Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(76,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.i (of order \(2\), degree \(1\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.3 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.76 |
Dual form | 1155.2.i.b.76.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.517638i | − | 0.366025i | −0.983111 | − | 0.183013i | \(-0.941415\pi\) | ||
0.983111 | − | 0.183013i | \(-0.0585849\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.73205 | 0.866025 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −0.517638 | −0.211325 | ||||||||
\(7\) | −2.63896 | + | 0.189469i | −0.997433 | + | 0.0716124i | ||||
\(8\) | − | 1.93185i | − | 0.683013i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.517638 | 0.163692 | ||||||||
\(11\) | −3.00000 | − | 1.41421i | −0.904534 | − | 0.426401i | ||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 0.0980762 | + | 1.36603i | 0.0262120 | + | 0.365086i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 2.46410 | 0.616025 | ||||||||
\(17\) | −2.44949 | −0.594089 | −0.297044 | − | 0.954864i | \(-0.596001\pi\) | ||||
−0.297044 | + | 0.954864i | \(0.596001\pi\) | |||||||
\(18\) | 0.517638i | 0.122008i | ||||||||
\(19\) | −1.03528 | −0.237509 | −0.118754 | − | 0.992924i | \(-0.537890\pi\) | ||||
−0.118754 | + | 0.992924i | \(0.537890\pi\) | |||||||
\(20\) | 1.73205i | 0.387298i | ||||||||
\(21\) | 0.189469 | + | 2.63896i | 0.0413455 | + | 0.575868i | ||||
\(22\) | −0.732051 | + | 1.55291i | −0.156074 | + | 0.331082i | ||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −1.93185 | −0.394338 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 2.19615i | 0.430701i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −4.57081 | + | 0.328169i | −0.863802 | + | 0.0620182i | ||||
\(29\) | − | 1.03528i | − | 0.192246i | −0.995369 | − | 0.0961230i | \(-0.969356\pi\) | ||
0.995369 | − | 0.0961230i | \(-0.0306442\pi\) | |||||||
\(30\) | − | 0.517638i | − | 0.0945074i | ||||||
\(31\) | 2.92820i | 0.525921i | 0.964807 | + | 0.262960i | \(0.0846989\pi\) | ||||
−0.964807 | + | 0.262960i | \(0.915301\pi\) | |||||||
\(32\) | − | 5.13922i | − | 0.908494i | ||||||
\(33\) | −1.41421 | + | 3.00000i | −0.246183 | + | 0.522233i | ||||
\(34\) | 1.26795i | 0.217451i | ||||||||
\(35\) | −0.189469 | − | 2.63896i | −0.0320261 | − | 0.446065i | ||||
\(36\) | −1.73205 | −0.288675 | ||||||||
\(37\) | −0.535898 | −0.0881012 | −0.0440506 | − | 0.999029i | \(-0.514026\pi\) | ||||
−0.0440506 | + | 0.999029i | \(0.514026\pi\) | |||||||
\(38\) | 0.535898i | 0.0869342i | ||||||||
\(39\) | 4.24264i | 0.679366i | ||||||||
\(40\) | 1.93185 | 0.305453 | ||||||||
\(41\) | −6.69213 | −1.04514 | −0.522568 | − | 0.852598i | \(-0.675026\pi\) | ||||
−0.522568 | + | 0.852598i | \(0.675026\pi\) | |||||||
\(42\) | 1.36603 | − | 0.0980762i | 0.210782 | − | 0.0151335i | ||||
\(43\) | − | 2.44949i | − | 0.373544i | −0.982403 | − | 0.186772i | \(-0.940197\pi\) | ||
0.982403 | − | 0.186772i | \(-0.0598025\pi\) | |||||||
\(44\) | −5.19615 | − | 2.44949i | −0.783349 | − | 0.369274i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 2.07055i | 0.305286i | ||||||||
\(47\) | − | 2.92820i | − | 0.427122i | −0.976930 | − | 0.213561i | \(-0.931494\pi\) | ||
0.976930 | − | 0.213561i | \(-0.0685063\pi\) | |||||||
\(48\) | − | 2.46410i | − | 0.355662i | ||||||
\(49\) | 6.92820 | − | 1.00000i | 0.989743 | − | 0.142857i | ||||
\(50\) | 0.517638i | 0.0732051i | ||||||||
\(51\) | 2.44949i | 0.342997i | ||||||||
\(52\) | −7.34847 | −1.01905 | ||||||||
\(53\) | −3.46410 | −0.475831 | −0.237915 | − | 0.971286i | \(-0.576464\pi\) | ||||
−0.237915 | + | 0.971286i | \(0.576464\pi\) | |||||||
\(54\) | 0.517638 | 0.0704416 | ||||||||
\(55\) | 1.41421 | − | 3.00000i | 0.190693 | − | 0.404520i | ||||
\(56\) | 0.366025 | + | 5.09808i | 0.0489122 | + | 0.681259i | ||||
\(57\) | 1.03528i | 0.137126i | ||||||||
\(58\) | −0.535898 | −0.0703669 | ||||||||
\(59\) | − | 12.9282i | − | 1.68311i | −0.540172 | − | 0.841554i | \(-0.681641\pi\) | ||
0.540172 | − | 0.841554i | \(-0.318359\pi\) | |||||||
\(60\) | 1.73205 | 0.223607 | ||||||||
\(61\) | 4.89898 | 0.627250 | 0.313625 | − | 0.949547i | \(-0.398457\pi\) | ||||
0.313625 | + | 0.949547i | \(0.398457\pi\) | |||||||
\(62\) | 1.51575 | 0.192500 | ||||||||
\(63\) | 2.63896 | − | 0.189469i | 0.332478 | − | 0.0238708i | ||||
\(64\) | 2.26795 | 0.283494 | ||||||||
\(65\) | − | 4.24264i | − | 0.526235i | ||||||
\(66\) | 1.55291 | + | 0.732051i | 0.191151 | + | 0.0901092i | ||||
\(67\) | −5.46410 | −0.667546 | −0.333773 | − | 0.942653i | \(-0.608322\pi\) | ||||
−0.333773 | + | 0.942653i | \(0.608322\pi\) | |||||||
\(68\) | −4.24264 | −0.514496 | ||||||||
\(69\) | 4.00000i | 0.481543i | ||||||||
\(70\) | −1.36603 | + | 0.0980762i | −0.163271 | + | 0.0117223i | ||||
\(71\) | 6.92820 | 0.822226 | 0.411113 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411113 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(72\) | 1.93185i | 0.227671i | ||||||||
\(73\) | 0.656339 | 0.0768186 | 0.0384093 | − | 0.999262i | \(-0.487771\pi\) | ||||
0.0384093 | + | 0.999262i | \(0.487771\pi\) | |||||||
\(74\) | 0.277401i | 0.0322473i | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | −1.79315 | −0.205689 | ||||||||
\(77\) | 8.18482 | + | 3.16364i | 0.932747 | + | 0.360531i | ||||
\(78\) | 2.19615 | 0.248665 | ||||||||
\(79\) | 3.86370i | 0.434701i | 0.976094 | + | 0.217350i | \(0.0697414\pi\) | ||||
−0.976094 | + | 0.217350i | \(0.930259\pi\) | |||||||
\(80\) | 2.46410i | 0.275495i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.46410i | 0.382546i | ||||||||
\(83\) | −1.41421 | −0.155230 | −0.0776151 | − | 0.996983i | \(-0.524731\pi\) | ||||
−0.0776151 | + | 0.996983i | \(0.524731\pi\) | |||||||
\(84\) | 0.328169 | + | 4.57081i | 0.0358062 | + | 0.498716i | ||||
\(85\) | − | 2.44949i | − | 0.265684i | ||||||
\(86\) | −1.26795 | −0.136726 | ||||||||
\(87\) | −1.03528 | −0.110993 | ||||||||
\(88\) | −2.73205 | + | 5.79555i | −0.291238 | + | 0.617808i | ||||
\(89\) | − | 4.92820i | − | 0.522388i | −0.965286 | − | 0.261194i | \(-0.915884\pi\) | ||
0.965286 | − | 0.261194i | \(-0.0841163\pi\) | |||||||
\(90\) | −0.517638 | −0.0545638 | ||||||||
\(91\) | 11.1962 | − | 0.803848i | 1.17368 | − | 0.0842661i | ||||
\(92\) | −6.92820 | −0.722315 | ||||||||
\(93\) | 2.92820 | 0.303641 | ||||||||
\(94\) | −1.51575 | −0.156338 | ||||||||
\(95\) | − | 1.03528i | − | 0.106217i | ||||||
\(96\) | −5.13922 | −0.524519 | ||||||||
\(97\) | 4.92820i | 0.500383i | 0.968196 | + | 0.250192i | \(0.0804936\pi\) | ||||
−0.968196 | + | 0.250192i | \(0.919506\pi\) | |||||||
\(98\) | −0.517638 | − | 3.58630i | −0.0522893 | − | 0.362271i | ||||
\(99\) | 3.00000 | + | 1.41421i | 0.301511 | + | 0.142134i | ||||
\(100\) | −1.73205 | −0.173205 | ||||||||
\(101\) | −11.5911 | −1.15336 | −0.576679 | − | 0.816971i | \(-0.695652\pi\) | ||||
−0.576679 | + | 0.816971i | \(0.695652\pi\) | |||||||
\(102\) | 1.26795 | 0.125546 | ||||||||
\(103\) | 12.3923i | 1.22105i | 0.791997 | + | 0.610525i | \(0.209042\pi\) | ||||
−0.791997 | + | 0.610525i | \(0.790958\pi\) | |||||||
\(104\) | 8.19615i | 0.803699i | ||||||||
\(105\) | −2.63896 | + | 0.189469i | −0.257536 | + | 0.0184903i | ||||
\(106\) | 1.79315i | 0.174166i | ||||||||
\(107\) | − | 10.4543i | − | 1.01066i | −0.862928 | − | 0.505328i | \(-0.831372\pi\) | ||
0.862928 | − | 0.505328i | \(-0.168628\pi\) | |||||||
\(108\) | 1.73205i | 0.166667i | ||||||||
\(109\) | 17.5254i | 1.67863i | 0.543649 | + | 0.839313i | \(0.317042\pi\) | ||||
−0.543649 | + | 0.839313i | \(0.682958\pi\) | |||||||
\(110\) | −1.55291 | − | 0.732051i | −0.148065 | − | 0.0697983i | ||||
\(111\) | 0.535898i | 0.0508652i | ||||||||
\(112\) | −6.50266 | + | 0.466870i | −0.614444 | + | 0.0441151i | ||||
\(113\) | 8.53590 | 0.802990 | 0.401495 | − | 0.915861i | \(-0.368491\pi\) | ||||
0.401495 | + | 0.915861i | \(0.368491\pi\) | |||||||
\(114\) | 0.535898 | 0.0501915 | ||||||||
\(115\) | − | 4.00000i | − | 0.373002i | ||||||
\(116\) | − | 1.79315i | − | 0.166490i | ||||||
\(117\) | 4.24264 | 0.392232 | ||||||||
