Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(299,525)]
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, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.q (of order \(6\), degree \(2\), not 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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 374.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.374 |
Dual form | 525.2.q.a.299.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 1.50000i | −0.612372 | − | 1.06066i | −0.990839 | − | 0.135045i | \(-0.956882\pi\) |
0.378467 | − | 0.925615i | \(-0.376451\pi\) | |||||||
\(3\) | 1.73205 | 1.00000 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.50000 | − | 2.59808i | −0.612372 | − | 1.06066i | ||||
\(7\) | 0.866025 | + | 2.50000i | 0.327327 | + | 0.944911i | ||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 1.73205i | 0.904534 | + | 0.522233i | 0.878668 | − | 0.477432i | \(-0.158432\pi\) |
0.0258656 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(12\) | −0.866025 | + | 1.50000i | −0.250000 | + | 0.433013i | ||||
\(13\) | 3.46410 | 0.960769 | 0.480384 | − | 0.877058i | \(-0.340497\pi\) | ||||
0.480384 | + | 0.877058i | \(0.340497\pi\) | |||||||
\(14\) | 3.00000 | − | 3.46410i | 0.801784 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.50000 | + | 4.33013i | 0.625000 | + | 1.08253i | ||||
\(17\) | −5.19615 | − | 3.00000i | −1.26025 | − | 0.727607i | −0.287129 | − | 0.957892i | \(-0.592701\pi\) |
−0.973123 | + | 0.230285i | \(0.926034\pi\) | |||||||
\(18\) | −2.59808 | − | 4.50000i | −0.612372 | − | 1.06066i | ||||
\(19\) | 6.00000 | − | 3.46410i | 1.37649 | − | 0.794719i | 0.384759 | − | 0.923017i | \(-0.374285\pi\) |
0.991736 | + | 0.128298i | \(0.0409513\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.50000 | + | 4.33013i | 0.327327 | + | 0.944911i | ||||
\(22\) | − | 6.00000i | − | 1.27920i | ||||||
\(23\) | −0.866025 | − | 1.50000i | −0.180579 | − | 0.312772i | 0.761499 | − | 0.648166i | \(-0.224464\pi\) |
−0.942078 | + | 0.335394i | \(0.891130\pi\) | |||||||
\(24\) | −3.00000 | −0.612372 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | − | 5.19615i | −0.588348 | − | 1.01905i | ||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | −2.59808 | − | 0.500000i | −0.490990 | − | 0.0944911i | ||||
\(29\) | 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 | \(0.767359\pi\) | |||||||
\(32\) | 2.59808 | − | 4.50000i | 0.459279 | − | 0.795495i | ||||
\(33\) | 5.19615 | + | 3.00000i | 0.904534 | + | 0.522233i | ||||
\(34\) | 10.3923i | 1.78227i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | + | 2.59808i | −0.250000 | + | 0.433013i | ||||
\(37\) | −3.46410 | + | 2.00000i | −0.569495 | + | 0.328798i | −0.756948 | − | 0.653476i | \(-0.773310\pi\) |
0.187453 | + | 0.982274i | \(0.439977\pi\) | |||||||
\(38\) | −10.3923 | − | 6.00000i | −1.68585 | − | 0.973329i | ||||
\(39\) | 6.00000 | 0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 5.19615 | − | 6.00000i | 0.801784 | − | 0.925820i | ||||
\(43\) | 1.00000i | 0.152499i | 0.997089 | + | 0.0762493i | \(0.0242945\pi\) | ||||
−0.997089 | + | 0.0762493i | \(0.975706\pi\) | |||||||
\(44\) | −3.00000 | + | 1.73205i | −0.452267 | + | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 4.33013 | + | 7.50000i | 0.625000 | + | 1.08253i | ||||
\(49\) | −5.50000 | + | 4.33013i | −0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.00000 | − | 5.19615i | −1.26025 | − | 0.727607i | ||||
\(52\) | −1.73205 | + | 3.00000i | −0.240192 | + | 0.416025i | ||||
\(53\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(54\) | −4.50000 | − | 7.79423i | −0.612372 | − | 1.06066i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.50000 | − | 4.33013i | −0.200446 | − | 0.578638i | ||||
\(57\) | 10.3923 | − | 6.00000i | 1.37649 | − | 0.794719i | ||||
\(58\) | 2.59808 | − | 1.50000i | 0.341144 | − | 0.196960i | ||||
\(59\) | 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 | \(0.441276\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | 2.59808 | + | 7.50000i | 0.327327 | + | 0.944911i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 10.3923i | − | 1.27920i | ||||||
\(67\) | −11.2583 | − | 6.50000i | −1.37542 | − | 0.794101i | −0.383819 | − | 0.923408i | \(-0.625391\pi\) |
−0.991605 | + | 0.129307i | \(0.958725\pi\) | |||||||
\(68\) | 5.19615 | − | 3.00000i | 0.630126 | − | 0.363803i | ||||
\(69\) | −1.50000 | − | 2.59808i | −0.180579 | − | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.92820i | − | 0.822226i | −0.911584 | − | 0.411113i | \(-0.865140\pi\) | ||
0.911584 | − | 0.411113i | \(-0.134860\pi\) | |||||||
\(72\) | −5.19615 | −0.612372 | ||||||||
\(73\) | −1.73205 | + | 3.00000i | −0.202721 | + | 0.351123i | −0.949404 | − | 0.314057i | \(-0.898312\pi\) |
0.746683 | + | 0.665180i | \(0.231645\pi\) | |||||||
\(74\) | 6.00000 | + | 3.46410i | 0.697486 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.92820i | 0.794719i | ||||||||
\(77\) | −1.73205 | + | 9.00000i | −0.197386 | + | 1.02565i | ||||
\(78\) | −5.19615 | − | 9.00000i | −0.588348 | − | 1.01905i | ||||
\(79\) | −8.00000 | − | 13.8564i | −0.900070 | − | 1.55897i | −0.827401 | − | 0.561611i | \(-0.810182\pi\) |
−0.0726692 | − | 0.997356i | \(-0.523152\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | −2.59808 | − | 4.50000i | −0.286910 | − | 0.496942i | ||||
\(83\) | 9.00000i | 0.987878i | 0.869496 | + | 0.493939i | \(0.164443\pi\) | ||||
−0.869496 | + | 0.493939i | \(0.835557\pi\) | |||||||
\(84\) | −4.50000 | − | 0.866025i | −0.490990 | − | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.50000 | − | 0.866025i | 0.161749 | − | 0.0933859i | ||||
\(87\) | 3.00000i | 0.321634i | ||||||||
\(88\) | −5.19615 | − | 3.00000i | −0.553912 | − | 0.319801i | ||||
\(89\) | −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 | ||||
\(92\) | 1.73205 | 0.180579 | ||||||||
\(93\) | −5.19615 | − | 3.00000i | −0.538816 | − | 0.311086i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.50000 | − | 7.79423i | 0.459279 | − | 0.795495i | ||||
\(97\) | 10.3923 | 1.05518 | 0.527589 | − | 0.849500i | \(-0.323096\pi\) | ||||
0.527589 | + | 0.849500i | \(0.323096\pi\) | |||||||
\(98\) | 11.2583 | + | 4.50000i | 1.13726 | + | 0.454569i | ||||
\(99\) | 9.00000 | + | 5.19615i | 0.904534 | + | 0.522233i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.50000 | + | 12.9904i | −0.746278 | + | 1.29259i | 0.203317 | + | 0.979113i | \(0.434828\pi\) |
−0.949595 | + | 0.313478i | \(0.898506\pi\) | |||||||
\(102\) | 18.0000i | 1.78227i | ||||||||
\(103\) | −2.59808 | − | 4.50000i | −0.255996 | − | 0.443398i | 0.709170 | − | 0.705038i | \(-0.249070\pi\) |
−0.965166 | + | 0.261640i | \(0.915737\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.59808 | + | 4.50000i | 0.251166 | + | 0.435031i | 0.963847 | − | 0.266456i | \(-0.0858528\pi\) |
−0.712681 | + | 0.701488i | \(0.752519\pi\) | |||||||
\(108\) | −2.59808 | + | 4.50000i | −0.250000 | + | 0.433013i | ||||
\(109\) | −2.50000 | + | 4.33013i | −0.239457 | + | 0.414751i | −0.960558 | − | 0.278078i | \(-0.910303\pi\) |
0.721102 | + | 0.692829i | \(0.243636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | + | 3.46410i | −0.569495 | + | 0.328798i | ||||
\(112\) | −8.66025 | + | 10.0000i | −0.818317 | + | 0.944911i | ||||
\(113\) | 6.92820 | 0.651751 | 0.325875 | − | 0.945413i | \(-0.394341\pi\) | ||||
0.325875 | + | 0.945413i | \(0.394341\pi\) | |||||||
\(114\) | −18.0000 | − | 10.3923i | −1.68585 | − | 0.973329i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.50000 | − | 0.866025i | −0.139272 | − | 0.0804084i | ||||
\(117\) | 10.3923 | 0.960769 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | − | 15.5885i | 0.275010 | − | 1.42899i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 7.79423 | + | 4.50000i | 0.705656 | + | 0.407411i | ||||
