Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(26,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
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: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.101 |
Dual form | 525.2.t.e.26.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50000 | − | 0.866025i | 1.06066 | − | 0.612372i | 0.135045 | − | 0.990839i | \(-0.456882\pi\) |
0.925615 | + | 0.378467i | \(0.123549\pi\) | |||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.50000 | − | 2.59808i | 0.612372 | − | 1.06066i | ||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | − | 1.73205i | −0.904534 | − | 0.522233i | −0.0258656 | − | 0.999665i | \(-0.508234\pi\) |
−0.878668 | + | 0.477432i | \(0.841568\pi\) | |||||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 3.00000 | − | 3.46410i | 0.801784 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.50000 | + | 4.33013i | 0.625000 | + | 1.08253i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | − | 5.19615i | − | 1.22474i | ||||||
\(19\) | −6.00000 | + | 3.46410i | −1.37649 | + | 0.794719i | −0.991736 | − | 0.128298i | \(-0.959049\pi\) |
−0.384759 | + | 0.923017i | \(0.625715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | − | 3.46410i | 0.654654 | − | 0.755929i | ||||
\(22\) | −6.00000 | −1.27920 | ||||||||
\(23\) | −1.50000 | + | 0.866025i | −0.312772 | + | 0.180579i | −0.648166 | − | 0.761499i | \(-0.724464\pi\) |
0.335394 | + | 0.942078i | \(0.391130\pi\) | |||||||
\(24\) | 1.50000 | + | 2.59808i | 0.306186 | + | 0.530330i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.00000 | + | 5.19615i | 0.588348 | + | 1.01905i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0.500000 | − | 2.59808i | 0.0944911 | − | 0.490990i | ||||
\(29\) | 1.73205i | 0.321634i | 0.986984 | + | 0.160817i | \(0.0514129\pi\) | ||||
−0.986984 | + | 0.160817i | \(0.948587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | − | 1.73205i | −0.538816 | − | 0.311086i | 0.205783 | − | 0.978598i | \(-0.434026\pi\) |
−0.744599 | + | 0.667512i | \(0.767359\pi\) | |||||||
\(32\) | 4.50000 | + | 2.59808i | 0.795495 | + | 0.459279i | ||||
\(33\) | −6.00000 | −1.04447 | ||||||||
\(34\) | − | 10.3923i | − | 1.78227i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | − | 2.59808i | −0.250000 | − | 0.433013i | ||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | −6.00000 | + | 10.3923i | −0.973329 | + | 1.68585i | ||||
\(39\) | 3.00000 | + | 5.19615i | 0.480384 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 1.50000 | − | 7.79423i | 0.231455 | − | 1.20268i | ||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | −3.00000 | + | 1.73205i | −0.452267 | + | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 7.50000 | + | 4.33013i | 1.08253 | + | 0.625000i | ||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 10.3923i | − | 1.45521i | ||||||
\(52\) | 3.00000 | + | 1.73205i | 0.416025 | + | 0.240192i | ||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | −4.50000 | − | 7.79423i | −0.612372 | − | 1.06066i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | + | 4.33013i | 0.200446 | + | 0.578638i | ||||
\(57\) | −6.00000 | + | 10.3923i | −0.794719 | + | 1.37649i | ||||
\(58\) | 1.50000 | + | 2.59808i | 0.196960 | + | 0.341144i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.50000 | + | 2.59808i | −0.576166 | + | 0.332650i | −0.759608 | − | 0.650381i | \(-0.774609\pi\) |
0.183442 | + | 0.983030i | \(0.441276\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 1.50000 | − | 7.79423i | 0.188982 | − | 0.981981i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.00000 | + | 5.19615i | −1.10782 | + | 0.639602i | ||||
\(67\) | −6.50000 | + | 11.2583i | −0.794101 | + | 1.37542i | 0.129307 | + | 0.991605i | \(0.458725\pi\) |
−0.923408 | + | 0.383819i | \(0.874609\pi\) | |||||||
\(68\) | −3.00000 | − | 5.19615i | −0.363803 | − | 0.630126i | ||||
\(69\) | −1.50000 | + | 2.59808i | −0.180579 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92820i | 0.822226i | 0.911584 | + | 0.411113i | \(0.134860\pi\) | ||||
−0.911584 | + | 0.411113i | \(0.865140\pi\) | |||||||
\(72\) | 4.50000 | + | 2.59808i | 0.530330 | + | 0.306186i | ||||
\(73\) | −3.00000 | − | 1.73205i | −0.351123 | − | 0.202721i | 0.314057 | − | 0.949404i | \(-0.398312\pi\) |
−0.665180 | + | 0.746683i | \(0.731645\pi\) | |||||||
\(74\) | 6.00000 | + | 3.46410i | 0.697486 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.92820i | 0.794719i | ||||||||
\(77\) | −9.00000 | − | 1.73205i | −1.02565 | − | 0.197386i | ||||
\(78\) | 9.00000 | + | 5.19615i | 1.01905 | + | 0.588348i | ||||
\(79\) | 8.00000 | + | 13.8564i | 0.900070 | + | 1.55897i | 0.827401 | + | 0.561611i | \(0.189818\pi\) |
0.0726692 | + | 0.997356i | \(0.476848\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −4.50000 | + | 2.59808i | −0.496942 | + | 0.286910i | ||||
\(83\) | 9.00000 | 0.987878 | 0.493939 | − | 0.869496i | \(-0.335557\pi\) | ||||
0.493939 | + | 0.869496i | \(0.335557\pi\) | |||||||
\(84\) | −1.50000 | − | 4.33013i | −0.163663 | − | 0.472456i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.50000 | + | 0.866025i | −0.161749 | + | 0.0933859i | ||||
\(87\) | 1.50000 | + | 2.59808i | 0.160817 | + | 0.278543i | ||||
\(88\) | 3.00000 | − | 5.19615i | 0.319801 | − | 0.553912i | ||||
\(89\) | −1.50000 | − | 2.59808i | −0.159000 | − | 0.275396i | 0.775509 | − | 0.631337i | \(-0.217494\pi\) |
−0.934508 | + | 0.355942i | \(0.884160\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000 | + | 8.66025i | 0.314485 | + | 0.907841i | ||||
\(92\) | 1.73205i | 0.180579i | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.00000 | 0.918559 | ||||||||
\(97\) | − | 10.3923i | − | 1.05518i | −0.849500 | − | 0.527589i | \(-0.823096\pi\) | ||
0.849500 | − | 0.527589i | \(-0.176904\pi\) | |||||||
\(98\) | 4.50000 | − | 11.2583i | 0.454569 | − | 1.13726i | ||||
\(99\) | −9.00000 | + | 5.19615i | −0.904534 | + | 0.522233i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.50000 | − | 12.9904i | 0.746278 | − | 1.29259i | −0.203317 | − | 0.979113i | \(-0.565172\pi\) |
0.949595 | − | 0.313478i | \(-0.101494\pi\) | |||||||
\(102\) | −9.00000 | − | 15.5885i | −0.891133 | − | 1.54349i | ||||
\(103\) | 4.50000 | − | 2.59808i | 0.443398 | − | 0.255996i | −0.261640 | − | 0.965166i | \(-0.584263\pi\) |
0.705038 | + | 0.709170i | \(0.250930\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.50000 | + | 2.59808i | −0.435031 | + | 0.251166i | −0.701488 | − | 0.712681i | \(-0.747481\pi\) |
0.266456 | + | 0.963847i | \(0.414147\pi\) | |||||||
\(108\) | −4.50000 | − | 2.59808i | −0.433013 | − | 0.250000i | ||||
\(109\) | 2.50000 | − | 4.33013i | 0.239457 | − | 0.414751i | −0.721102 | − | 0.692829i | \(-0.756364\pi\) |
0.960558 | + | 0.278078i | \(0.0896974\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | + | 3.46410i | 0.569495 | + | 0.328798i | ||||
\(112\) | 10.0000 | + | 8.66025i | 0.944911 | + | 0.818317i | ||||
\(113\) | − | 6.92820i | − | 0.651751i | −0.945413 | − | 0.325875i | \(-0.894341\pi\) | ||
0.945413 | − | 0.325875i | \(-0.105659\pi\) | |||||||
\(114\) | 20.7846i | 1.94666i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.50000 | + | 0.866025i | 0.139272 | + | 0.0804084i | ||||
\(117\) | 9.00000 | + | 5.19615i | 0.832050 | + | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | − | 15.5885i | 0.275010 | − | 1.42899i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | −4.50000 | + | 7.79423i | −0.407411 | + | 0.705656i | ||||
\(123\) | −4.50000 | + | 2.59808i | −0.405751 | + | 0.234261i | ||||
\(124\) | −3.00000 | + | 1.73205i | −0.269408 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.50000 | − | 12.9904i | −0.400892 | − | 1.15728i | ||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | −10.5000 | + | 6.06218i | −0.928078 | + | 0.535826i | ||||
\(129\) | −1.50000 | + | 0.866025i | −0.132068 | + | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | −3.00000 | + | 5.19615i | −0.261116 | + | 0.452267i | ||||
\(133\) | −12.0000 | + | 13.8564i | −1.04053 | + | 1.20150i | ||||