\(118\) | −6.69213 | −0.616061 | ||||||||
\(119\) | 6.46410 | − | 0.464102i | 0.592563 | − | 0.0425441i | ||||
\(120\) | − | 1.93185i | − | 0.176353i | ||||||
\(121\) | 7.00000 | + | 8.48528i | 0.636364 | + | 0.771389i | ||||
\(122\) | − | 2.53590i | − | 0.229589i | ||||||
\(123\) | 6.69213i | 0.603409i | ||||||||
\(124\) | 5.07180i | 0.455461i | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −0.0980762 | − | 1.36603i | −0.00873732 | − | 0.121695i | ||||
\(127\) | − | 12.2474i | − | 1.08679i | −0.839479 | − | 0.543393i | \(-0.817139\pi\) | ||
0.839479 | − | 0.543393i | \(-0.182861\pi\) | |||||||
\(128\) | − | 11.4524i | − | 1.01226i | ||||||
\(129\) | −2.44949 | −0.215666 | ||||||||
\(130\) | −2.19615 | −0.192615 | ||||||||
\(131\) | −4.89898 | −0.428026 | −0.214013 | − | 0.976831i | \(-0.568653\pi\) | ||||
−0.214013 | + | 0.976831i | \(0.568653\pi\) | |||||||
\(132\) | −2.44949 | + | 5.19615i | −0.213201 | + | 0.452267i | ||||
\(133\) | 2.73205 | − | 0.196152i | 0.236899 | − | 0.0170086i | ||||
\(134\) | 2.82843i | 0.244339i | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 4.73205i | 0.405770i | ||||||||
\(137\) | −20.9282 | −1.78802 | −0.894009 | − | 0.448050i | \(-0.852119\pi\) | ||||
−0.894009 | + | 0.448050i | \(0.852119\pi\) | |||||||
\(138\) | 2.07055 | 0.176257 | ||||||||
\(139\) | 21.3891 | 1.81420 | 0.907099 | − | 0.420918i | \(-0.138292\pi\) | ||||
0.907099 | + | 0.420918i | \(0.138292\pi\) | |||||||
\(140\) | −0.328169 | − | 4.57081i | −0.0277354 | − | 0.386304i | ||||
\(141\) | −2.92820 | −0.246599 | ||||||||
\(142\) | − | 3.58630i | − | 0.300956i | ||||||
\(143\) | 12.7279 | + | 6.00000i | 1.06436 | + | 0.501745i | ||||
\(144\) | −2.46410 | −0.205342 | ||||||||
\(145\) | 1.03528 | 0.0859750 | ||||||||
\(146\) | − | 0.339746i | − | 0.0281176i | ||||||
\(147\) | −1.00000 | − | 6.92820i | −0.0824786 | − | 0.571429i | ||||
\(148\) | −0.928203 | −0.0762978 | ||||||||
\(149\) | 18.7637i | 1.53718i | 0.639740 | + | 0.768592i | \(0.279042\pi\) | ||||
−0.639740 | + | 0.768592i | \(0.720958\pi\) | |||||||
\(150\) | 0.517638 | 0.0422650 | ||||||||
\(151\) | − | 5.93426i | − | 0.482923i | −0.970410 | − | 0.241461i | \(-0.922373\pi\) | ||
0.970410 | − | 0.241461i | \(-0.0776267\pi\) | |||||||
\(152\) | 2.00000i | 0.162221i | ||||||||
\(153\) | 2.44949 | 0.198030 | ||||||||
\(154\) | 1.63762 | − | 4.23678i | 0.131963 | − | 0.341409i | ||||
\(155\) | −2.92820 | −0.235199 | ||||||||
\(156\) | 7.34847i | 0.588348i | ||||||||
\(157\) | − | 6.39230i | − | 0.510161i | −0.966920 | − | 0.255081i | \(-0.917898\pi\) | ||
0.966920 | − | 0.255081i | \(-0.0821021\pi\) | |||||||
\(158\) | 2.00000 | 0.159111 | ||||||||
\(159\) | 3.46410i | 0.274721i | ||||||||
\(160\) | 5.13922 | 0.406291 | ||||||||
\(161\) | 10.5558 | − | 0.757875i | 0.831916 | − | 0.0597289i | ||||
\(162\) | − | 0.517638i | − | 0.0406695i | ||||||
\(163\) | −8.39230 | −0.657336 | −0.328668 | − | 0.944446i | \(-0.606600\pi\) | ||||
−0.328668 | + | 0.944446i | \(0.606600\pi\) | |||||||
\(164\) | −11.5911 | −0.905114 | ||||||||
\(165\) | −3.00000 | − | 1.41421i | −0.233550 | − | 0.110096i | ||||
\(166\) | 0.732051i | 0.0568182i | ||||||||
\(167\) | 7.07107 | 0.547176 | 0.273588 | − | 0.961847i | \(-0.411790\pi\) | ||||
0.273588 | + | 0.961847i | \(0.411790\pi\) | |||||||
\(168\) | 5.09808 | − | 0.366025i | 0.393325 | − | 0.0282395i | ||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | −1.26795 | −0.0972473 | ||||||||
\(171\) | 1.03528 | 0.0791695 | ||||||||
\(172\) | − | 4.24264i | − | 0.323498i | ||||||
\(173\) | −2.44949 | −0.186231 | −0.0931156 | − | 0.995655i | \(-0.529683\pi\) | ||||
−0.0931156 | + | 0.995655i | \(0.529683\pi\) | |||||||
\(174\) | 0.535898i | 0.0406264i | ||||||||
\(175\) | 2.63896 | − | 0.189469i | 0.199487 | − | 0.0143225i | ||||
\(176\) | −7.39230 | − | 3.48477i | −0.557216 | − | 0.262674i | ||||
\(177\) | −12.9282 | −0.971743 | ||||||||
\(178\) | −2.55103 | −0.191207 | ||||||||
\(179\) | −4.92820 | −0.368351 | −0.184176 | − | 0.982893i | \(-0.558962\pi\) | ||||
−0.184176 | + | 0.982893i | \(0.558962\pi\) | |||||||
\(180\) | − | 1.73205i | − | 0.129099i | ||||||
\(181\) | − | 16.9282i | − | 1.25826i | −0.777299 | − | 0.629132i | \(-0.783411\pi\) | ||
0.777299 | − | 0.629132i | \(-0.216589\pi\) | |||||||
\(182\) | −0.416102 | − | 5.79555i | −0.0308435 | − | 0.429595i | ||||
\(183\) | − | 4.89898i | − | 0.362143i | ||||||
\(184\) | 7.72741i | 0.569672i | ||||||||
\(185\) | − | 0.535898i | − | 0.0394000i | ||||||
\(186\) | − | 1.51575i | − | 0.111140i | ||||||
\(187\) | 7.34847 | + | 3.46410i | 0.537373 | + | 0.253320i | ||||
\(188\) | − | 5.07180i | − | 0.369899i | ||||||
\(189\) | −0.189469 | − | 2.63896i | −0.0137818 | − | 0.191956i | ||||
\(190\) | −0.535898 | −0.0388782 | ||||||||
\(191\) | −11.0718 | −0.801127 | −0.400564 | − | 0.916269i | \(-0.631186\pi\) | ||||
−0.400564 | + | 0.916269i | \(0.631186\pi\) | |||||||
\(192\) | − | 2.26795i | − | 0.163675i | ||||||
\(193\) | 21.2132i | 1.52696i | 0.645832 | + | 0.763480i | \(0.276511\pi\) | ||||
−0.645832 | + | 0.763480i | \(0.723489\pi\) | |||||||
\(194\) | 2.55103 | 0.183153 | ||||||||
\(195\) | −4.24264 | −0.303822 | ||||||||
\(196\) | 12.0000 | − | 1.73205i | 0.857143 | − | 0.123718i | ||||
\(197\) | − | 17.9043i | − | 1.27563i | −0.770190 | − | 0.637814i | \(-0.779839\pi\) | ||
0.770190 | − | 0.637814i | \(-0.220161\pi\) | |||||||
\(198\) | 0.732051 | − | 1.55291i | 0.0520246 | − | 0.110361i | ||||
\(199\) | − | 19.4641i | − | 1.37977i | −0.723917 | − | 0.689887i | \(-0.757660\pi\) | ||
0.723917 | − | 0.689887i | \(-0.242340\pi\) | |||||||
\(200\) | 1.93185i | 0.136603i | ||||||||
\(201\) | 5.46410i | 0.385408i | ||||||||
\(202\) | 6.00000i | 0.422159i | ||||||||
\(203\) | 0.196152 | + | 2.73205i | 0.0137672 | + | 0.191752i | ||||
\(204\) | 4.24264i | 0.297044i | ||||||||
\(205\) | − | 6.69213i | − | 0.467399i | ||||||
\(206\) | 6.41473 | 0.446935 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | −10.4543 | −0.724875 | ||||||||
\(209\) | 3.10583 | + | 1.46410i | 0.214835 | + | 0.101274i | ||||
\(210\) | 0.0980762 | + | 1.36603i | 0.00676790 | + | 0.0942647i | ||||
\(211\) | − | 8.00481i | − | 0.551074i | −0.961291 | − | 0.275537i | \(-0.911144\pi\) | ||
0.961291 | − | 0.275537i | \(-0.0888556\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | − | 6.92820i | − | 0.474713i | ||||||
\(214\) | −5.41154 | −0.369925 | ||||||||
\(215\) | 2.44949 | 0.167054 | ||||||||
\(216\) | 1.93185 | 0.131446 | ||||||||
\(217\) | −0.554803 | − | 7.72741i | −0.0376625 | − | 0.524571i | ||||
\(218\) | 9.07180 | 0.614420 | ||||||||
\(219\) | − | 0.656339i | − | 0.0443513i | ||||||
\(220\) | 2.44949 | − | 5.19615i | 0.165145 | − | 0.350325i | ||||
\(221\) | 10.3923 | 0.699062 | ||||||||
\(222\) | 0.277401 | 0.0186180 | ||||||||
\(223\) | − | 9.85641i | − | 0.660034i | −0.943975 | − | 0.330017i | \(-0.892946\pi\) | ||
0.943975 | − | 0.330017i | \(-0.107054\pi\) | |||||||
\(224\) | 0.973721 | + | 13.5622i | 0.0650594 | + | 0.906161i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | − | 4.41851i | − | 0.293915i | ||||||
\(227\) | 18.3848 | 1.22024 | 0.610120 | − | 0.792309i | \(-0.291121\pi\) | ||||
0.610120 | + | 0.792309i | \(0.291121\pi\) | |||||||
\(228\) | 1.79315i | 0.118754i | ||||||||
\(229\) | 17.8564i | 1.17998i | 0.807409 | + | 0.589992i | \(0.200869\pi\) | ||||
−0.807409 | + | 0.589992i | \(0.799131\pi\) | |||||||
\(230\) | −2.07055 | −0.136528 | ||||||||
\(231\) | 3.16364 | − | 8.18482i | 0.208153 | − | 0.538522i | ||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | 17.1464i | 1.12330i | 0.827375 | + | 0.561650i | \(0.189833\pi\) | ||||
−0.827375 | + | 0.561650i | \(0.810167\pi\) | |||||||
\(234\) | − | 2.19615i | − | 0.143567i | ||||||
\(235\) | 2.92820 | 0.191015 | ||||||||
\(236\) | − | 22.3923i | − | 1.45761i | ||||||
\(237\) | 3.86370 | 0.250974 | ||||||||
\(238\) | −0.240237 | − | 3.34607i | −0.0155722 | − | 0.216893i | ||||
\(239\) | − | 11.8685i | − | 0.767710i | −0.923393 | − | 0.383855i | \(-0.874596\pi\) | ||
0.923393 | − | 0.383855i | \(-0.125404\pi\) | |||||||
\(240\) | 2.46410 | 0.159057 | ||||||||
