Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.961 |
Dual form | 1960.2.q.d.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | − | 5.19615i | 0.688247 | − | 1.19208i | −0.284157 | − | 0.958778i | \(-0.591714\pi\) |
0.972404 | − | 0.233301i | \(-0.0749529\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50000 | + | 2.59808i | −0.312772 | + | 0.541736i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) |
0.666190 | + | 0.745782i | \(0.267924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | − | 1.73205i | 0.174078 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | − | 10.3923i | 0.986394 | − | 1.70848i | 0.350823 | − | 0.936442i | \(-0.385902\pi\) |
0.635571 | − | 0.772043i | \(-0.280765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | + | 3.46410i | 0.320256 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.00000 | 1.09322 | 0.546608 | − | 0.837389i | \(-0.315919\pi\) | ||||
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.00000 | −1.37249 | −0.686244 | − | 0.727372i | \(-0.740742\pi\) | ||||
−0.686244 | + | 0.727372i | \(0.740742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | + | 1.73205i | 0.149071 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | + | 5.19615i | 0.412082 | + | 0.713746i | 0.995117 | − | 0.0987002i | \(-0.0314685\pi\) |
−0.583036 | + | 0.812447i | \(0.698135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.00000 | −0.794719 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.00000 | − | 8.66025i | −0.650945 | − | 1.12747i | −0.982894 | − | 0.184172i | \(-0.941040\pi\) |
0.331949 | − | 0.943297i | \(-0.392294\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50000 | − | 4.33013i | 0.320092 | − | 0.554416i | −0.660415 | − | 0.750901i | \(-0.729619\pi\) |
0.980507 | + | 0.196485i | \(0.0629528\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | − | 3.46410i | 0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.50000 | − | 9.52628i | −0.671932 | − | 1.16382i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.305424 | − | 0.952217i | \(-0.401202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0000 | −1.18678 | −0.593391 | − | 0.804914i | \(-0.702211\pi\) | ||||
−0.593391 | + | 0.804914i | \(0.702211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | − | 6.92820i | −0.468165 | − | 0.810885i | 0.531174 | − | 0.847263i | \(-0.321751\pi\) |
−0.999338 | + | 0.0363782i | \(0.988418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00000 | + | 5.19615i | −0.337526 | + | 0.584613i | −0.983967 | − | 0.178352i | \(-0.942924\pi\) |
0.646440 | + | 0.762964i | \(0.276257\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.00000 | 0.329293 | 0.164646 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164646 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.50000 | + | 2.59808i | 0.160817 | + | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.50000 | − | 14.7224i | 0.900998 | − | 1.56057i | 0.0747975 | − | 0.997199i | \(-0.476169\pi\) |
0.826201 | − | 0.563376i | \(-0.190498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.00000 | + | 5.19615i | 0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.50000 | − | 14.7224i | −0.845782 | − | 1.46494i | −0.884941 | − | 0.465704i | \(-0.845801\pi\) |
0.0391591 | − | 0.999233i | \(-0.487532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.50000 | + | 12.9904i | −0.738997 | + | 1.27998i | 0.213950 | + | 0.976845i | \(0.431367\pi\) |
−0.952947 | + | 0.303136i | \(0.901966\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.500000 | − | 0.866025i | 0.0483368 | − | 0.0837218i | −0.840845 | − | 0.541276i | \(-0.817941\pi\) |
0.889182 | + | 0.457555i | \(0.151275\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.50000 | + | 4.33013i | 0.239457 | + | 0.414751i | 0.960558 | − | 0.278078i | \(-0.0896974\pi\) |
−0.721102 | + | 0.692829i | \(0.756364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.50000 | − | 2.59808i | −0.139876 | − | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.00000 | + | 6.92820i | −0.369800 | + | 0.640513i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.50000 | − | 6.06218i | −0.315584 | − | 0.546608i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.50000 | + | 7.79423i | 0.396203 | + | 0.686244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.50000 | − | 4.33013i | 0.215166 | − | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | + | 3.46410i | 0.170872 | + | 0.295958i | 0.938725 | − | 0.344668i | \(-0.112008\pi\) |