\(134\) | 22.5167i | 1.94514i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.00000 | + | 5.19615i | 0.771744 | + | 0.445566i | ||||
\(137\) | 18.0000 | + | 10.3923i | 1.53784 | + | 0.887875i | 0.998965 | + | 0.0454914i | \(0.0144854\pi\) |
0.538879 | + | 0.842383i | \(0.318848\pi\) | |||||||
\(138\) | 5.19615i | 0.442326i | ||||||||
\(139\) | − | 10.3923i | − | 0.881464i | −0.897639 | − | 0.440732i | \(-0.854719\pi\) | ||
0.897639 | − | 0.440732i | \(-0.145281\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | + | 10.3923i | 0.503509 | + | 0.872103i | ||||
\(143\) | 6.00000 | − | 10.3923i | 0.501745 | − | 0.869048i | ||||
\(144\) | 15.0000 | 1.25000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | 4.50000 | − | 11.2583i | 0.371154 | − | 0.928571i | ||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | −19.5000 | + | 11.2583i | −1.59750 | + | 0.922318i | −0.605536 | + | 0.795818i | \(0.707041\pi\) |
−0.991967 | + | 0.126500i | \(0.959626\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | − | 1.73205i | 0.0813788 | − | 0.140952i | −0.822464 | − | 0.568818i | \(-0.807401\pi\) |
0.903842 | + | 0.427865i | \(0.140734\pi\) | |||||||
\(152\) | −6.00000 | − | 10.3923i | −0.486664 | − | 0.842927i | ||||
\(153\) | −9.00000 | − | 15.5885i | −0.727607 | − | 1.26025i | ||||
\(154\) | −15.0000 | + | 5.19615i | −1.20873 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | 3.00000 | + | 1.73205i | 0.239426 | + | 0.138233i | 0.614913 | − | 0.788595i | \(-0.289191\pi\) |
−0.375487 | + | 0.926828i | \(0.622524\pi\) | |||||||
\(158\) | 24.0000 | + | 13.8564i | 1.90934 | + | 1.10236i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.00000 | + | 3.46410i | −0.236433 | + | 0.273009i | ||||
\(162\) | −13.5000 | − | 7.79423i | −1.06066 | − | 0.612372i | ||||
\(163\) | 4.00000 | + | 6.92820i | 0.313304 | + | 0.542659i | 0.979076 | − | 0.203497i | \(-0.0652307\pi\) |
−0.665771 | + | 0.746156i | \(0.731897\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.5000 | − | 7.79423i | 1.04780 | − | 0.604949i | ||||
\(167\) | −21.0000 | −1.62503 | −0.812514 | − | 0.582941i | \(-0.801902\pi\) | ||||
−0.812514 | + | 0.582941i | \(0.801902\pi\) | |||||||
\(168\) | 6.00000 | + | 5.19615i | 0.462910 | + | 0.400892i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.7846i | 1.58944i | ||||||||
\(172\) | −0.500000 | + | 0.866025i | −0.0381246 | + | 0.0660338i | ||||
\(173\) | −6.00000 | − | 10.3923i | −0.456172 | − | 0.790112i | 0.542583 | − | 0.840002i | \(-0.317446\pi\) |
−0.998755 | + | 0.0498898i | \(0.984113\pi\) | |||||||
\(174\) | 4.50000 | + | 2.59808i | 0.341144 | + | 0.196960i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 17.3205i | − | 1.30558i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.50000 | − | 2.59808i | −0.337289 | − | 0.194734i | ||||
\(179\) | −9.00000 | − | 5.19615i | −0.672692 | − | 0.388379i | 0.124404 | − | 0.992232i | \(-0.460298\pi\) |
−0.797096 | + | 0.603853i | \(0.793631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.19615i | − | 0.386227i | −0.981176 | − | 0.193113i | \(-0.938141\pi\) | ||
0.981176 | − | 0.193113i | \(-0.0618586\pi\) | |||||||
\(182\) | 12.0000 | + | 10.3923i | 0.889499 | + | 0.770329i | ||||
\(183\) | −4.50000 | + | 7.79423i | −0.332650 | + | 0.576166i | ||||
\(184\) | −1.50000 | − | 2.59808i | −0.110581 | − | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.00000 | + | 5.19615i | −0.659912 | + | 0.381000i | ||||
\(187\) | −18.0000 | + | 10.3923i | −1.31629 | + | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.50000 | − | 12.9904i | −0.327327 | − | 0.944911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | − | 5.19615i | 0.651217 | − | 0.375980i | −0.137705 | − | 0.990473i | \(-0.543973\pi\) |
0.788922 | + | 0.614493i | \(0.210639\pi\) | |||||||
\(192\) | −1.50000 | + | 0.866025i | −0.108253 | + | 0.0625000i | ||||
\(193\) | 11.0000 | − | 19.0526i | 0.791797 | − | 1.37143i | −0.133056 | − | 0.991109i | \(-0.542479\pi\) |
0.924853 | − | 0.380325i | \(-0.124188\pi\) | |||||||
\(194\) | −9.00000 | − | 15.5885i | −0.646162 | − | 1.11919i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | − | 3.46410i | − | 0.246807i | −0.992357 | − | 0.123404i | \(-0.960619\pi\) | ||
0.992357 | − | 0.123404i | \(-0.0393809\pi\) | |||||||
\(198\) | −9.00000 | + | 15.5885i | −0.639602 | + | 1.10782i | ||||
\(199\) | 6.00000 | + | 3.46410i | 0.425329 | + | 0.245564i | 0.697355 | − | 0.716726i | \(-0.254360\pi\) |
−0.272026 | + | 0.962290i | \(0.587694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.5167i | 1.58820i | ||||||||
\(202\) | − | 25.9808i | − | 1.82800i | ||||||
\(203\) | 1.50000 | + | 4.33013i | 0.105279 | + | 0.303915i | ||||
\(204\) | −9.00000 | − | 5.19615i | −0.630126 | − | 0.363803i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.50000 | − | 7.79423i | 0.313530 | − | 0.543050i | ||||
\(207\) | 5.19615i | 0.361158i | ||||||||
\(208\) | −15.0000 | + | 8.66025i | −1.04006 | + | 0.600481i | ||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | + | 10.3923i | 0.411113 | + | 0.712069i | ||||
\(214\) | −4.50000 | + | 7.79423i | −0.307614 | + | 0.532803i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.00000 | 0.612372 | ||||||||
\(217\) | −9.00000 | − | 1.73205i | −0.610960 | − | 0.117579i | ||||
\(218\) | − | 8.66025i | − | 0.586546i | ||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000 | + | 10.3923i | 1.21081 | + | 0.699062i | ||||
\(222\) | 12.0000 | 0.805387 | ||||||||
\(223\) | − | 3.46410i | − | 0.231973i | −0.993251 | − | 0.115987i | \(-0.962997\pi\) | ||
0.993251 | − | 0.115987i | \(-0.0370030\pi\) | |||||||
\(224\) | 13.5000 | + | 2.59808i | 0.902007 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | − | 10.3923i | −0.399114 | − | 0.691286i | ||||
\(227\) | 6.00000 | − | 10.3923i | 0.398234 | − | 0.689761i | −0.595274 | − | 0.803523i | \(-0.702957\pi\) |
0.993508 | + | 0.113761i | \(0.0362899\pi\) | |||||||
\(228\) | 6.00000 | + | 10.3923i | 0.397360 | + | 0.688247i | ||||
\(229\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.0000 | + | 5.19615i | −0.986928 | + | 0.341882i | ||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | −3.00000 | + | 1.73205i | −0.196537 | + | 0.113470i | −0.595039 | − | 0.803697i | \(-0.702863\pi\) |
0.398502 | + | 0.917167i | \(0.369530\pi\) | |||||||
\(234\) | 18.0000 | 1.17670 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.0000 | + | 13.8564i | 1.55897 | + | 0.900070i | ||||
\(238\) | −9.00000 | − | 25.9808i | −0.583383 | − | 1.68408i | ||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | − | 3.46410i | −0.386494 | − | 0.223142i | 0.294146 | − | 0.955761i | \(-0.404965\pi\) |
−0.680640 | + | 0.732618i | \(0.738298\pi\) | |||||||
\(242\) | 1.50000 | + | 0.866025i | 0.0964237 | + | 0.0556702i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 5.19615i | 0.332650i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.50000 | + | 7.79423i | −0.286910 | + | 0.496942i | ||||
\(247\) | −12.0000 | − | 20.7846i | −0.763542 | − | 1.32249i | ||||
\(248\) | 3.00000 | − | 5.19615i | 0.190500 | − | 0.329956i | ||||
\(249\) | 13.5000 | − | 7.79423i | 0.855528 | − | 0.493939i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | −6.00000 | − | 5.19615i | −0.377964 | − | 0.327327i | ||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 24.0000 | − | 13.8564i | 1.50589 | − | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.50000 | + | 16.4545i | −0.593750 | + | 1.02841i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | −1.50000 | + | 2.59808i | −0.0933859 | + | 0.161749i | ||||
\(259\) | 8.00000 | + | 6.92820i | 0.497096 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | + | 2.59808i | 0.278543 | + | 0.160817i | ||||
\(262\) | −18.0000 | − | 10.3923i | −1.11204 | − | 0.642039i | ||||
\(263\) | −1.50000 | − | 0.866025i | −0.0924940 | − | 0.0534014i | 0.453040 | − | 0.891490i | \(-0.350340\pi\) |
−0.545534 | + | 0.838089i | \(0.683673\pi\) | |||||||
\(264\) | − | 10.3923i | − | 0.639602i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.00000 | + | 31.1769i | −0.367884 | + | 1.91158i | ||||
