Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(881,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, 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("1176.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.k (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: | \(9.39040727770\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + 1332 x^{7} - 846 x^{6} - 1296 x^{5} + 5265 x^{4} - 10206 x^{3} + 13851 x^{2} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.5 | ||
Root | \(0.247636 - 1.71426i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.881 |
Dual form | 1176.2.k.a.881.6 |
$q$-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 \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −1.07159 | − | 1.36077i | −0.618681 | − | 0.785642i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.57910 | 1.15341 | 0.576704 | − | 0.816953i | \(-0.304338\pi\) | ||||
0.576704 | + | 0.816953i | \(0.304338\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.703402 | + | 2.91637i | −0.234467 | + | 0.972124i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.65352i | − | 0.498556i | −0.968432 | − | 0.249278i | \(-0.919807\pi\) | ||
0.968432 | − | 0.249278i | \(-0.0801934\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.71177i | 1.58416i | 0.610418 | + | 0.792080i | \(0.291002\pi\) | ||||
−0.610418 | + | 0.792080i | \(0.708998\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.76373 | − | 3.50957i | −0.713592 | − | 0.906167i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.58626 | 1.83994 | 0.919970 | − | 0.391990i | \(-0.128213\pi\) | ||||
0.919970 | + | 0.391990i | \(0.128213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.99022i | 0.686004i | 0.939335 | + | 0.343002i | \(0.111444\pi\) | ||||
−0.939335 | + | 0.343002i | \(0.888556\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.287913i | 0.0600341i | 0.999549 | + | 0.0300170i | \(0.00955615\pi\) | ||||
−0.999549 | + | 0.0300170i | \(0.990444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.65176 | 0.330352 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.72227 | − | 2.16798i | 0.908802 | − | 0.417227i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.05856i | 0.382265i | 0.981564 | + | 0.191133i | \(0.0612161\pi\) | ||||
−0.981564 | + | 0.191133i | \(0.938784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.01840i | 1.08094i | 0.841364 | + | 0.540468i | \(0.181753\pi\) | ||||
−0.841364 | + | 0.540468i | \(0.818247\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.25007 | + | 1.77190i | −0.391687 | + | 0.308447i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.75505 | 0.288528 | 0.144264 | − | 0.989539i | \(-0.453919\pi\) | ||||
0.144264 | + | 0.989539i | \(0.453919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.77242 | − | 6.12066i | 1.24458 | − | 0.980090i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.28635 | −0.669415 | −0.334708 | − | 0.942322i | \(-0.608638\pi\) | ||||
−0.334708 | + | 0.942322i | \(0.608638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.46537 | 0.375965 | 0.187982 | − | 0.982172i | \(-0.439805\pi\) | ||||
0.187982 | + | 0.982172i | \(0.439805\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.81414 | + | 7.52162i | −0.270437 | + | 1.12126i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.373172 | −0.0544327 | −0.0272163 | − | 0.999630i | \(-0.508664\pi\) | ||||
−0.0272163 | + | 0.999630i | \(0.508664\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.12934 | − | 10.3232i | −1.13834 | − | 1.44553i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.77418i | − | 1.06787i | −0.845527 | − | 0.533933i | \(-0.820713\pi\) | ||
0.845527 | − | 0.533933i | \(-0.179287\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.26461i | − | 0.575039i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.06901 | − | 3.20429i | 0.538954 | − | 0.424418i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.79219 | 1.27483 | 0.637417 | − | 0.770519i | \(-0.280003\pi\) | ||||
0.637417 | + | 0.770519i | \(0.280003\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.02745i | 0.131551i | 0.997834 | + | 0.0657755i | \(0.0209521\pi\) | ||||
−0.997834 | + | 0.0657755i | \(0.979048\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.7312i | 1.82718i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.36561 | 0.289005 | 0.144503 | − | 0.989504i | \(-0.453842\pi\) | ||||
0.144503 | + | 0.989504i | \(0.453842\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.391784 | − | 0.308524i | 0.0471653 | − | 0.0371419i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 15.6655i | − | 1.85915i | −0.368631 | − | 0.929576i | \(-0.620174\pi\) | ||
0.368631 | − | 0.929576i | \(-0.379826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.81247i | 0.446216i | 0.974794 | + | 0.223108i | \(0.0716202\pi\) | ||||
−0.974794 | + | 0.223108i | \(0.928380\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.77000 | − | 2.24767i | −0.204382 | − | 0.259538i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.12066 | −1.02615 | −0.513077 | − | 0.858343i | \(-0.671494\pi\) | ||||
−0.513077 | + | 0.858343i | \(0.671494\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.01045 | − | 4.10276i | −0.890050 | − | 0.455863i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.65166 | 0.730114 | 0.365057 | − | 0.930985i | \(-0.381049\pi\) | ||||
0.365057 | + | 0.930985i | \(0.381049\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.5657 | 2.12220 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.80123 | − | 2.20593i | 0.300324 | − | 0.236500i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.5145 | 1.53853 | 0.769265 | − | 0.638930i | \(-0.220623\pi\) | ||||
0.769265 | + | 0.638930i | \(0.220623\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.18967 | − | 6.44924i | 0.849229 | − | 0.668755i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.71209i | 0.791243i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.43739i | − | 0.450548i | −0.974295 | − | 0.225274i | \(-0.927672\pi\) | ||
0.974295 | − | 0.225274i | \(-0.0723278\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.82229 | + | 1.16309i | 0.484659 | + | 0.116895i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.07256 | −0.405235 | −0.202617 | − | 0.979258i | \(-0.564945\pi\) | ||||
−0.202617 | + | 0.979258i | \(0.564945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.43331i | − | 0.830959i | −0.909603 | − | 0.415479i | \(-0.863614\pi\) | ||
0.909603 | − | 0.415479i | \(-0.136386\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.5878i | 1.41025i | 0.709081 | + | 0.705127i | \(0.249110\pi\) | ||||