\(123\) | 5.19615 | 0.468521 | ||||||||
\(124\) | 3.00000 | − | 1.73205i | 0.269408 | − | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.00000 | − | 10.3923i | 0.801784 | − | 0.925820i | ||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | −6.06218 | − | 10.5000i | −0.535826 | − | 0.928078i | ||||
\(129\) | 1.73205i | 0.152499i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | + | 10.3923i | 0.524222 | + | 0.907980i | 0.999602 | + | 0.0281993i | \(0.00897729\pi\) |
−0.475380 | + | 0.879781i | \(0.657689\pi\) | |||||||
\(132\) | −5.19615 | + | 3.00000i | −0.452267 | + | 0.261116i | ||||
\(133\) | 13.8564 | + | 12.0000i | 1.20150 | + | 1.04053i | ||||
\(134\) | 22.5167i | 1.94514i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.00000 | + | 5.19615i | 0.771744 | + | 0.445566i | ||||
\(137\) | 10.3923 | − | 18.0000i | 0.887875 | − | 1.53784i | 0.0454914 | − | 0.998965i | \(-0.485515\pi\) |
0.842383 | − | 0.538879i | \(-0.181152\pi\) | |||||||
\(138\) | −2.59808 | + | 4.50000i | −0.221163 | + | 0.383065i | ||||
\(139\) | 10.3923i | 0.881464i | 0.897639 | + | 0.440732i | \(0.145281\pi\) | ||||
−0.897639 | + | 0.440732i | \(0.854719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.3923 | + | 6.00000i | −0.872103 | + | 0.503509i | ||||
\(143\) | 10.3923 | + | 6.00000i | 0.869048 | + | 0.501745i | ||||
\(144\) | 7.50000 | + | 12.9904i | 0.625000 | + | 1.08253i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | −9.52628 | + | 7.50000i | −0.785714 | + | 0.618590i | ||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | −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 | \(0.140734\pi\) | |||||||
\(152\) | −10.3923 | + | 6.00000i | −0.842927 | + | 0.486664i | ||||
\(153\) | −15.5885 | − | 9.00000i | −1.26025 | − | 0.727607i | ||||
\(154\) | 15.0000 | − | 5.19615i | 1.20873 | − | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.00000 | + | 5.19615i | −0.240192 | + | 0.416025i | ||||
\(157\) | −1.73205 | + | 3.00000i | −0.138233 | + | 0.239426i | −0.926828 | − | 0.375487i | \(-0.877476\pi\) |
0.788595 | + | 0.614913i | \(0.210809\pi\) | |||||||
\(158\) | −13.8564 | + | 24.0000i | −1.10236 | + | 1.90934i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.00000 | − | 3.46410i | 0.236433 | − | 0.273009i | ||||
\(162\) | −7.79423 | − | 13.5000i | −0.612372 | − | 1.06066i | ||||
\(163\) | 6.92820 | − | 4.00000i | 0.542659 | − | 0.313304i | −0.203497 | − | 0.979076i | \(-0.565231\pi\) |
0.746156 | + | 0.665771i | \(0.231897\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.5000 | − | 7.79423i | 1.04780 | − | 0.604949i | ||||
\(167\) | 21.0000i | 1.62503i | 0.582941 | + | 0.812514i | \(0.301902\pi\) | ||||
−0.582941 | + | 0.812514i | \(0.698098\pi\) | |||||||
\(168\) | −2.59808 | − | 7.50000i | −0.200446 | − | 0.578638i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.0000 | − | 10.3923i | 1.37649 | − | 0.794719i | ||||
\(172\) | −0.866025 | − | 0.500000i | −0.0660338 | − | 0.0381246i | ||||
\(173\) | 10.3923 | − | 6.00000i | 0.790112 | − | 0.456172i | −0.0498898 | − | 0.998755i | \(-0.515887\pi\) |
0.840002 | + | 0.542583i | \(0.182554\pi\) | |||||||
\(174\) | 4.50000 | − | 2.59808i | 0.341144 | − | 0.196960i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.3205i | 1.30558i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.59808 | + | 4.50000i | −0.194734 | + | 0.337289i | ||||
\(179\) | −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 | \(-0.0618586\pi\) | |||||||
\(182\) | 10.3923 | − | 12.0000i | 0.770329 | − | 0.889499i | ||||
\(183\) | −7.79423 | + | 4.50000i | −0.576166 | + | 0.332650i | ||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.3923i | 0.762001i | ||||||||
\(187\) | −10.3923 | − | 18.0000i | −0.759961 | − | 1.31629i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50000 | + | 12.9904i | 0.327327 | + | 0.944911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | + | 5.19615i | −0.651217 | + | 0.375980i | −0.788922 | − | 0.614493i | \(-0.789361\pi\) |
0.137705 | + | 0.990473i | \(0.456027\pi\) | |||||||
\(192\) | 1.73205 | 0.125000 | ||||||||
\(193\) | −19.0526 | − | 11.0000i | −1.37143 | − | 0.791797i | −0.380325 | − | 0.924853i | \(-0.624188\pi\) |
−0.991109 | + | 0.133056i | \(0.957521\pi\) | |||||||
\(194\) | −9.00000 | − | 15.5885i | −0.646162 | − | 1.11919i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | −3.46410 | −0.246807 | −0.123404 | − | 0.992357i | \(-0.539381\pi\) | ||||
−0.123404 | + | 0.992357i | \(0.539381\pi\) | |||||||
\(198\) | − | 18.0000i | − | 1.27920i | ||||||
\(199\) | −6.00000 | − | 3.46410i | −0.425329 | − | 0.245564i | 0.272026 | − | 0.962290i | \(-0.412306\pi\) |
−0.697355 | + | 0.716726i | \(0.745640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.5000 | − | 11.2583i | −1.37542 | − | 0.794101i | ||||
\(202\) | 25.9808 | 1.82800 | ||||||||
\(203\) | −4.33013 | + | 1.50000i | −0.303915 | + | 0.105279i | ||||
\(204\) | 9.00000 | − | 5.19615i | 0.630126 | − | 0.363803i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.50000 | + | 7.79423i | −0.313530 | + | 0.543050i | ||||
\(207\) | −2.59808 | − | 4.50000i | −0.180579 | − | 0.312772i | ||||
\(208\) | 8.66025 | + | 15.0000i | 0.600481 | + | 1.04006i | ||||
\(209\) | 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 | ||||||||
\(213\) | − | 12.0000i | − | 0.822226i | ||||||
\(214\) | 4.50000 | − | 7.79423i | 0.307614 | − | 0.532803i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −9.00000 | −0.612372 | ||||||||
\(217\) | 1.73205 | − | 9.00000i | 0.117579 | − | 0.610960i | ||||
\(218\) | 8.66025 | 0.586546 | ||||||||
\(219\) | −3.00000 | + | 5.19615i | −0.202721 | + | 0.351123i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0000 | − | 10.3923i | −1.21081 | − | 0.699062i | ||||
\(222\) | 10.3923 | + | 6.00000i | 0.697486 | + | 0.402694i | ||||
\(223\) | −3.46410 | −0.231973 | −0.115987 | − | 0.993251i | \(-0.537003\pi\) | ||||
−0.115987 | + | 0.993251i | \(0.537003\pi\) | |||||||
\(224\) | 13.5000 | + | 2.59808i | 0.902007 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | − | 10.3923i | −0.399114 | − | 0.691286i | ||||
\(227\) | −10.3923 | − | 6.00000i | −0.689761 | − | 0.398234i | 0.113761 | − | 0.993508i | \(-0.463710\pi\) |
−0.803523 | + | 0.595274i | \(0.797043\pi\) | |||||||
\(228\) | 12.0000i | 0.794719i | ||||||||
\(229\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | + | 15.5885i | −0.197386 | + | 1.02565i | ||||
\(232\) | − | 3.00000i | − | 0.196960i | ||||||
\(233\) | −1.73205 | − | 3.00000i | −0.113470 | − | 0.196537i | 0.803697 | − | 0.595039i | \(-0.202863\pi\) |
−0.917167 | + | 0.398502i | \(0.869530\pi\) | |||||||
\(234\) | −9.00000 | − | 15.5885i | −0.588348 | − | 1.01905i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.8564 | − | 24.0000i | −0.900070 | − | 1.55897i | ||||
\(238\) | −25.9808 | + | 9.00000i | −1.68408 | + | 0.583383i | ||||
\(239\) | − | 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 | \(0.738298\pi\) | |||||||
\(242\) | 0.866025 | − | 1.50000i | 0.0556702 | − | 0.0964237i | ||||
\(243\) | 15.5885 | 1.00000 | ||||||||
\(244\) | − | 5.19615i | − | 0.332650i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.50000 | − | 7.79423i | −0.286910 | − | 0.496942i | ||||
\(247\) | 20.7846 | − | 12.0000i | 1.32249 | − | 0.763542i | ||||
\(248\) | 5.19615 | + | 3.00000i | 0.329956 | + | 0.190500i | ||||
\(249\) | 15.5885i | 0.987878i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | −7.79423 | − | 1.50000i | −0.490990 | − | 0.0944911i | ||||
\(253\) | − | 6.00000i | − | 0.377217i | ||||||