\(241\) | 11.1106 | 0.715699 | 0.357850 | − | 0.933779i | \(-0.383510\pi\) | ||||
0.357850 | + | 0.933779i | \(0.383510\pi\) | |||||||
\(242\) | 4.39230 | − | 3.62347i | 0.282348 | − | 0.232925i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 8.48528 | 0.543214 | ||||||||
\(245\) | 1.00000 | + | 6.92820i | 0.0638877 | + | 0.442627i | ||||
\(246\) | 3.46410 | 0.220863 | ||||||||
\(247\) | 4.39230 | 0.279476 | ||||||||
\(248\) | 5.65685 | 0.359211 | ||||||||
\(249\) | 1.41421i | 0.0896221i | ||||||||
\(250\) | −0.517638 | −0.0327383 | ||||||||
\(251\) | − | 19.8564i | − | 1.25333i | −0.779291 | − | 0.626663i | \(-0.784420\pi\) | ||
0.779291 | − | 0.626663i | \(-0.215580\pi\) | |||||||
\(252\) | 4.57081 | − | 0.328169i | 0.287934 | − | 0.0206727i | ||||
\(253\) | 12.0000 | + | 5.65685i | 0.754434 | + | 0.355643i | ||||
\(254\) | −6.33975 | −0.397791 | ||||||||
\(255\) | −2.44949 | −0.153393 | ||||||||
\(256\) | −1.39230 | −0.0870191 | ||||||||
\(257\) | − | 14.0000i | − | 0.873296i | −0.899632 | − | 0.436648i | \(-0.856166\pi\) | ||
0.899632 | − | 0.436648i | \(-0.143834\pi\) | |||||||
\(258\) | 1.26795i | 0.0789391i | ||||||||
\(259\) | 1.41421 | − | 0.101536i | 0.0878750 | − | 0.00630914i | ||||
\(260\) | − | 7.34847i | − | 0.455733i | ||||||
\(261\) | 1.03528i | 0.0640820i | ||||||||
\(262\) | 2.53590i | 0.156668i | ||||||||
\(263\) | 6.31319i | 0.389288i | 0.980874 | + | 0.194644i | \(0.0623552\pi\) | ||||
−0.980874 | + | 0.194644i | \(0.937645\pi\) | |||||||
\(264\) | 5.79555 | + | 2.73205i | 0.356692 | + | 0.168146i | ||||
\(265\) | − | 3.46410i | − | 0.212798i | ||||||
\(266\) | −0.101536 | − | 1.41421i | −0.00622557 | − | 0.0867110i | ||||
\(267\) | −4.92820 | −0.301601 | ||||||||
\(268\) | −9.46410 | −0.578112 | ||||||||
\(269\) | 2.53590i | 0.154616i | 0.997007 | + | 0.0773082i | \(0.0246326\pi\) | ||||
−0.997007 | + | 0.0773082i | \(0.975367\pi\) | |||||||
\(270\) | 0.517638i | 0.0315025i | ||||||||
\(271\) | 21.5921 | 1.31163 | 0.655815 | − | 0.754922i | \(-0.272325\pi\) | ||||
0.655815 | + | 0.754922i | \(0.272325\pi\) | |||||||
\(272\) | −6.03579 | −0.365974 | ||||||||
\(273\) | −0.803848 | − | 11.1962i | −0.0486511 | − | 0.677622i | ||||
\(274\) | 10.8332i | 0.654460i | ||||||||
\(275\) | 3.00000 | + | 1.41421i | 0.180907 | + | 0.0852803i | ||||
\(276\) | 6.92820i | 0.417029i | ||||||||
\(277\) | − | 16.8690i | − | 1.01356i | −0.862075 | − | 0.506781i | \(-0.830835\pi\) | ||
0.862075 | − | 0.506781i | \(-0.169165\pi\) | |||||||
\(278\) | − | 11.0718i | − | 0.664042i | ||||||
\(279\) | − | 2.92820i | − | 0.175307i | ||||||
\(280\) | −5.09808 | + | 0.366025i | −0.304668 | + | 0.0218742i | ||||
\(281\) | − | 12.3490i | − | 0.736679i | −0.929691 | − | 0.368339i | \(-0.879926\pi\) | ||
0.929691 | − | 0.368339i | \(-0.120074\pi\) | |||||||
\(282\) | 1.51575i | 0.0902616i | ||||||||
\(283\) | 19.4201 | 1.15440 | 0.577201 | − | 0.816602i | \(-0.304145\pi\) | ||||
0.577201 | + | 0.816602i | \(0.304145\pi\) | |||||||
\(284\) | 12.0000 | 0.712069 | ||||||||
\(285\) | −1.03528 | −0.0613245 | ||||||||
\(286\) | 3.10583 | − | 6.58846i | 0.183651 | − | 0.389584i | ||||
\(287\) | 17.6603 | − | 1.26795i | 1.04245 | − | 0.0748447i | ||||
\(288\) | 5.13922i | 0.302831i | ||||||||
\(289\) | −11.0000 | −0.647059 | ||||||||
\(290\) | − | 0.535898i | − | 0.0314690i | ||||||
\(291\) | 4.92820 | 0.288896 | ||||||||
\(292\) | 1.13681 | 0.0665269 | ||||||||
\(293\) | 16.3886 | 0.957430 | 0.478715 | − | 0.877970i | \(-0.341103\pi\) | ||||
0.478715 | + | 0.877970i | \(0.341103\pi\) | |||||||
\(294\) | −3.58630 | + | 0.517638i | −0.209157 | + | 0.0301893i | ||||
\(295\) | 12.9282 | 0.752709 | ||||||||
\(296\) | 1.03528i | 0.0601742i | ||||||||
\(297\) | 1.41421 | − | 3.00000i | 0.0820610 | − | 0.174078i | ||||
\(298\) | 9.71281 | 0.562648 | ||||||||
\(299\) | 16.9706 | 0.981433 | ||||||||
\(300\) | 1.73205i | 0.100000i | ||||||||
\(301\) | 0.464102 | + | 6.46410i | 0.0267504 | + | 0.372585i | ||||
\(302\) | −3.07180 | −0.176762 | ||||||||
\(303\) | 11.5911i | 0.665892i | ||||||||
\(304\) | −2.55103 | −0.146311 | ||||||||
\(305\) | 4.89898i | 0.280515i | ||||||||
\(306\) | − | 1.26795i | − | 0.0724838i | ||||||
\(307\) | −15.0759 | −0.860426 | −0.430213 | − | 0.902727i | \(-0.641561\pi\) | ||||
−0.430213 | + | 0.902727i | \(0.641561\pi\) | |||||||
\(308\) | 14.1765 | + | 5.47959i | 0.807783 | + | 0.312229i | ||||
\(309\) | 12.3923 | 0.704974 | ||||||||
\(310\) | 1.51575i | 0.0860888i | ||||||||
\(311\) | 18.7846i | 1.06518i | 0.846374 | + | 0.532589i | \(0.178781\pi\) | ||||
−0.846374 | + | 0.532589i | \(0.821219\pi\) | |||||||
\(312\) | 8.19615 | 0.464016 | ||||||||
\(313\) | − | 31.8564i | − | 1.80063i | −0.435238 | − | 0.900315i | \(-0.643336\pi\) | ||
0.435238 | − | 0.900315i | \(-0.356664\pi\) | |||||||
\(314\) | −3.30890 | −0.186732 | ||||||||
\(315\) | 0.189469 | + | 2.63896i | 0.0106754 | + | 0.148688i | ||||
\(316\) | 6.69213i | 0.376462i | ||||||||
\(317\) | −28.2487 | −1.58661 | −0.793303 | − | 0.608827i | \(-0.791640\pi\) | ||||
−0.793303 | + | 0.608827i | \(0.791640\pi\) | |||||||
\(318\) | 1.79315 | 0.100555 | ||||||||
\(319\) | −1.46410 | + | 3.10583i | −0.0819740 | + | 0.173893i | ||||
\(320\) | 2.26795i | 0.126782i | ||||||||
\(321\) | −10.4543 | −0.583502 | ||||||||
\(322\) | −0.392305 | − | 5.46410i | −0.0218623 | − | 0.304502i | ||||
\(323\) | 2.53590 | 0.141101 | ||||||||
\(324\) | 1.73205 | 0.0962250 | ||||||||
\(325\) | 4.24264 | 0.235339 | ||||||||
\(326\) | 4.34418i | 0.240602i | ||||||||
\(327\) | 17.5254 | 0.969155 | ||||||||
\(328\) | 12.9282i | 0.713841i | ||||||||
\(329\) | 0.554803 | + | 7.72741i | 0.0305873 | + | 0.426026i | ||||
\(330\) | −0.732051 | + | 1.55291i | −0.0402981 | + | 0.0854851i | ||||
\(331\) | −32.2487 | −1.77255 | −0.886275 | − | 0.463160i | \(-0.846716\pi\) | ||||
−0.886275 | + | 0.463160i | \(0.846716\pi\) | |||||||
\(332\) | −2.44949 | −0.134433 | ||||||||
\(333\) | 0.535898 | 0.0293671 | ||||||||
\(334\) | − | 3.66025i | − | 0.200280i | ||||||
\(335\) | − | 5.46410i | − | 0.298536i | ||||||
\(336\) | 0.466870 | + | 6.50266i | 0.0254699 | + | 0.354749i | ||||
\(337\) | − | 6.31319i | − | 0.343902i | −0.985106 | − | 0.171951i | \(-0.944993\pi\) | ||
0.985106 | − | 0.171951i | \(-0.0550070\pi\) | |||||||
\(338\) | − | 2.58819i | − | 0.140779i | ||||||
\(339\) | − | 8.53590i | − | 0.463606i | ||||||
\(340\) | − | 4.24264i | − | 0.230089i | ||||||
\(341\) | 4.14110 | − | 8.78461i | 0.224253 | − | 0.475713i | ||||
\(342\) | − | 0.535898i | − | 0.0289781i | ||||||
\(343\) | −18.0938 | + | 3.95164i | −0.976972 | + | 0.213368i | ||||
\(344\) | −4.73205 | −0.255135 | ||||||||
\(345\) | −4.00000 | −0.215353 | ||||||||
\(346\) | 1.26795i | 0.0681654i | ||||||||
\(347\) | − | 9.14162i | − | 0.490748i | −0.969429 | − | 0.245374i | \(-0.921089\pi\) | ||
0.969429 | − | 0.245374i | \(-0.0789107\pi\) | |||||||
\(348\) | −1.79315 | −0.0961230 | ||||||||
\(349\) | −8.48528 | −0.454207 | −0.227103 | − | 0.973871i | \(-0.572926\pi\) | ||||
−0.227103 | + | 0.973871i | \(0.572926\pi\) | |||||||
\(350\) | −0.0980762 | − | 1.36603i | −0.00524239 | − | 0.0730171i | ||||
\(351\) | − | 4.24264i | − | 0.226455i | ||||||
\(352\) | −7.26795 | + | 15.4176i | −0.387383 | + | 0.821763i | ||||
\(353\) | 19.4641i | 1.03597i | 0.855390 | + | 0.517985i | \(0.173318\pi\) | ||||
−0.855390 | + | 0.517985i | \(0.826682\pi\) | |||||||
\(354\) | 6.69213i | 0.355683i | ||||||||
\(355\) | 6.92820i | 0.367711i | ||||||||
\(356\) | − | 8.53590i | − | 0.452402i | ||||||
\(357\) | −0.464102 | − | 6.46410i | −0.0245629 | − | 0.342117i | ||||
\(358\) | 2.55103i | 0.134826i | ||||||||
\(359\) | 14.9000i | 0.786392i | 0.919455 | + | 0.393196i | \(0.128631\pi\) | ||||
−0.919455 | + | 0.393196i | \(0.871369\pi\) | |||||||
\(360\) | −1.93185 | −0.101818 | ||||||||
\(361\) | −17.9282 | −0.943590 | ||||||||
\(362\) | −8.76268 | −0.460556 | ||||||||
\(363\) | 8.48528 | − | 7.00000i | 0.445362 | − | 0.367405i | ||||
\(364\) | 19.3923 | − | 1.39230i | 1.01643 | − | 0.0729766i | ||||
\(365\) | 0.656339i | 0.0343543i | ||||||||
\(366\) | −2.53590 | −0.132554 | ||||||||
