\(457\) | 11.0000 | − | 19.0526i | 0.514558 | − | 0.891241i | −0.485299 | − | 0.874348i | \(-0.661289\pi\) |
0.999857 | − | 0.0168929i | \(-0.00537742\pi\) | |||||||
\(458\) | 10.0000 | + | 17.3205i | 0.467269 | + | 0.809334i | ||||
\(459\) | 6.00000 | + | 10.3923i | 0.280056 | + | 0.485071i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0000 | −1.11779 | −0.558896 | − | 0.829238i | \(-0.688775\pi\) | ||||
−0.558896 | + | 0.829238i | \(0.688775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.0000 | −1.16185 | −0.580924 | − | 0.813958i | \(-0.697309\pi\) | ||||
−0.580924 | + | 0.813958i | \(0.697309\pi\) | |||||||
\(464\) | 3.00000 | − | 5.19615i | 0.139272 | − | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | 3.00000 | − | 5.19615i | 0.138823 | − | 0.240449i | −0.788228 | − | 0.615383i | \(-0.789001\pi\) |
0.927052 | + | 0.374934i | \(0.122335\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −4.00000 | − | 3.46410i | −0.184703 | − | 0.159957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.00000 | − | 3.46410i | 0.0921551 | − | 0.159617i | ||||
\(472\) | 6.00000 | + | 10.3923i | 0.276172 | + | 0.478345i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.00000 | + | 8.66025i | −0.229658 | + | 0.397779i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.50000 | − | 7.79423i | 0.0687524 | − | 0.357248i | ||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 7.50000 | − | 12.9904i | 0.343042 | − | 0.594166i | ||||
\(479\) | 13.5000 | + | 23.3827i | 0.616831 | + | 1.06838i | 0.990060 | + | 0.140643i | \(0.0449170\pi\) |
−0.373230 | + | 0.927739i | \(0.621750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | 22.0000 | 1.00207 | ||||||||
\(483\) | 45.0000 | − | 15.5885i | 2.04757 | − | 0.709299i | ||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.00000 | + | 8.66025i | 0.226805 | + | 0.392837i | ||||
\(487\) | −5.50000 | − | 9.52628i | −0.249229 | − | 0.431677i | 0.714083 | − | 0.700061i | \(-0.246844\pi\) |
−0.963312 | + | 0.268384i | \(0.913510\pi\) | |||||||
\(488\) | −2.00000 | + | 3.46410i | −0.0905357 | + | 0.156813i | ||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.0000 | 1.89543 | 0.947717 | − | 0.319113i | \(-0.103385\pi\) | ||||
0.947717 | + | 0.319113i | \(0.103385\pi\) | |||||||
\(492\) | −3.00000 | + | 5.19615i | −0.135250 | + | 0.234261i | ||||
\(493\) | −9.00000 | − | 15.5885i | −0.405340 | − | 0.702069i | ||||
\(494\) | 8.00000 | + | 13.8564i | 0.359937 | + | 0.623429i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.00000 | 0.224507 | ||||||||
\(497\) | −22.5000 | + | 7.79423i | −1.00926 | + | 0.349619i | ||||
\(498\) | −12.0000 | −0.537733 | ||||||||
\(499\) | 17.0000 | − | 29.4449i | 0.761025 | − | 1.31813i | −0.181298 | − | 0.983428i | \(-0.558030\pi\) |
0.942323 | − | 0.334705i | \(-0.108637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0000 | + | 41.5692i | 1.07224 | + | 1.85718i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0.500000 | − | 2.59808i | 0.0222718 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | − | 15.5885i | −0.399704 | − | 0.692308i | ||||
\(508\) | −4.00000 | − | 6.92820i | −0.177471 | − | 0.307389i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | + | 17.3205i | 0.884748 | + | 0.766214i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −16.0000 | + | 27.7128i | −0.706417 | + | 1.22355i | ||||
\(514\) | 9.00000 | + | 15.5885i | 0.396973 | + | 0.687577i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10.0000 | + | 17.3205i | −0.440225 | + | 0.762493i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 16.0000 | + | 13.8564i | 0.703000 | + | 0.608816i | ||||
\(519\) | 24.0000 | 1.05348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50000 | + | 2.59808i | 0.0657162 | + | 0.113824i | 0.897011 | − | 0.442007i | \(-0.145733\pi\) |
−0.831295 | + | 0.555831i | \(0.812400\pi\) | |||||||
\(522\) | −3.00000 | − | 5.19615i | −0.131306 | − | 0.227429i | ||||
\(523\) | 17.0000 | − | 29.4449i | 0.743358 | − | 1.28753i | −0.207600 | − | 0.978214i | \(-0.566565\pi\) |
0.950958 | − | 0.309320i | \(-0.100101\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.00000 | −0.392419 | ||||||||