−0.767853 | + | 0.640626i | \(0.778675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.0000 | −1.52674 | −0.763370 | − | 0.645961i | \(-0.776457\pi\) | ||||
−0.763370 | + | 0.645961i | \(0.776457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | − | 6.92820i | −0.334497 | − | 0.579365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.50000 | − | 2.59808i | 0.124568 | − | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.50000 | − | 14.7224i | 0.696347 | − | 1.20611i | −0.273377 | − | 0.961907i | \(-0.588141\pi\) |
0.969724 | − | 0.244202i | \(-0.0785259\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | − | 17.3205i | −0.813788 | − | 1.40952i | −0.910195 | − | 0.414181i | \(-0.864068\pi\) |
0.0964061 | − | 0.995342i | \(-0.469265\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | − | 12.1244i | −0.558661 | − | 0.967629i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.438948 | − | 0.898513i | \(-0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | − | 10.3923i | 0.469956 | − | 0.813988i | −0.529454 | − | 0.848339i | \(-0.677603\pi\) |
0.999410 | + | 0.0343508i | \(0.0109363\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.00000 | + | 1.73205i | 0.0778499 | + | 0.134840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | −0.232147 | −0.116073 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116073 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | − | 10.3923i | −0.458831 | − | 0.794719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.00000 | + | 6.92820i | −0.304114 | + | 0.526742i | −0.977064 | − | 0.212947i | \(-0.931694\pi\) |
0.672949 | + | 0.739689i | \(0.265027\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.00000 | + | 8.66025i | −0.375823 | + | 0.650945i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | + | 6.92820i | 0.298974 | + | 0.517838i | 0.975901 | − | 0.218212i | \(-0.0700223\pi\) |
−0.676927 | + | 0.736050i | \(0.736689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.00000 | −0.369611 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | + | 10.3923i | 0.441129 | + | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.00000 | + | 12.1244i | −0.506502 | + | 0.877288i | 0.493469 | + | 0.869763i | \(0.335728\pi\) |
−0.999972 | + | 0.00752447i | \(0.997605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0000 | + | 19.0526i | 0.791797 | + | 1.37143i | 0.924853 | + | 0.380325i | \(0.124188\pi\) |
−0.133056 | + | 0.991109i | \(0.542479\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.00000 | −0.286446 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.00000 | + | 10.3923i | 0.425329 | + | 0.736691i | 0.996451 | − | 0.0841740i | \(-0.0268252\pi\) |
−0.571122 | + | 0.820865i | \(0.693492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.50000 | + | 9.52628i | −0.387940 | + | 0.671932i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.50000 | + | 6.06218i | −0.244451 | + | 0.423401i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00000 | + | 5.19615i | 0.208514 | + | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.0000 | −0.963800 | −0.481900 | − | 0.876226i | \(-0.660053\pi\) | ||||
−0.481900 | + | 0.876226i | \(0.660053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.00000 | + | 8.66025i | 0.342594 | + | 0.593391i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.50000 | − | 7.79423i | 0.306897 | − | 0.531562i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.00000 | + | 6.92820i | −0.270295 | + | 0.468165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.00000 | − | 3.46410i | −0.132745 | − | 0.229920i | 0.791989 | − | 0.610535i | \(-0.209046\pi\) |
−0.924734 | + | 0.380615i | \(0.875712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | + | 1.73205i | −0.0660819 | + | 0.114457i | −0.897173 | − | 0.441679i | \(-0.854383\pi\) |
0.831092 | + | 0.556136i | \(0.187717\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.00000 | − | 3.46410i | 0.131024 | − | 0.226941i | −0.793047 | − | 0.609160i | \(-0.791507\pi\) |
0.924072 | + | 0.382219i | \(0.124840\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.00000 | 0.389742 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.00000 | + | 15.5885i | 0.579741 | + | 1.00414i | 0.995509 | + | 0.0946700i | \(0.0301796\pi\) |