\(367\) | − | 16.7846i | − | 0.876149i | −0.898939 | − | 0.438075i | \(-0.855661\pi\) | ||
0.898939 | − | 0.438075i | \(-0.144339\pi\) | |||||||
\(368\) | −9.85641 | −0.513801 | ||||||||
\(369\) | 6.69213 | 0.348378 | ||||||||
\(370\) | −0.277401 | −0.0144214 | ||||||||
\(371\) | 9.14162 | − | 0.656339i | 0.474609 | − | 0.0340754i | ||||
\(372\) | 5.07180 | 0.262960 | ||||||||
\(373\) | 35.9101i | 1.85936i | 0.368372 | + | 0.929678i | \(0.379915\pi\) | ||||
−0.368372 | + | 0.929678i | \(0.620085\pi\) | |||||||
\(374\) | 1.79315 | − | 3.80385i | 0.0927216 | − | 0.196692i | ||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −5.65685 | −0.291730 | ||||||||
\(377\) | 4.39230i | 0.226215i | ||||||||
\(378\) | −1.36603 | + | 0.0980762i | −0.0702608 | + | 0.00504450i | ||||
\(379\) | 6.14359 | 0.315575 | 0.157788 | − | 0.987473i | \(-0.449564\pi\) | ||||
0.157788 | + | 0.987473i | \(0.449564\pi\) | |||||||
\(380\) | − | 1.79315i | − | 0.0919867i | ||||||
\(381\) | −12.2474 | −0.627456 | ||||||||
\(382\) | 5.73118i | 0.293233i | ||||||||
\(383\) | 3.60770i | 0.184345i | 0.995743 | + | 0.0921723i | \(0.0293811\pi\) | ||||
−0.995743 | + | 0.0921723i | \(0.970619\pi\) | |||||||
\(384\) | −11.4524 | −0.584428 | ||||||||
\(385\) | −3.16364 | + | 8.18482i | −0.161234 | + | 0.417137i | ||||
\(386\) | 10.9808 | 0.558906 | ||||||||
\(387\) | 2.44949i | 0.124515i | ||||||||
\(388\) | 8.53590i | 0.433345i | ||||||||
\(389\) | 30.7846 | 1.56084 | 0.780421 | − | 0.625255i | \(-0.215005\pi\) | ||||
0.780421 | + | 0.625255i | \(0.215005\pi\) | |||||||
\(390\) | 2.19615i | 0.111207i | ||||||||
\(391\) | 9.79796 | 0.495504 | ||||||||
\(392\) | −1.93185 | − | 13.3843i | −0.0975732 | − | 0.676007i | ||||
\(393\) | 4.89898i | 0.247121i | ||||||||
\(394\) | −9.26795 | −0.466913 | ||||||||
\(395\) | −3.86370 | −0.194404 | ||||||||
\(396\) | 5.19615 | + | 2.44949i | 0.261116 | + | 0.123091i | ||||
\(397\) | 4.92820i | 0.247339i | 0.992323 | + | 0.123670i | \(0.0394663\pi\) | ||||
−0.992323 | + | 0.123670i | \(0.960534\pi\) | |||||||
\(398\) | −10.0754 | −0.505032 | ||||||||
\(399\) | −0.196152 | − | 2.73205i | −0.00981990 | − | 0.136774i | ||||
\(400\) | −2.46410 | −0.123205 | ||||||||
\(401\) | −17.4641 | −0.872116 | −0.436058 | − | 0.899919i | \(-0.643626\pi\) | ||||
−0.436058 | + | 0.899919i | \(0.643626\pi\) | |||||||
\(402\) | 2.82843 | 0.141069 | ||||||||
\(403\) | − | 12.4233i | − | 0.618849i | ||||||
\(404\) | −20.0764 | −0.998838 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 1.41421 | − | 0.101536i | 0.0701862 | − | 0.00503915i | ||||
\(407\) | 1.60770 | + | 0.757875i | 0.0796905 | + | 0.0375665i | ||||
\(408\) | 4.73205 | 0.234271 | ||||||||
\(409\) | −30.3548 | −1.50095 | −0.750475 | − | 0.660899i | \(-0.770175\pi\) | ||||
−0.750475 | + | 0.660899i | \(0.770175\pi\) | |||||||
\(410\) | −3.46410 | −0.171080 | ||||||||
\(411\) | 20.9282i | 1.03231i | ||||||||
\(412\) | 21.4641i | 1.05746i | ||||||||
\(413\) | 2.44949 | + | 34.1170i | 0.120532 | + | 1.67879i | ||||
\(414\) | − | 2.07055i | − | 0.101762i | ||||||
\(415\) | − | 1.41421i | − | 0.0694210i | ||||||
\(416\) | 21.8038i | 1.06902i | ||||||||
\(417\) | − | 21.3891i | − | 1.04743i | ||||||
\(418\) | 0.757875 | − | 1.60770i | 0.0370689 | − | 0.0786349i | ||||
\(419\) | − | 17.0718i | − | 0.834012i | −0.908904 | − | 0.417006i | \(-0.863079\pi\) | ||
0.908904 | − | 0.417006i | \(-0.136921\pi\) | |||||||
\(420\) | −4.57081 | + | 0.328169i | −0.223033 | + | 0.0160130i | ||||
\(421\) | −1.85641 | −0.0904757 | −0.0452379 | − | 0.998976i | \(-0.514405\pi\) | ||||
−0.0452379 | + | 0.998976i | \(0.514405\pi\) | |||||||
\(422\) | −4.14359 | −0.201707 | ||||||||
\(423\) | 2.92820i | 0.142374i | ||||||||
\(424\) | 6.69213i | 0.324999i | ||||||||
\(425\) | 2.44949 | 0.118818 | ||||||||
\(426\) | −3.58630 | −0.173757 | ||||||||
\(427\) | −12.9282 | + | 0.928203i | −0.625640 | + | 0.0449189i | ||||
\(428\) | − | 18.1074i | − | 0.875253i | ||||||
\(429\) | 6.00000 | − | 12.7279i | 0.289683 | − | 0.614510i | ||||
\(430\) | − | 1.26795i | − | 0.0611459i | ||||||
\(431\) | − | 24.4949i | − | 1.17988i | −0.807448 | − | 0.589939i | \(-0.799152\pi\) | ||
0.807448 | − | 0.589939i | \(-0.200848\pi\) | |||||||
\(432\) | 2.46410i | 0.118554i | ||||||||
\(433\) | 16.9282i | 0.813518i | 0.913536 | + | 0.406759i | \(0.133341\pi\) | ||||
−0.913536 | + | 0.406759i | \(0.866659\pi\) | |||||||
\(434\) | −4.00000 | + | 0.287187i | −0.192006 | + | 0.0137854i | ||||
\(435\) | − | 1.03528i | − | 0.0496377i | ||||||
\(436\) | 30.3548i | 1.45373i | ||||||||
\(437\) | 4.14110 | 0.198096 | ||||||||
\(438\) | −0.339746 | −0.0162337 | ||||||||
\(439\) | −38.3596 | −1.83081 | −0.915403 | − | 0.402539i | \(-0.868128\pi\) | ||||
−0.915403 | + | 0.402539i | \(0.868128\pi\) | |||||||
\(440\) | −5.79555 | − | 2.73205i | −0.276292 | − | 0.130245i | ||||
\(441\) | −6.92820 | + | 1.00000i | −0.329914 | + | 0.0476190i | ||||
\(442\) | − | 5.37945i | − | 0.255874i | ||||||
\(443\) | −4.78461 | −0.227324 | −0.113662 | − | 0.993519i | \(-0.536258\pi\) | ||||
−0.113662 | + | 0.993519i | \(0.536258\pi\) | |||||||
\(444\) | 0.928203i | 0.0440506i | ||||||||
\(445\) | 4.92820 | 0.233619 | ||||||||
\(446\) | −5.10205 | −0.241589 | ||||||||
\(447\) | 18.7637 | 0.887493 | ||||||||
\(448\) | −5.98502 | + | 0.429705i | −0.282766 | + | 0.0203017i | ||||
\(449\) | 23.3205 | 1.10056 | 0.550281 | − | 0.834979i | \(-0.314520\pi\) | ||||
0.550281 | + | 0.834979i | \(0.314520\pi\) | |||||||
\(450\) | − | 0.517638i | − | 0.0244017i | ||||||
\(451\) | 20.0764 | + | 9.46410i | 0.945360 | + | 0.445647i | ||||
\(452\) | 14.7846 | 0.695410 | ||||||||
\(453\) | −5.93426 | −0.278816 | ||||||||
\(454\) | − | 9.51666i | − | 0.446639i | ||||||
\(455\) | 0.803848 | + | 11.1962i | 0.0376850 | + | 0.524884i | ||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | − | 40.2543i | − | 1.88302i | −0.336988 | − | 0.941509i | \(-0.609408\pi\) | ||
0.336988 | − | 0.941509i | \(-0.390592\pi\) | |||||||
\(458\) | 9.24316 | 0.431904 | ||||||||
\(459\) | − | 2.44949i | − | 0.114332i | ||||||
\(460\) | − | 6.92820i | − | 0.323029i | ||||||
\(461\) | −36.8439 | −1.71599 | −0.857995 | − | 0.513657i | \(-0.828290\pi\) | ||||
−0.857995 | + | 0.513657i | \(0.828290\pi\) | |||||||
\(462\) | −4.23678 | − | 1.63762i | −0.197113 | − | 0.0761891i | ||||
\(463\) | 31.7128 | 1.47382 | 0.736910 | − | 0.675991i | \(-0.236284\pi\) | ||||
0.736910 | + | 0.675991i | \(0.236284\pi\) | |||||||
\(464\) | − | 2.55103i | − | 0.118428i | ||||||
\(465\) | 2.92820i | 0.135792i | ||||||||
\(466\) | 8.87564 | 0.411156 | ||||||||
\(467\) | − | 26.2487i | − | 1.21465i | −0.794455 | − | 0.607323i | \(-0.792243\pi\) | ||
0.794455 | − | 0.607323i | \(-0.207757\pi\) | |||||||
\(468\) | 7.34847 | 0.339683 | ||||||||
\(469\) | 14.4195 | − | 1.03528i | 0.665832 | − | 0.0478046i | ||||
\(470\) | − | 1.51575i | − | 0.0699163i | ||||||
\(471\) | −6.39230 | −0.294542 | ||||||||
\(472\) | −24.9754 | −1.14958 | ||||||||
\(473\) | −3.46410 | + | 7.34847i | −0.159280 | + | 0.337883i | ||||
\(474\) | − | 2.00000i | − | 0.0918630i | ||||||
\(475\) | 1.03528 | 0.0475017 | ||||||||
\(476\) | 11.1962 | − | 0.803848i | 0.513175 | − | 0.0368443i | ||||
\(477\) | 3.46410 | 0.158610 | ||||||||
\(478\) | −6.14359 | −0.281001 | ||||||||
\(479\) | −2.82843 | −0.129234 | −0.0646171 | − | 0.997910i | \(-0.520583\pi\) | ||||
−0.0646171 | + | 0.997910i | \(0.520583\pi\) | |||||||
\(480\) | − | 5.13922i | − | 0.234572i | ||||||
\(481\) | 2.27362 | 0.103668 | ||||||||
\(482\) | − | 5.75129i | − | 0.261964i | ||||||
\(483\) | −0.757875 | − | 10.5558i | −0.0344845 | − | 0.480307i | ||||
\(484\) | 12.1244 | + | 14.6969i | 0.551107 | + | 0.668043i | ||||
\(485\) | −4.92820 | −0.223778 | ||||||||
\(486\) | −0.517638 | −0.0234805 | ||||||||
\(487\) | −15.3205 | −0.694238 | −0.347119 | − | 0.937821i | \(-0.612840\pi\) | ||||
−0.347119 | + | 0.937821i | \(0.612840\pi\) | |||||||
\(488\) | − | 9.46410i | − | 0.428420i | ||||||
\(489\) | 8.39230i | 0.379513i | ||||||||
\(490\) | 3.58630 | − | 0.517638i | 0.162013 | − | 0.0233845i | ||||
\(491\) | 2.82843i | 0.127645i | 0.997961 | + | 0.0638226i | \(0.0203292\pi\) | ||||