\(254\) | 24.0000 | − | 13.8564i | 1.50589 | − | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.50000 | + | 16.4545i | −0.593750 | + | 1.02841i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 2.59808 | − | 1.50000i | 0.161749 | − | 0.0933859i | ||||
\(259\) | −8.00000 | − | 6.92820i | −0.497096 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.19615i | 0.321634i | ||||||||
\(262\) | 10.3923 | − | 18.0000i | 0.642039 | − | 1.11204i | ||||
\(263\) | 0.866025 | − | 1.50000i | 0.0534014 | − | 0.0924940i | −0.838089 | − | 0.545534i | \(-0.816327\pi\) |
0.891490 | + | 0.453040i | \(0.149660\pi\) | |||||||
\(264\) | −9.00000 | − | 5.19615i | −0.553912 | − | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.00000 | − | 31.1769i | 0.367884 | − | 1.91158i | ||||
\(267\) | −2.59808 | − | 4.50000i | −0.159000 | − | 0.275396i | ||||
\(268\) | 11.2583 | − | 6.50000i | 0.687712 | − | 0.397051i | ||||
\(269\) | 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 | \(0.265847\pi\) | |||||||
\(272\) | − | 30.0000i | − | 1.81902i | ||||||
\(273\) | 5.19615 | + | 15.0000i | 0.314485 | + | 0.907841i | ||||
\(274\) | −36.0000 | −2.17484 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.00000 | 0.180579 | ||||||||
\(277\) | 22.5167 | + | 13.0000i | 1.35290 | + | 0.781094i | 0.988654 | − | 0.150210i | \(-0.0479951\pi\) |
0.364241 | + | 0.931305i | \(0.381328\pi\) | |||||||
\(278\) | 15.5885 | − | 9.00000i | 0.934934 | − | 0.539784i | ||||
\(279\) | −9.00000 | − | 5.19615i | −0.538816 | − | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.92820i | − | 0.413302i | −0.978415 | − | 0.206651i | \(-0.933744\pi\) | ||
0.978415 | − | 0.206651i | \(-0.0662565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5885 | − | 27.0000i | 0.926638 | − | 1.60498i | 0.137732 | − | 0.990470i | \(-0.456019\pi\) |
0.788906 | − | 0.614514i | \(-0.210648\pi\) | |||||||
\(284\) | 6.00000 | + | 3.46410i | 0.356034 | + | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 20.7846i | − | 1.22902i | ||||||
\(287\) | 2.59808 | + | 7.50000i | 0.153360 | + | 0.442711i | ||||
\(288\) | 7.79423 | − | 13.5000i | 0.459279 | − | 0.795495i | ||||
\(289\) | 9.50000 | + | 16.4545i | 0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.0000 | 1.05518 | ||||||||
\(292\) | −1.73205 | − | 3.00000i | −0.101361 | − | 0.175562i | ||||
\(293\) | − | 24.0000i | − | 1.40209i | −0.713115 | − | 0.701047i | \(-0.752716\pi\) | ||
0.713115 | − | 0.701047i | \(-0.247284\pi\) | |||||||
\(294\) | 19.5000 | + | 7.79423i | 1.13726 | + | 0.454569i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.00000 | − | 3.46410i | 0.348743 | − | 0.201347i | ||||
\(297\) | 15.5885 | + | 9.00000i | 0.904534 | + | 0.522233i | ||||
\(298\) | 33.7750 | + | 19.5000i | 1.95653 | + | 1.12960i | ||||
\(299\) | −3.00000 | − | 5.19615i | −0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.50000 | + | 0.866025i | −0.144098 | + | 0.0499169i | ||||
\(302\) | −3.46410 | −0.199337 | ||||||||
\(303\) | −12.9904 | + | 22.5000i | −0.746278 | + | 1.29259i | ||||
\(304\) | 30.0000 | + | 17.3205i | 1.72062 | + | 0.993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 31.1769i | 1.78227i | ||||||||
\(307\) | −22.5167 | −1.28509 | −0.642547 | − | 0.766246i | \(-0.722122\pi\) | ||||
−0.642547 | + | 0.766246i | \(0.722122\pi\) | |||||||
\(308\) | −6.92820 | − | 6.00000i | −0.394771 | − | 0.341882i | ||||
\(309\) | −4.50000 | − | 7.79423i | −0.255996 | − | 0.443398i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | + | 20.7846i | −0.680458 | + | 1.17859i | 0.294384 | + | 0.955687i | \(0.404886\pi\) |
−0.974841 | + | 0.222900i | \(0.928448\pi\) | |||||||
\(312\) | −10.3923 | −0.588348 | ||||||||
\(313\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(314\) | 6.00000 | 0.338600 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | −8.66025 | − | 15.0000i | −0.486408 | − | 0.842484i | 0.513470 | − | 0.858108i | \(-0.328360\pi\) |
−0.999878 | + | 0.0156238i | \(0.995027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.50000 | + | 7.79423i | 0.251166 | + | 0.435031i | ||||
\(322\) | −7.79423 | − | 1.50000i | −0.434355 | − | 0.0835917i | ||||
\(323\) | −41.5692 | −2.31297 | ||||||||
\(324\) | −4.50000 | + | 7.79423i | −0.250000 | + | 0.433013i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.0000 | − | 6.92820i | −0.664619 | − | 0.383718i | ||||
\(327\) | −4.33013 | + | 7.50000i | −0.239457 | + | 0.414751i | ||||
\(328\) | −5.19615 | −0.286910 | ||||||||
\(329\) | 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 | \(0.921953\pi\) | |||||||
\(332\) | −7.79423 | − | 4.50000i | −0.427764 | − | 0.246970i | ||||
\(333\) | −10.3923 | + | 6.00000i | −0.569495 | + | 0.328798i | ||||
\(334\) | 31.5000 | − | 18.1865i | 1.72360 | − | 0.995123i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −15.0000 | + | 17.3205i | −0.818317 | + | 0.944911i | ||||
\(337\) | 32.0000i | 1.74315i | 0.490261 | + | 0.871576i | \(0.336901\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 0.866025 | + | 1.50000i | 0.0471056 | + | 0.0815892i | ||||
\(339\) | 12.0000 | 0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | − | 10.3923i | −0.324918 | − | 0.562775i | ||||
\(342\) | −31.1769 | − | 18.0000i | −1.68585 | − | 0.973329i | ||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | − | 1.73205i | − | 0.0933859i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | − | 10.3923i | −0.967686 | − | 0.558694i | ||||
\(347\) | −9.52628 | + | 16.5000i | −0.511397 | + | 0.885766i | 0.488515 | + | 0.872555i | \(0.337539\pi\) |
−0.999913 | + | 0.0132111i | \(0.995795\pi\) | |||||||
\(348\) | −2.59808 | − | 1.50000i | −0.139272 | − | 0.0804084i | ||||
\(349\) | − | 8.66025i | − | 0.463573i | −0.972767 | − | 0.231786i | \(-0.925543\pi\) | ||
0.972767 | − | 0.231786i | \(-0.0744570\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | 0.960769 | ||||||||
\(352\) | 15.5885 | − | 9.00000i | 0.830868 | − | 0.479702i | ||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.00000 | 0.159000 | ||||||||
\(357\) | 5.19615 | − | 27.0000i | 0.275010 | − | 1.42899i | ||||
\(358\) | 18.0000i | 0.951330i | ||||||||
\(359\) | −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 | ||||
\(362\) | −7.79423 | + | 4.50000i | −0.409656 | + | 0.236515i | ||||
\(363\) | 0.866025 | + | 1.50000i | 0.0454545 | + | 0.0787296i | ||||
\(364\) | −9.00000 | − | 1.73205i | −0.471728 | − | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.5000 | + | 7.79423i | 0.705656 | + | 0.407411i | ||||
\(367\) | 7.79423 | − | 13.5000i | 0.406855 | − | 0.704694i | −0.587680 | − | 0.809093i | \(-0.699959\pi\) |
0.994535 | + | 0.104399i | \(0.0332919\pi\) | |||||||
\(368\) | 4.33013 | − | 7.50000i | 0.225723 | − | 0.390965i | ||||
\(369\) | 9.00000 | 0.468521 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.19615 | − | 3.00000i | 0.269408 | − | 0.155543i | ||||
\(373\) | −3.46410 | + | 2.00000i | −0.179364 | + | 0.103556i | −0.586994 | − | 0.809591i | \(-0.699689\pi\) |
0.407630 | + | 0.913147i | \(0.366355\pi\) | |||||||
\(374\) | −18.0000 | + | 31.1769i | −0.930758 | + | 1.61212i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | 15.5885 | − | 18.0000i | 0.801784 | − | 0.925820i | ||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.7128i | 1.41977i | ||||||||
\(382\) | 15.5885 | + | 9.00000i | 0.797575 | + | 0.460480i | ||||
\(383\) | −18.1865 | + | 10.5000i | −0.929288 | + | 0.536525i | −0.886586 | − | 0.462563i | \(-0.846930\pi\) |
−0.0427020 | + | 0.999088i | \(0.513597\pi\) | |||||||
\(384\) | −10.5000 | − | 18.1865i | −0.535826 | − | 0.928078i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 38.1051i | 1.93950i | ||||||||
\(387\) | 3.00000i | 0.152499i | ||||||||
\(388\) | −5.19615 | + | 9.00000i | −0.263795 | + | 0.456906i | ||||
\(389\) | 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 | ||||||||