−0.709081 | + | 0.705127i | \(0.750890\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.2999 | 1.65703 | 0.828514 | − | 0.559969i | \(-0.189187\pi\) | ||||
0.828514 | + | 0.559969i | \(0.189187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.88068 | − | 2.38822i | −0.178507 | − | 0.226680i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000i | 0.376288i | 0.982141 | + | 0.188144i | \(0.0602472\pi\) | ||||
−0.982141 | + | 0.188144i | \(0.939753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.742557i | 0.0692438i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.6576 | − | 4.01767i | −1.54000 | − | 0.371434i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.26586 | 0.751441 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.59320 | + | 5.83274i | 0.414155 | + | 0.525921i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.63545 | −0.772378 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6481 | −1.47728 | −0.738641 | − | 0.674099i | \(-0.764532\pi\) | ||||
−0.738641 | + | 0.674099i | \(0.764532\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.64185 | − | 3.35480i | −0.232602 | − | 0.295374i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5949 | 1.44990 | 0.724951 | − | 0.688800i | \(-0.241862\pi\) | ||||
0.724951 | + | 0.688800i | \(0.241862\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.1792 | − | 5.59143i | 1.04822 | − | 0.481234i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 9.94987i | − | 0.850075i | −0.905176 | − | 0.425037i | \(-0.860261\pi\) | ||
0.905176 | − | 0.425037i | \(-0.139739\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.11952i | − | 0.264594i | −0.991210 | − | 0.132297i | \(-0.957765\pi\) | ||
0.991210 | − | 0.132297i | \(-0.0422353\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.399886 | + | 0.507801i | 0.0336765 | + | 0.0427646i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.44455 | 0.789793 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.30924i | 0.440908i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.13979i | − | 0.0933755i | −0.998910 | − | 0.0466877i | \(-0.985133\pi\) | ||
0.998910 | − | 0.0466877i | \(-0.0148666\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7724 | −1.03940 | −0.519702 | − | 0.854347i | \(-0.673957\pi\) | ||||
−0.519702 | + | 0.854347i | \(0.673957\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.33619 | + | 22.1244i | −0.431406 | + | 1.78865i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.5221i | 1.24676i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.03037i | − | 0.720702i | −0.932817 | − | 0.360351i | \(-0.882657\pi\) | ||
0.932817 | − | 0.360351i | \(-0.117343\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.5789 | + | 8.33071i | −0.838961 | + | 0.660669i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0997549 | 0.00781340 | 0.00390670 | − | 0.999992i | \(-0.498756\pi\) | ||||
0.00390670 | + | 0.999992i | \(0.498756\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.80316 | + | 4.56990i | −0.451775 | + | 0.355766i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.08612 | −0.238811 | −0.119406 | − | 0.992846i | \(-0.538099\pi\) | ||||
−0.119406 | + | 0.992846i | \(0.538099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.6243 | −1.50956 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.72060 | − | 2.10333i | −0.666881 | − | 0.160846i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.46075 | −0.567231 | −0.283615 | − | 0.958938i | \(-0.591534\pi\) | ||||
−0.283615 | + | 0.958938i | \(0.591534\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.4932 | − | 13.3249i | −0.788716 | − | 1.00156i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.01914i | 0.225661i | 0.993614 | + | 0.112830i | \(0.0359917\pi\) | ||||
−0.993614 | + | 0.112830i | \(0.964008\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.762552i | 0.0566801i | 0.999598 | + | 0.0283400i | \(0.00902212\pi\) | ||||
−0.999598 | + | 0.0283400i | \(0.990978\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.39812 | − | 1.10100i | 0.103352 | − | 0.0813881i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.52644 | 0.332790 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 12.5441i | − | 0.917313i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.22218i | − | 0.0884337i | −0.999022 | − | 0.0442169i | \(-0.985921\pi\) | ||
0.999022 | − | 0.0442169i | \(-0.0140793\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.5174 | −1.69282 | −0.846409 | − | 0.532534i | \(-0.821240\pi\) | ||||
−0.846409 | + | 0.532534i | \(0.821240\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.0458 | − | 15.7858i | 1.43551 | − | 1.13044i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7312i | 1.04956i | 0.851239 | + | 0.524778i | \(0.175852\pi\) | ||||
−0.851239 | + | 0.524778i | \(0.824148\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.88238i | − | 0.487879i | −0.969790 | − | 0.243940i | \(-0.921560\pi\) | ||
0.969790 | − | 0.243940i | \(-0.0784399\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.53496 | − | 3.21906i | −0.178802 | − | 0.227055i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.0549 | −0.772109 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.839662 | − | 0.202519i | −0.0583606 | − | 0.0140760i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.94441 | 0.342012 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0897 | −1.31419 | −0.657093 | − | 0.753809i | \(-0.728214\pi\) | ||||
−0.657093 | + | 0.753809i | \(0.728214\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.3172 | + | 16.7869i | −1.46063 | + | 1.15022i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.35843 | 0.433641 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.18790 | − | 4.08539i | 0.350566 | − | 0.276065i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 43.3310i | 2.91476i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9876i | 0.735785i | 0.929868 | + | 0.367892i | \(0.119921\pi\) | ||||
−0.929868 | + | 0.367892i | \(0.880079\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.16185 | + | 4.81714i | −0.0774567 | + | 0.321143i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.9084 | −1.25499 | −0.627496 | − | 0.778620i | \(-0.715920\pi\) | ||||
−0.627496 | + | 0.778620i | \(0.715920\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.2909i | 1.14261i | 0.820736 | + | 0.571307i | \(0.193564\pi\) | ||||
−0.820736 | + | 0.571307i | \(0.806436\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5.13979i | − | 0.336719i | −0.985726 | − | 0.168360i | \(-0.946153\pi\) | ||