−0.997961 | + | 0.0638226i | \(0.979671\pi\) | |||||||
\(492\) | 11.5911i | 0.522568i | ||||||||
\(493\) | 2.53590i | 0.114211i | ||||||||
\(494\) | − | 2.27362i | − | 0.102295i | ||||||
\(495\) | −1.41421 | + | 3.00000i | −0.0635642 | + | 0.134840i | ||||
\(496\) | 7.21539i | 0.323981i | ||||||||
\(497\) | −18.2832 | + | 1.31268i | −0.820115 | + | 0.0588816i | ||||
\(498\) | 0.732051 | 0.0328040 | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | − | 1.73205i | − | 0.0774597i | ||||||
\(501\) | − | 7.07107i | − | 0.315912i | ||||||
\(502\) | −10.2784 | −0.458749 | ||||||||
\(503\) | 19.4944 | 0.869212 | 0.434606 | − | 0.900621i | \(-0.356888\pi\) | ||||
0.434606 | + | 0.900621i | \(0.356888\pi\) | |||||||
\(504\) | −0.366025 | − | 5.09808i | −0.0163041 | − | 0.227086i | ||||
\(505\) | − | 11.5911i | − | 0.515798i | ||||||
\(506\) | 2.92820 | − | 6.21166i | 0.130175 | − | 0.276142i | ||||
\(507\) | − | 5.00000i | − | 0.222058i | ||||||
\(508\) | − | 21.2132i | − | 0.941184i | ||||||
\(509\) | 18.2487i | 0.808860i | 0.914569 | + | 0.404430i | \(0.132530\pi\) | ||||
−0.914569 | + | 0.404430i | \(0.867470\pi\) | |||||||
\(510\) | 1.26795i | 0.0561457i | ||||||||
\(511\) | −1.73205 | + | 0.124356i | −0.0766214 | + | 0.00550117i | ||||
\(512\) | − | 22.1841i | − | 0.980408i | ||||||
\(513\) | − | 1.03528i | − | 0.0457086i | ||||||
\(514\) | −7.24693 | −0.319649 | ||||||||
\(515\) | −12.3923 | −0.546070 | ||||||||
\(516\) | −4.24264 | −0.186772 | ||||||||
\(517\) | −4.14110 | + | 8.78461i | −0.182126 | + | 0.386347i | ||||
\(518\) | −0.0525589 | − | 0.732051i | −0.00230930 | − | 0.0321645i | ||||
\(519\) | 2.44949i | 0.107521i | ||||||||
\(520\) | −8.19615 | −0.359425 | ||||||||
\(521\) | 31.8564i | 1.39565i | 0.716266 | + | 0.697827i | \(0.245850\pi\) | ||||
−0.716266 | + | 0.697827i | \(0.754150\pi\) | |||||||
\(522\) | 0.535898 | 0.0234556 | ||||||||
\(523\) | 1.13681 | 0.0497093 | 0.0248547 | − | 0.999691i | \(-0.492088\pi\) | ||||
0.0248547 | + | 0.999691i | \(0.492088\pi\) | |||||||
\(524\) | −8.48528 | −0.370681 | ||||||||
\(525\) | −0.189469 | − | 2.63896i | −0.00826909 | − | 0.115174i | ||||
\(526\) | 3.26795 | 0.142489 | ||||||||
\(527\) | − | 7.17260i | − | 0.312444i | ||||||
\(528\) | −3.48477 | + | 7.39230i | −0.151655 | + | 0.321709i | ||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −1.79315 | −0.0778895 | ||||||||
\(531\) | 12.9282i | 0.561036i | ||||||||
\(532\) | 4.73205 | − | 0.339746i | 0.205160 | − | 0.0147299i | ||||
\(533\) | 28.3923 | 1.22981 | ||||||||
\(534\) | 2.55103i | 0.110394i | ||||||||
\(535\) | 10.4543 | 0.451979 | ||||||||
\(536\) | 10.5558i | 0.455943i | ||||||||
\(537\) | 4.92820i | 0.212668i | ||||||||
\(538\) | 1.31268 | 0.0565935 | ||||||||
\(539\) | −22.1988 | − | 6.79796i | −0.956171 | − | 0.292809i | ||||
\(540\) | −1.73205 | −0.0745356 | ||||||||
\(541\) | − | 33.9411i | − | 1.45924i | −0.683851 | − | 0.729621i | \(-0.739696\pi\) | ||
0.683851 | − | 0.729621i | \(-0.260304\pi\) | |||||||
\(542\) | − | 11.1769i | − | 0.480090i | ||||||
\(543\) | −16.9282 | −0.726459 | ||||||||
\(544\) | 12.5885i | 0.539726i | ||||||||
\(545\) | −17.5254 | −0.750704 | ||||||||
\(546\) | −5.79555 | + | 0.416102i | −0.248027 | + | 0.0178075i | ||||
\(547\) | 3.76217i | 0.160859i | 0.996760 | + | 0.0804293i | \(0.0256291\pi\) | ||||
−0.996760 | + | 0.0804293i | \(0.974371\pi\) | |||||||
\(548\) | −36.2487 | −1.54847 | ||||||||
\(549\) | −4.89898 | −0.209083 | ||||||||
\(550\) | 0.732051 | − | 1.55291i | 0.0312148 | − | 0.0662165i | ||||
\(551\) | 1.07180i | 0.0456601i | ||||||||
\(552\) | 7.72741 | 0.328900 | ||||||||
\(553\) | −0.732051 | − | 10.1962i | −0.0311300 | − | 0.433585i | ||||
\(554\) | −8.73205 | −0.370989 | ||||||||
\(555\) | −0.535898 | −0.0227476 | ||||||||
\(556\) | 37.0470 | 1.57114 | ||||||||
\(557\) | 17.3495i | 0.735122i | 0.929999 | + | 0.367561i | \(0.119807\pi\) | ||||
−0.929999 | + | 0.367561i | \(0.880193\pi\) | |||||||
\(558\) | −1.51575 | −0.0641668 | ||||||||
\(559\) | 10.3923i | 0.439548i | ||||||||
\(560\) | −0.466870 | − | 6.50266i | −0.0197289 | − | 0.274788i | ||||
\(561\) | 3.46410 | − | 7.34847i | 0.146254 | − | 0.310253i | ||||
\(562\) | −6.39230 | −0.269643 | ||||||||
\(563\) | −21.7680 | −0.917412 | −0.458706 | − | 0.888588i | \(-0.651687\pi\) | ||||
−0.458706 | + | 0.888588i | \(0.651687\pi\) | |||||||
\(564\) | −5.07180 | −0.213561 | ||||||||
\(565\) | 8.53590i | 0.359108i | ||||||||
\(566\) | − | 10.0526i | − | 0.422541i | ||||||
\(567\) | −2.63896 | + | 0.189469i | −0.110826 | + | 0.00795694i | ||||
\(568\) | − | 13.3843i | − | 0.561591i | ||||||
\(569\) | 23.4596i | 0.983478i | 0.870743 | + | 0.491739i | \(0.163639\pi\) | ||||
−0.870743 | + | 0.491739i | \(0.836361\pi\) | |||||||
\(570\) | 0.535898i | 0.0224463i | ||||||||
\(571\) | 43.2586i | 1.81032i | 0.425075 | + | 0.905158i | \(0.360248\pi\) | ||||
−0.425075 | + | 0.905158i | \(0.639752\pi\) | |||||||
\(572\) | 22.0454 | + | 10.3923i | 0.921765 | + | 0.434524i | ||||
\(573\) | 11.0718i | 0.462531i | ||||||||
\(574\) | −0.656339 | − | 9.14162i | −0.0273951 | − | 0.381564i | ||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | −2.26795 | −0.0944979 | ||||||||
\(577\) | 35.1769i | 1.46443i | 0.681071 | + | 0.732217i | \(0.261514\pi\) | ||||
−0.681071 | + | 0.732217i | \(0.738486\pi\) | |||||||
\(578\) | 5.69402i | 0.236840i | ||||||||
\(579\) | 21.2132 | 0.881591 | ||||||||
\(580\) | 1.79315 | 0.0744565 | ||||||||
\(581\) | 3.73205 | − | 0.267949i | 0.154832 | − | 0.0111164i | ||||
\(582\) | − | 2.55103i | − | 0.105743i | ||||||
\(583\) | 10.3923 | + | 4.89898i | 0.430405 | + | 0.202895i | ||||
\(584\) | − | 1.26795i | − | 0.0524681i | ||||||
\(585\) | 4.24264i | 0.175412i | ||||||||
\(586\) | − | 8.48334i | − | 0.350444i | ||||||
\(587\) | − | 15.6077i | − | 0.644199i | −0.946706 | − | 0.322099i | \(-0.895612\pi\) | ||
0.946706 | − | 0.322099i | \(-0.104388\pi\) | |||||||
\(588\) | −1.73205 | − | 12.0000i | −0.0714286 | − | 0.494872i | ||||
\(589\) | − | 3.03150i | − | 0.124911i | ||||||
\(590\) | − | 6.69213i | − | 0.275511i | ||||||
\(591\) | −17.9043 | −0.736485 | ||||||||
\(592\) | −1.32051 | −0.0542725 | ||||||||
\(593\) | −39.2190 | −1.61053 | −0.805267 | − | 0.592913i | \(-0.797978\pi\) | ||||
−0.805267 | + | 0.592913i | \(0.797978\pi\) | |||||||
\(594\) | −1.55291 | − | 0.732051i | −0.0637168 | − | 0.0300364i | ||||
\(595\) | 0.464102 | + | 6.46410i | 0.0190263 | + | 0.265002i | ||||
\(596\) | 32.4997i | 1.33124i | ||||||||
\(597\) | −19.4641 | −0.796613 | ||||||||
\(598\) | − | 8.78461i | − | 0.359229i | ||||||
\(599\) | 7.85641 | 0.321004 | 0.160502 | − | 0.987036i | \(-0.448689\pi\) | ||||
0.160502 | + | 0.987036i | \(0.448689\pi\) | |||||||
\(600\) | 1.93185 | 0.0788675 | ||||||||
\(601\) | 13.5873 | 0.554239 | 0.277119 | − | 0.960835i | \(-0.410620\pi\) | ||||
0.277119 | + | 0.960835i | \(0.410620\pi\) | |||||||
\(602\) | 3.34607 | − | 0.240237i | 0.136375 | − | 0.00979132i | ||||
\(603\) | 5.46410 | 0.222515 | ||||||||
\(604\) | − | 10.2784i | − | 0.418223i | ||||||
\(605\) | −8.48528 | + | 7.00000i | −0.344976 | + | 0.284590i | ||||
\(606\) | 6.00000 | 0.243733 | ||||||||
\(607\) | −21.6937 | −0.880519 | −0.440260 | − | 0.897871i | \(-0.645114\pi\) | ||||
−0.440260 | + | 0.897871i | \(0.645114\pi\) | |||||||
\(608\) | 5.32051i | 0.215775i | ||||||||
\(609\) | 2.73205 | − | 0.196152i | 0.110708 | − | 0.00794850i | ||||
\(610\) | 2.53590 | 0.102676 | ||||||||
\(611\) | 12.4233i | 0.502593i | ||||||||
\(612\) | 4.24264 | 0.171499 | ||||||||
\(613\) | − | 35.9101i | − | 1.45040i | −0.688540 | − | 0.725198i | \(-0.741748\pi\) | ||
0.688540 | − | 0.725198i | \(-0.258252\pi\) | |||||||
\(614\) | 7.80385i | 0.314938i | ||||||||
\(615\) | −6.69213 | −0.269853 | ||||||||
\(616\) | 6.11169 | − | 15.8119i | 0.246247 | − | 0.637078i | ||||
\(617\) | 20.5359 | 0.826744 | 0.413372 | − | 0.910562i | \(-0.364351\pi\) | ||||
0.413372 | + | 0.910562i | \(0.364351\pi\) | |||||||
\(618\) | − | 6.41473i | − | 0.258038i | ||||||
\(619\) | 9.85641i | 0.396162i | 0.980186 | + | 0.198081i | \(0.0634710\pi\) | ||||