\(267\) | −4.50000 | − | 2.59808i | −0.275396 | − | 0.159000i | ||||
\(268\) | 6.50000 | + | 11.2583i | 0.397051 | + | 0.687712i | ||||
\(269\) | 1.50000 | − | 2.59808i | 0.0914566 | − | 0.158408i | −0.816668 | − | 0.577108i | \(-0.804181\pi\) |
0.908124 | + | 0.418701i | \(0.137514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.00000 | − | 3.46410i | 0.364474 | − | 0.210429i | −0.306568 | − | 0.951849i | \(-0.599181\pi\) |
0.671042 | + | 0.741420i | \(0.265847\pi\) | |||||||
\(272\) | 30.0000 | 1.81902 | ||||||||
\(273\) | 12.0000 | + | 10.3923i | 0.726273 | + | 0.628971i | ||||
\(274\) | 36.0000 | 2.17484 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.50000 | + | 2.59808i | 0.0902894 | + | 0.156386i | ||||
\(277\) | 13.0000 | − | 22.5167i | 0.781094 | − | 1.35290i | −0.150210 | − | 0.988654i | \(-0.547995\pi\) |
0.931305 | − | 0.364241i | \(-0.118672\pi\) | |||||||
\(278\) | −9.00000 | − | 15.5885i | −0.539784 | − | 0.934934i | ||||
\(279\) | −9.00000 | + | 5.19615i | −0.538816 | + | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.92820i | 0.413302i | 0.978415 | + | 0.206651i | \(0.0662565\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.0000 | + | 15.5885i | 1.60498 | + | 0.926638i | 0.990470 | + | 0.137732i | \(0.0439811\pi\) |
0.614514 | + | 0.788906i | \(0.289352\pi\) | |||||||
\(284\) | 6.00000 | + | 3.46410i | 0.356034 | + | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 20.7846i | − | 1.22902i | ||||||
\(287\) | −7.50000 | + | 2.59808i | −0.442711 | + | 0.153360i | ||||
\(288\) | 13.5000 | − | 7.79423i | 0.795495 | − | 0.459279i | ||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.00000 | − | 15.5885i | −0.527589 | − | 0.913812i | ||||
\(292\) | −3.00000 | + | 1.73205i | −0.175562 | + | 0.101361i | ||||
\(293\) | −24.0000 | −1.40209 | −0.701047 | − | 0.713115i | \(-0.747284\pi\) | ||||
−0.701047 | + | 0.713115i | \(0.747284\pi\) | |||||||
\(294\) | −3.00000 | − | 20.7846i | −0.174964 | − | 1.21218i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.00000 | + | 3.46410i | −0.348743 | + | 0.201347i | ||||
\(297\) | −9.00000 | + | 15.5885i | −0.522233 | + | 0.904534i | ||||
\(298\) | −19.5000 | + | 33.7750i | −1.12960 | + | 1.95653i | ||||
\(299\) | −3.00000 | − | 5.19615i | −0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.50000 | + | 0.866025i | −0.144098 | + | 0.0499169i | ||||
\(302\) | − | 3.46410i | − | 0.199337i | ||||||
\(303\) | − | 25.9808i | − | 1.49256i | ||||||
\(304\) | −30.0000 | − | 17.3205i | −1.72062 | − | 0.993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −27.0000 | − | 15.5885i | −1.54349 | − | 0.891133i | ||||
\(307\) | 22.5167i | 1.28509i | 0.766246 | + | 0.642547i | \(0.222122\pi\) | ||||
−0.766246 | + | 0.642547i | \(0.777878\pi\) | |||||||
\(308\) | −6.00000 | + | 6.92820i | −0.341882 | + | 0.394771i | ||||
\(309\) | 4.50000 | − | 7.79423i | 0.255996 | − | 0.443398i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | − | 20.7846i | 0.680458 | − | 1.17859i | −0.294384 | − | 0.955687i | \(-0.595114\pi\) |
0.974841 | − | 0.222900i | \(-0.0715523\pi\) | |||||||
\(312\) | −9.00000 | + | 5.19615i | −0.509525 | + | 0.294174i | ||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | 6.00000 | 0.338600 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | 15.0000 | − | 8.66025i | 0.842484 | − | 0.486408i | −0.0156238 | − | 0.999878i | \(-0.504973\pi\) |
0.858108 | + | 0.513470i | \(0.171640\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | − | 5.19615i | 0.167968 | − | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | + | 7.79423i | −0.251166 | + | 0.435031i | ||||
\(322\) | −1.50000 | + | 7.79423i | −0.0835917 | + | 0.434355i | ||||
\(323\) | 41.5692i | 2.31297i | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.0000 | + | 6.92820i | 0.664619 | + | 0.383718i | ||||
\(327\) | − | 8.66025i | − | 0.478913i | ||||||
\(328\) | − | 5.19615i | − | 0.286910i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | − | 8.66025i | −0.274825 | − | 0.476011i | 0.695266 | − | 0.718752i | \(-0.255287\pi\) |
−0.970091 | + | 0.242742i | \(0.921953\pi\) | |||||||
\(332\) | 4.50000 | − | 7.79423i | 0.246970 | − | 0.427764i | ||||
\(333\) | 12.0000 | 0.657596 | ||||||||
\(334\) | −31.5000 | + | 18.1865i | −1.72360 | + | 0.995123i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 22.5000 | + | 4.33013i | 1.22748 | + | 0.236228i | ||||
\(337\) | 32.0000 | 1.74315 | 0.871576 | − | 0.490261i | \(-0.163099\pi\) | ||||
0.871576 | + | 0.490261i | \(0.163099\pi\) | |||||||
\(338\) | 1.50000 | − | 0.866025i | 0.0815892 | − | 0.0471056i | ||||
\(339\) | −6.00000 | − | 10.3923i | −0.325875 | − | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | + | 10.3923i | 0.324918 | + | 0.562775i | ||||
\(342\) | 18.0000 | + | 31.1769i | 0.973329 | + | 1.68585i | ||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | − | 1.73205i | − | 0.0933859i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | − | 10.3923i | −0.967686 | − | 0.558694i | ||||
\(347\) | −16.5000 | − | 9.52628i | −0.885766 | − | 0.511397i | −0.0132111 | − | 0.999913i | \(-0.504205\pi\) |
−0.872555 | + | 0.488515i | \(0.837539\pi\) | |||||||
\(348\) | 3.00000 | 0.160817 | ||||||||
\(349\) | 8.66025i | 0.463573i | 0.972767 | + | 0.231786i | \(0.0744570\pi\) | ||||
−0.972767 | + | 0.231786i | \(0.925543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | 0.960769 | ||||||||
\(352\) | −9.00000 | − | 15.5885i | −0.479702 | − | 0.830868i | ||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.00000 | −0.159000 | ||||||||
\(357\) | −9.00000 | − | 25.9808i | −0.476331 | − | 1.37505i | ||||
\(358\) | −18.0000 | −0.951330 | ||||||||
\(359\) | −21.0000 | + | 12.1244i | −1.10834 | + | 0.639899i | −0.938398 | − | 0.345556i | \(-0.887690\pi\) |
−0.169939 | + | 0.985455i | \(0.554357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5000 | − | 25.1147i | 0.763158 | − | 1.32183i | ||||
\(362\) | −4.50000 | − | 7.79423i | −0.236515 | − | 0.409656i | ||||
\(363\) | 1.50000 | + | 0.866025i | 0.0787296 | + | 0.0454545i | ||||
\(364\) | 9.00000 | + | 1.73205i | 0.471728 | + | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 15.5885i | 0.814822i | ||||||||
\(367\) | −13.5000 | − | 7.79423i | −0.704694 | − | 0.406855i | 0.104399 | − | 0.994535i | \(-0.466708\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | −7.50000 | − | 4.33013i | −0.390965 | − | 0.225723i | ||||
\(369\) | −4.50000 | + | 7.79423i | −0.234261 | + | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.00000 | + | 5.19615i | −0.155543 | + | 0.269408i | ||||
\(373\) | −2.00000 | − | 3.46410i | −0.103556 | − | 0.179364i | 0.809591 | − | 0.586994i | \(-0.199689\pi\) |
−0.913147 | + | 0.407630i | \(0.866355\pi\) | |||||||
\(374\) | −18.0000 | + | 31.1769i | −0.930758 | + | 1.61212i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00000 | −0.309016 | ||||||||
\(378\) | −18.0000 | − | 15.5885i | −0.925820 | − | 0.801784i | ||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.0000 | − | 13.8564i | 1.22956 | − | 0.709885i | ||||
\(382\) | 9.00000 | − | 15.5885i | 0.460480 | − | 0.797575i | ||||
\(383\) | 10.5000 | + | 18.1865i | 0.536525 | + | 0.929288i | 0.999088 | + | 0.0427020i | \(0.0135966\pi\) |
−0.462563 | + | 0.886586i | \(0.653070\pi\) | |||||||
\(384\) | −10.5000 | + | 18.1865i | −0.535826 | + | 0.928078i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 38.1051i | − | 1.93950i | ||||||
\(387\) | −1.50000 | + | 2.59808i | −0.0762493 | + | 0.132068i | ||||
\(388\) | −9.00000 | − | 5.19615i | −0.456906 | − | 0.263795i | ||||
\(389\) | 24.0000 | + | 13.8564i | 1.21685 | + | 0.702548i | 0.964242 | − | 0.265022i | \(-0.0853791\pi\) |
0.252606 | + | 0.967569i | \(0.418712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3923i | 0.525561i | ||||||||
\(392\) | 7.50000 | + | 9.52628i | 0.378807 | + | 0.481150i | ||||
\(393\) | −18.0000 | − | 10.3923i | −0.907980 | − | 0.524222i | ||||
\(394\) | −3.00000 | − | 5.19615i | −0.151138 | − | 0.261778i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.3923i | 0.522233i | ||||||||