0.985726 | − | 0.168360i | \(-0.0538470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.962447 | −0.0627831 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.77358 | + | 12.4111i | 0.634862 | + | 0.806190i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.67983i | 0.367398i | 0.982983 | + | 0.183699i | \(0.0588071\pi\) | ||||
−0.982983 | + | 0.183699i | \(0.941193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.2792i | − | 1.49955i | −0.661695 | − | 0.749773i | \(-0.730163\pi\) | ||
0.661695 | − | 0.749773i | \(-0.269837\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.00097 | + | 15.2969i | 0.192512 | + | 0.981295i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.0795 | −1.08674 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.12783 | − | 9.05139i | −0.451708 | − | 0.573609i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.3799 | −1.34949 | −0.674744 | − | 0.738052i | \(-0.735746\pi\) | ||||
−0.674744 | + | 0.738052i | \(0.735746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.476072 | 0.0299304 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.9664 | − | 26.6245i | −1.31297 | − | 1.66729i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.1861 | −0.884904 | −0.442452 | − | 0.896792i | \(-0.645891\pi\) | ||||
−0.442452 | + | 0.896792i | \(0.645891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00353 | − | 1.44800i | −0.371609 | − | 0.0896288i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.20199i | − | 0.135781i | −0.997693 | − | 0.0678904i | \(-0.978373\pi\) | ||
0.997693 | − | 0.0678904i | \(-0.0216268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 20.0504i | − | 1.23169i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.5535 | − | 19.7509i | −0.951860 | − | 1.20873i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.6655 | −0.894172 | −0.447086 | − | 0.894491i | \(-0.647538\pi\) | ||||
−0.447086 | + | 0.894491i | \(0.647538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4021i | 1.23934i | 0.784863 | + | 0.619669i | \(0.212733\pi\) | ||||
−0.784863 | + | 0.619669i | \(0.787267\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.73122i | − | 0.164699i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.0107055 | 0.000643231 | 0.000321615 | − | 1.00000i | \(-0.499898\pi\) | ||||
0.000321615 | 1.00000i | \(0.499898\pi\) | ||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.5519 | − | 4.23335i | −1.05080 | − | 0.253444i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.11712i | − | 0.484227i | −0.970248 | − | 0.242114i | \(-0.922159\pi\) | ||
0.970248 | − | 0.242114i | \(-0.0778406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.86208i | 0.229577i | 0.993390 | + | 0.114788i | \(0.0366190\pi\) | ||||
−0.993390 | + | 0.114788i | \(0.963381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.4944 | − | 8.26417i | 0.621634 | − | 0.489527i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.5514 | 2.38538 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.03827 | + | 4.75505i | −0.353970 | + | 0.278746i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.75351 | −0.336123 | −0.168062 | − | 0.985776i | \(-0.553751\pi\) | ||||
−0.168062 | + | 0.985776i | \(0.553751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.2550 | 1.47041 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.58480 | − | 7.80840i | −0.208011 | − | 0.453089i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.64449 | −0.0951035 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.36410 | + | 5.54182i | 0.250711 | + | 0.318369i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.64989i | 0.151732i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.9041i | 1.36428i | 0.731221 | + | 0.682140i | \(0.238951\pi\) | ||||
−0.731221 | + | 0.682140i | \(0.761049\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.4758 | + | 9.03703i | −0.652836 | + | 0.514099i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.1578 | 1.19975 | 0.599874 | − | 0.800095i | \(-0.295217\pi\) | ||||
0.599874 | + | 0.800095i | \(0.295217\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 21.1150i | − | 1.19349i | −0.802430 | − | 0.596746i | \(-0.796460\pi\) | ||
0.802430 | − | 0.596746i | \(-0.203540\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.0155i | 0.899520i | 0.893149 | + | 0.449760i | \(0.148490\pi\) | ||||
−0.893149 | + | 0.449760i | \(0.851510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.40388 | 0.190581 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.8507 | − | 15.6321i | 1.10796 | − | 0.872498i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.6846i | 1.26221i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.43446i | 0.523330i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.5383 | − | 23.5412i | −1.02517 | − | 1.30183i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9797 | 1.04322 | 0.521610 | − | 0.853184i | \(-0.325332\pi\) | ||||
0.521610 | + | 0.853184i | \(0.325332\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.23450 | + | 5.11837i | −0.0676503 | + | 0.280485i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.10115 | 0.333341 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.151144 | 0.00823337 | 0.00411668 | − | 0.999992i | \(-0.498690\pi\) | ||||
0.00411668 | + | 0.999992i | \(0.498690\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.44309 | − | 4.28635i | 0.295628 | − | 0.232802i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.95157 | 0.538908 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.01045 | − | 0.795715i | 0.0544009 | − | 0.0428398i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.3919i | 0.718916i | 0.933161 | + | 0.359458i | \(0.117038\pi\) | ||||
−0.933161 | + | 0.359458i | \(0.882962\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.4025i | − | 0.717421i | −0.933449 | − | 0.358710i | \(-0.883217\pi\) | ||
0.933449 | − | 0.358710i | \(-0.116783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.3830 | + | 26.9725i | 0.660955 | + | 1.43969i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.4937 | 1.14400 | 0.571998 | − | 0.820255i | \(-0.306169\pi\) | ||||
0.571998 | + | 0.820255i | \(0.306169\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 40.4029i | − | 2.14436i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 28.1947i | − | 1.48806i | −0.668146 | − | 0.744030i | \(-0.732912\pi\) | ||
0.668146 | − | 0.744030i | \(-0.267088\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.0586 | 0.529398 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.85759 | − | 11.2479i | −0.464903 | − | 0.590364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.83274i | 0.514669i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.7256i | 1.18627i | 0.805103 | + | 0.593135i | \(0.202110\pi\) | ||||