−0.980186 | + | 0.198081i | \(0.936529\pi\) | |||||||
\(620\) | −5.07180 | −0.203688 | ||||||||
\(621\) | − | 4.00000i | − | 0.160514i | ||||||
\(622\) | 9.72363 | 0.389882 | ||||||||
\(623\) | 0.933740 | + | 13.0053i | 0.0374095 | + | 0.521047i | ||||
\(624\) | 10.4543i | 0.418507i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −16.4901 | −0.659077 | ||||||||
\(627\) | 1.46410 | − | 3.10583i | 0.0584706 | − | 0.124035i | ||||
\(628\) | − | 11.0718i | − | 0.441813i | ||||||
\(629\) | 1.31268 | 0.0523399 | ||||||||
\(630\) | 1.36603 | − | 0.0980762i | 0.0544238 | − | 0.00390745i | ||||
\(631\) | −43.7128 | −1.74018 | −0.870090 | − | 0.492893i | \(-0.835939\pi\) | ||||
−0.870090 | + | 0.492893i | \(0.835939\pi\) | |||||||
\(632\) | 7.46410 | 0.296906 | ||||||||
\(633\) | −8.00481 | −0.318163 | ||||||||
\(634\) | 14.6226i | 0.580738i | ||||||||
\(635\) | 12.2474 | 0.486025 | ||||||||
\(636\) | 6.00000i | 0.237915i | ||||||||
\(637\) | −29.3939 | + | 4.24264i | −1.16463 | + | 0.168100i | ||||
\(638\) | 1.60770 | + | 0.757875i | 0.0636493 | + | 0.0300045i | ||||
\(639\) | −6.92820 | −0.274075 | ||||||||
\(640\) | 11.4524 | 0.452696 | ||||||||
\(641\) | 11.3205 | 0.447133 | 0.223567 | − | 0.974689i | \(-0.428230\pi\) | ||||
0.223567 | + | 0.974689i | \(0.428230\pi\) | |||||||
\(642\) | 5.41154i | 0.213577i | ||||||||
\(643\) | 22.5359i | 0.888729i | 0.895846 | + | 0.444365i | \(0.146570\pi\) | ||||
−0.895846 | + | 0.444365i | \(0.853430\pi\) | |||||||
\(644\) | 18.2832 | − | 1.31268i | 0.720461 | − | 0.0517267i | ||||
\(645\) | − | 2.44949i | − | 0.0964486i | ||||||
\(646\) | − | 1.31268i | − | 0.0516466i | ||||||
\(647\) | 19.6077i | 0.770858i | 0.922737 | + | 0.385429i | \(0.125947\pi\) | ||||
−0.922737 | + | 0.385429i | \(0.874053\pi\) | |||||||
\(648\) | − | 1.93185i | − | 0.0758903i | ||||||
\(649\) | −18.2832 | + | 38.7846i | −0.717680 | + | 1.52243i | ||||
\(650\) | − | 2.19615i | − | 0.0861402i | ||||||
\(651\) | −7.72741 | + | 0.554803i | −0.302861 | + | 0.0217444i | ||||
\(652\) | −14.5359 | −0.569270 | ||||||||
\(653\) | 39.5692 | 1.54846 | 0.774232 | − | 0.632902i | \(-0.218137\pi\) | ||||
0.774232 | + | 0.632902i | \(0.218137\pi\) | |||||||
\(654\) | − | 9.07180i | − | 0.354735i | ||||||
\(655\) | − | 4.89898i | − | 0.191419i | ||||||
\(656\) | −16.4901 | −0.643830 | ||||||||
\(657\) | −0.656339 | −0.0256062 | ||||||||
\(658\) | 4.00000 | − | 0.287187i | 0.155936 | − | 0.0111957i | ||||
\(659\) | 5.45378i | 0.212449i | 0.994342 | + | 0.106225i | \(0.0338763\pi\) | ||||
−0.994342 | + | 0.106225i | \(0.966124\pi\) | |||||||
\(660\) | −5.19615 | − | 2.44949i | −0.202260 | − | 0.0953463i | ||||
\(661\) | − | 41.5692i | − | 1.61686i | −0.588596 | − | 0.808428i | \(-0.700319\pi\) | ||
0.588596 | − | 0.808428i | \(-0.299681\pi\) | |||||||
\(662\) | 16.6932i | 0.648798i | ||||||||
\(663\) | − | 10.3923i | − | 0.403604i | ||||||
\(664\) | 2.73205i | 0.106024i | ||||||||
\(665\) | 0.196152 | + | 2.73205i | 0.00760646 | + | 0.105944i | ||||
\(666\) | − | 0.277401i | − | 0.0107491i | ||||||
\(667\) | 4.14110i | 0.160344i | ||||||||
\(668\) | 12.2474 | 0.473868 | ||||||||
\(669\) | −9.85641 | −0.381071 | ||||||||
\(670\) | −2.82843 | −0.109272 | ||||||||
\(671\) | −14.6969 | − | 6.92820i | −0.567369 | − | 0.267460i | ||||
\(672\) | 13.5622 | − | 0.973721i | 0.523172 | − | 0.0375621i | ||||
\(673\) | − | 31.2142i | − | 1.20322i | −0.798790 | − | 0.601610i | \(-0.794526\pi\) | ||
0.798790 | − | 0.601610i | \(-0.205474\pi\) | |||||||
\(674\) | −3.26795 | −0.125877 | ||||||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | 8.66025 | 0.333087 | ||||||||
\(677\) | 29.0149 | 1.11513 | 0.557567 | − | 0.830132i | \(-0.311735\pi\) | ||||
0.557567 | + | 0.830132i | \(0.311735\pi\) | |||||||
\(678\) | −4.41851 | −0.169692 | ||||||||
\(679\) | −0.933740 | − | 13.0053i | −0.0358337 | − | 0.499099i | ||||
\(680\) | −4.73205 | −0.181466 | ||||||||
\(681\) | − | 18.3848i | − | 0.704506i | ||||||
\(682\) | −4.54725 | − | 2.14359i | −0.174123 | − | 0.0820824i | ||||
\(683\) | −44.1051 | −1.68764 | −0.843818 | − | 0.536630i | \(-0.819697\pi\) | ||||
−0.843818 | + | 0.536630i | \(0.819697\pi\) | |||||||
\(684\) | 1.79315 | 0.0685628 | ||||||||
\(685\) | − | 20.9282i | − | 0.799626i | ||||||
\(686\) | 2.04552 | + | 9.36603i | 0.0780982 | + | 0.357597i | ||||
\(687\) | 17.8564 | 0.681264 | ||||||||
\(688\) | − | 6.03579i | − | 0.230112i | ||||||
\(689\) | 14.6969 | 0.559909 | ||||||||
\(690\) | 2.07055i | 0.0788246i | ||||||||
\(691\) | − | 23.1769i | − | 0.881691i | −0.897583 | − | 0.440846i | \(-0.854679\pi\) | ||
0.897583 | − | 0.440846i | \(-0.145321\pi\) | |||||||
\(692\) | −4.24264 | −0.161281 | ||||||||
\(693\) | −8.18482 | − | 3.16364i | −0.310916 | − | 0.120177i | ||||
\(694\) | −4.73205 | −0.179626 | ||||||||
\(695\) | 21.3891i | 0.811334i | ||||||||
\(696\) | 2.00000i | 0.0758098i | ||||||||
\(697\) | 16.3923 | 0.620903 | ||||||||
\(698\) | 4.39230i | 0.166251i | ||||||||
\(699\) | 17.1464 | 0.648537 | ||||||||
\(700\) | 4.57081 | − | 0.328169i | 0.172760 | − | 0.0124036i | ||||
\(701\) | 34.5703i | 1.30570i | 0.757487 | + | 0.652850i | \(0.226427\pi\) | ||||
−0.757487 | + | 0.652850i | \(0.773573\pi\) | |||||||
\(702\) | −2.19615 | −0.0828884 | ||||||||
\(703\) | 0.554803 | 0.0209248 | ||||||||
\(704\) | −6.80385 | − | 3.20736i | −0.256430 | − | 0.120882i | ||||
\(705\) | − | 2.92820i | − | 0.110283i | ||||||
\(706\) | 10.0754 | 0.379191 | ||||||||
\(707\) | 30.5885 | − | 2.19615i | 1.15040 | − | 0.0825948i | ||||
\(708\) | −22.3923 | −0.841554 | ||||||||
\(709\) | −10.9282 | −0.410417 | −0.205209 | − | 0.978718i | \(-0.565787\pi\) | ||||
−0.205209 | + | 0.978718i | \(0.565787\pi\) | |||||||
\(710\) | 3.58630 | 0.134592 | ||||||||
\(711\) | − | 3.86370i | − | 0.144900i | ||||||
\(712\) | −9.52056 | −0.356798 | ||||||||
\(713\) | − | 11.7128i | − | 0.438648i | ||||||
\(714\) | −3.34607 | + | 0.240237i | −0.125223 | + | 0.00899063i | ||||
\(715\) | −6.00000 | + | 12.7279i | −0.224387 | + | 0.475997i | ||||
\(716\) | −8.53590 | −0.319002 | ||||||||
\(717\) | −11.8685 | −0.443238 | ||||||||
\(718\) | 7.71281 | 0.287840 | ||||||||
\(719\) | 5.85641i | 0.218407i | 0.994019 | + | 0.109204i | \(0.0348300\pi\) | ||||
−0.994019 | + | 0.109204i | \(0.965170\pi\) | |||||||
\(720\) | − | 2.46410i | − | 0.0918316i | ||||||
\(721\) | −2.34795 | − | 32.7028i | −0.0874424 | − | 1.21792i | ||||
\(722\) | 9.28032i | 0.345378i | ||||||||
\(723\) | − | 11.1106i | − | 0.413209i | ||||||
\(724\) | − | 29.3205i | − | 1.08969i | ||||||
\(725\) | 1.03528i | 0.0384492i | ||||||||
\(726\) | −3.62347 | − | 4.39230i | −0.134479 | − | 0.163014i | ||||
\(727\) | 45.5692i | 1.69007i | 0.534712 | + | 0.845034i | \(0.320420\pi\) | ||||
−0.534712 | + | 0.845034i | \(0.679580\pi\) | |||||||
\(728\) | −1.55291 | − | 21.6293i | −0.0575548 | − | 0.801635i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0.339746 | 0.0125746 | ||||||||
\(731\) | 6.00000i | 0.221918i | ||||||||
\(732\) | − | 8.48528i | − | 0.313625i | ||||||
\(733\) | −0.101536 | −0.00375032 | −0.00187516 | − | 0.999998i | \(-0.500597\pi\) | ||||
−0.00187516 | + | 0.999998i | \(0.500597\pi\) | |||||||
\(734\) | −8.68835 | −0.320693 | ||||||||
\(735\) | 6.92820 | − | 1.00000i | 0.255551 | − | 0.0368856i | ||||
\(736\) | 20.5569i | 0.757736i | ||||||||
\(737\) | 16.3923 | + | 7.72741i | 0.603818 | + | 0.284643i | ||||
\(738\) | − | 3.46410i | − | 0.127515i | ||||||
\(739\) | − | 51.5408i | − | 1.89596i | −0.318330 | − | 0.947980i | \(-0.603122\pi\) | ||
0.318330 | − | 0.947980i | \(-0.396878\pi\) | |||||||
\(740\) | − | 0.928203i | − | 0.0341214i | ||||||
\(741\) | − | 4.39230i | − | 0.161355i | ||||||
\(742\) | −0.339746 | − | 4.73205i | −0.0124725 | − | 0.173719i | ||||
\(743\) | 32.3238i | 1.18585i | 0.805259 | + | 0.592923i | \(0.202026\pi\) | ||||
−0.805259 | + | 0.592923i | \(0.797974\pi\) | |||||||
\(744\) | − | 5.65685i | − | 0.207390i | ||||||
\(745\) | −18.7637 | −0.687449 | ||||||||
\(746\) | 18.5885 | 0.680572 | ||||||||
\(747\) | 1.41421 | 0.0517434 | ||||||||
\(748\) | 12.7279 | + | 6.00000i | 0.465379 | + | 0.219382i | ||||