\(527\) | 7.50000 | − | 12.9904i | 0.326705 | − | 0.565870i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.0000 | − | 50.2295i | −1.26087 | − | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 20.0000 | − | 6.92820i | 0.867110 | − | 0.300376i | ||||
\(533\) | −6.00000 | −0.259889 | ||||||||
\(534\) | −3.00000 | + | 5.19615i | −0.129823 | + | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | 24.0000 | − | 41.5692i | 1.03568 | − | 1.79384i | ||||
\(538\) | 30.0000 | 1.29339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | 5.50000 | + | 9.52628i | 0.236245 | + | 0.409189i | ||||
\(543\) | 20.0000 | + | 34.6410i | 0.858282 | + | 1.48659i | ||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.0000 | − | 3.46410i | 0.427960 | − | 0.148250i | ||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | −4.50000 | + | 7.79423i | −0.192230 | + | 0.332953i | ||||
\(549\) | 2.00000 | + | 3.46410i | 0.0853579 | + | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0000 | − | 41.5692i | 1.02243 | − | 1.77091i | ||||
\(552\) | −18.0000 | −0.766131 | ||||||||
\(553\) | −2.50000 | + | 12.9904i | −0.106311 | + | 0.552407i | ||||
\(554\) | 4.00000 | 0.169944 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | − | 1.73205i | −0.0424094 | − | 0.0734553i | ||||
\(557\) | −12.0000 | − | 20.7846i | −0.508456 | − | 0.880672i | −0.999952 | − | 0.00979220i | \(-0.996883\pi\) |
0.491496 | − | 0.870880i | \(-0.336450\pi\) | |||||||
\(558\) | 2.50000 | − | 4.33013i | 0.105833 | − | 0.183309i | ||||
\(559\) | −20.0000 | −0.845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.50000 | − | 2.59808i | 0.0632737 | − | 0.109593i | ||||
\(563\) | 3.00000 | + | 5.19615i | 0.126435 | + | 0.218992i | 0.922293 | − | 0.386492i | \(-0.126313\pi\) |
−0.795858 | + | 0.605483i | \(0.792980\pi\) | |||||||
\(564\) | −3.00000 | − | 5.19615i | −0.126323 | − | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.00000 | −0.0840663 | ||||||||
\(567\) | 22.0000 | + | 19.0526i | 0.923913 | + | 0.800132i | ||||
\(568\) | 9.00000 | 0.377632 | ||||||||
\(569\) | 1.50000 | − | 2.59808i | 0.0628833 | − | 0.108917i | −0.832870 | − | 0.553469i | \(-0.813304\pi\) |
0.895753 | + | 0.444552i | \(0.146637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.0000 | −1.25327 | ||||||||
\(574\) | −1.50000 | + | 7.79423i | −0.0626088 | + | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 17.0000 | + | 29.4449i | 0.707719 | + | 1.22581i | 0.965701 | + | 0.259656i | \(0.0836092\pi\) |
−0.257982 | + | 0.966150i | \(0.583058\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | 5.00000 | − | 8.66025i | 0.207793 | − | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | + | 5.19615i | −0.622305 | + | 0.215573i | ||||
\(582\) | 10.0000 | 0.414513 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.00000 | − | 8.66025i | −0.206901 | − | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.00000 | − | 5.19615i | 0.123929 | − | 0.214651i | ||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | −2.00000 | − | 13.8564i | −0.0824786 | − | 0.571429i | ||||
\(589\) | 40.0000 | 1.64817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | + | 31.1769i | 0.740421 | + | 1.28245i | ||||
\(592\) | −4.00000 | − | 6.92820i | −0.164399 | − | 0.284747i | ||||
\(593\) | −1.50000 | + | 2.59808i | −0.0615976 | + | 0.106690i | −0.895180 | − | 0.445705i | \(-0.852953\pi\) |
0.833582 | + | 0.552396i | \(0.186286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.0000 | − | 29.4449i | 0.695764 | − | 1.20510i | ||||
\(598\) | −9.00000 | − | 15.5885i | −0.368037 | − | 0.637459i | ||||
\(599\) | −10.5000 | − | 18.1865i | −0.429018 | − | 0.743082i | 0.567768 | − | 0.823189i | \(-0.307807\pi\) |
−0.996786 | + | 0.0801071i | \(0.974474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | −5.00000 | + | 25.9808i | −0.203785 | + | 1.05890i | ||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 2.00000 | − | 3.46410i | 0.0813788 | − | 0.140952i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5000 | − | 21.6506i | 0.507359 | − | 0.878772i | −0.492604 | − | 0.870253i | \(-0.663955\pi\) |
0.999964 | − | 0.00851879i | \(-0.00271165\pi\) | |||||||