\(392\) | 9.52628 | − | 7.50000i | 0.481150 | − | 0.378807i | ||||
\(393\) | 10.3923 | + | 18.0000i | 0.524222 | + | 0.907980i | ||||
\(394\) | 3.00000 | + | 5.19615i | 0.151138 | + | 0.261778i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.00000 | + | 5.19615i | −0.452267 | + | 0.261116i | ||||
\(397\) | 12.1244 | + | 21.0000i | 0.608504 | + | 1.05396i | 0.991487 | + | 0.130204i | \(0.0415634\pi\) |
−0.382983 | + | 0.923755i | \(0.625103\pi\) | |||||||
\(398\) | 12.0000i | 0.601506i | ||||||||
\(399\) | 24.0000 | + | 20.7846i | 1.20150 | + | 1.04053i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5000 | − | 9.52628i | 0.823971 | − | 0.475720i | −0.0278131 | − | 0.999613i | \(-0.508854\pi\) |
0.851784 | + | 0.523893i | \(0.175521\pi\) | |||||||
\(402\) | 39.0000i | 1.94514i | ||||||||
\(403\) | −10.3923 | − | 6.00000i | −0.517678 | − | 0.298881i | ||||
\(404\) | −7.50000 | − | 12.9904i | −0.373139 | − | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 5.19615i | 0.297775 | + | 0.257881i | ||||
\(407\) | −13.8564 | −0.686837 | ||||||||
\(408\) | 15.5885 | + | 9.00000i | 0.771744 | + | 0.445566i | ||||
\(409\) | −19.5000 | − | 11.2583i | −0.964213 | − | 0.556689i | −0.0667458 | − | 0.997770i | \(-0.521262\pi\) |
−0.897467 | + | 0.441081i | \(0.854595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0000 | − | 31.1769i | 0.887875 | − | 1.53784i | ||||
\(412\) | 5.19615 | 0.255996 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.50000 | + | 7.79423i | −0.221163 | + | 0.383065i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.00000 | − | 15.5885i | 0.441261 | − | 0.764287i | ||||
\(417\) | 18.0000i | 0.881464i | ||||||||
\(418\) | −20.7846 | − | 36.0000i | −1.01661 | − | 1.76082i | ||||
\(419\) | 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 | \(0.174843\pi\) | |||||||
\(422\) | 17.3205 | + | 30.0000i | 0.843149 | + | 1.46038i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −18.0000 | + | 10.3923i | −0.872103 | + | 0.503509i | ||||
\(427\) | −10.3923 | − | 9.00000i | −0.502919 | − | 0.435541i | ||||
\(428\) | −5.19615 | −0.251166 | ||||||||
\(429\) | 18.0000 | + | 10.3923i | 0.869048 | + | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.00000 | − | 5.19615i | −0.433515 | − | 0.250290i | 0.267328 | − | 0.963606i | \(-0.413859\pi\) |
−0.700843 | + | 0.713316i | \(0.747193\pi\) | |||||||
\(432\) | 12.9904 | + | 22.5000i | 0.625000 | + | 1.08253i | ||||
\(433\) | 13.8564 | 0.665896 | 0.332948 | − | 0.942945i | \(-0.391957\pi\) | ||||
0.332948 | + | 0.942945i | \(0.391957\pi\) | |||||||
\(434\) | −15.0000 | + | 5.19615i | −0.720023 | + | 0.249423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.50000 | − | 4.33013i | −0.119728 | − | 0.207375i | ||||
\(437\) | −10.3923 | − | 6.00000i | −0.497131 | − | 0.287019i | ||||
\(438\) | 10.3923 | 0.496564 | ||||||||
\(439\) | 6.00000 | − | 3.46410i | 0.286364 | − | 0.165333i | −0.349937 | − | 0.936773i | \(-0.613797\pi\) |
0.636301 | + | 0.771441i | \(0.280464\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.5000 | + | 12.9904i | −0.785714 | + | 0.618590i | ||||
\(442\) | 36.0000i | 1.71235i | ||||||||
\(443\) | −7.79423 | − | 13.5000i | −0.370315 | − | 0.641404i | 0.619299 | − | 0.785155i | \(-0.287417\pi\) |
−0.989614 | + | 0.143751i | \(0.954084\pi\) | |||||||
\(444\) | − | 6.92820i | − | 0.328798i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.00000 | + | 5.19615i | 0.142054 | + | 0.246045i | ||||
\(447\) | −33.7750 | + | 19.5000i | −1.59750 | + | 0.922318i | ||||
\(448\) | 0.866025 | + | 2.50000i | 0.0409159 | + | 0.118114i | ||||
\(449\) | − | 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 | ||||
\(452\) | −3.46410 | + | 6.00000i | −0.162938 | + | 0.282216i | ||||
\(453\) | 1.73205 | − | 3.00000i | 0.0813788 | − | 0.140952i | ||||
\(454\) | 20.7846i | 0.975470i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.0000 | + | 10.3923i | −0.842927 | + | 0.486664i | ||||
\(457\) | 6.92820 | − | 4.00000i | 0.324088 | − | 0.187112i | −0.329125 | − | 0.944286i | \(-0.606754\pi\) |
0.653213 | + | 0.757174i | \(0.273421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.0000 | − | 15.5885i | −1.26025 | − | 0.727607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0000 | 1.39724 | 0.698620 | − | 0.715493i | \(-0.253798\pi\) | ||||
0.698620 | + | 0.715493i | \(0.253798\pi\) | |||||||
\(462\) | 25.9808 | − | 9.00000i | 1.20873 | − | 0.418718i | ||||
\(463\) | 29.0000i | 1.34774i | 0.738848 | + | 0.673872i | \(0.235370\pi\) | ||||
−0.738848 | + | 0.673872i | \(0.764630\pi\) | |||||||
\(464\) | −7.50000 | + | 4.33013i | −0.348179 | + | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | 18.1865 | − | 10.5000i | 0.841572 | − | 0.485882i | −0.0162260 | − | 0.999868i | \(-0.505165\pi\) |
0.857798 | + | 0.513986i | \(0.171832\pi\) | |||||||
\(468\) | −5.19615 | + | 9.00000i | −0.240192 | + | 0.416025i | ||||
\(469\) | 6.50000 | − | 33.7750i | 0.300142 | − | 1.55958i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | + | 5.19615i | −0.138233 | + | 0.239426i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.73205 | + | 3.00000i | −0.0796398 | + | 0.137940i | ||||
\(474\) | −24.0000 | + | 41.5692i | −1.10236 | + | 1.90934i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | + | 10.3923i | 0.550019 | + | 0.476331i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.5885 | + | 9.00000i | −0.712999 | + | 0.411650i | ||||
\(479\) | 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 | ||||
\(482\) | 12.0000i | 0.546585i | ||||||||
\(483\) | 5.19615 | − | 6.00000i | 0.236433 | − | 0.273009i | ||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.5000 | − | 23.3827i | −0.612372 | − | 1.06066i | ||||
\(487\) | −27.7128 | − | 16.0000i | −1.25579 | − | 0.725029i | −0.283535 | − | 0.958962i | \(-0.591507\pi\) |
−0.972253 | + | 0.233933i | \(0.924840\pi\) | |||||||
\(488\) | 7.79423 | − | 4.50000i | 0.352828 | − | 0.203705i | ||||
\(489\) | 12.0000 | − | 6.92820i | 0.542659 | − | 0.313304i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 38.1051i | − | 1.71966i | −0.510581 | − | 0.859830i | \(-0.670569\pi\) | ||
0.510581 | − | 0.859830i | \(-0.329431\pi\) | |||||||
\(492\) | −2.59808 | + | 4.50000i | −0.117130 | + | 0.202876i | ||||
\(493\) | 5.19615 | − | 9.00000i | 0.234023 | − | 0.405340i | ||||
\(494\) | −36.0000 | − | 20.7846i | −1.61972 | − | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 17.3205i | − | 0.777714i | ||||||
\(497\) | 17.3205 | − | 6.00000i | 0.776931 | − | 0.269137i | ||||
\(498\) | 23.3827 | − | 13.5000i | 1.04780 | − | 0.604949i | ||||
\(499\) | −7.00000 | − | 12.1244i | −0.313363 | − | 0.542761i | 0.665725 | − | 0.746197i | \(-0.268122\pi\) |
−0.979088 | + | 0.203436i | \(0.934789\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 36.3731i | 1.62503i | ||||||||
\(502\) | −15.5885 | − | 27.0000i | −0.695747 | − | 1.20507i | ||||
\(503\) | 15.0000i | 0.668817i | 0.942428 | + | 0.334408i | \(0.108537\pi\) | ||||
−0.942428 | + | 0.334408i | \(0.891463\pi\) | |||||||
\(504\) | −4.50000 | − | 12.9904i | −0.200446 | − | 0.578638i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00000 | + | 5.19615i | −0.400099 | + | 0.230997i | ||||
\(507\) | −1.73205 | −0.0769231 | ||||||||
\(508\) | −13.8564 | − | 8.00000i | −0.614779 | − | 0.354943i | ||||
\(509\) | 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 | ||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | 31.1769 | − | 18.0000i | 1.37649 | − | 0.794719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.50000 | − | 0.866025i | −0.0660338 | − | 0.0381246i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.46410 | + | 18.0000i | −0.152204 | + | 0.790875i | ||||