\(749\) | 1.98076 | + | 27.5885i | 0.0723755 | + | 1.00806i | ||||
\(750\) | 0.517638i | 0.0189015i | ||||||||
\(751\) | 18.9282 | 0.690700 | 0.345350 | − | 0.938474i | \(-0.387760\pi\) | ||||
0.345350 | + | 0.938474i | \(0.387760\pi\) | |||||||
\(752\) | − | 7.21539i | − | 0.263118i | ||||||
\(753\) | −19.8564 | −0.723608 | ||||||||
\(754\) | 2.27362 | 0.0828005 | ||||||||
\(755\) | 5.93426 | 0.215970 | ||||||||
\(756\) | −0.328169 | − | 4.57081i | −0.0119354 | − | 0.166239i | ||||
\(757\) | 20.6410 | 0.750210 | 0.375105 | − | 0.926982i | \(-0.377607\pi\) | ||||
0.375105 | + | 0.926982i | \(0.377607\pi\) | |||||||
\(758\) | − | 3.18016i | − | 0.115509i | ||||||
\(759\) | 5.65685 | − | 12.0000i | 0.205331 | − | 0.435572i | ||||
\(760\) | −2.00000 | −0.0725476 | ||||||||
\(761\) | −52.8535 | −1.91594 | −0.957969 | − | 0.286872i | \(-0.907385\pi\) | ||||
−0.957969 | + | 0.286872i | \(0.907385\pi\) | |||||||
\(762\) | 6.33975i | 0.229665i | ||||||||
\(763\) | −3.32051 | − | 46.2487i | −0.120210 | − | 1.67432i | ||||
\(764\) | −19.1769 | −0.693796 | ||||||||
\(765\) | 2.44949i | 0.0885615i | ||||||||
\(766\) | 1.86748 | 0.0674748 | ||||||||
\(767\) | 54.8497i | 1.98051i | ||||||||
\(768\) | 1.39230i | 0.0502405i | ||||||||
\(769\) | −46.5675 | −1.67927 | −0.839634 | − | 0.543153i | \(-0.817230\pi\) | ||||
−0.839634 | + | 0.543153i | \(0.817230\pi\) | |||||||
\(770\) | 4.23678 | + | 1.63762i | 0.152683 | + | 0.0590158i | ||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 36.7423i | 1.32239i | ||||||||
\(773\) | 42.0000i | 1.51064i | 0.655359 | + | 0.755318i | \(0.272517\pi\) | ||||
−0.655359 | + | 0.755318i | \(0.727483\pi\) | |||||||
\(774\) | 1.26795 | 0.0455755 | ||||||||
\(775\) | − | 2.92820i | − | 0.105184i | ||||||
\(776\) | 9.52056 | 0.341768 | ||||||||
\(777\) | −0.101536 | − | 1.41421i | −0.00364258 | − | 0.0507346i | ||||
\(778\) | − | 15.9353i | − | 0.571308i | ||||||
\(779\) | 6.92820 | 0.248229 | ||||||||
\(780\) | −7.34847 | −0.263117 | ||||||||
\(781\) | −20.7846 | − | 9.79796i | −0.743732 | − | 0.350599i | ||||
\(782\) | − | 5.07180i | − | 0.181367i | ||||||
\(783\) | 1.03528 | 0.0369978 | ||||||||
\(784\) | 17.0718 | − | 2.46410i | 0.609707 | − | 0.0880036i | ||||
\(785\) | 6.39230 | 0.228151 | ||||||||
\(786\) | 2.53590 | 0.0904525 | ||||||||
\(787\) | −3.96524 | −0.141346 | −0.0706728 | − | 0.997500i | \(-0.522515\pi\) | ||||
−0.0706728 | + | 0.997500i | \(0.522515\pi\) | |||||||
\(788\) | − | 31.0112i | − | 1.10473i | ||||||
\(789\) | 6.31319 | 0.224756 | ||||||||
\(790\) | 2.00000i | 0.0711568i | ||||||||
\(791\) | −22.5259 | + | 1.61729i | −0.800928 | + | 0.0575041i | ||||
\(792\) | 2.73205 | − | 5.79555i | 0.0970792 | − | 0.205936i | ||||
\(793\) | −20.7846 | −0.738083 | ||||||||
\(794\) | 2.55103 | 0.0905325 | ||||||||
\(795\) | −3.46410 | −0.122859 | ||||||||
\(796\) | − | 33.7128i | − | 1.19492i | ||||||
\(797\) | 18.3923i | 0.651489i | 0.945458 | + | 0.325744i | \(0.105615\pi\) | ||||
−0.945458 | + | 0.325744i | \(0.894385\pi\) | |||||||
\(798\) | −1.41421 | + | 0.101536i | −0.0500626 | + | 0.00359433i | ||||
\(799\) | 7.17260i | 0.253748i | ||||||||
\(800\) | 5.13922i | 0.181699i | ||||||||
\(801\) | 4.92820i | 0.174129i | ||||||||
\(802\) | 9.04008i | 0.319216i | ||||||||
\(803\) | −1.96902 | − | 0.928203i | −0.0694851 | − | 0.0327556i | ||||
\(804\) | 9.46410i | 0.333773i | ||||||||
\(805\) | 0.757875 | + | 10.5558i | 0.0267116 | + | 0.372044i | ||||
\(806\) | −6.43078 | −0.226515 | ||||||||
\(807\) | 2.53590 | 0.0892679 | ||||||||
\(808\) | 22.3923i | 0.787759i | ||||||||
\(809\) | 31.3901i | 1.10362i | 0.833971 | + | 0.551809i | \(0.186062\pi\) | ||||
−0.833971 | + | 0.551809i | \(0.813938\pi\) | |||||||
\(810\) | 0.517638 | 0.0181879 | ||||||||
\(811\) | 28.0069 | 0.983454 | 0.491727 | − | 0.870749i | \(-0.336366\pi\) | ||||
0.491727 | + | 0.870749i | \(0.336366\pi\) | |||||||
\(812\) | 0.339746 | + | 4.73205i | 0.0119227 | + | 0.166062i | ||||
\(813\) | − | 21.5921i | − | 0.757269i | ||||||
\(814\) | 0.392305 | − | 0.832204i | 0.0137503 | − | 0.0291687i | ||||
\(815\) | − | 8.39230i | − | 0.293970i | ||||||
\(816\) | 6.03579i | 0.211295i | ||||||||
\(817\) | 2.53590i | 0.0887199i | ||||||||
\(818\) | 15.7128i | 0.549386i | ||||||||
\(819\) | −11.1962 | + | 0.803848i | −0.391225 | + | 0.0280887i | ||||
\(820\) | − | 11.5911i | − | 0.404779i | ||||||
\(821\) | 42.7038i | 1.49037i | 0.666856 | + | 0.745187i | \(0.267640\pi\) | ||||
−0.666856 | + | 0.745187i | \(0.732360\pi\) | |||||||
\(822\) | 10.8332 | 0.377852 | ||||||||
\(823\) | 13.1769 | 0.459318 | 0.229659 | − | 0.973271i | \(-0.426239\pi\) | ||||
0.229659 | + | 0.973271i | \(0.426239\pi\) | |||||||
\(824\) | 23.9401 | 0.833993 | ||||||||
\(825\) | 1.41421 | − | 3.00000i | 0.0492366 | − | 0.104447i | ||||
\(826\) | 17.6603 | − | 1.26795i | 0.614479 | − | 0.0441176i | ||||
\(827\) | 37.4259i | 1.30143i | 0.759324 | + | 0.650713i | \(0.225530\pi\) | ||||
−0.759324 | + | 0.650713i | \(0.774470\pi\) | |||||||
\(828\) | 6.92820 | 0.240772 | ||||||||
\(829\) | − | 12.1436i | − | 0.421764i | −0.977511 | − | 0.210882i | \(-0.932366\pi\) | ||
0.977511 | − | 0.210882i | \(-0.0676337\pi\) | |||||||
\(830\) | −0.732051 | −0.0254099 | ||||||||
\(831\) | −16.8690 | −0.585180 | ||||||||
\(832\) | −9.62209 | −0.333586 | ||||||||
\(833\) | −16.9706 | + | 2.44949i | −0.587995 | + | 0.0848698i | ||||
\(834\) | −11.0718 | −0.383385 | ||||||||
\(835\) | 7.07107i | 0.244704i | ||||||||
\(836\) | 5.37945 | + | 2.53590i | 0.186052 | + | 0.0877059i | ||||
\(837\) | −2.92820 | −0.101214 | ||||||||
\(838\) | −8.83701 | −0.305270 | ||||||||
\(839\) | − | 46.7846i | − | 1.61518i | −0.589742 | − | 0.807592i | \(-0.700770\pi\) | ||
0.589742 | − | 0.807592i | \(-0.299230\pi\) | |||||||
\(840\) | 0.366025 | + | 5.09808i | 0.0126291 | + | 0.175900i | ||||
\(841\) | 27.9282 | 0.963041 | ||||||||
\(842\) | 0.960947i | 0.0331164i | ||||||||
\(843\) | −12.3490 | −0.425322 | ||||||||
\(844\) | − | 13.8647i | − | 0.477244i | ||||||
\(845\) | 5.00000i | 0.172005i | ||||||||
\(846\) | 1.51575 | 0.0521125 | ||||||||
\(847\) | −20.0804 | − | 21.0660i | −0.689971 | − | 0.723837i | ||||
\(848\) | −8.53590 | −0.293124 | ||||||||
\(849\) | − | 19.4201i | − | 0.666494i | ||||||
\(850\) | − | 1.26795i | − | 0.0434903i | ||||||
\(851\) | 2.14359 | 0.0734814 | ||||||||
\(852\) | − | 12.0000i | − | 0.411113i | ||||||
\(853\) | 3.48477 | 0.119316 | 0.0596581 | − | 0.998219i | \(-0.480999\pi\) | ||||
0.0596581 | + | 0.998219i | \(0.480999\pi\) | |||||||
\(854\) | 0.480473 | + | 6.69213i | 0.0164415 | + | 0.229000i | ||||
\(855\) | 1.03528i | 0.0354057i | ||||||||
\(856\) | −20.1962 | −0.690290 | ||||||||
\(857\) | 9.62209 | 0.328684 | 0.164342 | − | 0.986403i | \(-0.447450\pi\) | ||||
0.164342 | + | 0.986403i | \(0.447450\pi\) | |||||||
\(858\) | −6.58846 | − | 3.10583i | −0.224926 | − | 0.106031i | ||||
\(859\) | 26.6410i | 0.908980i | 0.890752 | + | 0.454490i | \(0.150178\pi\) | ||||
−0.890752 | + | 0.454490i | \(0.849822\pi\) | |||||||
\(860\) | 4.24264 | 0.144673 | ||||||||
\(861\) | −1.26795 | − | 17.6603i | −0.0432116 | − | 0.601860i | ||||
\(862\) | −12.6795 | −0.431865 | ||||||||
\(863\) | 16.7846 | 0.571355 | 0.285677 | − | 0.958326i | \(-0.407781\pi\) | ||||
0.285677 | + | 0.958326i | \(0.407781\pi\) | |||||||
\(864\) | 5.13922 | 0.174840 | ||||||||
\(865\) | − | 2.44949i | − | 0.0832851i | ||||||
\(866\) | 8.76268 | 0.297768 | ||||||||
\(867\) | 11.0000i | 0.373580i | ||||||||
\(868\) | −0.960947 | − | 13.3843i | −0.0326167 | − | 0.454291i | ||||
\(869\) | 5.46410 | − | 11.5911i | 0.185357 | − | 0.393201i | ||||
\(870\) | −0.535898 | −0.0181687 | ||||||||
\(871\) | 23.1822 | 0.785500 | ||||||||
\(872\) | 33.8564 | 1.14652 | ||||||||
\(873\) | − | 4.92820i | − | 0.166794i | ||||||
\(874\) | − | 2.14359i | − | 0.0725081i | ||||||
\(875\) | 0.189469 | + | 2.63896i | 0.00640521 | + | 0.0892131i | ||||
\(876\) | − | 1.13681i | − | 0.0384093i | ||||||
\(877\) | − | 1.96902i | − | 0.0664890i | −0.999447 | − | 0.0332445i | \(-0.989416\pi\) | ||
0.999447 | − | 0.0332445i | \(-0.0105840\pi\) | |||||||