−0.805103 | + | 0.593135i | \(0.797890\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.01503 | − | 12.5006i | 0.156956 | − | 0.650755i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.9140 | −0.720438 | −0.360219 | − | 0.932868i | \(-0.617298\pi\) | ||||
−0.360219 | + | 0.932868i | \(0.617298\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.25364 | + | 11.7509i | 0.477856 | + | 0.606813i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.7580 | −0.605569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8656 | 1.07179 | 0.535897 | − | 0.844283i | \(-0.319973\pi\) | ||||
0.535897 | + | 0.844283i | \(0.319973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.8399 | + | 22.6543i | 0.913966 | + | 1.16061i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.47155 | −0.126290 | −0.0631451 | − | 0.998004i | \(-0.520113\pi\) | ||||
−0.0631451 | + | 0.998004i | \(0.520113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.73414 | + | 7.18992i | −0.0881515 | + | 0.365484i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 23.5842i | − | 1.19576i | −0.801584 | − | 0.597882i | \(-0.796009\pi\) | ||
0.801584 | − | 0.597882i | \(-0.203991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.18419i | 0.110459i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.7829 | − | 22.5819i | −0.897027 | − | 1.13910i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.5231 | −1.18358 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.06877i | − | 0.103828i | −0.998652 | − | 0.0519142i | \(-0.983468\pi\) | ||
0.998652 | − | 0.0519142i | \(-0.0165322\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.45996i | 0.372533i | 0.982499 | + | 0.186266i | \(0.0596387\pi\) | ||||
−0.982499 | + | 0.186266i | \(0.940361\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.3757 | −1.71238 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.6598 | − | 10.5814i | −1.02659 | − | 0.525796i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.90201i | − | 0.143847i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 33.8208i | − | 1.67233i | −0.548477 | − | 0.836166i | \(-0.684792\pi\) | ||
0.548477 | − | 0.836166i | \(-0.315208\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.5395 | + | 10.6622i | −0.667854 | + | 0.525925i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.1553 | 0.842120 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.24495 | + | 3.34284i | −0.207876 | + | 0.163699i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.2980 | 0.747358 | 0.373679 | − | 0.927558i | \(-0.378096\pi\) | ||||
0.373679 | + | 0.927558i | \(0.378096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.8931 | 0.579633 | 0.289816 | − | 0.957082i | \(-0.406406\pi\) | ||||
0.289816 | + | 0.957082i | \(0.406406\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.262490 | − | 1.08831i | 0.0127627 | − | 0.0529153i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.5307 | 0.607827 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.1207 | − | 12.8519i | −0.488630 | − | 0.620495i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.2222i | − | 0.829563i | −0.909921 | − | 0.414782i | \(-0.863858\pi\) | ||
0.909921 | − | 0.414782i | \(-0.136142\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.55093i | − | 0.0745329i | −0.999305 | − | 0.0372664i | \(-0.988135\pi\) | ||
0.999305 | − | 0.0372664i | \(-0.0118650\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.22466 | − | 5.68931i | 0.346396 | − | 0.272782i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.860925 | −0.0411836 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.4310i | 0.927392i | 0.885994 | + | 0.463696i | \(0.153477\pi\) | ||||
−0.885994 | + | 0.463696i | \(0.846523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.56761i | 0.169502i | 0.996402 | + | 0.0847510i | \(0.0270095\pi\) | ||||
−0.996402 | + | 0.0847510i | \(0.972991\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37.4343 | 1.77455 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.55100 | + | 1.22139i | −0.0733597 | + | 0.0577697i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.5796i | − | 1.39595i | −0.716124 | − | 0.697973i | \(-0.754085\pi\) | ||
0.716124 | − | 0.697973i | \(-0.245915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.08758i | 0.333741i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.6868 | + | 17.3803i | 0.643060 | + | 0.816600i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.4624 | −1.05075 | −0.525374 | − | 0.850871i | \(-0.676075\pi\) | ||||
−0.525374 | + | 0.850871i | \(0.676075\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 35.8244 | − | 16.4468i | 1.67214 | − | 0.767673i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.31904 | 0.434031 | 0.217015 | − | 0.976168i | \(-0.430368\pi\) | ||||
0.217015 | + | 0.976168i | \(0.430368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.6243 | −0.772597 | −0.386298 | − | 0.922374i | \(-0.626246\pi\) | ||||
−0.386298 | + | 0.922374i | \(0.626246\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.1220 | − | 16.6332i | 0.979508 | − | 0.771348i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.1312 | −0.561365 | −0.280683 | − | 0.959801i | \(-0.590561\pi\) | ||||
−0.280683 | + | 0.959801i | \(0.590561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.2883 | + | 9.67682i | −0.566214 | + | 0.445885i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4.07654i | − | 0.187440i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.93913i | 0.226623i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.6724 | + | 5.46838i | 1.03810 | + | 0.250380i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.5188 | −1.21168 | −0.605839 | − | 0.795588i | \(-0.707162\pi\) | ||||
−0.605839 | + | 0.795588i | \(0.707162\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0244i | 0.457074i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 11.4445i | − | 0.519666i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.1972 | −1.59494 | −0.797469 | − | 0.603360i | \(-0.793828\pi\) | ||||
−0.797469 | + | 0.603360i | \(0.793828\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.106896 | − | 0.135744i | −0.00483401 | − | 0.00613854i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.5795i | − | 1.47029i | −0.677910 | − | 0.735145i | \(-0.737114\pi\) | ||
0.677910 | − | 0.735145i | \(-0.262886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.6168i | 0.703345i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.4372 | + | 2.99973i | 0.559010 | + | 0.134828i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.93790 | 0.221051 | 0.110525 | − | 0.993873i | \(-0.464747\pi\) | ||||