\(397\) | 21.0000 | − | 12.1244i | 1.05396 | − | 0.608504i | 0.130204 | − | 0.991487i | \(-0.458437\pi\) |
0.923755 | + | 0.382983i | \(0.125103\pi\) | |||||||
\(398\) | 12.0000 | 0.601506 | ||||||||
\(399\) | −6.00000 | + | 31.1769i | −0.300376 | + | 1.56080i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.5000 | + | 9.52628i | −0.823971 | + | 0.475720i | −0.851784 | − | 0.523893i | \(-0.824479\pi\) |
0.0278131 | + | 0.999613i | \(0.491146\pi\) | |||||||
\(402\) | 19.5000 | + | 33.7750i | 0.972572 | + | 1.68454i | ||||
\(403\) | 6.00000 | − | 10.3923i | 0.298881 | − | 0.517678i | ||||
\(404\) | −7.50000 | − | 12.9904i | −0.373139 | − | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 5.19615i | 0.297775 | + | 0.257881i | ||||
\(407\) | − | 13.8564i | − | 0.686837i | ||||||
\(408\) | 18.0000 | 0.891133 | ||||||||
\(409\) | 19.5000 | + | 11.2583i | 0.964213 | + | 0.556689i | 0.897467 | − | 0.441081i | \(-0.145405\pi\) |
0.0667458 | + | 0.997770i | \(0.478738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.0000 | 1.77575 | ||||||||
\(412\) | − | 5.19615i | − | 0.255996i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.50000 | + | 7.79423i | 0.221163 | + | 0.383065i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.00000 | + | 15.5885i | −0.441261 | + | 0.764287i | ||||
\(417\) | −9.00000 | − | 15.5885i | −0.440732 | − | 0.763370i | ||||
\(418\) | 36.0000 | − | 20.7846i | 1.76082 | − | 1.01661i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0000 | 1.70580 | 0.852898 | − | 0.522078i | \(-0.174843\pi\) | ||||
0.852898 | + | 0.522078i | \(0.174843\pi\) | |||||||
\(422\) | −30.0000 | + | 17.3205i | −1.46038 | + | 0.843149i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 18.0000 | + | 10.3923i | 0.872103 | + | 0.503509i | ||||
\(427\) | −9.00000 | + | 10.3923i | −0.435541 | + | 0.502919i | ||||
\(428\) | 5.19615i | 0.251166i | ||||||||
\(429\) | − | 20.7846i | − | 1.00349i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.00000 | + | 5.19615i | 0.433515 | + | 0.250290i | 0.700843 | − | 0.713316i | \(-0.252807\pi\) |
−0.267328 | + | 0.963606i | \(0.586141\pi\) | |||||||
\(432\) | 22.5000 | − | 12.9904i | 1.08253 | − | 0.625000i | ||||
\(433\) | 13.8564i | 0.665896i | 0.942945 | + | 0.332948i | \(0.108043\pi\) | ||||
−0.942945 | + | 0.332948i | \(0.891957\pi\) | |||||||
\(434\) | −15.0000 | + | 5.19615i | −0.720023 | + | 0.249423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.50000 | − | 4.33013i | −0.119728 | − | 0.207375i | ||||
\(437\) | 6.00000 | − | 10.3923i | 0.287019 | − | 0.497131i | ||||
\(438\) | −9.00000 | + | 5.19615i | −0.430037 | + | 0.248282i | ||||
\(439\) | −6.00000 | + | 3.46410i | −0.286364 | + | 0.165333i | −0.636301 | − | 0.771441i | \(-0.719536\pi\) |
0.349937 | + | 0.936773i | \(0.386203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 36.0000 | 1.71235 | ||||||||
\(443\) | −13.5000 | + | 7.79423i | −0.641404 | + | 0.370315i | −0.785155 | − | 0.619299i | \(-0.787417\pi\) |
0.143751 | + | 0.989614i | \(0.454084\pi\) | |||||||
\(444\) | 6.00000 | − | 3.46410i | 0.284747 | − | 0.164399i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.00000 | − | 5.19615i | −0.142054 | − | 0.246045i | ||||
\(447\) | −19.5000 | + | 33.7750i | −0.922318 | + | 1.59750i | ||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | − | 12.1244i | − | 0.572184i | −0.958202 | − | 0.286092i | \(-0.907644\pi\) | ||
0.958202 | − | 0.286092i | \(-0.0923563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | + | 5.19615i | 0.423793 | + | 0.244677i | ||||
\(452\) | −6.00000 | − | 3.46410i | −0.282216 | − | 0.162938i | ||||
\(453\) | − | 3.46410i | − | 0.162758i | ||||||
\(454\) | − | 20.7846i | − | 0.975470i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.0000 | − | 10.3923i | −0.842927 | − | 0.486664i | ||||
\(457\) | −4.00000 | − | 6.92820i | −0.187112 | − | 0.324088i | 0.757174 | − | 0.653213i | \(-0.226579\pi\) |
−0.944286 | + | 0.329125i | \(0.893246\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.0000 | − | 15.5885i | −1.26025 | − | 0.727607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | −18.0000 | + | 20.7846i | −0.837436 | + | 0.966988i | ||||
\(463\) | −29.0000 | −1.34774 | −0.673872 | − | 0.738848i | \(-0.735370\pi\) | ||||
−0.673872 | + | 0.738848i | \(0.735370\pi\) | |||||||
\(464\) | −7.50000 | + | 4.33013i | −0.348179 | + | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | 10.5000 | + | 18.1865i | 0.485882 | + | 0.841572i | 0.999868 | − | 0.0162260i | \(-0.00516512\pi\) |
−0.513986 | + | 0.857798i | \(0.671832\pi\) | |||||||
\(468\) | 9.00000 | − | 5.19615i | 0.416025 | − | 0.240192i | ||||
\(469\) | −6.50000 | + | 33.7750i | −0.300142 | + | 1.55958i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | 0.276465 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | + | 1.73205i | 0.137940 | + | 0.0796398i | ||||
\(474\) | 48.0000 | 2.20471 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.0000 | − | 10.3923i | −0.550019 | − | 0.476331i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.00000 | − | 15.5885i | −0.411650 | − | 0.712999i | ||||
\(479\) | 3.00000 | − | 5.19615i | 0.137073 | − | 0.237418i | −0.789314 | − | 0.613990i | \(-0.789564\pi\) |
0.926388 | + | 0.376571i | \(0.122897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | + | 6.92820i | −0.547153 | + | 0.315899i | ||||
\(482\) | −12.0000 | −0.546585 | ||||||||
\(483\) | −1.50000 | + | 7.79423i | −0.0682524 | + | 0.354650i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −27.0000 | −1.22474 | ||||||||
\(487\) | −16.0000 | + | 27.7128i | −0.725029 | + | 1.25579i | 0.233933 | + | 0.972253i | \(0.424840\pi\) |
−0.958962 | + | 0.283535i | \(0.908493\pi\) | |||||||
\(488\) | −4.50000 | − | 7.79423i | −0.203705 | − | 0.352828i | ||||
\(489\) | 12.0000 | + | 6.92820i | 0.542659 | + | 0.313304i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.1051i | 1.71966i | 0.510581 | + | 0.859830i | \(0.329431\pi\) | ||||
−0.510581 | + | 0.859830i | \(0.670569\pi\) | |||||||
\(492\) | 5.19615i | 0.234261i | ||||||||
\(493\) | 9.00000 | + | 5.19615i | 0.405340 | + | 0.234023i | ||||
\(494\) | −36.0000 | − | 20.7846i | −1.61972 | − | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 17.3205i | − | 0.777714i | ||||||
\(497\) | 6.00000 | + | 17.3205i | 0.269137 | + | 0.776931i | ||||
\(498\) | 13.5000 | − | 23.3827i | 0.604949 | − | 1.04780i | ||||
\(499\) | 7.00000 | + | 12.1244i | 0.313363 | + | 0.542761i | 0.979088 | − | 0.203436i | \(-0.0652110\pi\) |
−0.665725 | + | 0.746197i | \(0.731878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.5000 | + | 18.1865i | −1.40732 | + | 0.812514i | ||||
\(502\) | −27.0000 | + | 15.5885i | −1.20507 | + | 0.695747i | ||||
\(503\) | 15.0000 | 0.668817 | 0.334408 | − | 0.942428i | \(-0.391463\pi\) | ||||
0.334408 | + | 0.942428i | \(0.391463\pi\) | |||||||
\(504\) | 13.5000 | + | 2.59808i | 0.601338 | + | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | − | 5.19615i | 0.400099 | − | 0.230997i | ||||
\(507\) | 1.50000 | − | 0.866025i | 0.0666173 | − | 0.0384615i | ||||
\(508\) | 8.00000 | − | 13.8564i | 0.354943 | − | 0.614779i | ||||
\(509\) | 22.5000 | + | 38.9711i | 0.997295 | + | 1.72737i | 0.562303 | + | 0.826931i | \(0.309915\pi\) |
0.434992 | + | 0.900434i | \(0.356751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.00000 | − | 1.73205i | −0.398137 | − | 0.0766214i | ||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 18.0000 | + | 31.1769i | 0.794719 | + | 1.37649i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.73205i | 0.0762493i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 18.0000 | + | 3.46410i | 0.790875 | + | 0.152204i | ||||
\(519\) | −18.0000 | − | 10.3923i | −0.790112 | − | 0.456172i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0000 | + | 25.9808i | −0.657162 | + | 1.13824i | 0.324185 | + | 0.945994i | \(0.394910\pi\) |
−0.981347 | + | 0.192244i | \(0.938423\pi\) | |||||||
\(522\) | 9.00000 | 0.393919 | ||||||||
\(523\) | −21.0000 | + | 12.1244i | −0.918266 | + | 0.530161i | −0.883081 | − | 0.469220i | \(-0.844535\pi\) |