\(608\) | −8.00000 | −0.324443 | ||||||||
\(609\) | −24.0000 | − | 20.7846i | −0.972529 | − | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | − | 5.19615i | 0.121367 | − | 0.210214i | ||||
\(612\) | 1.50000 | + | 2.59808i | 0.0606339 | + | 0.105021i | ||||
\(613\) | −1.00000 | − | 1.73205i | −0.0403896 | − | 0.0699569i | 0.845124 | − | 0.534570i | \(-0.179527\pi\) |
−0.885514 | + | 0.464614i | \(0.846193\pi\) | |||||||
\(614\) | −8.00000 | + | 13.8564i | −0.322854 | + | 0.559199i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0000 | 0.603877 | 0.301939 | − | 0.953327i | \(-0.402366\pi\) | ||||
0.301939 | + | 0.953327i | \(0.402366\pi\) | |||||||
\(618\) | −11.0000 | + | 19.0526i | −0.442485 | + | 0.766406i | ||||
\(619\) | 5.00000 | + | 8.66025i | 0.200967 | + | 0.348085i | 0.948840 | − | 0.315757i | \(-0.102258\pi\) |
−0.747873 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0000 | − | 31.1769i | 0.722315 | − | 1.25109i | ||||
\(622\) | −21.0000 | −0.842023 | ||||||||
\(623\) | −1.50000 | + | 7.79423i | −0.0600962 | + | 0.312269i | ||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.50000 | + | 14.7224i | 0.339728 | + | 0.588427i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | + | 1.73205i | −0.0399043 | + | 0.0691164i | ||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0000 | −0.756378 | −0.378189 | − | 0.925728i | \(-0.623453\pi\) | ||||
−0.378189 | + | 0.925728i | \(0.623453\pi\) | |||||||
\(632\) | 2.50000 | − | 4.33013i | 0.0994447 | − | 0.172243i | ||||
\(633\) | 2.00000 | + | 3.46410i | 0.0794929 | + | 0.137686i | ||||
\(634\) | −6.00000 | − | 10.3923i | −0.238290 | − | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.0000 | −0.475831 | ||||||||
\(637\) | 11.0000 | − | 8.66025i | 0.435836 | − | 0.343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.50000 | − | 7.79423i | 0.178017 | − | 0.308335i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.5000 | − | 38.9711i | −0.888697 | − | 1.53927i | −0.841417 | − | 0.540386i | \(-0.818278\pi\) |
−0.0472793 | − | 0.998882i | \(-0.515055\pi\) | |||||||
\(642\) | −12.0000 | + | 20.7846i | −0.473602 | + | 0.820303i | ||||
\(643\) | 20.0000 | 0.788723 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(644\) | −22.5000 | + | 7.79423i | −0.886624 | + | 0.307136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | + | 20.7846i | −0.472134 | + | 0.817760i | ||||
\(647\) | −12.0000 | − | 20.7846i | −0.471769 | − | 0.817127i | 0.527710 | − | 0.849425i | \(-0.323051\pi\) |
−0.999478 | + | 0.0322975i | \(0.989718\pi\) | |||||||
\(648\) | −5.50000 | − | 9.52628i | −0.216060 | − | 0.374228i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.00000 | − | 25.9808i | 0.195965 | − | 1.01827i | ||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 10.0000 | + | 17.3205i | 0.391031 | + | 0.677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.50000 | − | 2.59808i | 0.0585652 | − | 0.101438i | ||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | −6.00000 | − | 5.19615i | −0.233904 | − | 0.202567i | ||||
\(659\) | 30.0000 | 1.16863 | 0.584317 | − | 0.811525i | \(-0.301362\pi\) | ||||
0.584317 | + | 0.811525i | \(0.301362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.00000 | + | 13.8564i | 0.311164 | + | 0.538952i | 0.978615 | − | 0.205702i | \(-0.0659478\pi\) |
−0.667451 | + | 0.744654i | \(0.732615\pi\) | |||||||
\(662\) | 7.00000 | + | 12.1244i | 0.272063 | + | 0.471226i | ||||
\(663\) | −6.00000 | + | 10.3923i | −0.233021 | + | 0.403604i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | −27.0000 | + | 46.7654i | −1.04544 | + | 1.81076i | ||||
\(668\) | −12.0000 | − | 20.7846i | −0.464294 | − | 0.804181i | ||||
\(669\) | 23.0000 | + | 39.8372i | 0.889231 | + | 1.54019i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.00000 | + | 5.19615i | −0.0385758 | + | 0.200446i | ||||
\(673\) | 5.00000 | 0.192736 | 0.0963679 | − | 0.995346i | \(-0.469277\pi\) | ||||
0.0963679 | + | 0.995346i | \(0.469277\pi\) | |||||||
\(674\) | −6.50000 | + | 11.2583i | −0.250371 | + | 0.433655i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | −21.0000 | + | 36.3731i | −0.807096 | + | 1.39793i | 0.107772 | + | 0.994176i | \(0.465628\pi\) |