0.110525 | + | 0.993873i | \(0.464747\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.30705 | + | 4.19951i | 0.147748 | + | 0.187620i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.7907 | 0.748661 | 0.374331 | − | 0.927295i | \(-0.377873\pi\) | ||||
0.374331 | + | 0.927295i | \(0.377873\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5035 | −0.467401 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.0291 | + | 26.7042i | 0.933937 | + | 1.18597i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.26298 | −0.0559806 | −0.0279903 | − | 0.999608i | \(-0.508911\pi\) | ||||
−0.0279903 | + | 0.999608i | \(0.508911\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.48274 | + | 14.1207i | 0.286220 | + | 0.623442i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 21.7504i | − | 0.958435i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.617048i | 0.0271378i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.99485 | + | 10.1524i | 0.350935 | + | 0.445640i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.9891 | −1.31384 | −0.656922 | − | 0.753958i | \(-0.728142\pi\) | ||||
−0.656922 | + | 0.753958i | \(0.728142\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.5171i | 1.55306i | 0.630083 | + | 0.776528i | \(0.283021\pi\) | ||||
−0.630083 | + | 0.776528i | \(0.716979\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 45.6572i | 1.98886i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9171 | 0.996396 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.88785 | + | 28.5577i | −0.298907 | + | 1.23930i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 24.4826i | − | 1.06046i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.6234i | 1.62660i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.10836 | − | 3.23527i | 0.177289 | − | 0.139612i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.8316 | −1.02460 | −0.512300 | − | 0.858807i | \(-0.671206\pi\) | ||||
−0.512300 | + | 0.858807i | \(0.671206\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.03766 | − | 0.817141i | 0.0445302 | − | 0.0350669i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44.6181 | 1.91123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.1040 | 0.902342 | 0.451171 | − | 0.892437i | \(-0.351006\pi\) | ||||
0.451171 | + | 0.892437i | \(0.351006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.99641 | − | 0.722707i | −0.127884 | − | 0.0308444i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.15556 | −0.262236 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.85047 | − | 6.15945i | −0.205891 | − | 0.261454i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.2880i | 0.944374i | 0.881499 | + | 0.472187i | \(0.156535\pi\) | ||||
−0.881499 | + | 0.472187i | \(0.843465\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.0816i | 0.595588i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.0696 | + | 13.4421i | −0.720680 | + | 0.567525i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.4393 | 1.70431 | 0.852157 | − | 0.523286i | \(-0.175294\pi\) | ||||
0.852157 | + | 0.523286i | \(0.175294\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3164i | 0.434014i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 25.1398i | − | 1.05391i | −0.849892 | − | 0.526957i | \(-0.823333\pi\) | ||
0.849892 | − | 0.526957i | \(-0.176667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.31069 | 0.0548506 | 0.0274253 | − | 0.999624i | \(-0.491269\pi\) | ||||
0.0274253 | + | 0.999624i | \(0.491269\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.66311 | + | 1.30967i | −0.0694773 | + | 0.0547123i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.475563i | 0.0198324i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6.02452i | − | 0.250804i | −0.992106 | − | 0.125402i | \(-0.959978\pi\) | ||
0.992106 | − | 0.125402i | \(-0.0400221\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.2009 | + | 32.0018i | 1.04731 | + | 1.32995i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.8548 | −0.532391 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −42.9617 | − | 10.3620i | −1.77625 | − | 0.428415i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.5131 | −1.63088 | −0.815439 | − | 0.578843i | \(-0.803504\pi\) | ||||
−0.815439 | + | 0.578843i | \(0.803504\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.9964 | −0.741527 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.0458 | − | 15.7858i | 0.824576 | − | 0.649341i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.5171 | −0.555081 | −0.277540 | − | 0.960714i | \(-0.589519\pi\) | ||||
−0.277540 | + | 0.960714i | \(0.589519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.36536 | + | 7.37507i | −0.383299 | + | 0.301842i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 6.56750i | − | 0.268341i | −0.990958 | − | 0.134170i | \(-0.957163\pi\) | ||
0.990958 | − | 0.134170i | \(-0.0428369\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0499i | 0.409946i | 0.978768 | + | 0.204973i | \(0.0657106\pi\) | ||||
−0.978768 | + | 0.204973i | \(0.934289\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.66398 | + | 6.89900i | −0.0677623 | + | 0.280949i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.3185 | 0.866719 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 0.778176i | − | 0.0315852i | −0.999875 | − | 0.0157926i | \(-0.994973\pi\) | ||
0.999875 | − | 0.0157926i | \(-0.00502715\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2.13147i | − | 0.0862300i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.6697 | 1.56186 | 0.780928 | − | 0.624621i | \(-0.214747\pi\) | ||||
0.780928 | + | 0.624621i | \(0.214747\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.8463 | + | 15.0432i | 0.477689 | + | 0.606602i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.83523i | − | 0.315434i | −0.987484 | − | 0.157717i | \(-0.949587\pi\) | ||
0.987484 | − | 0.157717i | \(-0.0504134\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 20.6963i | − | 0.831854i | −0.909398 | − | 0.415927i | \(-0.863457\pi\) | ||
0.909398 | − | 0.415927i | \(-0.136543\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.624189 | + | 1.35961i | 0.0250479 | + | 0.0545591i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.5305 | −1.22122 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.29836 | − | 6.72821i | −0.211596 | − | 0.268699i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.3142 | 0.530874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.21022 | −0.287034 | −0.143517 | − | 0.989648i | \(-0.545841\pi\) | ||||