\(519\) | 18.0000 | − | 10.3923i | 0.790112 | − | 0.456172i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0000 | − | 25.9808i | 0.657162 | − | 1.13824i | −0.324185 | − | 0.945994i | \(-0.605090\pi\) |
0.981347 | − | 0.192244i | \(-0.0615766\pi\) | |||||||
\(522\) | 7.79423 | − | 4.50000i | 0.341144 | − | 0.196960i | ||||
\(523\) | 12.1244 | + | 21.0000i | 0.530161 | + | 0.918266i | 0.999381 | + | 0.0351845i | \(0.0112019\pi\) |
−0.469220 | + | 0.883081i | \(0.655465\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | −0.130806 | ||||||||
\(527\) | 10.3923 | + | 18.0000i | 0.452696 | + | 0.784092i | ||||
\(528\) | 30.0000i | 1.30558i | ||||||||
\(529\) | 10.0000 | − | 17.3205i | 0.434783 | − | 0.753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.3205 | + | 6.00000i | −0.750939 | + | 0.260133i | ||||
\(533\) | 10.3923 | 0.450141 | ||||||||
\(534\) | −4.50000 | + | 7.79423i | −0.194734 | + | 0.337289i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 19.5000 | + | 11.2583i | 0.842272 | + | 0.486286i | ||||
\(537\) | −15.5885 | − | 9.00000i | −0.672692 | − | 0.388379i | ||||
\(538\) | −5.19615 | −0.224022 | ||||||||
\(539\) | −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 | \(-0.380917\pi\) | |||||||
\(542\) | −10.3923 | − | 6.00000i | −0.446388 | − | 0.257722i | ||||
\(543\) | − | 9.00000i | − | 0.386227i | ||||||
\(544\) | −27.0000 | + | 15.5885i | −1.15762 | + | 0.668350i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 18.0000 | − | 20.7846i | 0.770329 | − | 0.889499i | ||||
\(547\) | 1.00000i | 0.0427569i | 0.999771 | + | 0.0213785i | \(0.00680549\pi\) | ||||
−0.999771 | + | 0.0213785i | \(0.993195\pi\) | |||||||
\(548\) | 10.3923 | + | 18.0000i | 0.443937 | + | 0.768922i | ||||
\(549\) | −13.5000 | + | 7.79423i | −0.576166 | + | 0.332650i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | + | 10.3923i | 0.255609 | + | 0.442727i | ||||
\(552\) | 2.59808 | + | 4.50000i | 0.110581 | + | 0.191533i | ||||
\(553\) | 27.7128 | − | 32.0000i | 1.17847 | − | 1.36078i | ||||
\(554\) | − | 45.0333i | − | 1.91328i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.00000 | − | 5.19615i | −0.381685 | − | 0.220366i | ||||
\(557\) | 8.66025 | − | 15.0000i | 0.366947 | − | 0.635570i | −0.622140 | − | 0.782906i | \(-0.713736\pi\) |
0.989087 | + | 0.147336i | \(0.0470698\pi\) | |||||||
\(558\) | 18.0000i | 0.762001i | ||||||||
\(559\) | 3.46410i | 0.146516i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.0000 | − | 31.1769i | −0.759961 | − | 1.31629i | ||||
\(562\) | −10.3923 | + | 6.00000i | −0.438373 | + | 0.253095i | ||||
\(563\) | 18.1865 | + | 10.5000i | 0.766471 | + | 0.442522i | 0.831614 | − | 0.555354i | \(-0.187417\pi\) |
−0.0651433 | + | 0.997876i | \(0.520750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −54.0000 | −2.26979 | ||||||||
\(567\) | 7.79423 | + | 22.5000i | 0.327327 | + | 0.944911i | ||||
\(568\) | 12.0000i | 0.503509i | ||||||||
\(569\) | 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 | \(0.139994\pi\) | |||||||
\(572\) | −10.3923 | + | 6.00000i | −0.434524 | + | 0.250873i | ||||
\(573\) | −15.5885 | + | 9.00000i | −0.651217 | + | 0.375980i | ||||
\(574\) | 9.00000 | − | 10.3923i | 0.375653 | − | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | 12.1244 | − | 21.0000i | 0.504744 | − | 0.874241i | −0.495241 | − | 0.868755i | \(-0.664920\pi\) |
0.999985 | − | 0.00548605i | \(-0.00174627\pi\) | |||||||
\(578\) | 16.4545 | − | 28.5000i | 0.684416 | − | 1.18544i | ||||
\(579\) | −33.0000 | − | 19.0526i | −1.37143 | − | 0.791797i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.5000 | + | 7.79423i | −0.933457 | + | 0.323359i | ||||
\(582\) | −15.5885 | − | 27.0000i | −0.646162 | − | 1.11919i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.00000 | − | 5.19615i | 0.124141 | − | 0.215018i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.0000 | + | 20.7846i | −1.48715 | + | 0.858604i | ||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | −1.73205 | − | 12.0000i | −0.0714286 | − | 0.494872i | ||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | −17.3205 | − | 10.0000i | −0.711868 | − | 0.410997i | ||||
\(593\) | −41.5692 | + | 24.0000i | −1.70704 | + | 0.985562i | −0.768864 | + | 0.639413i | \(0.779178\pi\) |
−0.938179 | + | 0.346149i | \(0.887489\pi\) | |||||||
\(594\) | − | 31.1769i | − | 1.27920i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 22.5167i | − | 0.922318i | ||||||
\(597\) | −10.3923 | − | 6.00000i | −0.425329 | − | 0.245564i | ||||
\(598\) | −5.19615 | + | 9.00000i | −0.212486 | + | 0.368037i | ||||
\(599\) | −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 | \(0.860657\pi\) | |||||||
\(602\) | 3.46410 | + | 3.00000i | 0.141186 | + | 0.122271i | ||||
\(603\) | −33.7750 | − | 19.5000i | −1.37542 | − | 0.794101i | ||||
\(604\) | 1.00000 | + | 1.73205i | 0.0406894 | + | 0.0704761i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 45.0000 | 1.82800 | ||||||||
\(607\) | 0.866025 | + | 1.50000i | 0.0351509 | + | 0.0608831i | 0.883066 | − | 0.469249i | \(-0.155475\pi\) |
−0.847915 | + | 0.530133i | \(0.822142\pi\) | |||||||
\(608\) | − | 36.0000i | − | 1.45999i | ||||||
\(609\) | −7.50000 | + | 2.59808i | −0.303915 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 15.5885 | − | 9.00000i | 0.630126 | − | 0.363803i | ||||
\(613\) | −1.73205 | − | 1.00000i | −0.0699569 | − | 0.0403896i | 0.464614 | − | 0.885514i | \(-0.346193\pi\) |
−0.534570 | + | 0.845124i | \(0.679527\pi\) | |||||||
\(614\) | 19.5000 | + | 33.7750i | 0.786956 | + | 1.36305i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | − | 15.5885i | 0.120873 | − | 0.628077i | ||||
\(617\) | 34.6410 | 1.39459 | 0.697297 | − | 0.716782i | \(-0.254386\pi\) | ||||
0.697297 | + | 0.716782i | \(0.254386\pi\) | |||||||
\(618\) | −7.79423 | + | 13.5000i | −0.313530 | + | 0.543050i | ||||
\(619\) | 21.0000 | + | 12.1244i | 0.844061 | + | 0.487319i | 0.858643 | − | 0.512575i | \(-0.171308\pi\) |
−0.0145814 | + | 0.999894i | \(0.504642\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.50000 | − | 7.79423i | −0.180579 | − | 0.312772i | ||||
\(622\) | 41.5692 | 1.66677 | ||||||||
\(623\) | 5.19615 | − | 6.00000i | 0.208179 | − | 0.240385i | ||||
\(624\) | 15.0000 | + | 25.9808i | 0.600481 | + | 1.04006i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 41.5692 | 1.66011 | ||||||||
\(628\) | −1.73205 | − | 3.00000i | −0.0691164 | − | 0.119713i | ||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 13.8564 | + | 24.0000i | 0.551178 | + | 0.954669i | ||||
\(633\) | −34.6410 | −1.37686 | ||||||||
\(634\) | −15.0000 | + | 25.9808i | −0.595726 | + | 1.03183i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.0526 | + | 15.0000i | −0.754890 | + | 0.594322i | ||||
\(638\) | 10.3923 | 0.411435 | ||||||||
\(639\) | − | 20.7846i | − | 0.822226i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 6.06218i | −0.414725 | − | 0.239442i | 0.278093 | − | 0.960554i | \(-0.410298\pi\) |
−0.692818 | + | 0.721113i | \(0.743631\pi\) | |||||||
\(642\) | 7.79423 | − | 13.5000i | 0.307614 | − | 0.532803i | ||||
\(643\) | 17.3205 | 0.683054 | 0.341527 | − | 0.939872i | \(-0.389056\pi\) | ||||
0.341527 | + | 0.939872i | \(0.389056\pi\) | |||||||
\(644\) | 1.50000 | + | 4.33013i | 0.0591083 | + | 0.170631i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 36.0000 | + | 62.3538i | 1.41640 | + | 2.45328i | ||||
\(647\) | −2.59808 | − | 1.50000i | −0.102141 | − | 0.0589711i | 0.448059 | − | 0.894004i | \(-0.352115\pi\) |
−0.550200 | + | 0.835033i | \(0.685449\pi\) | |||||||
\(648\) | −15.5885 | −0.612372 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.00000 | − | 15.5885i | 0.117579 | − | 0.610960i | ||||
\(652\) | 8.00000i | 0.313304i | ||||||||