−0.415768 | + | 0.909471i | \(0.636487\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0000 | + | 20.7846i | −0.763542 | + | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.50000 | − | 2.59808i | −0.0950586 | − | 0.164646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.0000 | − | 20.7846i | 0.748539 | − | 1.29651i | −0.199983 | − | 0.979799i | \(-0.564089\pi\) |
0.948523 | − | 0.316709i | \(-0.102578\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | + | 5.19615i | −0.185695 | + | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5000 | − | 18.1865i | −0.647458 | − | 1.12143i | −0.983728 | − | 0.179664i | \(-0.942499\pi\) |
0.336270 | − | 0.941766i | \(-0.390834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.0000 | −1.04038 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.5000 | + | 26.8468i | 0.945052 | + | 1.63688i | 0.755648 | + | 0.654978i | \(0.227322\pi\) |
0.189404 | + | 0.981899i | \(0.439344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | + | 1.73205i | −0.0607457 | + | 0.105215i | −0.894799 | − | 0.446469i | \(-0.852681\pi\) |
0.834053 | + | 0.551684i | \(0.186015\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | − | 1.73205i | 0.0603023 | − | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | − | 6.92820i | −0.240337 | − | 0.416275i | 0.720473 | − | 0.693482i | \(-0.243925\pi\) |
−0.960810 | + | 0.277207i | \(0.910591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0000 | − | 24.2487i | −0.832214 | − | 1.44144i | −0.896279 | − | 0.443491i | \(-0.853740\pi\) |
0.0640654 | − | 0.997946i | \(-0.479593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.00000 | − | 5.19615i | 0.177705 | − | 0.307794i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00000 | − | 1.73205i | −0.0586210 | − | 0.101535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0000 | 0.582223 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.00000 | − | 8.66025i | −0.290129 | − | 0.502519i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | − | 10.3923i | 0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.50000 | + | 14.7224i | −0.488312 | + | 0.845782i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.50000 | + | 4.33013i | 0.143150 | + | 0.247942i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.0000 | 1.19853 | 0.599267 | − | 0.800549i | \(-0.295459\pi\) | ||||
0.599267 | + | 0.800549i | \(0.295459\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0000 | 0.853320 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.00000 | + | 8.66025i | 0.283524 | + | 0.491078i | 0.972250 | − | 0.233944i | \(-0.0751631\pi\) |
−0.688726 | + | 0.725022i | \(0.741830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.00000 | + | 13.8564i | −0.452187 | + | 0.783210i | −0.998522 | − | 0.0543564i | \(-0.982689\pi\) |
0.546335 | + | 0.837567i | \(0.316023\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | − | 10.3923i | 0.336994 | − | 0.583690i | −0.646872 | − | 0.762598i | \(-0.723923\pi\) |
0.983866 | + | 0.178908i | \(0.0572566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | − | 5.19615i | −0.167968 | − | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.00000 | −0.0558146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | + | 3.46410i | 0.110940 | + | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.50000 | − | 4.33013i | 0.138250 | − | 0.239457i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.0000 | − | 20.7846i | −0.657596 | − | 1.13899i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.0000 | 0.600994 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0000 | 0.544735 | 0.272367 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272367 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.00000 | + | 15.5885i | 0.488813 | + | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.50000 | + | 2.59808i | −0.0807573 | + | 0.139876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5000 | + | 21.6506i | 0.671035 | + | 1.16227i | 0.977611 | + | 0.210421i | \(0.0674834\pi\) |
−0.306576 | + | 0.951846i | \(0.599183\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.0000 | −0.909989 | −0.454995 | − | 0.890494i | \(-0.650359\pi\) | ||||