−0.143517 | + | 0.989648i | \(0.545841\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.4562 | + | 25.9767i | 0.813062 | + | 1.03248i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42.9372 | −1.70391 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 45.6864 | + | 11.0191i | 1.80733 | + | 0.435910i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 36.8529i | − | 1.45560i | −0.685788 | − | 0.727802i | \(-0.740542\pi\) | ||
0.685788 | − | 0.727802i | \(-0.259458\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.5183i | 0.414801i | 0.978256 | + | 0.207400i | \(0.0665003\pi\) | ||||
−0.978256 | + | 0.207400i | \(0.933500\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.81361 | − | 8.65237i | −0.268286 | − | 0.340687i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.4114 | −0.802456 | −0.401228 | − | 0.915978i | \(-0.631417\pi\) | ||||
−0.401228 | + | 0.915978i | \(0.631417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 16.1916i | − | 0.635577i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 33.1840i | − | 1.29859i | −0.760536 | − | 0.649295i | \(-0.775064\pi\) | ||
0.760536 | − | 0.649295i | \(-0.224936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 42.7999 | 1.67233 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.1186 | − | 2.68170i | −0.433777 | − | 0.104623i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.18286i | 0.279804i | 0.990165 | + | 0.139902i | \(0.0446788\pi\) | ||||
−0.990165 | + | 0.139902i | \(0.955321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.0571i | 0.819025i | 0.912304 | + | 0.409513i | \(0.134301\pi\) | ||||
−0.912304 | + | 0.409513i | \(0.865699\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 58.9636 | − | 46.4329i | 2.28996 | − | 1.80331i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.592687 | −0.0229489 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.9516 | − | 11.7742i | 0.578064 | − | 0.455216i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.69891 | 0.0655856 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.5441 | −0.830464 | −0.415232 | − | 0.909715i | \(-0.636300\pi\) | ||||
−0.415232 | + | 0.909715i | \(0.636300\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.80006 | − | 3.58097i | 0.300224 | − | 0.137832i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.39752 | 0.207444 | 0.103722 | − | 0.994606i | \(-0.466925\pi\) | ||||
0.103722 | + | 0.994606i | \(0.466925\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.2620 | + | 25.7300i | 0.776440 | + | 0.985975i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 33.3716i | − | 1.27693i | −0.769651 | − | 0.638465i | \(-0.779570\pi\) | ||
0.769651 | − | 0.638465i | \(-0.220430\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 25.6617i | − | 0.980483i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.5290 | − | 18.5287i | 0.897686 | − | 0.706914i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 44.4043 | 1.69167 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 39.8020i | − | 1.51414i | −0.653334 | − | 0.757070i | \(-0.726630\pi\) | ||
0.653334 | − | 0.757070i | \(-0.273370\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.04555i | − | 0.305185i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.5174 | −1.23168 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.99409 | + | 5.50774i | −0.264541 | + | 0.208322i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.6583i | 0.402559i | 0.979534 | + | 0.201280i | \(0.0645100\pi\) | ||||
−0.979534 | + | 0.201280i | \(0.935490\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.24798i | 0.197931i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.03135 | + | 1.30967i | 0.0388427 | + | 0.0493251i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.1453 | 1.31991 | 0.659955 | − | 0.751305i | \(-0.270575\pi\) | ||||
0.659955 | + | 0.751305i | \(0.270575\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.41549 | − | 26.5992i | 0.240600 | − | 0.997549i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.73278 | −0.0648930 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.3584 | 0.910954 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.72896 | − | 6.08644i | 0.288643 | − | 0.227302i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.2617 | 1.16586 | 0.582932 | − | 0.812521i | \(-0.301905\pi\) | ||||
0.582932 | + | 0.812521i | \(0.301905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −31.6777 | + | 24.9457i | −1.17811 | + | 0.927741i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.40025i | 0.126282i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 39.7975i | − | 1.47601i | −0.674797 | − | 0.738003i | \(-0.735769\pi\) | ||
0.674797 | − | 0.738003i | \(-0.264231\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.5998 | − | 20.4756i | 0.651843 | − | 0.758354i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.7029 | 0.691752 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.2258i | 0.451570i | 0.974177 | + | 0.225785i | \(0.0724947\pi\) | ||||
−0.974177 | + | 0.225785i | \(0.927505\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.91160i | − | 0.144086i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.0001 | 1.06679 | 0.533393 | − | 0.845868i | \(-0.320917\pi\) | ||||
0.533393 | + | 0.845868i | \(0.320917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.3021 | + | 23.2413i | 0.672346 | + | 0.853789i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.4864i | 1.22850i | 0.789113 | + | 0.614248i | \(0.210541\pi\) | ||||
−0.789113 | + | 0.614248i | \(0.789459\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2.93964i | − | 0.107700i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.67879 | + | 19.3987i | −0.171188 | + | 0.709762i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7204 | 0.427684 | 0.213842 | − | 0.976868i | \(-0.431402\pi\) | ||||
0.213842 | + | 0.976868i | \(0.431402\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.9104 | + | 29.0932i | 0.834903 | + | 1.06021i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.9413 | −1.19886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2688 | 0.409571 | 0.204785 | − | 0.978807i | \(-0.434350\pi\) | ||||
0.204785 | + | 0.978807i | \(0.434350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.510152 | − | 0.647825i | −0.0185174 | − | 0.0235146i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.1265 | −0.729587 | −0.364793 | − | 0.931088i | \(-0.618860\pi\) | ||||
−0.364793 | + | 0.931088i | \(0.618860\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.7626 | + | 57.0610i | −0.497587 | + | 2.06304i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 55.9307i | 2.01954i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 7.95157i | − | 0.286741i | −0.989669 | − | 0.143370i | \(-0.954206\pi\) | ||