\(653\) | 15.5885 | + | 27.0000i | 0.610023 | + | 1.05659i | 0.991236 | + | 0.132104i | \(0.0421733\pi\) |
−0.381212 | + | 0.924487i | \(0.624493\pi\) | |||||||
\(654\) | 15.0000 | 0.586546 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.50000 | + | 12.9904i | 0.292826 | + | 0.507189i | ||||
\(657\) | −5.19615 | + | 9.00000i | −0.202721 | + | 0.351123i | ||||
\(658\) | 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 | \(0.445599\pi\) | |||||||
\(662\) | −8.66025 | + | 15.0000i | −0.336590 | + | 0.582992i | ||||
\(663\) | −31.1769 | − | 18.0000i | −1.21081 | − | 0.699062i | ||||
\(664\) | − | 15.5885i | − | 0.604949i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.0000 | + | 10.3923i | 0.697486 | + | 0.402694i | ||||
\(667\) | 2.59808 | − | 1.50000i | 0.100598 | − | 0.0580802i | ||||
\(668\) | −18.1865 | − | 10.5000i | −0.703658 | − | 0.406257i | ||||
\(669\) | −6.00000 | −0.231973 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.0000 | −0.694882 | ||||||||
\(672\) | 23.3827 | + | 4.50000i | 0.902007 | + | 0.173591i | ||||
\(673\) | 4.00000i | 0.154189i | 0.997024 | + | 0.0770943i | \(0.0245643\pi\) | ||||
−0.997024 | + | 0.0770943i | \(0.975436\pi\) | |||||||
\(674\) | 48.0000 | − | 27.7128i | 1.84889 | − | 1.06746i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | − | 0.866025i | 0.0192308 | − | 0.0333087i | ||||
\(677\) | 5.19615 | − | 3.00000i | 0.199704 | − | 0.115299i | −0.396813 | − | 0.917899i | \(-0.629884\pi\) |
0.596518 | + | 0.802600i | \(0.296551\pi\) | |||||||
\(678\) | −10.3923 | − | 18.0000i | −0.399114 | − | 0.691286i | ||||
\(679\) | 9.00000 | + | 25.9808i | 0.345388 | + | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0000 | − | 10.3923i | −0.689761 | − | 0.398234i | ||||
\(682\) | −10.3923 | + | 18.0000i | −0.397942 | + | 0.689256i | ||||
\(683\) | 19.9186 | − | 34.5000i | 0.762163 | − | 1.32011i | −0.179570 | − | 0.983745i | \(-0.557471\pi\) |
0.941733 | − | 0.336361i | \(-0.109196\pi\) | |||||||
\(684\) | 20.7846i | 0.794719i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.50000 | + | 32.0429i | −0.0572703 | + | 1.22341i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.33013 | + | 2.50000i | −0.165085 | + | 0.0953116i | ||||
\(689\) | 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 | \(0.312345\pi\) | |||||||
\(692\) | 12.0000i | 0.456172i | ||||||||
\(693\) | −5.19615 | + | 27.0000i | −0.197386 | + | 1.02565i | ||||
\(694\) | 33.0000 | 1.25266 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 5.19615i | − | 0.196960i | ||||||
\(697\) | −15.5885 | − | 9.00000i | −0.590455 | − | 0.340899i | ||||
\(698\) | −12.9904 | + | 7.50000i | −0.491693 | + | 0.283879i | ||||
\(699\) | −3.00000 | − | 5.19615i | −0.113470 | − | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.9808i | 0.981280i | 0.871362 | + | 0.490640i | \(0.163237\pi\) | ||||
−0.871362 | + | 0.490640i | \(0.836763\pi\) | |||||||
\(702\) | −15.5885 | − | 27.0000i | −0.588348 | − | 1.01905i | ||||
\(703\) | −13.8564 | + | 24.0000i | −0.522604 | + | 0.905177i | ||||
\(704\) | 3.00000 | + | 1.73205i | 0.113067 | + | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.9711 | − | 7.50000i | −1.46566 | − | 0.282067i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.50000 | + | 16.4545i | 0.356780 | + | 0.617961i | 0.987421 | − | 0.158114i | \(-0.0505412\pi\) |
−0.630641 | + | 0.776075i | \(0.717208\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.0000 | − | 41.5692i | −0.900070 | − | 1.55897i | ||||
\(712\) | 2.59808 | + | 4.50000i | 0.0973670 | + | 0.168645i | ||||
\(713\) | 6.00000i | 0.224702i | ||||||||
\(714\) | −45.0000 | + | 15.5885i | −1.68408 | + | 0.583383i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.00000 | − | 5.19615i | 0.336346 | − | 0.194189i | ||||
\(717\) | − | 18.0000i | − | 0.672222i | ||||||
\(718\) | 36.3731 | + | 21.0000i | 1.35743 | + | 0.783713i | ||||
\(719\) | −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 | ||||
\(722\) | −50.2295 | −1.86935 | ||||||||
\(723\) | −10.3923 | − | 6.00000i | −0.386494 | − | 0.223142i | ||||
\(724\) | 4.50000 | + | 2.59808i | 0.167241 | + | 0.0965567i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.50000 | − | 2.59808i | 0.0556702 | − | 0.0964237i | ||||
\(727\) | 5.19615 | 0.192715 | 0.0963573 | − | 0.995347i | \(-0.469281\pi\) | ||||
0.0963573 | + | 0.995347i | \(0.469281\pi\) | |||||||
\(728\) | −5.19615 | − | 15.0000i | −0.192582 | − | 0.555937i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | − | 5.19615i | 0.110959 | − | 0.192187i | ||||
\(732\) | − | 9.00000i | − | 0.332650i | ||||||
\(733\) | −8.66025 | − | 15.0000i | −0.319874 | − | 0.554038i | 0.660588 | − | 0.750749i | \(-0.270307\pi\) |
−0.980461 | + | 0.196711i | \(0.936974\pi\) | |||||||
\(734\) | −27.0000 | −0.996588 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.00000 | −0.331744 | ||||||||
\(737\) | −22.5167 | − | 39.0000i | −0.829412 | − | 1.43658i | ||||
\(738\) | −7.79423 | − | 13.5000i | −0.286910 | − | 0.496942i | ||||
\(739\) | 19.0000 | − | 32.9090i | 0.698926 | − | 1.21058i | −0.269913 | − | 0.962885i | \(-0.586995\pi\) |
0.968839 | − | 0.247691i | \(-0.0796718\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.0000 | − | 20.7846i | 1.32249 | − | 0.763542i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.7654 | 1.71566 | 0.857828 | − | 0.513938i | \(-0.171814\pi\) | ||||
0.857828 | + | 0.513938i | \(0.171814\pi\) | |||||||
\(744\) | 9.00000 | + | 5.19615i | 0.329956 | + | 0.190500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.00000 | + | 3.46410i | 0.219676 | + | 0.126830i | ||||
\(747\) | 27.0000i | 0.987878i | ||||||||
\(748\) | 20.7846 | 0.759961 | ||||||||
\(749\) | −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 | ||||||||
\(753\) | 31.1769 | 1.13615 | ||||||||
\(754\) | 9.00000 | − | 5.19615i | 0.327761 | − | 0.189233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.5000 | − | 2.59808i | −0.490990 | − | 0.0944911i | ||||
\(757\) | − | 22.0000i | − | 0.799604i | −0.916602 | − | 0.399802i | \(-0.869079\pi\) | ||
0.916602 | − | 0.399802i | \(-0.130921\pi\) | |||||||
\(758\) | 13.8564 | + | 24.0000i | 0.503287 | + | 0.871719i | ||||
\(759\) | − | 10.3923i | − | 0.377217i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.00000 | + | 15.5885i | 0.326250 | + | 0.565081i | 0.981764 | − | 0.190101i | \(-0.0608816\pi\) |
−0.655515 | + | 0.755182i | \(0.727548\pi\) | |||||||
\(762\) | 41.5692 | − | 24.0000i | 1.50589 | − | 0.869428i | ||||
\(763\) | −12.9904 | − | 2.50000i | −0.470283 | − | 0.0905061i | ||||
\(764\) | − | 10.3923i | − | 0.375980i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.5000 | + | 18.1865i | 1.13814 | + | 0.657106i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −16.4545 | + | 28.5000i | −0.593750 | + | 1.02841i | ||||
\(769\) | 41.5692i | 1.49902i | 0.661991 | + | 0.749512i | \(0.269712\pi\) | ||||
−0.661991 | + | 0.749512i | \(0.730288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.0526 | − | 11.0000i | 0.685717 | − | 0.395899i | ||||
\(773\) | −15.5885 | − | 9.00000i | −0.560678 | − | 0.323708i | 0.192740 | − | 0.981250i | \(-0.438263\pi\) |
−0.753418 | + | 0.657542i | \(0.771596\pi\) | |||||||
\(774\) | 4.50000 | − | 2.59808i | 0.161749 | − | 0.0933859i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.0000 | −0.646162 | ||||||||
\(777\) | −13.8564 | − | 12.0000i | −0.497096 | − | 0.430498i | ||||
\(778\) | − | 48.0000i | − | 1.72088i | ||||||
\(779\) | 18.0000 | − | 10.3923i | 0.644917 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | − | 20.7846i | 0.429394 | − | 0.743732i | ||||
\(782\) | 15.5885 | − | 9.00000i | 0.557442 | − | 0.321839i | ||||
\(783\) | 9.00000i | 0.321634i | ||||||||