−0.454995 | + | 0.890494i | \(0.650359\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | + | 15.5885i | 0.479022 | + | 0.829690i | 0.999711 | − | 0.0240566i | \(-0.00765819\pi\) |
−0.520689 | + | 0.853746i | \(0.674325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.00000 | − | 8.66025i | 0.265372 | − | 0.459639i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0000 | − | 20.7846i | 0.633336 | − | 1.09697i | −0.353529 | − | 0.935423i | \(-0.615019\pi\) |
0.986865 | − | 0.161546i | \(-0.0516481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.00000 | 0.418739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.50000 | + | 11.2583i | 0.339297 | + | 0.587680i | 0.984301 | − | 0.176500i | \(-0.0564774\pi\) |
−0.645003 | + | 0.764180i | \(0.723144\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.00000 | − | 12.1244i | 0.364405 | − | 0.631169i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0000 | + | 31.1769i | −0.932005 | + | 1.61428i | −0.152115 | + | 0.988363i | \(0.548608\pi\) |
−0.779890 | + | 0.625917i | \(0.784725\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.0000 | 1.74646 | 0.873231 | − | 0.487306i | \(-0.162020\pi\) | ||||
0.873231 | + | 0.487306i | \(0.162020\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | − | 6.92820i | −0.204926 | − | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.5000 | + | 28.5788i | −0.843111 | + | 1.46031i | 0.0441413 | + | 0.999025i | \(0.485945\pi\) |
−0.887252 | + | 0.461285i | \(0.847389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.00000 | + | 15.5885i | −0.457496 | + | 0.792406i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.00000 | + | 12.1244i | 0.354914 | + | 0.614729i | 0.987103 | − | 0.160085i | \(-0.0511768\pi\) |
−0.632189 | + | 0.774814i | \(0.717843\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.00000 | − | 5.19615i | −0.150946 | − | 0.261447i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00000 | + | 1.73205i | −0.0501886 | + | 0.0869291i | −0.890028 | − | 0.455905i | \(-0.849316\pi\) |
0.839840 | + | 0.542834i | \(0.182649\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5000 | − | 28.5788i | 0.823971 | − | 1.42716i | −0.0787327 | − | 0.996896i | \(-0.525087\pi\) |
0.902703 | − | 0.430263i | \(-0.141579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.50000 | − | 11.2583i | −0.321404 | − | 0.556689i | 0.659374 | − | 0.751815i | \(-0.270822\pi\) |
−0.980778 | + | 0.195127i | \(0.937488\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | − | 3.46410i | 0.0986527 | − | 0.170872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.50000 | + | 2.59808i | −0.0736321 | + | 0.127535i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.00000 | + | 15.5885i | 0.440732 | + | 0.763370i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.0000 | −1.51085 | −0.755424 | − | 0.655237i | \(-0.772569\pi\) | ||||
−0.755424 | + | 0.655237i | \(0.772569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | + | 6.92820i | −0.193122 | + | 0.334497i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.0000 | + | 19.0526i | 0.529851 | + | 0.917729i | 0.999394 | + | 0.0348195i | \(0.0110856\pi\) |
−0.469542 | + | 0.882910i | \(0.655581\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.0000 | −0.865025 | −0.432512 | − | 0.901628i | \(-0.642373\pi\) | ||||
−0.432512 | + | 0.901628i | \(0.642373\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.00000 | −0.143839 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.00000 | + | 15.5885i | 0.430528 | + | 0.745697i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.00000 | + | 3.46410i | −0.0954548 | + | 0.165333i | −0.909798 | − | 0.415051i | \(-0.863764\pi\) |
0.814344 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5000 | − | 18.1865i | 0.498870 | − | 0.864068i | −0.501129 | − | 0.865373i | \(-0.667082\pi\) |
0.999999 | + | 0.00130426i | \(0.000415158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.50000 | + | 14.7224i | 0.402939 | + | 0.697910i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.0000 | −0.804072 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.0000 | 1.84052 | 0.920262 | − | 0.391303i | \(-0.127976\pi\) | ||||
0.920262 | + | 0.391303i | \(0.127976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.00000 | + | 12.1244i | 0.329617 | + | 0.570914i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.0000 | + | 17.3205i | −0.469841 | + | 0.813788i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.00000 | + | 6.92820i | −0.187112 | + | 0.324088i | −0.944286 | − | 0.329125i | \(-0.893246\pi\) |