−0.914867 | + | 0.403755i | \(0.867705\pi\) | |||||||
\(678\) | 30.0000 | 1.15214 | ||||||||
\(679\) | 12.5000 | − | 4.33013i | 0.479706 | − | 0.166175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.0000 | − | 31.1769i | 0.689761 | − | 1.19470i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0000 | + | 25.9808i | 0.573959 | + | 0.994126i | 0.996154 | + | 0.0876211i | \(0.0279265\pi\) |
−0.422195 | + | 0.906505i | \(0.638740\pi\) | |||||||
\(684\) | −4.00000 | + | 6.92820i | −0.152944 | + | 0.264906i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | −40.0000 | −1.52610 | ||||||||
\(688\) | 5.00000 | − | 8.66025i | 0.190623 | − | 0.330169i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0000 | + | 43.3013i | −0.951045 | + | 1.64726i | −0.207875 | + | 0.978155i | \(0.566655\pi\) |
−0.743170 | + | 0.669102i | \(0.766679\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.00000 | + | 10.3923i | 0.227429 | + | 0.393919i | ||||
\(697\) | −4.50000 | − | 7.79423i | −0.170450 | − | 0.295227i | ||||
\(698\) | 13.0000 | − | 22.5167i | 0.492057 | − | 0.852268i | ||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.0000 | −1.35970 | −0.679851 | − | 0.733351i | \(-0.737955\pi\) | ||||
−0.679851 | + | 0.733351i | \(0.737955\pi\) | |||||||
\(702\) | 4.00000 | − | 6.92820i | 0.150970 | − | 0.261488i | ||||
\(703\) | −32.0000 | − | 55.4256i | −1.20690 | − | 2.09042i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.00000 | 0.338719 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −24.0000 | −0.901975 | ||||||||
\(709\) | 2.00000 | − | 3.46410i | 0.0751116 | − | 0.130097i | −0.826023 | − | 0.563636i | \(-0.809402\pi\) |
0.901135 | + | 0.433539i | \(0.142735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | − | 4.33013i | −0.0937573 | − | 0.162392i | ||||
\(712\) | 1.50000 | − | 2.59808i | 0.0562149 | − | 0.0973670i | ||||
\(713\) | −45.0000 | −1.68526 | ||||||||
\(714\) | 12.0000 | + | 10.3923i | 0.449089 | + | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | + | 20.7846i | −0.448461 | + | 0.776757i | ||||
\(717\) | 15.0000 | + | 25.9808i | 0.560185 | + | 0.970269i | ||||
\(718\) | −12.0000 | − | 20.7846i | −0.447836 | − | 0.775675i | ||||
\(719\) | 7.50000 | − | 12.9904i | 0.279703 | − | 0.484459i | −0.691608 | − | 0.722273i | \(-0.743097\pi\) |
0.971311 | + | 0.237814i | \(0.0764307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.50000 | + | 28.5788i | −0.204831 | + | 1.06433i | ||||
\(722\) | −45.0000 | −1.67473 | ||||||||
\(723\) | −22.0000 | + | 38.1051i | −0.818189 | + | 1.41714i | ||||
\(724\) | −10.0000 | − | 17.3205i | −0.371647 | − | 0.643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.0000 | − | 19.0526i | 0.408248 | − | 0.707107i | ||||
\(727\) | −31.0000 | −1.14973 | −0.574863 | − | 0.818250i | \(-0.694945\pi\) | ||||
−0.574863 | + | 0.818250i | \(0.694945\pi\) | |||||||
\(728\) | −5.00000 | + | 1.73205i | −0.185312 | + | 0.0641941i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.0000 | − | 25.9808i | −0.554795 | − | 0.960933i | ||||
\(732\) | −4.00000 | − | 6.92820i | −0.147844 | − | 0.256074i | ||||
\(733\) | 17.0000 | − | 29.4449i | 0.627909 | − | 1.08757i | −0.360061 | − | 0.932929i | \(-0.617244\pi\) |
0.987971 | − | 0.154642i | \(-0.0494225\pi\) | |||||||
\(734\) | −8.00000 | −0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.00000 | 0.331744 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.50000 | − | 2.59808i | −0.0552158 | − | 0.0956365i | ||||
\(739\) | −4.00000 | − | 6.92820i | −0.147142 | − | 0.254858i | 0.783028 | − | 0.621987i | \(-0.213674\pi\) |
−0.930170 | + | 0.367129i | \(0.880341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32.0000 | −1.17555 | ||||||||
\(742\) | −15.0000 | + | 5.19615i | −0.550667 | + | 0.190757i | ||||
\(743\) | 33.0000 | 1.21065 | 0.605326 | − | 0.795977i | \(-0.293043\pi\) | ||||
0.605326 | + | 0.795977i | \(0.293043\pi\) | |||||||
\(744\) | −5.00000 | + | 8.66025i | −0.183309 | + | 0.317500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.00000 | + | 1.73205i | 0.0366126 | + | 0.0634149i | ||||