−0.0351845 | + | 0.999381i | \(0.511202\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | −0.130806 | ||||||||
\(527\) | −18.0000 | + | 10.3923i | −0.784092 | + | 0.452696i | ||||
\(528\) | −15.0000 | − | 25.9808i | −0.652791 | − | 1.13067i | ||||
\(529\) | −10.0000 | + | 17.3205i | −0.434783 | + | 0.753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.00000 | + | 17.3205i | 0.260133 | + | 0.750939i | ||||
\(533\) | − | 10.3923i | − | 0.450141i | ||||||
\(534\) | −9.00000 | −0.389468 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19.5000 | − | 11.2583i | −0.842272 | − | 0.486286i | ||||
\(537\) | −18.0000 | −0.776757 | ||||||||
\(538\) | − | 5.19615i | − | 0.224022i | ||||||
\(539\) | −24.0000 | + | 3.46410i | −1.03375 | + | 0.149209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.5000 | − | 25.1147i | −0.623404 | − | 1.07977i | −0.988847 | − | 0.148933i | \(-0.952416\pi\) |
0.365444 | − | 0.930834i | \(-0.380917\pi\) | |||||||
\(542\) | 6.00000 | − | 10.3923i | 0.257722 | − | 0.446388i | ||||
\(543\) | −4.50000 | − | 7.79423i | −0.193113 | − | 0.334482i | ||||
\(544\) | 27.0000 | − | 15.5885i | 1.15762 | − | 0.668350i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 27.0000 | + | 5.19615i | 1.15549 | + | 0.222375i | ||||
\(547\) | 1.00000 | 0.0427569 | 0.0213785 | − | 0.999771i | \(-0.493195\pi\) | ||||
0.0213785 | + | 0.999771i | \(0.493195\pi\) | |||||||
\(548\) | 18.0000 | − | 10.3923i | 0.768922 | − | 0.443937i | ||||
\(549\) | 15.5885i | 0.665299i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | − | 10.3923i | −0.255609 | − | 0.442727i | ||||
\(552\) | −4.50000 | − | 2.59808i | −0.191533 | − | 0.110581i | ||||
\(553\) | 32.0000 | + | 27.7128i | 1.36078 | + | 1.17847i | ||||
\(554\) | − | 45.0333i | − | 1.91328i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.00000 | − | 5.19615i | −0.381685 | − | 0.220366i | ||||
\(557\) | 15.0000 | + | 8.66025i | 0.635570 | + | 0.366947i | 0.782906 | − | 0.622140i | \(-0.213736\pi\) |
−0.147336 | + | 0.989087i | \(0.547070\pi\) | |||||||
\(558\) | −9.00000 | + | 15.5885i | −0.381000 | + | 0.659912i | ||||
\(559\) | − | 3.46410i | − | 0.146516i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | + | 31.1769i | −0.759961 | + | 1.31629i | ||||
\(562\) | 6.00000 | + | 10.3923i | 0.253095 | + | 0.438373i | ||||
\(563\) | 10.5000 | − | 18.1865i | 0.442522 | − | 0.766471i | −0.555354 | − | 0.831614i | \(-0.687417\pi\) |
0.997876 | + | 0.0651433i | \(0.0207504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 54.0000 | 2.26979 | ||||||||
\(567\) | −18.0000 | − | 15.5885i | −0.755929 | − | 0.654654i | ||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 6.00000 | − | 3.46410i | 0.251533 | − | 0.145223i | −0.368933 | − | 0.929456i | \(-0.620277\pi\) |
0.620466 | + | 0.784233i | \(0.286943\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | −6.00000 | − | 10.3923i | −0.250873 | − | 0.434524i | ||||
\(573\) | 9.00000 | − | 15.5885i | 0.375980 | − | 0.651217i | ||||
\(574\) | −9.00000 | + | 10.3923i | −0.375653 | + | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.50000 | + | 2.59808i | −0.0625000 | + | 0.108253i | ||||
\(577\) | −21.0000 | − | 12.1244i | −0.874241 | − | 0.504744i | −0.00548605 | − | 0.999985i | \(-0.501746\pi\) |
−0.868755 | + | 0.495241i | \(0.835080\pi\) | |||||||
\(578\) | −28.5000 | − | 16.4545i | −1.18544 | − | 0.684416i | ||||
\(579\) | − | 38.1051i | − | 1.58359i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.5000 | − | 7.79423i | 0.933457 | − | 0.323359i | ||||
\(582\) | −27.0000 | − | 15.5885i | −1.11919 | − | 0.646162i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.00000 | − | 5.19615i | 0.124141 | − | 0.215018i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.0000 | + | 20.7846i | −1.48715 | + | 0.858604i | ||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | −7.50000 | − | 9.52628i | −0.309295 | − | 0.392857i | ||||
\(589\) | 24.0000 | 0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | − | 5.19615i | −0.123404 | − | 0.213741i | ||||
\(592\) | −10.0000 | + | 17.3205i | −0.410997 | + | 0.711868i | ||||
\(593\) | 24.0000 | + | 41.5692i | 0.985562 | + | 1.70704i | 0.639413 | + | 0.768864i | \(0.279178\pi\) |
0.346149 | + | 0.938179i | \(0.387489\pi\) | |||||||
\(594\) | 31.1769i | 1.27920i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.5167i | 0.922318i | ||||||||
\(597\) | 12.0000 | 0.491127 | ||||||||
\(598\) | −9.00000 | − | 5.19615i | −0.368037 | − | 0.212486i | ||||
\(599\) | −12.0000 | − | 6.92820i | −0.490307 | − | 0.283079i | 0.234395 | − | 0.972141i | \(-0.424689\pi\) |
−0.724702 | + | 0.689063i | \(0.758022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.7846i | 0.847822i | 0.905704 | + | 0.423911i | \(0.139343\pi\) | ||||
−0.905704 | + | 0.423911i | \(0.860657\pi\) | |||||||
\(602\) | −3.00000 | + | 3.46410i | −0.122271 | + | 0.141186i | ||||
\(603\) | 19.5000 | + | 33.7750i | 0.794101 | + | 1.37542i | ||||
\(604\) | −1.00000 | − | 1.73205i | −0.0406894 | − | 0.0704761i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −22.5000 | − | 38.9711i | −0.914000 | − | 1.58309i | ||||
\(607\) | 1.50000 | − | 0.866025i | 0.0608831 | − | 0.0351509i | −0.469249 | − | 0.883066i | \(-0.655475\pi\) |
0.530133 | + | 0.847915i | \(0.322142\pi\) | |||||||
\(608\) | −36.0000 | −1.45999 | ||||||||
\(609\) | 6.00000 | + | 5.19615i | 0.243132 | + | 0.210559i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −18.0000 | −0.727607 | ||||||||
\(613\) | 1.00000 | − | 1.73205i | 0.0403896 | − | 0.0699569i | −0.845124 | − | 0.534570i | \(-0.820473\pi\) |
0.885514 | + | 0.464614i | \(0.153807\pi\) | |||||||
\(614\) | 19.5000 | + | 33.7750i | 0.786956 | + | 1.36305i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | − | 15.5885i | 0.120873 | − | 0.628077i | ||||
\(617\) | 34.6410i | 1.39459i | 0.716782 | + | 0.697297i | \(0.245614\pi\) | ||||
−0.716782 | + | 0.697297i | \(0.754386\pi\) | |||||||
\(618\) | − | 15.5885i | − | 0.627060i | ||||||
\(619\) | −21.0000 | − | 12.1244i | −0.844061 | − | 0.487319i | 0.0145814 | − | 0.999894i | \(-0.495358\pi\) |
−0.858643 | + | 0.512575i | \(0.828692\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.50000 | + | 7.79423i | 0.180579 | + | 0.312772i | ||||
\(622\) | − | 41.5692i | − | 1.66677i | ||||||
\(623\) | −6.00000 | − | 5.19615i | −0.240385 | − | 0.208179i | ||||
\(624\) | −15.0000 | + | 25.9808i | −0.600481 | + | 1.04006i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 36.0000 | − | 20.7846i | 1.43770 | − | 0.830057i | ||||
\(628\) | 3.00000 | − | 1.73205i | 0.119713 | − | 0.0691164i | ||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | −24.0000 | + | 13.8564i | −0.954669 | + | 0.551178i | ||||
\(633\) | −30.0000 | + | 17.3205i | −1.19239 | + | 0.688428i | ||||
\(634\) | 15.0000 | − | 25.9808i | 0.595726 | − | 1.03183i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | + | 19.0526i | 0.594322 | + | 0.754890i | ||||
\(638\) | − | 10.3923i | − | 0.411435i | ||||||
\(639\) | 18.0000 | + | 10.3923i | 0.712069 | + | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.5000 | + | 6.06218i | 0.414725 | + | 0.239442i | 0.692818 | − | 0.721113i | \(-0.256369\pi\) |
−0.278093 | + | 0.960554i | \(0.589702\pi\) | |||||||
\(642\) | 15.5885i | 0.615227i | ||||||||
\(643\) | 17.3205i | 0.683054i | 0.939872 | + | 0.341527i | \(0.110944\pi\) | ||||
−0.939872 | + | 0.341527i | \(0.889056\pi\) | |||||||
\(644\) | 1.50000 | + | 4.33013i | 0.0591083 | + | 0.170631i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.0000 | + | 62.3538i | 1.41640 | + | 2.45328i | ||||
\(647\) | 1.50000 | − | 2.59808i | 0.0589711 | − | 0.102141i | −0.835033 | − | 0.550200i | \(-0.814551\pi\) |
0.894004 | + | 0.448059i | \(0.147885\pi\) | |||||||
\(648\) | 13.5000 | − | 7.79423i | 0.530330 | − | 0.306186i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.0000 | + | 5.19615i | −0.587896 | + | 0.203653i | ||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | 27.0000 | − | 15.5885i | 1.05659 | − | 0.610023i | 0.132104 | − | 0.991236i | \(-0.457827\pi\) |
0.924487 | + | 0.381212i | \(0.124493\pi\) | |||||||