\(784\) | −32.5000 | − | 12.9904i | −1.16071 | − | 0.463942i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.0000 | − | 31.1769i | 0.642039 | − | 1.11204i | ||||
\(787\) | −12.9904 | + | 22.5000i | −0.463057 | + | 0.802038i | −0.999112 | − | 0.0421450i | \(-0.986581\pi\) |
0.536054 | + | 0.844183i | \(0.319914\pi\) | |||||||
\(788\) | 1.73205 | − | 3.00000i | 0.0617018 | − | 0.106871i | ||||
\(789\) | 1.50000 | − | 2.59808i | 0.0534014 | − | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.00000 | + | 17.3205i | 0.213335 | + | 0.615846i | ||||
\(792\) | −15.5885 | − | 9.00000i | −0.553912 | − | 0.319801i | ||||
\(793\) | −15.5885 | + | 9.00000i | −0.553562 | + | 0.319599i | ||||
\(794\) | 21.0000 | − | 36.3731i | 0.745262 | − | 1.29083i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.00000 | − | 3.46410i | 0.212664 | − | 0.122782i | ||||
\(797\) | 12.0000i | 0.425062i | 0.977154 | + | 0.212531i | \(0.0681706\pi\) | ||||
−0.977154 | + | 0.212531i | \(0.931829\pi\) | |||||||
\(798\) | 10.3923 | − | 54.0000i | 0.367884 | − | 1.91158i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.50000 | − | 7.79423i | −0.159000 | − | 0.275396i | ||||
\(802\) | −28.5788 | − | 16.5000i | −1.00915 | − | 0.582635i | ||||
\(803\) | −10.3923 | + | 6.00000i | −0.366736 | + | 0.211735i | ||||
\(804\) | 19.5000 | − | 11.2583i | 0.687712 | − | 0.397051i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.7846i | 0.732107i | ||||||||
\(807\) | 2.59808 | − | 4.50000i | 0.0914566 | − | 0.158408i | ||||
\(808\) | 12.9904 | − | 22.5000i | 0.457000 | − | 0.791547i | ||||
\(809\) | 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 | \(0.709734\pi\) | |||||||
\(812\) | 0.866025 | − | 4.50000i | 0.0303915 | − | 0.157919i | ||||
\(813\) | 10.3923 | − | 6.00000i | 0.364474 | − | 0.210429i | ||||
\(814\) | 12.0000 | + | 20.7846i | 0.420600 | + | 0.728500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 51.9615i | − | 1.81902i | ||||||
\(817\) | 3.46410 | + | 6.00000i | 0.121194 | + | 0.209913i | ||||
\(818\) | 39.0000i | 1.36360i | ||||||||
\(819\) | 9.00000 | + | 25.9808i | 0.314485 | + | 0.907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.0000 | + | 20.7846i | −1.25641 | + | 0.725388i | −0.972375 | − | 0.233426i | \(-0.925006\pi\) |
−0.284034 | + | 0.958814i | \(0.591673\pi\) | |||||||
\(822\) | −62.3538 | −2.17484 | ||||||||
\(823\) | −19.9186 | − | 11.5000i | −0.694318 | − | 0.400865i | 0.110910 | − | 0.993831i | \(-0.464624\pi\) |
−0.805228 | + | 0.592966i | \(0.797957\pi\) | |||||||
\(824\) | 4.50000 | + | 7.79423i | 0.156765 | + | 0.271525i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.5167 | 0.782981 | 0.391491 | − | 0.920182i | \(-0.371960\pi\) | ||||
0.391491 | + | 0.920182i | \(0.371960\pi\) | |||||||
\(828\) | 5.19615 | 0.180579 | ||||||||
\(829\) | 12.0000 | + | 6.92820i | 0.416777 | + | 0.240626i | 0.693698 | − | 0.720266i | \(-0.255980\pi\) |
−0.276920 | + | 0.960893i | \(0.589314\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.0000 | + | 22.5167i | 1.35290 | + | 0.781094i | ||||
\(832\) | 3.46410 | 0.120096 | ||||||||
\(833\) | 41.5692 | − | 6.00000i | 1.44029 | − | 0.207888i | ||||
\(834\) | 27.0000 | − | 15.5885i | 0.934934 | − | 0.539784i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | + | 20.7846i | −0.415029 | + | 0.718851i | ||||
\(837\) | −15.5885 | − | 9.00000i | −0.538816 | − | 0.311086i | ||||
\(838\) | 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 | ||||||||
\(842\) | −30.3109 | − | 52.5000i | −1.04458 | − | 1.80927i | ||||
\(843\) | − | 12.0000i | − | 0.413302i | ||||||
\(844\) | 10.0000 | − | 17.3205i | 0.344214 | − | 0.596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.73205 | + | 2.00000i | −0.0595140 | + | 0.0687208i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.0000 | − | 46.7654i | 0.926638 | − | 1.60498i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | + | 3.46410i | 0.205677 | + | 0.118748i | ||||
\(852\) | 10.3923 | + | 6.00000i | 0.356034 | + | 0.205557i | ||||
\(853\) | 20.7846 | 0.711651 | 0.355826 | − | 0.934552i | \(-0.384200\pi\) | ||||
0.355826 | + | 0.934552i | \(0.384200\pi\) | |||||||
\(854\) | −4.50000 | + | 23.3827i | −0.153987 | + | 0.800139i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.50000 | − | 7.79423i | −0.153807 | − | 0.266401i | ||||
\(857\) | 36.3731 | + | 21.0000i | 1.24248 | + | 0.717346i | 0.969599 | − | 0.244701i | \(-0.0786899\pi\) |
0.272882 | + | 0.962048i | \(0.412023\pi\) | |||||||
\(858\) | − | 36.0000i | − | 1.22902i | ||||||
\(859\) | −24.0000 | + | 13.8564i | −0.818869 | + | 0.472774i | −0.850026 | − | 0.526740i | \(-0.823414\pi\) |
0.0311570 | + | 0.999515i | \(0.490081\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.50000 | + | 12.9904i | 0.153360 | + | 0.442711i | ||||
\(862\) | 18.0000i | 0.613082i | ||||||||
\(863\) | −4.33013 | − | 7.50000i | −0.147399 | − | 0.255303i | 0.782866 | − | 0.622190i | \(-0.213757\pi\) |
−0.930265 | + | 0.366887i | \(0.880424\pi\) | |||||||
\(864\) | 13.5000 | − | 23.3827i | 0.459279 | − | 0.795495i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.0000 | − | 20.7846i | −0.407777 | − | 0.706290i | ||||
\(867\) | 16.4545 | + | 28.5000i | 0.558824 | + | 0.967911i | ||||
\(868\) | 6.92820 | + | 6.00000i | 0.235159 | + | 0.203653i | ||||
\(869\) | − | 55.4256i | − | 1.88019i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.0000 | − | 22.5167i | −1.32146 | − | 0.762948i | ||||
\(872\) | 4.33013 | − | 7.50000i | 0.146637 | − | 0.253982i | ||||
\(873\) | 31.1769 | 1.05518 | ||||||||
\(874\) | 20.7846i | 0.703050i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.00000 | − | 5.19615i | −0.101361 | − | 0.175562i | ||||
\(877\) | −27.7128 | + | 16.0000i | −0.935795 | + | 0.540282i | −0.888640 | − | 0.458606i | \(-0.848349\pi\) |
−0.0471555 | + | 0.998888i | \(0.515016\pi\) | |||||||
\(878\) | −10.3923 | − | 6.00000i | −0.350723 | − | 0.202490i | ||||
\(879\) | − | 41.5692i | − | 1.40209i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.00000 | 0.303218 | 0.151609 | − | 0.988441i | \(-0.451555\pi\) | ||||
0.151609 | + | 0.988441i | \(0.451555\pi\) | |||||||
\(882\) | 33.7750 | + | 13.5000i | 1.13726 | + | 0.454569i | ||||
\(883\) | − | 20.0000i | − | 0.673054i | −0.941674 | − | 0.336527i | \(-0.890748\pi\) | ||
0.941674 | − | 0.336527i | \(-0.109252\pi\) | |||||||
\(884\) | 18.0000 | − | 10.3923i | 0.605406 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.5000 | + | 23.3827i | −0.453541 | + | 0.785557i | ||||
\(887\) | 7.79423 | − | 4.50000i | 0.261705 | − | 0.151095i | −0.363407 | − | 0.931630i | \(-0.618387\pi\) |
0.625112 | + | 0.780535i | \(0.285053\pi\) | |||||||
\(888\) | 10.3923 | − | 6.00000i | 0.348743 | − | 0.201347i | ||||
\(889\) | −40.0000 | + | 13.8564i | −1.34156 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.0000 | + | 15.5885i | 0.904534 | + | 0.522233i | ||||
\(892\) | 1.73205 | − | 3.00000i | 0.0579934 | − | 0.100447i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 58.5000 | + | 33.7750i | 1.95653 | + | 1.12960i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 21.0000 | − | 24.2487i | 0.701561 | − | 0.810093i | ||||
\(897\) | −5.19615 | − | 9.00000i | −0.173494 | − | 0.300501i | ||||
\(898\) | −18.1865 | + | 10.5000i | −0.606892 | + | 0.350390i | ||||
\(899\) | 3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | − | 18.0000i | − | 0.599334i | ||||||
\(903\) | −4.33013 | + | 1.50000i | −0.144098 | + | 0.0499169i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.00000 | −0.199337 | ||||||||
\(907\) | 32.0429 | + | 18.5000i | 1.06397 | + | 0.614282i | 0.926527 | − | 0.376228i | \(-0.122779\pi\) |
0.137441 | + | 0.990510i | \(0.456112\pi\) | |||||||
\(908\) | 10.3923 | − | 6.00000i | 0.344881 | − | 0.199117i | ||||