\(747\) | 3.00000 | − | 5.19615i | 0.109764 | − | 0.190117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | + | 31.1769i | −0.219235 | + | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | − | 13.8564i | 0.291924 | − | 0.505627i | −0.682341 | − | 0.731034i | \(-0.739038\pi\) |
0.974265 | + | 0.225407i | \(0.0723712\pi\) | |||||||
\(752\) | 1.50000 | + | 2.59808i | 0.0546994 | + | 0.0947421i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.00000 | + | 10.3923i | −0.218507 | + | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.00000 | − | 6.92820i | −0.290957 | − | 0.251976i | ||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 4.00000 | − | 6.92820i | 0.145287 | − | 0.251644i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5000 | + | 38.9711i | −0.815624 | + | 1.41270i | 0.0932544 | + | 0.995642i | \(0.470273\pi\) |
−0.908879 | + | 0.417061i | \(0.863060\pi\) | |||||||
\(762\) | 16.0000 | 0.579619 | ||||||||
\(763\) | 20.0000 | + | 17.3205i | 0.724049 | + | 0.627044i | ||||
\(764\) | 15.0000 | 0.542681 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.50000 | + | 7.79423i | 0.162592 | + | 0.281617i | ||||
\(767\) | −12.0000 | − | 20.7846i | −0.433295 | − | 0.750489i | ||||
\(768\) | 1.00000 | − | 1.73205i | 0.0360844 | − | 0.0625000i | ||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.0000 | −1.29651 | ||||||||
\(772\) | −2.50000 | + | 4.33013i | −0.0899770 | + | 0.155845i | ||||
\(773\) | 6.00000 | + | 10.3923i | 0.215805 | + | 0.373785i | 0.953521 | − | 0.301326i | \(-0.0974291\pi\) |
−0.737716 | + | 0.675111i | \(0.764096\pi\) | |||||||
\(774\) | −5.00000 | − | 8.66025i | −0.179721 | − | 0.311286i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.00000 | −0.179490 | ||||||||
\(777\) | −40.0000 | + | 13.8564i | −1.43499 | + | 0.497096i | ||||
\(778\) | 18.0000 | 0.645331 | ||||||||
\(779\) | 12.0000 | − | 20.7846i | 0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 13.5000 | − | 23.3827i | 0.482759 | − | 0.836163i | ||||
\(783\) | −24.0000 | −0.857690 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.00000 | + | 13.8564i | 0.285169 | + | 0.493928i | 0.972650 | − | 0.232275i | \(-0.0746169\pi\) |
−0.687481 | + | 0.726202i | \(0.741284\pi\) | |||||||
\(788\) | −9.00000 | − | 15.5885i | −0.320612 | − | 0.555316i | ||||
\(789\) | 9.00000 | − | 15.5885i | 0.320408 | − | 0.554964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.5000 | − | 12.9904i | 1.33335 | − | 0.461885i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | − | 6.92820i | 0.142044 | − | 0.246028i | ||||
\(794\) | 1.00000 | + | 1.73205i | 0.0354887 | + | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.50000 | + | 14.7224i | −0.301275 | + | 0.521823i | ||||
\(797\) | −12.0000 | −0.425062 | −0.212531 | − | 0.977154i | \(-0.568171\pi\) | ||||
−0.212531 | + | 0.977154i | \(0.568171\pi\) | |||||||
\(798\) | −8.00000 | + | 41.5692i | −0.283197 | + | 1.47153i | ||||
\(799\) | 9.00000 | 0.318397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.50000 | − | 2.59808i | −0.0529999 | − | 0.0917985i | ||||
\(802\) | 9.00000 | + | 15.5885i | 0.317801 | + | 0.550448i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.0000 | −0.352235 | ||||||||
\(807\) | −30.0000 | + | 51.9615i | −1.05605 | + | 1.82913i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.0000 | + | 25.9808i | 0.527372 | + | 0.913435i | 0.999491 | + | 0.0319002i | \(0.0101559\pi\) |
−0.472119 | + | 0.881535i | \(0.656511\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.0000 | 0.912983 | 0.456492 | − | 0.889728i | \(-0.349106\pi\) | ||||
0.456492 | + | 0.889728i | \(0.349106\pi\) | |||||||
\(812\) | 12.0000 | + | 10.3923i | 0.421117 | + | 0.364698i | ||||
\(813\) | −22.0000 | −0.771574 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.00000 | − | 5.19615i | −0.105021 | − | 0.181902i | ||||
\(817\) | 40.0000 | − | 69.2820i | 1.39942 | − | 2.42387i | ||||
\(818\) | 7.00000 | 0.244749 | ||||||||
\(819\) | −1.00000 | + | 5.19615i | −0.0349428 | + | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | − | 10.3923i | 0.209401 | − | 0.362694i | −0.742125 | − | 0.670262i | \(-0.766182\pi\) |