0.757174 | + | 0.653213i | \(0.226579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0000 | 1.39724 | 0.698620 | − | 0.715493i | \(-0.253798\pi\) | ||||
0.698620 | + | 0.715493i | \(0.253798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.0000 | 1.34774 | 0.673872 | − | 0.738848i | \(-0.264630\pi\) | ||||
0.673872 | + | 0.738848i | \(0.264630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.5000 | + | 28.5788i | −0.763529 | + | 1.32247i | 0.177492 | + | 0.984122i | \(0.443202\pi\) |
−0.941021 | + | 0.338349i | \(0.890132\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | + | 12.1244i | −0.322543 | + | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.00000 | − | 15.5885i | −0.413820 | − | 0.716758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | −0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.0000 | + | 31.1769i | 0.822441 | + | 1.42451i | 0.903859 | + | 0.427830i | \(0.140722\pi\) |
−0.0814184 | + | 0.996680i | \(0.525945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | + | 41.5692i | −1.09431 | + | 1.89539i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.00000 | + | 1.73205i | −0.0454077 | + | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | − | 27.7128i | −0.725029 | − | 1.25579i | −0.958962 | − | 0.283535i | \(-0.908493\pi\) |
0.233933 | − | 0.972253i | \(-0.424840\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | + | 3.46410i | −0.0898933 | + | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.00000 | − | 8.66025i | 0.223831 | − | 0.387686i | −0.732137 | − | 0.681157i | \(-0.761477\pi\) |
0.955968 | + | 0.293471i | \(0.0948104\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.50000 | + | 2.59808i | 0.0670151 | + | 0.116073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.0000 | 1.64975 | 0.824874 | − | 0.565316i | \(-0.191246\pi\) | ||||
0.824874 | + | 0.565316i | \(0.191246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.0000 | 0.756490 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.50000 | − | 2.59808i | −0.0666173 | − | 0.115385i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5000 | − | 18.1865i | 0.465404 | − | 0.806104i | −0.533815 | − | 0.845601i | \(-0.679242\pi\) |
0.999220 | + | 0.0394971i | \(0.0125756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.0000 | + | 25.9808i | −0.662266 | + | 1.14708i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.50000 | − | 12.9904i | −0.330489 | − | 0.572425i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.00000 | 0.351161 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | − | 15.5885i | −0.394297 | − | 0.682943i | 0.598714 | − | 0.800963i | \(-0.295679\pi\) |
−0.993011 | + | 0.118020i | \(0.962345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0000 | − | 24.2487i | 0.612177 | − | 1.06032i | −0.378695 | − | 0.925521i | \(-0.623627\pi\) |
0.990873 | − | 0.134801i | \(-0.0430394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.0000 | −0.867926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.0000 | −1.21281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.500000 | + | 0.866025i | 0.0216169 | + | 0.0374415i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.00000 | − | 6.92820i | 0.172613 | − | 0.298974i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.5000 | + | 33.7750i | −0.838370 | + | 1.45210i | 0.0528859 | + | 0.998601i | \(0.483158\pi\) |
−0.891256 | + | 0.453500i | \(0.850175\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.50000 | − | 4.33013i | −0.107285 | − | 0.185824i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.00000 | −0.214176 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.0000 | −0.555840 | −0.277920 | − | 0.960604i | \(-0.589645\pi\) | ||||
−0.277920 | + | 0.960604i | \(0.589645\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.00000 | − | 8.66025i | −0.213395 | − | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.00000 | + | 15.5885i | −0.383413 | + | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.00000 | − | 10.3923i | 0.254686 | − | 0.441129i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0000 | − | 25.9808i | −0.635570 | − | 1.10084i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.350824 | − | 0.936442i | \(-0.385902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.0000 | 1.52264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.50000 | − | 9.52628i | −0.231797 | − | 0.401485i | 0.726540 | − | 0.687124i | \(-0.241127\pi\) |