0.989669 | − | 0.143370i | \(-0.0457940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.2016 | + | 19.3040i | 0.547473 | + | 0.695218i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.7854 | −1.14324 | −0.571620 | − | 0.820518i | \(-0.693685\pi\) | ||||
−0.571620 | + | 0.820518i | \(0.693685\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.94094i | 0.357089i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 12.8171i | − | 0.459222i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.9033 | −0.926892 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.46291 | + | 9.72110i | 0.159492 | + | 0.347404i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 23.2902i | − | 0.831264i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 30.4344i | − | 1.08487i | −0.840099 | − | 0.542434i | \(-0.817503\pi\) | ||
0.840099 | − | 0.542434i | \(-0.182497\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.99641 | + | 2.35963i | −0.106675 | + | 0.0840050i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.86853 | −0.208398 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.2840 | + | 21.4857i | −0.967664 | + | 0.762021i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.0924 | 1.42015 | 0.710074 | − | 0.704127i | \(-0.248662\pi\) | ||||
0.710074 | + | 0.704127i | \(0.248662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.83098 | −0.100153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.2095 | + | 42.3296i | −0.360735 | + | 1.49564i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.30401 | 0.222464 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.7154 | + | 19.9564i | 0.553207 | + | 0.702499i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 39.2952i | − | 1.38155i | −0.723072 | − | 0.690773i | \(-0.757271\pi\) | ||
0.723072 | − | 0.690773i | \(-0.242729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.6789i | 0.831480i | 0.909484 | + | 0.415740i | \(0.136477\pi\) | ||||
−0.909484 | + | 0.415740i | \(0.863523\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.7626 | − | 21.8626i | 0.973676 | − | 0.766755i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.257278 | 0.00901205 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.37200i | 0.257914i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 43.2749i | − | 1.51030i | −0.655550 | − | 0.755152i | \(-0.727563\pi\) | ||
0.655550 | − | 0.755152i | \(-0.272437\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.969513 | −0.0337951 | −0.0168975 | − | 0.999857i | \(-0.505379\pi\) | ||||
−0.0168975 | + | 0.999857i | \(0.505379\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.71657 | + | 2.92674i | −0.129394 | + | 0.101896i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 43.9510i | − | 1.52833i | −0.645023 | − | 0.764163i | \(-0.723152\pi\) | ||
0.645023 | − | 0.764163i | \(-0.276848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.58776i | 0.263534i | 0.991281 | + | 0.131767i | \(0.0420650\pi\) | ||||
−0.991281 | + | 0.131767i | \(0.957935\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.0114719 | − | 0.0145677i | −0.000397955 | − | 0.000505349i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.95942 | −0.275447 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.0478 | + | 28.4205i | 0.450996 | + | 0.982357i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.87477 | −0.306391 | −0.153196 | − | 0.988196i | \(-0.548956\pi\) | ||||
−0.153196 | + | 0.988196i | \(0.548956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.7623 | 0.853873 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.0456 | + | 8.69821i | −0.380429 | + | 0.299582i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −50.6130 | −1.74114 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.25541 | − | 4.13855i | 0.180365 | − | 0.142035i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.505301i | 0.0173215i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.208510i | 0.00713924i | 0.999994 | + | 0.00356962i | \(0.00113625\pi\) | ||||
−0.999994 | + | 0.00356962i | \(0.998864\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.4913 | − | 5.42470i | −0.769187 | − | 0.185521i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.9891 | −1.02441 | −0.512204 | − | 0.858864i | \(-0.671171\pi\) | ||||
−0.512204 | + | 0.858864i | \(0.671171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.6953i | 0.706115i | 0.935602 | + | 0.353057i | \(0.114858\pi\) | ||||
−0.935602 | + | 0.353057i | \(0.885142\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 17.1051i | − | 0.582263i | −0.956683 | − | 0.291131i | \(-0.905968\pi\) | ||
0.956683 | − | 0.291131i | \(-0.0940317\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.2420 | −0.654249 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.4543 | − | 55.1812i | −1.47579 | − | 1.87405i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.0812i | 0.511596i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.5118i | 0.457831i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.9411 | + | 3.12127i | 0.437989 | + | 0.105639i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.4343 | 0.656248 | 0.328124 | − | 0.944635i | \(-0.393584\pi\) | ||||
0.328124 | + | 0.944635i | \(0.393584\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.16538 | + | 7.82921i | 0.207953 | + | 0.264073i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0526 | −1.01250 | −0.506249 | − | 0.862387i | \(-0.668968\pi\) | ||||
−0.506249 | + | 0.862387i | \(0.668968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.8382 | −0.566649 | −0.283324 | − | 0.959024i | \(-0.591437\pi\) | ||||
−0.283324 | + | 0.959024i | \(0.591437\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.0630 | − | 34.3664i | −0.909712 | − | 1.15521i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.6566 | −0.895041 | −0.447520 | − | 0.894274i | \(-0.647693\pi\) | ||||
−0.447520 | + | 0.894274i | \(0.647693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.78402 | + | 13.2455i | −0.227273 | + | 0.443740i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.11587i | − | 0.0373410i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.78665i | 0.260279i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.76222 | + | 2.23778i | 0.0588388 | + | 0.0747174i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.3892 | −0.413205 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 58.9770i | − | 1.96481i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.96670i | 0.0653753i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.45506 | 0.280746 | 0.140373 | − | 0.990099i | \(-0.455170\pi\) | ||||