0.951526 | + | 0.307568i | \(0.0995151\pi\) | |||||||
\(822\) | −9.00000 | − | 15.5885i | −0.313911 | − | 0.543710i | ||||
\(823\) | −10.0000 | − | 17.3205i | −0.348578 | − | 0.603755i | 0.637419 | − | 0.770517i | \(-0.280002\pi\) |
−0.985997 | + | 0.166762i | \(0.946669\pi\) | |||||||
\(824\) | 5.50000 | − | 9.52628i | 0.191602 | − | 0.331864i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.0000 | + | 10.3923i | −1.04383 | + | 0.361595i | ||||
\(827\) | −18.0000 | −0.625921 | −0.312961 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312961 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(828\) | 4.50000 | − | 7.79423i | 0.156386 | − | 0.270868i | ||||
\(829\) | −22.0000 | − | 38.1051i | −0.764092 | − | 1.32345i | −0.940726 | − | 0.339169i | \(-0.889854\pi\) |
0.176634 | − | 0.984277i | \(-0.443479\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | + | 6.92820i | −0.138758 | + | 0.240337i | ||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | 19.5000 | + | 7.79423i | 0.675635 | + | 0.270054i | ||||
\(834\) | 4.00000 | 0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0000 | − | 17.3205i | −0.345651 | − | 0.598684i | ||||
\(838\) | −15.0000 | + | 25.9808i | −0.518166 | + | 0.897491i | ||||
\(839\) | −33.0000 | −1.13929 | −0.569643 | − | 0.821892i | \(-0.692919\pi\) | ||||
−0.569643 | + | 0.821892i | \(0.692919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −2.00000 | + | 3.46410i | −0.0689246 | + | 0.119381i | ||||
\(843\) | 3.00000 | + | 5.19615i | 0.103325 | + | 0.178965i | ||||
\(844\) | −1.00000 | − | 1.73205i | −0.0344214 | − | 0.0596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | 5.50000 | − | 28.5788i | 0.188982 | − | 0.981981i | ||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 2.00000 | − | 3.46410i | 0.0686398 | − | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.0000 | + | 62.3538i | 1.23406 | + | 2.13746i | ||||
\(852\) | −9.00000 | + | 15.5885i | −0.308335 | + | 0.534052i | ||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | −8.00000 | − | 6.92820i | −0.273754 | − | 0.237078i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | − | 10.3923i | 0.205076 | − | 0.355202i | ||||
\(857\) | −27.0000 | − | 46.7654i | −0.922302 | − | 1.59747i | −0.795843 | − | 0.605503i | \(-0.792972\pi\) |
−0.126459 | − | 0.991972i | \(-0.540361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | − | 34.6410i | 0.682391 | − | 1.18194i | −0.291858 | − | 0.956462i | \(-0.594273\pi\) |
0.974249 | − | 0.225475i | \(-0.0723932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | − | 10.3923i | −0.408959 | − | 0.354169i | ||||
\(862\) | 3.00000 | 0.102180 | ||||||||
\(863\) | −10.5000 | + | 18.1865i | −0.357424 | + | 0.619077i | −0.987530 | − | 0.157433i | \(-0.949678\pi\) |
0.630106 | + | 0.776509i | \(0.283012\pi\) | |||||||
\(864\) | 2.00000 | + | 3.46410i | 0.0680414 | + | 0.117851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.5000 | − | 25.1147i | 0.492730 | − | 0.853433i | ||||
\(867\) | 16.0000 | 0.543388 | ||||||||
\(868\) | −2.50000 | + | 12.9904i | −0.0848555 | + | 0.440922i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00000 | − | 3.46410i | −0.0677674 | − | 0.117377i | ||||
\(872\) | −5.00000 | − | 8.66025i | −0.169321 | − | 0.293273i | ||||
\(873\) | −2.50000 | + | 4.33013i | −0.0846122 | + | 0.146553i | ||||
\(874\) | 72.0000 | 2.43544 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.0000 | 0.675737 | ||||||||
\(877\) | 8.00000 | − | 13.8564i | 0.270141 | − | 0.467898i | −0.698757 | − | 0.715359i | \(-0.746263\pi\) |
0.968898 | + | 0.247462i | \(0.0795964\pi\) | |||||||
\(878\) | 11.5000 | + | 19.9186i | 0.388106 | + | 0.672220i | ||||
\(879\) | 6.00000 | + | 10.3923i | 0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.0000 | 0.909653 | 0.454827 | − | 0.890580i | \(-0.349701\pi\) | ||||
0.454827 | + | 0.890580i | \(0.349701\pi\) | |||||||
\(882\) | 6.50000 | + | 2.59808i | 0.218866 | + | 0.0874818i | ||||
\(883\) | 26.0000 | 0.874970 | 0.437485 | − | 0.899226i | \(-0.355869\pi\) | ||||
0.437485 | + | 0.899226i | \(0.355869\pi\) | |||||||