−0.958337 | + | 0.285640i | \(0.907794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00000 | − | 15.5885i | 0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.0000 | + | 19.0526i | −0.461144 | + | 0.798725i | −0.999018 | − | 0.0443003i | \(-0.985894\pi\) |
0.537874 | + | 0.843025i | \(0.319228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.00000 | + | 15.5885i | 0.376638 | + | 0.652357i | 0.990571 | − | 0.137002i | \(-0.0437466\pi\) |
−0.613933 | + | 0.789359i | \(0.710413\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.0000 | 0.584858 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.00000 | 0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.00000 | + | 1.73205i | 0.0416305 | + | 0.0721062i | 0.886090 | − | 0.463513i | \(-0.153411\pi\) |
−0.844459 | + | 0.535620i | \(0.820078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.0000 | − | 19.0526i | 0.457144 | − | 0.791797i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | + | 10.3923i | −0.248495 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.00000 | − | 6.92820i | −0.165380 | − | 0.286446i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.0000 | −0.825488 | −0.412744 | − | 0.910847i | \(-0.635430\pi\) | ||||
−0.412744 | + | 0.910847i | \(0.635430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | + | 5.19615i | 0.123404 | + | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.00000 | + | 8.66025i | −0.205325 | + | 0.355634i | −0.950236 | − | 0.311530i | \(-0.899159\pi\) |
0.744911 | + | 0.667164i | \(0.232492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.00000 | − | 10.3923i | 0.245564 | − | 0.425329i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | + | 10.3923i | 0.245153 | + | 0.424618i | 0.962175 | − | 0.272433i | \(-0.0878284\pi\) |
−0.717021 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.00000 | −0.0815817 | −0.0407909 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407909 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.0000 | −0.895909 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.50000 | + | 6.06218i | 0.142295 | + | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.50000 | + | 6.06218i | −0.142061 | + | 0.246056i | −0.928272 | − | 0.371901i | \(-0.878706\pi\) |
0.786212 | + | 0.617957i | \(0.212039\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00000 | − | 6.92820i | −0.161558 | − | 0.279827i | 0.773869 | − | 0.633345i | \(-0.218319\pi\) |
−0.935428 | + | 0.353518i | \(0.884985\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.00000 | 0.282267 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.0000 | −0.805170 | −0.402585 | − | 0.915383i | \(-0.631888\pi\) | ||||
−0.402585 | + | 0.915383i | \(0.631888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.0000 | + | 22.5167i | 0.522514 | + | 0.905021i | 0.999657 | + | 0.0261952i | \(0.00833914\pi\) |
−0.477143 | + | 0.878826i | \(0.658328\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.50000 | − | 12.9904i | 0.300965 | − | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.00000 | − | 10.3923i | −0.239617 | − | 0.415029i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.00000 | −0.238856 | −0.119428 | − | 0.992843i | \(-0.538106\pi\) | ||||
−0.119428 | + | 0.992843i | \(0.538106\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.00000 | + | 12.1244i | 0.278225 | + | 0.481900i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | + | 6.92820i | −0.158735 | + | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.0000 | + | 17.3205i | −0.395594 | + | 0.685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.50000 | − | 11.2583i | −0.256735 | − | 0.444677i | 0.708631 | − | 0.705580i | \(-0.249313\pi\) |
−0.965365 | + | 0.260902i | \(0.915980\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.00000 | 0.157745 | 0.0788723 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788723 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.00000 | −0.354375 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.5000 | + | 38.9711i | 0.884566 | + | 1.53211i | 0.846210 | + | 0.532850i | \(0.178879\pi\) |