\(909\) | −22.5000 | + | 38.9711i | −0.746278 | + | 1.29259i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24.2487i | − | 0.803396i | −0.915772 | − | 0.401698i | \(-0.868420\pi\) | ||
0.915772 | − | 0.401698i | \(-0.131580\pi\) | |||||||
\(912\) | 51.9615 | + | 30.0000i | 1.72062 | + | 0.993399i | ||||
\(913\) | −15.5885 | + | 27.0000i | −0.515903 | + | 0.893570i | ||||
\(914\) | −12.0000 | − | 6.92820i | −0.396925 | − | 0.229165i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.7846 | + | 24.0000i | −0.686368 | + | 0.792550i | ||||
\(918\) | 54.0000i | 1.78227i | ||||||||
\(919\) | 8.00000 | + | 13.8564i | 0.263896 | + | 0.457081i | 0.967274 | − | 0.253735i | \(-0.0816592\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −39.0000 | −1.28509 | ||||||||
\(922\) | −25.9808 | − | 45.0000i | −0.855631 | − | 1.48200i | ||||
\(923\) | − | 24.0000i | − | 0.789970i | ||||||
\(924\) | −12.0000 | − | 10.3923i | −0.394771 | − | 0.341882i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 43.5000 | − | 25.1147i | 1.42950 | − | 0.825321i | ||||
\(927\) | −7.79423 | − | 13.5000i | −0.255996 | − | 0.443398i | ||||
\(928\) | 7.79423 | + | 4.50000i | 0.255858 | + | 0.147720i | ||||
\(929\) | −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 | ||||
\(932\) | 3.46410 | 0.113470 | ||||||||
\(933\) | −20.7846 | + | 36.0000i | −0.680458 | + | 1.17859i | ||||
\(934\) | −31.5000 | − | 18.1865i | −1.03071 | − | 0.595082i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18.0000 | −0.588348 | ||||||||
\(937\) | 48.4974 | 1.58434 | 0.792171 | − | 0.610299i | \(-0.208951\pi\) | ||||
0.792171 | + | 0.610299i | \(0.208951\pi\) | |||||||
\(938\) | −56.2917 | + | 19.5000i | −1.83799 | + | 0.636698i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.00000 | − | 15.5885i | 0.293392 | − | 0.508169i | −0.681218 | − | 0.732081i | \(-0.738549\pi\) |
0.974609 | + | 0.223912i | \(0.0718827\pi\) | |||||||
\(942\) | 10.3923 | 0.338600 | ||||||||
\(943\) | −2.59808 | − | 4.50000i | −0.0846050 | − | 0.146540i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | −12.9904 | − | 22.5000i | −0.422131 | − | 0.731152i | 0.574017 | − | 0.818843i | \(-0.305384\pi\) |
−0.996148 | + | 0.0876916i | \(0.972051\pi\) | |||||||
\(948\) | 27.7128 | 0.900070 | ||||||||
\(949\) | −6.00000 | + | 10.3923i | −0.194768 | + | 0.337348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.0000 | − | 25.9808i | −0.486408 | − | 0.842484i | ||||
\(952\) | −5.19615 | + | 27.0000i | −0.168408 | + | 0.875075i | ||||
\(953\) | 6.92820 | 0.224427 | 0.112213 | − | 0.993684i | \(-0.464206\pi\) | ||||
0.112213 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.00000 | + | 5.19615i | 0.291081 | + | 0.168056i | ||||
\(957\) | −5.19615 | + | 9.00000i | −0.167968 | + | 0.290929i | ||||
\(958\) | −10.3923 | −0.335760 | ||||||||
\(959\) | 54.0000 | + | 10.3923i | 1.74375 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50000 | − | 16.4545i | −0.306452 | − | 0.530790i | ||||
\(962\) | 20.7846 | + | 12.0000i | 0.670123 | + | 0.386896i | ||||
\(963\) | 7.79423 | + | 13.5000i | 0.251166 | + | 0.435031i | ||||
\(964\) | 6.00000 | − | 3.46410i | 0.193247 | − | 0.111571i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.5000 | − | 2.59808i | −0.434355 | − | 0.0835917i | ||||
\(967\) | − | 23.0000i | − | 0.739630i | −0.929105 | − | 0.369815i | \(-0.879421\pi\) | ||
0.929105 | − | 0.369815i | \(-0.120579\pi\) | |||||||
\(968\) | −0.866025 | − | 1.50000i | −0.0278351 | − | 0.0482118i | ||||
\(969\) | −72.0000 | −2.31297 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.00000 | − | 10.3923i | −0.192549 | − | 0.333505i | 0.753545 | − | 0.657396i | \(-0.228342\pi\) |
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(972\) | −7.79423 | + | 13.5000i | −0.250000 | + | 0.433013i | ||||
\(973\) | −25.9808 | + | 9.00000i | −0.832905 | + | 0.288527i | ||||
\(974\) | 55.4256i | 1.77595i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.5000 | − | 12.9904i | −0.720207 | − | 0.415812i | ||||
\(977\) | 12.1244 | − | 21.0000i | 0.387893 | − | 0.671850i | −0.604273 | − | 0.796777i | \(-0.706537\pi\) |
0.992166 | + | 0.124928i | \(0.0398698\pi\) | |||||||
\(978\) | −20.7846 | − | 12.0000i | −0.664619 | − | 0.383718i | ||||
\(979\) | − | 10.3923i | − | 0.332140i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.50000 | + | 12.9904i | −0.239457 | + | 0.414751i | ||||
\(982\) | −57.1577 | + | 33.0000i | −1.82397 | + | 1.05307i | ||||
\(983\) | 49.3634 | + | 28.5000i | 1.57445 | + | 0.909009i | 0.995613 | + | 0.0935651i | \(0.0298263\pi\) |
0.578836 | + | 0.815444i | \(0.303507\pi\) | |||||||
\(984\) | −9.00000 | −0.286910 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.0000 | −0.573237 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.0000i | 0.763542i | ||||||||
\(989\) | 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 | \(0.985082\pi\) | |||||||
\(992\) | −15.5885 | + | 9.00000i | −0.494934 | + | 0.285750i | ||||
\(993\) | −8.66025 | − | 15.0000i | −0.274825 | − | 0.476011i | ||||
\(994\) | −24.0000 | − | 20.7846i | −0.761234 | − | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.5000 | − | 7.79423i | −0.427764 | − | 0.246970i | ||||
\(997\) | 3.46410 | − | 6.00000i | 0.109709 | − | 0.190022i | −0.805943 | − | 0.591993i | \(-0.798341\pi\) |
0.915652 | + | 0.401971i | \(0.131675\pi\) | |||||||
\(998\) | −12.1244 | + | 21.0000i | −0.383790 | + | 0.664743i | ||||
\(999\) | −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.q.a.374.1 | 4 | ||
3.2 | odd | 2 | 525.2.q.b.374.2 | 4 | |||
5.2 | odd | 4 | 105.2.s.b.101.1 | yes | 2 | ||
5.3 | odd | 4 | 525.2.t.a.101.1 | 2 | |||
5.4 | even | 2 | inner | 525.2.q.a.374.2 | 4 | ||
7.5 | odd | 6 | 525.2.q.b.299.1 | 4 | |||
15.2 | even | 4 | 105.2.s.a.101.1 | yes | 2 | ||
15.8 | even | 4 | 525.2.t.e.101.1 | 2 | |||
15.14 | odd | 2 | 525.2.q.b.374.1 | 4 | |||
21.5 | even | 6 | inner | 525.2.q.a.299.2 | 4 | ||
35.2 | odd | 12 | 735.2.s.c.656.1 | 2 | |||
35.12 | even | 12 | 105.2.s.a.26.1 | ✓ | 2 | ||
35.17 | even | 12 | 735.2.b.b.146.2 | 2 | |||
35.19 | odd | 6 | 525.2.q.b.299.2 | 4 | |||
35.27 | even | 4 | 735.2.s.e.521.1 | 2 | |||
35.32 | odd | 12 | 735.2.b.a.146.2 | 2 | |||
35.33 | even | 12 | 525.2.t.e.26.1 | 2 | |||
105.2 | even | 12 | 735.2.s.e.656.1 | 2 | |||
105.17 | odd | 12 | 735.2.b.a.146.1 | 2 | |||
105.32 | even | 12 | 735.2.b.b.146.1 | 2 | |||
105.47 | odd | 12 | 105.2.s.b.26.1 | yes | 2 | ||
105.62 | odd | 4 | 735.2.s.c.521.1 | 2 | |||
105.68 | odd | 12 | 525.2.t.a.26.1 | 2 | |||
105.89 | even | 6 | inner | 525.2.q.a.299.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.s.a.26.1 | ✓ | 2 | 35.12 | even | 12 | ||
105.2.s.a.101.1 | yes | 2 | 15.2 | even | 4 | ||
105.2.s.b.26.1 | yes | 2 | 105.47 | odd | 12 | ||
105.2.s.b.101.1 | yes | 2 | 5.2 | odd | 4 | ||
525.2.q.a.299.1 | 4 | 105.89 | even | 6 | inner | ||
525.2.q.a.299.2 | 4 | 21.5 | even | 6 | inner | ||
525.2.q.a.374.1 | 4 | 1.1 | even | 1 | trivial | ||
525.2.q.a.374.2 | 4 | 5.4 | even | 2 | inner | ||
525.2.q.b.299.1 | 4 | 7.5 | odd | 6 | |||
525.2.q.b.299.2 | 4 | 35.19 | odd | 6 | |||
525.2.q.b.374.1 | 4 | 15.14 | odd | 2 | |||
525.2.q.b.374.2 | 4 | 3.2 | odd | 2 | |||
525.2.t.a.26.1 | 2 | 105.68 | odd | 12 | |||
525.2.t.a.101.1 | 2 | 5.3 | odd | 4 | |||
525.2.t.e.26.1 | 2 | 35.33 | even | 12 | |||
525.2.t.e.101.1 | 2 | 15.8 | even | 4 | |||
735.2.b.a.146.1 | 2 | 105.17 | odd | 12 | |||
735.2.b.a.146.2 | 2 | 35.32 | odd | 12 | |||
735.2.b.b.146.1 | 2 | 105.32 | even | 12 | |||
735.2.b.b.146.2 | 2 | 35.17 | even | 12 | |||
735.2.s.c.521.1 | 2 | 105.62 | odd | 4 | |||
735.2.s.c.656.1 | 2 | 35.2 | odd | 12 | |||
735.2.s.e.521.1 | 2 | 35.27 | even | 4 | |||
735.2.s.e.656.1 | 2 | 105.2 | even | 12 |