\(654\) | −7.50000 | − | 12.9904i | −0.293273 | − | 0.507964i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.50000 | − | 12.9904i | −0.292826 | − | 0.507189i | ||||
\(657\) | −9.00000 | + | 5.19615i | −0.351123 | + | 0.202721i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.5692i | 1.61931i | 0.586908 | + | 0.809653i | \(0.300345\pi\) | ||||
−0.586908 | + | 0.809653i | \(0.699655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.5000 | + | 16.4545i | 1.10852 | + | 0.640005i | 0.938446 | − | 0.345426i | \(-0.112266\pi\) |
0.170075 | + | 0.985431i | \(0.445599\pi\) | |||||||
\(662\) | −15.0000 | − | 8.66025i | −0.582992 | − | 0.336590i | ||||
\(663\) | 36.0000 | 1.39812 | ||||||||
\(664\) | 15.5885i | 0.604949i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.0000 | − | 10.3923i | 0.697486 | − | 0.402694i | ||||
\(667\) | −1.50000 | − | 2.59808i | −0.0580802 | − | 0.100598i | ||||
\(668\) | −10.5000 | + | 18.1865i | −0.406257 | + | 0.703658i | ||||
\(669\) | −3.00000 | − | 5.19615i | −0.115987 | − | 0.200895i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | 22.5000 | − | 7.79423i | 0.867956 | − | 0.300669i | ||||
\(673\) | −4.00000 | −0.154189 | −0.0770943 | − | 0.997024i | \(-0.524564\pi\) | ||||
−0.0770943 | + | 0.997024i | \(0.524564\pi\) | |||||||
\(674\) | 48.0000 | − | 27.7128i | 1.84889 | − | 1.06746i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | − | 0.866025i | 0.0192308 | − | 0.0333087i | ||||
\(677\) | 3.00000 | + | 5.19615i | 0.115299 | + | 0.199704i | 0.917899 | − | 0.396813i | \(-0.129884\pi\) |
−0.802600 | + | 0.596518i | \(0.796551\pi\) | |||||||
\(678\) | −18.0000 | − | 10.3923i | −0.691286 | − | 0.399114i | ||||
\(679\) | −9.00000 | − | 25.9808i | −0.345388 | − | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 20.7846i | − | 0.796468i | ||||||
\(682\) | 18.0000 | + | 10.3923i | 0.689256 | + | 0.397942i | ||||
\(683\) | −34.5000 | − | 19.9186i | −1.32011 | − | 0.762163i | −0.336361 | − | 0.941733i | \(-0.609196\pi\) |
−0.983745 | + | 0.179570i | \(0.942529\pi\) | |||||||
\(684\) | 18.0000 | + | 10.3923i | 0.688247 | + | 0.397360i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.50000 | − | 32.0429i | 0.0572703 | − | 1.22341i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.50000 | − | 4.33013i | −0.0953116 | − | 0.165085i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.00000 | − | 1.73205i | 0.114125 | − | 0.0658903i | −0.441851 | − | 0.897089i | \(-0.645678\pi\) |
0.555976 | + | 0.831198i | \(0.312345\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | −18.0000 | + | 20.7846i | −0.683763 | + | 0.789542i | ||||
\(694\) | −33.0000 | −1.25266 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.50000 | + | 2.59808i | −0.170572 | + | 0.0984798i | ||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | 7.50000 | + | 12.9904i | 0.283879 | + | 0.491693i | ||||
\(699\) | −3.00000 | + | 5.19615i | −0.113470 | + | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.9808i | − | 0.981280i | −0.871362 | − | 0.490640i | \(-0.836763\pi\) | ||
0.871362 | − | 0.490640i | \(-0.163237\pi\) | |||||||
\(702\) | 27.0000 | − | 15.5885i | 1.01905 | − | 0.588348i | ||||
\(703\) | −24.0000 | − | 13.8564i | −0.905177 | − | 0.522604i | ||||
\(704\) | 3.00000 | + | 1.73205i | 0.113067 | + | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.50000 | − | 38.9711i | 0.282067 | − | 1.46566i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.50000 | − | 16.4545i | −0.356780 | − | 0.617961i | 0.630641 | − | 0.776075i | \(-0.282792\pi\) |
−0.987421 | + | 0.158114i | \(0.949459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.0000 | 1.80014 | ||||||||
\(712\) | 4.50000 | − | 2.59808i | 0.168645 | − | 0.0973670i | ||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | −36.0000 | − | 31.1769i | −1.34727 | − | 1.16677i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.00000 | + | 5.19615i | −0.336346 | + | 0.194189i | ||||
\(717\) | −9.00000 | − | 15.5885i | −0.336111 | − | 0.582162i | ||||
\(718\) | −21.0000 | + | 36.3731i | −0.783713 | + | 1.35743i | ||||
\(719\) | −3.00000 | − | 5.19615i | −0.111881 | − | 0.193784i | 0.804648 | − | 0.593753i | \(-0.202354\pi\) |
−0.916529 | + | 0.399969i | \(0.869021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.00000 | − | 10.3923i | 0.335178 | − | 0.387030i | ||||
\(722\) | − | 50.2295i | − | 1.86935i | ||||||
\(723\) | −12.0000 | −0.446285 | ||||||||
\(724\) | −4.50000 | − | 2.59808i | −0.167241 | − | 0.0965567i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.00000 | 0.111340 | ||||||||
\(727\) | − | 5.19615i | − | 0.192715i | −0.995347 | − | 0.0963573i | \(-0.969281\pi\) | ||
0.995347 | − | 0.0963573i | \(-0.0307191\pi\) | |||||||
\(728\) | −15.0000 | + | 5.19615i | −0.555937 | + | 0.192582i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.00000 | + | 5.19615i | −0.110959 | + | 0.192187i | ||||
\(732\) | 4.50000 | + | 7.79423i | 0.166325 | + | 0.288083i | ||||
\(733\) | 15.0000 | − | 8.66025i | 0.554038 | − | 0.319874i | −0.196711 | − | 0.980461i | \(-0.563026\pi\) |
0.750749 | + | 0.660588i | \(0.229693\pi\) | |||||||
\(734\) | −27.0000 | −0.996588 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.00000 | −0.331744 | ||||||||
\(737\) | 39.0000 | − | 22.5167i | 1.43658 | − | 0.829412i | ||||
\(738\) | 15.5885i | 0.573819i | ||||||||
\(739\) | −19.0000 | + | 32.9090i | −0.698926 | + | 1.21058i | 0.269913 | + | 0.962885i | \(0.413005\pi\) |
−0.968839 | + | 0.247691i | \(0.920328\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.0000 | − | 20.7846i | −1.32249 | − | 0.763542i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 46.7654i | − | 1.71566i | −0.513938 | − | 0.857828i | \(-0.671814\pi\) | ||
0.513938 | − | 0.857828i | \(-0.328186\pi\) | |||||||
\(744\) | − | 10.3923i | − | 0.381000i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.00000 | − | 3.46410i | −0.219676 | − | 0.126830i | ||||
\(747\) | 13.5000 | − | 23.3827i | 0.493939 | − | 0.855528i | ||||
\(748\) | 20.7846i | 0.759961i | ||||||||
\(749\) | −9.00000 | + | 10.3923i | −0.328853 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000 | + | 17.3205i | 0.364905 | + | 0.632034i | 0.988761 | − | 0.149505i | \(-0.0477681\pi\) |
−0.623856 | + | 0.781540i | \(0.714435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.0000 | + | 15.5885i | −0.983935 | + | 0.568075i | ||||
\(754\) | −9.00000 | + | 5.19615i | −0.327761 | + | 0.189233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.5000 | − | 2.59808i | −0.490990 | − | 0.0944911i | ||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 24.0000 | − | 13.8564i | 0.871719 | − | 0.503287i | ||||
\(759\) | 9.00000 | − | 5.19615i | 0.326679 | − | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | − | 15.5885i | −0.326250 | − | 0.565081i | 0.655515 | − | 0.755182i | \(-0.272452\pi\) |
−0.981764 | + | 0.190101i | \(0.939118\pi\) | |||||||
\(762\) | 24.0000 | − | 41.5692i | 0.869428 | − | 1.50589i | ||||
\(763\) | 2.50000 | − | 12.9904i | 0.0905061 | − | 0.470283i | ||||
\(764\) | − | 10.3923i | − | 0.375980i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.5000 | + | 18.1865i | 1.13814 | + | 0.657106i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 32.9090i | 1.18750i | ||||||||
\(769\) | − | 41.5692i | − | 1.49902i | −0.661991 | − | 0.749512i | \(-0.730288\pi\) | ||
0.661991 | − | 0.749512i | \(-0.269712\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.0000 | − | 19.0526i | −0.395899 | − | 0.685717i | ||||
\(773\) | −9.00000 | + | 15.5885i | −0.323708 | + | 0.560678i | −0.981250 | − | 0.192740i | \(-0.938263\pi\) |
0.657542 | + | 0.753418i | \(0.271596\pi\) | |||||||
\(774\) | 5.19615i | 0.186772i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.0000 | 0.646162 | ||||||||
\(777\) | 18.0000 | + | 3.46410i | 0.645746 | + | 0.124274i | ||||
\(778\) | 48.0000 | 1.72088 | ||||||||
\(779\) | 18.0000 | − | 10.3923i | 0.644917 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | − | 20.7846i | 0.429394 | − | 0.743732i | ||||
\(782\) | 9.00000 | + | 15.5885i | 0.321839 | + | 0.557442i | ||||