0.0383563 | + | 0.999264i | \(0.487788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000 | − | 17.3205i | 0.392534 | − | 0.679889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.0000 | −0.624219 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.0000 | −1.79191 | −0.895953 | − | 0.444149i | \(-0.853506\pi\) | ||||
−0.895953 | + | 0.444149i | \(0.853506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.50000 | − | 6.06218i | −0.136134 | − | 0.235791i | 0.789896 | − | 0.613241i | \(-0.210135\pi\) |
−0.926030 | + | 0.377450i | \(0.876801\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.50000 | − | 7.79423i | 0.174241 | − | 0.301794i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.00000 | − | 3.46410i | −0.0773245 | − | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0000 | 0.386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.0000 | −0.616755 | −0.308377 | − | 0.951264i | \(-0.599786\pi\) | ||||
−0.308377 | + | 0.951264i | \(0.599786\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0000 | + | 31.1769i | −0.691796 | + | 1.19823i | 0.279453 | + | 0.960159i | \(0.409847\pi\) |
−0.971249 | + | 0.238067i | \(0.923486\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.00000 | + | 3.46410i | −0.0766402 | + | 0.132745i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.50000 | − | 6.06218i | −0.133924 | − | 0.231963i | 0.791262 | − | 0.611477i | \(-0.209424\pi\) |
−0.925186 | + | 0.379514i | \(0.876091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.00000 | −0.152832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00000 | 0.0763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | − | 20.7846i | −0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.00000 | + | 8.66025i | −0.190209 | + | 0.329452i | −0.945319 | − | 0.326146i | \(-0.894250\pi\) |
0.755110 | + | 0.655598i | \(0.227583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.00000 | − | 15.5885i | 0.341389 | − | 0.591304i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.00000 | −0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.0000 | 1.69963 | 0.849813 | − | 0.527084i | \(-0.176715\pi\) | ||||
0.849813 | + | 0.527084i | \(0.176715\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.0000 | − | 62.3538i | −1.35777 | − | 2.35172i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.500000 | + | 0.866025i | −0.0187779 | + | 0.0325243i | −0.875262 | − | 0.483650i | \(-0.839311\pi\) |
0.856484 | + | 0.516174i | \(0.172644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.00000 | + | 10.3923i | 0.225018 | + | 0.389742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00000 | 0.299183 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.0000 | − | 17.3205i | −0.373457 | − | 0.646846i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.0000 | − | 22.5167i | 0.484818 | − | 0.839730i | −0.515030 | − | 0.857172i | \(-0.672219\pi\) |
0.999848 | + | 0.0174426i | \(0.00555244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.00000 | − | 15.5885i | 0.334714 | − | 0.579741i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.50000 | + | 2.59808i | 0.0557086 | + | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.0000 | 0.482143 | 0.241072 | − | 0.970507i | \(-0.422501\pi\) | ||||
0.241072 | + | 0.970507i | \(0.422501\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.00000 | − | 12.1244i | 0.258551 | − | 0.447823i | −0.707303 | − | 0.706910i | \(-0.750088\pi\) |
0.965854 | + | 0.259087i | \(0.0834217\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.0000 | − | 19.0526i | 0.405190 | − | 0.701810i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.00000 | + | 8.66025i | 0.183928 | + | 0.318573i | 0.943215 | − | 0.332184i | \(-0.107785\pi\) |
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.0000 | 0.881662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.00000 | 0.330178 | 0.165089 | − | 0.986279i | \(-0.447209\pi\) | ||||
0.165089 | + | 0.986279i | \(0.447209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.50000 | + | 14.7224i | 0.311416 | + | 0.539388i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.00000 | − | 5.19615i | 0.109764 | − | 0.190117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0000 | + | 24.2487i | −0.510867 | + | 0.884848i | 0.489053 | + | 0.872254i | \(0.337342\pi\) |