\(884\) | 3.00000 | − | 5.19615i | 0.100901 | − | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | − | 10.3923i | −0.201574 | − | 0.349136i | ||||
\(887\) | −18.0000 | + | 31.1769i | −0.604381 | + | 1.04682i | 0.387768 | + | 0.921757i | \(0.373246\pi\) |
−0.992149 | + | 0.125061i | \(0.960087\pi\) | |||||||
\(888\) | 16.0000 | 0.536925 | ||||||||
\(889\) | 20.0000 | − | 6.92820i | 0.670778 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.5000 | − | 19.9186i | −0.385048 | − | 0.666924i | ||||
\(893\) | 12.0000 | + | 20.7846i | 0.401565 | + | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | − | 2.59808i | 0.0167038 | − | 0.0867956i | ||||
\(897\) | 36.0000 | 1.20201 | ||||||||
\(898\) | −13.5000 | + | 23.3827i | −0.450501 | + | 0.780290i | ||||
\(899\) | 15.0000 | + | 25.9808i | 0.500278 | + | 0.866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | − | 15.5885i | 0.299833 | − | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −40.0000 | − | 34.6410i | −1.33112 | − | 1.15278i | ||||
\(904\) | −15.0000 | −0.498893 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.00000 | + | 6.92820i | 0.132891 | + | 0.230174i | ||||
\(907\) | 20.0000 | + | 34.6410i | 0.664089 | + | 1.15024i | 0.979531 | + | 0.201291i | \(0.0645138\pi\) |
−0.315442 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(908\) | −9.00000 | + | 15.5885i | −0.298675 | + | 0.517321i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.00000 | 0.0993944 | 0.0496972 | − | 0.998764i | \(-0.484174\pi\) | ||||
0.0496972 | + | 0.998764i | \(0.484174\pi\) | |||||||
\(912\) | 8.00000 | − | 13.8564i | 0.264906 | − | 0.458831i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −11.0000 | − | 19.0526i | −0.363848 | − | 0.630203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.0000 | 0.396059 | ||||||||
\(919\) | −5.50000 | + | 9.52628i | −0.181428 | + | 0.314243i | −0.942367 | − | 0.334581i | \(-0.891405\pi\) |
0.760939 | + | 0.648824i | \(0.224739\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0000 | − | 27.7128i | −0.527218 | − | 0.913168i | ||||
\(922\) | −12.0000 | + | 20.7846i | −0.395199 | + | 0.684505i | ||||
\(923\) | −18.0000 | −0.592477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.5000 | + | 21.6506i | −0.410775 | + | 0.711484i | ||||
\(927\) | −5.50000 | − | 9.52628i | −0.180644 | − | 0.312884i | ||||
\(928\) | −3.00000 | − | 5.19615i | −0.0984798 | − | 0.170572i | ||||
\(929\) | −21.0000 | + | 36.3731i | −0.688988 | + | 1.19336i | 0.283178 | + | 0.959067i | \(0.408611\pi\) |
−0.972166 | + | 0.234294i | \(0.924722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00000 | + | 55.4256i | 0.262189 | + | 1.81650i | ||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 21.0000 | − | 36.3731i | 0.687509 | − | 1.19080i | ||||
\(934\) | −3.00000 | − | 5.19615i | −0.0981630 | − | 0.170023i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.00000 | − | 1.73205i | 0.0326860 | − | 0.0566139i | ||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | −5.00000 | + | 1.73205i | −0.163256 | + | 0.0565535i | ||||
\(939\) | −34.0000 | −1.10955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00000 | + | 5.19615i | 0.0977972 | + | 0.169390i | 0.910773 | − | 0.412908i | \(-0.135487\pi\) |
−0.812975 | + | 0.582298i | \(0.802154\pi\) | |||||||
\(942\) | −2.00000 | − | 3.46410i | −0.0651635 | − | 0.112867i | ||||
\(943\) | −13.5000 | + | 23.3827i | −0.439620 | + | 0.761445i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.00000 | − | 10.3923i | 0.194974 | − | 0.337705i | −0.751918 | − | 0.659256i | \(-0.770871\pi\) |
0.946892 | + | 0.321552i | \(0.104204\pi\) | |||||||
\(948\) | 5.00000 | + | 8.66025i | 0.162392 | + | 0.281272i | ||||
\(949\) | 10.0000 | + | 17.3205i | 0.324614 | + | 0.562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.0000 | 0.778253 | ||||||||
\(952\) | −6.00000 | − | 5.19615i | −0.194461 | − | 0.168408i | ||||
\(953\) | 54.0000 | 1.74923 | 0.874616 | − | 0.484817i | \(-0.161114\pi\) | ||||
0.874616 | + | 0.484817i | \(0.161114\pi\) | |||||||
\(954\) | 3.00000 | − | 5.19615i | 0.0971286 | − | 0.168232i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.50000 | − | 12.9904i | −0.242567 | − | 0.420139i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.0000 | 0.872330 | ||||||||