\(783\) | 9.00000 | 0.321634 | ||||||||
\(784\) | 32.5000 | + | 12.9904i | 1.16071 | + | 0.463942i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −36.0000 | −1.28408 | ||||||||
\(787\) | 22.5000 | + | 12.9904i | 0.802038 | + | 0.463057i | 0.844183 | − | 0.536054i | \(-0.180086\pi\) |
−0.0421450 | + | 0.999112i | \(0.513419\pi\) | |||||||
\(788\) | −3.00000 | − | 1.73205i | −0.106871 | − | 0.0617018i | ||||
\(789\) | −3.00000 | −0.106803 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.00000 | − | 17.3205i | −0.213335 | − | 0.615846i | ||||
\(792\) | −9.00000 | − | 15.5885i | −0.319801 | − | 0.553912i | ||||
\(793\) | −9.00000 | − | 15.5885i | −0.319599 | − | 0.553562i | ||||
\(794\) | 21.0000 | − | 36.3731i | 0.745262 | − | 1.29083i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.00000 | − | 3.46410i | 0.212664 | − | 0.122782i | ||||
\(797\) | −12.0000 | −0.425062 | −0.212531 | − | 0.977154i | \(-0.568171\pi\) | ||||
−0.212531 | + | 0.977154i | \(0.568171\pi\) | |||||||
\(798\) | 18.0000 | + | 51.9615i | 0.637193 | + | 1.83942i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00000 | −0.317999 | ||||||||
\(802\) | −16.5000 | + | 28.5788i | −0.582635 | + | 1.00915i | ||||
\(803\) | 6.00000 | + | 10.3923i | 0.211735 | + | 0.366736i | ||||
\(804\) | 19.5000 | + | 11.2583i | 0.687712 | + | 0.397051i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 20.7846i | − | 0.732107i | ||||||
\(807\) | − | 5.19615i | − | 0.182913i | ||||||
\(808\) | 22.5000 | + | 12.9904i | 0.791547 | + | 0.457000i | ||||
\(809\) | 16.5000 | + | 9.52628i | 0.580109 | + | 0.334926i | 0.761177 | − | 0.648544i | \(-0.224622\pi\) |
−0.181068 | + | 0.983471i | \(0.557955\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.0333i | 1.58133i | 0.612247 | + | 0.790667i | \(0.290266\pi\) | ||||
−0.612247 | + | 0.790667i | \(0.709734\pi\) | |||||||
\(812\) | 4.50000 | + | 0.866025i | 0.157919 | + | 0.0303915i | ||||
\(813\) | 6.00000 | − | 10.3923i | 0.210429 | − | 0.364474i | ||||
\(814\) | −12.0000 | − | 20.7846i | −0.420600 | − | 0.728500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 45.0000 | − | 25.9808i | 1.57532 | − | 0.909509i | ||||
\(817\) | 6.00000 | − | 3.46410i | 0.209913 | − | 0.121194i | ||||
\(818\) | 39.0000 | 1.36360 | ||||||||
\(819\) | 27.0000 | + | 5.19615i | 0.943456 | + | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.0000 | − | 20.7846i | 1.25641 | − | 0.725388i | 0.284034 | − | 0.958814i | \(-0.408327\pi\) |
0.972375 | + | 0.233426i | \(0.0749938\pi\) | |||||||
\(822\) | 54.0000 | − | 31.1769i | 1.88347 | − | 1.08742i | ||||
\(823\) | 11.5000 | − | 19.9186i | 0.400865 | − | 0.694318i | −0.592966 | − | 0.805228i | \(-0.702043\pi\) |
0.993831 | + | 0.110910i | \(0.0353764\pi\) | |||||||
\(824\) | 4.50000 | + | 7.79423i | 0.156765 | + | 0.271525i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.5167i | 0.782981i | 0.920182 | + | 0.391491i | \(0.128040\pi\) | ||||
−0.920182 | + | 0.391491i | \(0.871960\pi\) | |||||||
\(828\) | 4.50000 | + | 2.59808i | 0.156386 | + | 0.0902894i | ||||
\(829\) | −12.0000 | − | 6.92820i | −0.416777 | − | 0.240626i | 0.276920 | − | 0.960893i | \(-0.410686\pi\) |
−0.693698 | + | 0.720266i | \(0.744020\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 45.0333i | − | 1.56219i | ||||||
\(832\) | − | 3.46410i | − | 0.120096i | ||||||
\(833\) | −6.00000 | − | 41.5692i | −0.207888 | − | 1.44029i | ||||
\(834\) | −27.0000 | − | 15.5885i | −0.934934 | − | 0.539784i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.0000 | − | 20.7846i | 0.415029 | − | 0.718851i | ||||
\(837\) | −9.00000 | + | 15.5885i | −0.311086 | + | 0.538816i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.0000 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.0000 | 0.896552 | ||||||||
\(842\) | 52.5000 | − | 30.3109i | 1.80927 | − | 1.04458i | ||||
\(843\) | 6.00000 | + | 10.3923i | 0.206651 | + | 0.357930i | ||||
\(844\) | −10.0000 | + | 17.3205i | −0.344214 | + | 0.596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | + | 1.73205i | 0.0687208 | + | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 54.0000 | 1.85328 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | − | 3.46410i | −0.205677 | − | 0.118748i | ||||
\(852\) | 12.0000 | 0.411113 | ||||||||
\(853\) | 20.7846i | 0.711651i | 0.934552 | + | 0.355826i | \(0.115800\pi\) | ||||
−0.934552 | + | 0.355826i | \(0.884200\pi\) | |||||||
\(854\) | −4.50000 | + | 23.3827i | −0.153987 | + | 0.800139i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.50000 | − | 7.79423i | −0.153807 | − | 0.266401i | ||||
\(857\) | −21.0000 | + | 36.3731i | −0.717346 | + | 1.24248i | 0.244701 | + | 0.969599i | \(0.421310\pi\) |
−0.962048 | + | 0.272882i | \(0.912023\pi\) | |||||||
\(858\) | −18.0000 | − | 31.1769i | −0.614510 | − | 1.06436i | ||||
\(859\) | 24.0000 | − | 13.8564i | 0.818869 | − | 0.472774i | −0.0311570 | − | 0.999515i | \(-0.509919\pi\) |
0.850026 | + | 0.526740i | \(0.176586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.00000 | + | 10.3923i | −0.306719 | + | 0.354169i | ||||
\(862\) | 18.0000 | 0.613082 | ||||||||
\(863\) | −7.50000 | + | 4.33013i | −0.255303 | + | 0.147399i | −0.622190 | − | 0.782866i | \(-0.713757\pi\) |
0.366887 | + | 0.930265i | \(0.380424\pi\) | |||||||
\(864\) | 13.5000 | − | 23.3827i | 0.459279 | − | 0.795495i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.0000 | + | 20.7846i | 0.407777 | + | 0.706290i | ||||
\(867\) | −28.5000 | − | 16.4545i | −0.967911 | − | 0.558824i | ||||
\(868\) | −6.00000 | + | 6.92820i | −0.203653 | + | 0.235159i | ||||
\(869\) | − | 55.4256i | − | 1.88019i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.0000 | − | 22.5167i | −1.32146 | − | 0.762948i | ||||
\(872\) | 7.50000 | + | 4.33013i | 0.253982 | + | 0.146637i | ||||
\(873\) | −27.0000 | − | 15.5885i | −0.913812 | − | 0.527589i | ||||
\(874\) | − | 20.7846i | − | 0.703050i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.00000 | + | 5.19615i | −0.101361 | + | 0.175562i | ||||
\(877\) | 16.0000 | + | 27.7128i | 0.540282 | + | 0.935795i | 0.998888 | + | 0.0471555i | \(0.0150156\pi\) |
−0.458606 | + | 0.888640i | \(0.651651\pi\) | |||||||
\(878\) | −6.00000 | + | 10.3923i | −0.202490 | + | 0.350723i | ||||
\(879\) | −36.0000 | + | 20.7846i | −1.21425 | + | 0.701047i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.00000 | −0.303218 | −0.151609 | − | 0.988441i | \(-0.548445\pi\) | ||||
−0.151609 | + | 0.988441i | \(0.548445\pi\) | |||||||
\(882\) | −22.5000 | − | 28.5788i | −0.757614 | − | 0.962300i | ||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 18.0000 | − | 10.3923i | 0.605406 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.5000 | + | 23.3827i | −0.453541 | + | 0.785557i | ||||
\(887\) | 4.50000 | + | 7.79423i | 0.151095 | + | 0.261705i | 0.931630 | − | 0.363407i | \(-0.118387\pi\) |
−0.780535 | + | 0.625112i | \(0.785053\pi\) | |||||||
\(888\) | −6.00000 | + | 10.3923i | −0.201347 | + | 0.348743i | ||||
\(889\) | 40.0000 | − | 13.8564i | 1.34156 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.1769i | 1.04447i | ||||||||
\(892\) | −3.00000 | − | 1.73205i | −0.100447 | − | 0.0579934i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 67.5500i | 2.25921i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21.0000 | + | 24.2487i | −0.701561 | + | 0.810093i | ||||
\(897\) | −9.00000 | − | 5.19615i | −0.300501 | − | 0.173494i | ||||
\(898\) | −10.5000 | − | 18.1865i | −0.350390 | − | 0.606892i | ||||
\(899\) | 3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 18.0000 | 0.599334 | ||||||||
\(903\) | −3.00000 | + | 3.46410i | −0.0998337 | + | 0.115278i | ||||
\(904\) | 12.0000 | 0.399114 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.00000 | − | 5.19615i | −0.0996683 | − | 0.172631i | ||||
\(907\) | 18.5000 | − | 32.0429i | 0.614282 | − | 1.06397i | −0.376228 | − | 0.926527i | \(-0.622779\pi\) |
0.990510 | − | 0.137441i | \(-0.0438878\pi\) | |||||||
\(908\) | −6.00000 | − | 10.3923i | −0.199117 | − | 0.344881i | ||||