0.140373 | + | 0.990099i | \(0.455170\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.86464 | − | 11.8771i | 0.0950143 | − | 0.393938i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15.4171i | − | 0.510792i | −0.966837 | − | 0.255396i | \(-0.917794\pi\) | ||
0.966837 | − | 0.255396i | \(-0.0822058\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 10.9987i | − | 0.364003i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.60589 | − | 2.83958i | 0.119207 | − | 0.0938737i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −57.5865 | −1.89960 | −0.949802 | − | 0.312851i | \(-0.898716\pi\) | ||||
−0.949802 | + | 0.312851i | \(0.898716\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.5281 | − | 25.6154i | 1.07184 | − | 0.844055i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 89.4776 | 2.94519 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.89891 | 0.0953156 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.5947 | + | 5.93201i | 0.807795 | + | 0.194833i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.3759 | 1.55435 | 0.777176 | − | 0.629283i | \(-0.216652\pi\) | ||||
0.777176 | + | 0.629283i | \(0.216652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.6724 | − | 28.7909i | −0.742261 | − | 0.942572i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 32.3524i | − | 1.05804i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 40.6136i | − | 1.32679i | −0.748270 | − | 0.663394i | \(-0.769115\pi\) | ||
0.748270 | − | 0.663394i | \(-0.230885\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.7327 | + | 22.6266i | −0.937657 | + | 0.738391i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.8284 | −0.972379 | −0.486189 | − | 0.873854i | \(-0.661613\pi\) | ||||
−0.486189 | + | 0.873854i | \(0.661613\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.23410i | − | 0.0401877i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 40.5461i | − | 1.31757i | −0.752331 | − | 0.658785i | \(-0.771071\pi\) | ||
0.752331 | − | 0.658785i | \(-0.228929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.7759 | −0.706877 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.7934 | − | 17.1620i | 0.706701 | − | 0.556516i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.7169i | 1.18938i | 0.803956 | + | 0.594688i | \(0.202724\pi\) | ||||
−0.803956 | + | 0.594688i | \(0.797276\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 3.15212i | − | 0.102000i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.64756 | − | 4.63191i | −0.117909 | − | 0.149728i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.22113 | −0.168424 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.5434 | − | 10.2611i | −1.37094 | − | 0.330659i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −60.6536 | −1.95251 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.1106 | 0.968290 | 0.484145 | − | 0.874988i | \(-0.339131\pi\) | ||||
0.484145 | + | 0.874988i | \(0.339131\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.8686 | − | 24.3086i | 0.991642 | − | 0.780903i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.2580 | −0.714294 | −0.357147 | − | 0.934048i | \(-0.616250\pi\) | ||||
−0.357147 | + | 0.934048i | \(0.616250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.8382 | − | 10.1098i | 0.411150 | − | 0.323774i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.8781i | 1.78770i | 0.448368 | + | 0.893849i | \(0.352005\pi\) | ||||
−0.448368 | + | 0.893849i | \(0.647995\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 24.0000i | − | 0.767044i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.1688 | + | 50.4529i | −0.388519 | + | 1.61084i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.7757 | −1.39623 | −0.698114 | − | 0.715987i | \(-0.745977\pi\) | ||||
−0.698114 | + | 0.715987i | \(0.745977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.9933i | 1.21057i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.709812i | 0.0225707i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.5471 | −0.747999 | −0.374000 | − | 0.927429i | \(-0.622014\pi\) | ||||
−0.374000 | + | 0.927429i | \(0.622014\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.3384 | − | 25.8271i | −0.645420 | − | 0.819597i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 17.7504i | − | 0.562724i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0437i | 0.603120i | 0.953447 | + | 0.301560i | \(0.0975074\pi\) | ||||
−0.953447 | + | 0.301560i | \(0.902493\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.28781 | − | 3.80490i | 0.262215 | − | 0.120382i |
(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 | 1176.2.k.a.881.5 | 16 | ||
3.2 | odd | 2 | inner | 1176.2.k.a.881.11 | 16 | ||
4.3 | odd | 2 | 2352.2.k.i.881.12 | 16 | |||
7.2 | even | 3 | 168.2.u.a.17.8 | yes | 16 | ||
7.3 | odd | 6 | 168.2.u.a.89.6 | yes | 16 | ||
7.4 | even | 3 | 1176.2.u.b.1097.3 | 16 | |||
7.5 | odd | 6 | 1176.2.u.b.521.1 | 16 | |||
7.6 | odd | 2 | inner | 1176.2.k.a.881.12 | 16 | ||
12.11 | even | 2 | 2352.2.k.i.881.6 | 16 | |||
21.2 | odd | 6 | 168.2.u.a.17.6 | ✓ | 16 | ||
21.5 | even | 6 | 1176.2.u.b.521.3 | 16 | |||
21.11 | odd | 6 | 1176.2.u.b.1097.1 | 16 | |||
21.17 | even | 6 | 168.2.u.a.89.8 | yes | 16 | ||
21.20 | even | 2 | inner | 1176.2.k.a.881.6 | 16 | ||
28.3 | even | 6 | 336.2.bc.f.257.3 | 16 | |||
28.23 | odd | 6 | 336.2.bc.f.17.1 | 16 | |||
28.27 | even | 2 | 2352.2.k.i.881.5 | 16 | |||
84.23 | even | 6 | 336.2.bc.f.17.3 | 16 | |||
84.59 | odd | 6 | 336.2.bc.f.257.1 | 16 | |||
84.83 | odd | 2 | 2352.2.k.i.881.11 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.u.a.17.6 | ✓ | 16 | 21.2 | odd | 6 | ||
168.2.u.a.17.8 | yes | 16 | 7.2 | even | 3 | ||
168.2.u.a.89.6 | yes | 16 | 7.3 | odd | 6 | ||
168.2.u.a.89.8 | yes | 16 | 21.17 | even | 6 | ||
336.2.bc.f.17.1 | 16 | 28.23 | odd | 6 | |||
336.2.bc.f.17.3 | 16 | 84.23 | even | 6 | |||
336.2.bc.f.257.1 | 16 | 84.59 | odd | 6 | |||
336.2.bc.f.257.3 | 16 | 28.3 | even | 6 | |||
1176.2.k.a.881.5 | 16 | 1.1 | even | 1 | trivial | ||
1176.2.k.a.881.6 | 16 | 21.20 | even | 2 | inner | ||
1176.2.k.a.881.11 | 16 | 3.2 | odd | 2 | inner | ||
1176.2.k.a.881.12 | 16 | 7.6 | odd | 2 | inner | ||
1176.2.u.b.521.1 | 16 | 7.5 | odd | 6 | |||
1176.2.u.b.521.3 | 16 | 21.5 | even | 6 | |||
1176.2.u.b.1097.1 | 16 | 21.11 | odd | 6 | |||
1176.2.u.b.1097.3 | 16 | 7.4 | even | 3 | |||
2352.2.k.i.881.5 | 16 | 28.27 | even | 2 | |||
2352.2.k.i.881.6 | 16 | 12.11 | even | 2 | |||
2352.2.k.i.881.11 | 16 | 84.83 | odd | 2 | |||
2352.2.k.i.881.12 | 16 | 4.3 | odd | 2 |