\(878\) | 19.8564i | 0.670121i | ||||||||
\(879\) | − | 16.3886i | − | 0.552772i | ||||||
\(880\) | 3.48477 | − | 7.39230i | 0.117471 | − | 0.249195i | ||||
\(881\) | − | 6.24871i | − | 0.210524i | −0.994445 | − | 0.105262i | \(-0.966432\pi\) | ||
0.994445 | − | 0.105262i | \(-0.0335682\pi\) | |||||||
\(882\) | 0.517638 | + | 3.58630i | 0.0174298 | + | 0.120757i | ||||
\(883\) | 6.92820 | 0.233153 | 0.116576 | − | 0.993182i | \(-0.462808\pi\) | ||||
0.116576 | + | 0.993182i | \(0.462808\pi\) | |||||||
\(884\) | 18.0000 | 0.605406 | ||||||||
\(885\) | − | 12.9282i | − | 0.434577i | ||||||
\(886\) | 2.47670i | 0.0832062i | ||||||||
\(887\) | 15.9081 | 0.534141 | 0.267071 | − | 0.963677i | \(-0.413944\pi\) | ||||
0.267071 | + | 0.963677i | \(0.413944\pi\) | |||||||
\(888\) | 1.03528 | 0.0347416 | ||||||||
\(889\) | 2.32051 | + | 32.3205i | 0.0778273 | + | 1.08400i | ||||
\(890\) | − | 2.55103i | − | 0.0855106i | ||||||
\(891\) | −3.00000 | − | 1.41421i | −0.100504 | − | 0.0473779i | ||||
\(892\) | − | 17.0718i | − | 0.571606i | ||||||
\(893\) | 3.03150i | 0.101445i | ||||||||
\(894\) | − | 9.71281i | − | 0.324845i | ||||||
\(895\) | − | 4.92820i | − | 0.164732i | ||||||
\(896\) | 2.16987 | + | 30.2224i | 0.0724904 | + | 1.00966i | ||||
\(897\) | − | 16.9706i | − | 0.566631i | ||||||
\(898\) | − | 12.0716i | − | 0.402834i | ||||||
\(899\) | 3.03150 | 0.101106 | ||||||||
\(900\) | 1.73205 | 0.0577350 | ||||||||
\(901\) | 8.48528 | 0.282686 | ||||||||
\(902\) | 4.89898 | − | 10.3923i | 0.163118 | − | 0.346026i | ||||
\(903\) | 6.46410 | − | 0.464102i | 0.215112 | − | 0.0154443i | ||||
\(904\) | − | 16.4901i | − | 0.548452i | ||||||
\(905\) | 16.9282 | 0.562713 | ||||||||
\(906\) | 3.07180i | 0.102054i | ||||||||
\(907\) | −4.00000 | −0.132818 | −0.0664089 | − | 0.997792i | \(-0.521154\pi\) | ||||
−0.0664089 | + | 0.997792i | \(0.521154\pi\) | |||||||
\(908\) | 31.8434 | 1.05676 | ||||||||
\(909\) | 11.5911 | 0.384453 | ||||||||
\(910\) | 5.79555 | − | 0.416102i | 0.192121 | − | 0.0137937i | ||||
\(911\) | 20.9282 | 0.693382 | 0.346691 | − | 0.937979i | \(-0.387305\pi\) | ||||
0.346691 | + | 0.937979i | \(0.387305\pi\) | |||||||
\(912\) | 2.55103i | 0.0844729i | ||||||||
\(913\) | 4.24264 | + | 2.00000i | 0.140411 | + | 0.0661903i | ||||
\(914\) | −20.8372 | −0.689232 | ||||||||
\(915\) | 4.89898 | 0.161955 | ||||||||
\(916\) | 30.9282i | 1.02190i | ||||||||
\(917\) | 12.9282 | − | 0.928203i | 0.426927 | − | 0.0306520i | ||||
\(918\) | −1.26795 | −0.0418486 | ||||||||
\(919\) | − | 22.1469i | − | 0.730560i | −0.930898 | − | 0.365280i | \(-0.880973\pi\) | ||
0.930898 | − | 0.365280i | \(-0.119027\pi\) | |||||||
\(920\) | −7.72741 | −0.254765 | ||||||||
\(921\) | 15.0759i | 0.496767i | ||||||||
\(922\) | 19.0718i | 0.628096i | ||||||||
\(923\) | −29.3939 | −0.967511 | ||||||||
\(924\) | 5.47959 | − | 14.1765i | 0.180265 | − | 0.466374i | ||||
\(925\) | 0.535898 | 0.0176202 | ||||||||
\(926\) | − | 16.4158i | − | 0.539455i | ||||||
\(927\) | − | 12.3923i | − | 0.407017i | ||||||
\(928\) | −5.32051 | −0.174654 | ||||||||
\(929\) | − | 9.46410i | − | 0.310507i | −0.987875 | − | 0.155254i | \(-0.950381\pi\) | ||
0.987875 | − | 0.155254i | \(-0.0496195\pi\) | |||||||
\(930\) | 1.51575 | 0.0497034 | ||||||||
\(931\) | −7.17260 | + | 1.03528i | −0.235073 | + | 0.0339298i | ||||
\(932\) | 29.6985i | 0.972806i | ||||||||
\(933\) | 18.7846 | 0.614981 | ||||||||
\(934\) | −13.5873 | −0.444591 | ||||||||
\(935\) | −3.46410 | + | 7.34847i | −0.113288 | + | 0.240321i | ||||
\(936\) | − | 8.19615i | − | 0.267900i | ||||||
\(937\) | −43.6375 | −1.42558 | −0.712788 | − | 0.701379i | \(-0.752568\pi\) | ||||
−0.712788 | + | 0.701379i | \(0.752568\pi\) | |||||||
\(938\) | −0.535898 | − | 7.46410i | −0.0174977 | − | 0.243712i | ||||
\(939\) | −31.8564 | −1.03959 | ||||||||
\(940\) | 5.07180 | 0.165424 | ||||||||
\(941\) | −22.3500 | −0.728590 | −0.364295 | − | 0.931284i | \(-0.618690\pi\) | ||||
−0.364295 | + | 0.931284i | \(0.618690\pi\) | |||||||
\(942\) | 3.30890i | 0.107810i | ||||||||
\(943\) | 26.7685 | 0.871703 | ||||||||
\(944\) | − | 31.8564i | − | 1.03684i | ||||||
\(945\) | 2.63896 | − | 0.189469i | 0.0858453 | − | 0.00616342i | ||||
\(946\) | 3.80385 | + | 1.79315i | 0.123674 | + | 0.0583004i | ||||
\(947\) | −4.39230 | −0.142731 | −0.0713654 | − | 0.997450i | \(-0.522736\pi\) | ||||
−0.0713654 | + | 0.997450i | \(0.522736\pi\) | |||||||
\(948\) | 6.69213 | 0.217350 | ||||||||
\(949\) | −2.78461 | −0.0903923 | ||||||||
\(950\) | − | 0.535898i | − | 0.0173868i | ||||||
\(951\) | 28.2487i | 0.916027i | ||||||||
\(952\) | −0.896575 | − | 12.4877i | −0.0290582 | − | 0.404728i | ||||
\(953\) | 15.0759i | 0.488356i | 0.969730 | + | 0.244178i | \(0.0785180\pi\) | ||||
−0.969730 | + | 0.244178i | \(0.921482\pi\) | |||||||
\(954\) | − | 1.79315i | − | 0.0580554i | ||||||
\(955\) | − | 11.0718i | − | 0.358275i | ||||||
\(956\) | − | 20.5569i | − | 0.664857i | ||||||
\(957\) | 3.10583 | + | 1.46410i | 0.100397 | + | 0.0473277i | ||||
\(958\) | 1.46410i | 0.0473030i | ||||||||
\(959\) | 55.2287 | − | 3.96524i | 1.78343 | − | 0.128044i | ||||
\(960\) | 2.26795 | 0.0731977 | ||||||||
\(961\) | 22.4256 | 0.723407 | ||||||||
\(962\) | − | 1.17691i | − | 0.0379452i | ||||||
\(963\) | 10.4543i | 0.336885i | ||||||||
\(964\) | 19.2442 | 0.619814 | ||||||||
\(965\) | −21.2132 | −0.682877 | ||||||||
\(966\) | −5.46410 | + | 0.392305i | −0.175805 | + | 0.0126222i | ||||
\(967\) | 36.7423i | 1.18155i | 0.806835 | + | 0.590777i | \(0.201179\pi\) | ||||
−0.806835 | + | 0.590777i | \(0.798821\pi\) | |||||||
\(968\) | 16.3923 | − | 13.5230i | 0.526869 | − | 0.434644i | ||||
\(969\) | − | 2.53590i | − | 0.0814648i | ||||||
\(970\) | 2.55103i | 0.0819085i | ||||||||
\(971\) | − | 10.1436i | − | 0.325523i | −0.986665 | − | 0.162762i | \(-0.947960\pi\) | ||
0.986665 | − | 0.162762i | \(-0.0520402\pi\) | |||||||
\(972\) | − | 1.73205i | − | 0.0555556i | ||||||
\(973\) | −56.4449 | + | 4.05256i | −1.80954 | + | 0.129919i | ||||
\(974\) | 7.93048i | 0.254109i | ||||||||
\(975\) | − | 4.24264i | − | 0.135873i | ||||||
\(976\) | 12.0716 | 0.386402 | ||||||||
\(977\) | −23.0718 | −0.738132 | −0.369066 | − | 0.929403i | \(-0.620322\pi\) | ||||
−0.369066 | + | 0.929403i | \(0.620322\pi\) | |||||||
\(978\) | 4.34418 | 0.138911 | ||||||||
\(979\) | −6.96953 | + | 14.7846i | −0.222747 | + | 0.472518i | ||||
\(980\) | 1.73205 | + | 12.0000i | 0.0553283 | + | 0.383326i | ||||
\(981\) | − | 17.5254i | − | 0.559542i | ||||||
\(982\) | 1.46410 | 0.0467214 | ||||||||
\(983\) | 16.3923i | 0.522833i | 0.965226 | + | 0.261417i | \(0.0841897\pi\) | ||||
−0.965226 | + | 0.261417i | \(0.915810\pi\) | |||||||
\(984\) | 12.9282 | 0.412136 | ||||||||
\(985\) | 17.9043 | 0.570479 | ||||||||
\(986\) | 1.31268 | 0.0418042 | ||||||||
\(987\) | 7.72741 | − | 0.554803i | 0.245966 | − | 0.0176596i | ||||
\(988\) | 7.60770 | 0.242033 | ||||||||
\(989\) | 9.79796i | 0.311557i | ||||||||
\(990\) | 1.55291 | + | 0.732051i | 0.0493549 | + | 0.0232661i | ||||
\(991\) | −18.1051 | −0.575128 | −0.287564 | − | 0.957761i | \(-0.592845\pi\) | ||||
−0.287564 | + | 0.957761i | \(0.592845\pi\) | |||||||
\(992\) | 15.0487 | 0.477796 | ||||||||
\(993\) | 32.2487i | 1.02338i | ||||||||
\(994\) | 0.679492 | + | 9.46410i | 0.0215522 | + | 0.300183i | ||||
\(995\) | 19.4641 | 0.617054 | ||||||||
\(996\) | 2.44949i | 0.0776151i | ||||||||
\(997\) | 26.1122 | 0.826981 | 0.413491 | − | 0.910508i | \(-0.364309\pi\) | ||||
0.413491 | + | 0.910508i | \(0.364309\pi\) | |||||||
\(998\) | 2.07055i | 0.0655422i | ||||||||
\(999\) | − | 0.535898i | − | 0.0169551i |
(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 | 1155.2.i.b.76.3 | ✓ | 8 | |
7.6 | odd | 2 | inner | 1155.2.i.b.76.4 | yes | 8 | |
11.10 | odd | 2 | inner | 1155.2.i.b.76.5 | yes | 8 | |
77.76 | even | 2 | inner | 1155.2.i.b.76.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.i.b.76.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1155.2.i.b.76.4 | yes | 8 | 7.6 | odd | 2 | inner | |
1155.2.i.b.76.5 | yes | 8 | 11.10 | odd | 2 | inner | |
1155.2.i.b.76.6 | yes | 8 | 77.76 | even | 2 | inner |