\(909\) | −22.5000 | − | 38.9711i | −0.746278 | − | 1.29259i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.2487i | 0.803396i | 0.915772 | + | 0.401698i | \(0.131580\pi\) | ||||
−0.915772 | + | 0.401698i | \(0.868420\pi\) | |||||||
\(912\) | −60.0000 | −1.98680 | ||||||||
\(913\) | −27.0000 | − | 15.5885i | −0.893570 | − | 0.515903i | ||||
\(914\) | −12.0000 | − | 6.92820i | −0.396925 | − | 0.229165i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.0000 | − | 20.7846i | −0.792550 | − | 0.686368i | ||||
\(918\) | −54.0000 | −1.78227 | ||||||||
\(919\) | −8.00000 | − | 13.8564i | −0.263896 | − | 0.457081i | 0.703378 | − | 0.710816i | \(-0.251674\pi\) |
−0.967274 | + | 0.253735i | \(0.918341\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.5000 | + | 33.7750i | 0.642547 | + | 1.11292i | ||||
\(922\) | −45.0000 | + | 25.9808i | −1.48200 | + | 0.855631i | ||||
\(923\) | −24.0000 | −0.789970 | ||||||||
\(924\) | −3.00000 | + | 15.5885i | −0.0986928 | + | 0.512823i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −43.5000 | + | 25.1147i | −1.42950 | + | 0.825321i | ||||
\(927\) | − | 15.5885i | − | 0.511992i | ||||||
\(928\) | −4.50000 | + | 7.79423i | −0.147720 | + | 0.255858i | ||||
\(929\) | −10.5000 | − | 18.1865i | −0.344494 | − | 0.596681i | 0.640768 | − | 0.767735i | \(-0.278616\pi\) |
−0.985262 | + | 0.171054i | \(0.945283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | + | 45.0333i | −0.589926 | + | 1.47591i | ||||
\(932\) | 3.46410i | 0.113470i | ||||||||
\(933\) | − | 41.5692i | − | 1.36092i | ||||||
\(934\) | 31.5000 | + | 18.1865i | 1.03071 | + | 0.595082i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.00000 | + | 15.5885i | −0.294174 | + | 0.509525i | ||||
\(937\) | − | 48.4974i | − | 1.58434i | −0.610299 | − | 0.792171i | \(-0.708951\pi\) | ||
0.610299 | − | 0.792171i | \(-0.291049\pi\) | |||||||
\(938\) | 19.5000 | + | 56.2917i | 0.636698 | + | 1.83799i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.00000 | + | 15.5885i | −0.293392 | + | 0.508169i | −0.974609 | − | 0.223912i | \(-0.928117\pi\) |
0.681218 | + | 0.732081i | \(0.261451\pi\) | |||||||
\(942\) | 9.00000 | − | 5.19615i | 0.293236 | − | 0.169300i | ||||
\(943\) | 4.50000 | − | 2.59808i | 0.146540 | − | 0.0846050i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | 22.5000 | − | 12.9904i | 0.731152 | − | 0.422131i | −0.0876916 | − | 0.996148i | \(-0.527949\pi\) |
0.818843 | + | 0.574017i | \(0.194616\pi\) | |||||||
\(948\) | 24.0000 | − | 13.8564i | 0.779484 | − | 0.450035i | ||||
\(949\) | 6.00000 | − | 10.3923i | 0.194768 | − | 0.337348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.0000 | − | 25.9808i | 0.486408 | − | 0.842484i | ||||
\(952\) | 27.0000 | + | 5.19615i | 0.875075 | + | 0.168408i | ||||
\(953\) | − | 6.92820i | − | 0.224427i | −0.993684 | − | 0.112213i | \(-0.964206\pi\) | ||
0.993684 | − | 0.112213i | \(-0.0357940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.00000 | − | 5.19615i | −0.291081 | − | 0.168056i | ||||
\(957\) | − | 10.3923i | − | 0.335936i | ||||||
\(958\) | − | 10.3923i | − | 0.335760i | ||||||
\(959\) | 54.0000 | + | 10.3923i | 1.74375 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50000 | − | 16.4545i | −0.306452 | − | 0.530790i | ||||
\(962\) | −12.0000 | + | 20.7846i | −0.386896 | + | 0.670123i | ||||
\(963\) | 15.5885i | 0.502331i | ||||||||
\(964\) | −6.00000 | + | 3.46410i | −0.193247 | + | 0.111571i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.50000 | + | 12.9904i | 0.144785 | + | 0.417959i | ||||
\(967\) | −23.0000 | −0.739630 | −0.369815 | − | 0.929105i | \(-0.620579\pi\) | ||||
−0.369815 | + | 0.929105i | \(0.620579\pi\) | |||||||
\(968\) | −1.50000 | + | 0.866025i | −0.0482118 | + | 0.0278351i | ||||
\(969\) | 36.0000 | + | 62.3538i | 1.15649 | + | 2.00309i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.00000 | + | 10.3923i | 0.192549 | + | 0.333505i | 0.946094 | − | 0.323891i | \(-0.104991\pi\) |
−0.753545 | + | 0.657396i | \(0.771658\pi\) | |||||||
\(972\) | −13.5000 | + | 7.79423i | −0.433013 | + | 0.250000i | ||||
\(973\) | −9.00000 | − | 25.9808i | −0.288527 | − | 0.832905i | ||||
\(974\) | 55.4256i | 1.77595i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.5000 | − | 12.9904i | −0.720207 | − | 0.415812i | ||||
\(977\) | 21.0000 | + | 12.1244i | 0.671850 | + | 0.387893i | 0.796777 | − | 0.604273i | \(-0.206537\pi\) |
−0.124928 | + | 0.992166i | \(0.539870\pi\) | |||||||
\(978\) | 24.0000 | 0.767435 | ||||||||
\(979\) | 10.3923i | 0.332140i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.50000 | − | 12.9904i | −0.239457 | − | 0.414751i | ||||
\(982\) | 33.0000 | + | 57.1577i | 1.05307 | + | 1.82397i | ||||
\(983\) | 28.5000 | − | 49.3634i | 0.909009 | − | 1.57445i | 0.0935651 | − | 0.995613i | \(-0.470174\pi\) |
0.815444 | − | 0.578836i | \(-0.196493\pi\) | |||||||
\(984\) | −4.50000 | − | 7.79423i | −0.143455 | − | 0.248471i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.0000 | 0.573237 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.0000 | −0.763542 | ||||||||
\(989\) | 1.50000 | − | 0.866025i | 0.0476972 | − | 0.0275380i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.0000 | + | 29.4449i | −0.540023 | + | 0.935347i | 0.458879 | + | 0.888499i | \(0.348251\pi\) |
−0.998902 | + | 0.0468483i | \(0.985082\pi\) | |||||||
\(992\) | −9.00000 | − | 15.5885i | −0.285750 | − | 0.494934i | ||||
\(993\) | −15.0000 | − | 8.66025i | −0.476011 | − | 0.274825i | ||||
\(994\) | 24.0000 | + | 20.7846i | 0.761234 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 15.5885i | − | 0.493939i | ||||||
\(997\) | −6.00000 | − | 3.46410i | −0.190022 | − | 0.109709i | 0.401971 | − | 0.915652i | \(-0.368325\pi\) |
−0.591993 | + | 0.805943i | \(0.701659\pi\) | |||||||
\(998\) | 21.0000 | + | 12.1244i | 0.664743 | + | 0.383790i | ||||
\(999\) | 18.0000 | − | 10.3923i | 0.569495 | − | 0.328798i |
(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 | 525.2.t.e.101.1 | 2 | ||
3.2 | odd | 2 | 525.2.t.a.101.1 | 2 | |||
5.2 | odd | 4 | 525.2.q.b.374.2 | 4 | |||
5.3 | odd | 4 | 525.2.q.b.374.1 | 4 | |||
5.4 | even | 2 | 105.2.s.a.101.1 | yes | 2 | ||
7.5 | odd | 6 | 525.2.t.a.26.1 | 2 | |||
15.2 | even | 4 | 525.2.q.a.374.1 | 4 | |||
15.8 | even | 4 | 525.2.q.a.374.2 | 4 | |||
15.14 | odd | 2 | 105.2.s.b.101.1 | yes | 2 | ||
21.5 | even | 6 | inner | 525.2.t.e.26.1 | 2 | ||
35.4 | even | 6 | 735.2.b.b.146.1 | 2 | |||
35.9 | even | 6 | 735.2.s.e.656.1 | 2 | |||
35.12 | even | 12 | 525.2.q.a.299.2 | 4 | |||
35.19 | odd | 6 | 105.2.s.b.26.1 | yes | 2 | ||
35.24 | odd | 6 | 735.2.b.a.146.1 | 2 | |||
35.33 | even | 12 | 525.2.q.a.299.1 | 4 | |||
35.34 | odd | 2 | 735.2.s.c.521.1 | 2 | |||
105.44 | odd | 6 | 735.2.s.c.656.1 | 2 | |||
105.47 | odd | 12 | 525.2.q.b.299.1 | 4 | |||
105.59 | even | 6 | 735.2.b.b.146.2 | 2 | |||
105.68 | odd | 12 | 525.2.q.b.299.2 | 4 | |||
105.74 | odd | 6 | 735.2.b.a.146.2 | 2 | |||
105.89 | even | 6 | 105.2.s.a.26.1 | ✓ | 2 | ||
105.104 | even | 2 | 735.2.s.e.521.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.s.a.26.1 | ✓ | 2 | 105.89 | even | 6 | ||
105.2.s.a.101.1 | yes | 2 | 5.4 | even | 2 | ||
105.2.s.b.26.1 | yes | 2 | 35.19 | odd | 6 | ||
105.2.s.b.101.1 | yes | 2 | 15.14 | odd | 2 | ||
525.2.q.a.299.1 | 4 | 35.33 | even | 12 | |||
525.2.q.a.299.2 | 4 | 35.12 | even | 12 | |||
525.2.q.a.374.1 | 4 | 15.2 | even | 4 | |||
525.2.q.a.374.2 | 4 | 15.8 | even | 4 | |||
525.2.q.b.299.1 | 4 | 105.47 | odd | 12 | |||
525.2.q.b.299.2 | 4 | 105.68 | odd | 12 | |||
525.2.q.b.374.1 | 4 | 5.3 | odd | 4 | |||
525.2.q.b.374.2 | 4 | 5.2 | odd | 4 | |||
525.2.t.a.26.1 | 2 | 7.5 | odd | 6 | |||
525.2.t.a.101.1 | 2 | 3.2 | odd | 2 | |||
525.2.t.e.26.1 | 2 | 21.5 | even | 6 | inner | ||
525.2.t.e.101.1 | 2 | 1.1 | even | 1 | trivial | ||
735.2.b.a.146.1 | 2 | 35.24 | odd | 6 | |||
735.2.b.a.146.2 | 2 | 105.74 | odd | 6 | |||
735.2.b.b.146.1 | 2 | 35.4 | even | 6 | |||
735.2.b.b.146.2 | 2 | 105.59 | even | 6 | |||
735.2.s.c.521.1 | 2 | 35.34 | odd | 2 | |||
735.2.s.c.656.1 | 2 | 105.44 | odd | 6 | |||
735.2.s.e.521.1 | 2 | 105.104 | even | 2 | |||
735.2.s.e.656.1 | 2 | 35.9 | even | 6 |