\(959\) | −18.0000 | − | 15.5885i | −0.581250 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 8.00000 | + | 13.8564i | 0.257930 | + | 0.446748i | ||||
\(963\) | −6.00000 | − | 10.3923i | −0.193347 | − | 0.334887i | ||||
\(964\) | 11.0000 | − | 19.0526i | 0.354286 | − | 0.613642i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.00000 | − | 46.7654i | 0.289570 | − | 1.50465i | ||||
\(967\) | −7.00000 | −0.225105 | −0.112552 | − | 0.993646i | \(-0.535903\pi\) | ||||
−0.112552 | + | 0.993646i | \(0.535903\pi\) | |||||||
\(968\) | −5.50000 | + | 9.52628i | −0.176777 | + | 0.306186i | ||||
\(969\) | −24.0000 | − | 41.5692i | −0.770991 | − | 1.33540i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0000 | + | 25.9808i | −0.481373 | + | 0.833762i | −0.999771 | − | 0.0213768i | \(-0.993195\pi\) |
0.518399 | + | 0.855139i | \(0.326528\pi\) | |||||||
\(972\) | 10.0000 | 0.320750 | ||||||||
\(973\) | 5.00000 | − | 1.73205i | 0.160293 | − | 0.0555270i | ||||
\(974\) | −11.0000 | −0.352463 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | + | 3.46410i | 0.0640184 | + | 0.110883i | ||||
\(977\) | 25.5000 | + | 44.1673i | 0.815817 | + | 1.41304i | 0.908740 | + | 0.417364i | \(0.137046\pi\) |
−0.0929223 | + | 0.995673i | \(0.529621\pi\) | |||||||
\(978\) | −8.00000 | + | 13.8564i | −0.255812 | + | 0.443079i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | 21.0000 | − | 36.3731i | 0.670137 | − | 1.16071i | ||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 3.00000 | + | 5.19615i | 0.0956365 | + | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.0000 | −0.573237 | ||||||||
\(987\) | 15.0000 | − | 5.19615i | 0.477455 | − | 0.165395i | ||||
\(988\) | 16.0000 | 0.509028 | ||||||||
\(989\) | −45.0000 | + | 77.9423i | −1.43092 | + | 2.47842i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.5000 | − | 25.1147i | −0.460608 | − | 0.797796i | 0.538384 | − | 0.842700i | \(-0.319035\pi\) |
−0.998991 | + | 0.0449040i | \(0.985702\pi\) | |||||||
\(992\) | 2.50000 | − | 4.33013i | 0.0793751 | − | 0.137482i | ||||
\(993\) | −28.0000 | −0.888553 | ||||||||
\(994\) | −4.50000 | + | 23.3827i | −0.142731 | + | 0.741654i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | + | 10.3923i | −0.190117 | + | 0.329293i | ||||
\(997\) | 2.00000 | + | 3.46410i | 0.0633406 | + | 0.109709i | 0.895957 | − | 0.444141i | \(-0.146491\pi\) |
−0.832616 | + | 0.553851i | \(0.813158\pi\) | |||||||
\(998\) | −17.0000 | − | 29.4449i | −0.538126 | − | 0.932061i | ||||
\(999\) | −16.0000 | + | 27.7128i | −0.506218 | + | 0.876795i |
(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 | 350.2.e.k.51.1 | yes | 2 | |
5.2 | odd | 4 | 350.2.j.e.149.2 | 4 | |||
5.3 | odd | 4 | 350.2.j.e.149.1 | 4 | |||
5.4 | even | 2 | 350.2.e.a.51.1 | ✓ | 2 | ||
7.2 | even | 3 | 2450.2.a.e.1.1 | 1 | |||
7.4 | even | 3 | inner | 350.2.e.k.151.1 | yes | 2 | |
7.5 | odd | 6 | 2450.2.a.o.1.1 | 1 | |||
35.2 | odd | 12 | 2450.2.c.o.99.1 | 2 | |||
35.4 | even | 6 | 350.2.e.a.151.1 | yes | 2 | ||
35.9 | even | 6 | 2450.2.a.be.1.1 | 1 | |||
35.12 | even | 12 | 2450.2.c.d.99.1 | 2 | |||
35.18 | odd | 12 | 350.2.j.e.249.2 | 4 | |||
35.19 | odd | 6 | 2450.2.a.u.1.1 | 1 | |||
35.23 | odd | 12 | 2450.2.c.o.99.2 | 2 | |||
35.32 | odd | 12 | 350.2.j.e.249.1 | 4 | |||
35.33 | even | 12 | 2450.2.c.d.99.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.e.a.51.1 | ✓ | 2 | 5.4 | even | 2 | ||
350.2.e.a.151.1 | yes | 2 | 35.4 | even | 6 | ||
350.2.e.k.51.1 | yes | 2 | 1.1 | even | 1 | trivial | |
350.2.e.k.151.1 | yes | 2 | 7.4 | even | 3 | inner | |
350.2.j.e.149.1 | 4 | 5.3 | odd | 4 | |||
350.2.j.e.149.2 | 4 | 5.2 | odd | 4 | |||
350.2.j.e.249.1 | 4 | 35.32 | odd | 12 | |||
350.2.j.e.249.2 | 4 | 35.18 | odd | 12 | |||
2450.2.a.e.1.1 | 1 | 7.2 | even | 3 | |||
2450.2.a.o.1.1 | 1 | 7.5 | odd | 6 | |||
2450.2.a.u.1.1 | 1 | 35.19 | odd | 6 | |||
2450.2.a.be.1.1 | 1 | 35.9 | even | 6 | |||
2450.2.c.d.99.1 | 2 | 35.12 | even | 12 | |||
2450.2.c.d.99.2 | 2 | 35.33 | even | 12 | |||
2450.2.c.o.99.1 | 2 | 35.2 | odd | 12 | |||
2450.2.c.o.99.2 | 2 | 35.23 | odd | 12 |