−0.999921 | + | 0.0125942i | \(0.995991\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.00000 | − | 3.46410i | −0.0728841 | − | 0.126239i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.0000 | 0.727875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.0000 | 0.726912 | 0.363456 | − | 0.931611i | \(-0.381597\pi\) | ||||
0.363456 | + | 0.931611i | \(0.381597\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.00000 | + | 5.19615i | 0.108893 | + | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0000 | + | 19.0526i | −0.398750 | + | 0.690655i | −0.993572 | − | 0.113203i | \(-0.963889\pi\) |
0.594822 | + | 0.803857i | \(0.297222\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.0000 | + | 34.6410i | 0.722158 | + | 1.25081i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.00000 | + | 3.46410i | 0.0719350 | + | 0.124595i | 0.899749 | − | 0.436407i | \(-0.143749\pi\) |
−0.827814 | + | 0.561002i | \(0.810416\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.0000 | − | 36.3731i | 0.752403 | − | 1.30320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0000 | − | 17.3205i | −0.357828 | − | 0.619777i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.0000 | 0.536056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0000 | 0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.5000 | − | 32.0429i | −0.659454 | − | 1.14221i | −0.980757 | − | 0.195231i | \(-0.937454\pi\) |
0.321303 | − | 0.946976i | \(-0.395879\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.5000 | + | 18.1865i | −0.373810 | + | 0.647458i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0000 | + | 17.3205i | −0.355110 | + | 0.615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.00000 | + | 5.19615i | 0.106399 | + | 0.184289i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.00000 | −0.283375 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.0000 | − | 29.4449i | −0.600665 | − | 1.04038i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.00000 | − | 13.8564i | 0.282314 | − | 0.488982i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.5000 | − | 26.8468i | 0.545626 | − | 0.945052i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.50000 | + | 9.52628i | 0.193370 | + | 0.334926i | 0.946365 | − | 0.323100i | \(-0.104725\pi\) |
−0.752995 | + | 0.658026i | \(0.771392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.0000 | −1.12367 | −0.561836 | − | 0.827249i | \(-0.689905\pi\) | ||||
−0.561836 | + | 0.827249i | \(0.689905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.00000 | 0.0701431 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | + | 10.3923i | 0.210171 | + | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.0000 | + | 46.7654i | −0.944610 | + | 1.63611i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.0000 | − | 29.4449i | 0.593304 | − | 1.02763i | −0.400480 | − | 0.916306i | \(-0.631157\pi\) |
0.993784 | − | 0.111327i | \(-0.0355102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.50000 | + | 11.2583i | 0.226576 | + | 0.392441i | 0.956791 | − | 0.290776i | \(-0.0939136\pi\) |
−0.730215 | + | 0.683217i | \(0.760580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.00000 | −0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.0000 | −1.07798 | −0.538988 | − | 0.842314i | \(-0.681193\pi\) | ||||
−0.538988 | + | 0.842314i | \(0.681193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00000 | − | 12.1244i | −0.243120 | − | 0.421096i | 0.718481 | − | 0.695546i | \(-0.244838\pi\) |
−0.961601 | + | 0.274450i | \(0.911504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | + | 6.92820i | −0.138758 | + | 0.240337i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.0000 | −1.58810 | −0.794048 | − | 0.607855i | \(-0.792030\pi\) | ||||
−0.794048 | + | 0.607855i | \(0.792030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.0000 | − | 22.5167i | −0.447744 | − | 0.775515i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.50000 | + | 2.59808i | −0.0516016 | + | 0.0893765i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.0000 | + | 24.2487i | −0.480479 | + | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0000 | + | 31.1769i | 0.617032 | + | 1.06873i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.0000 | −1.16414 | −0.582069 | − | 0.813139i | \(-0.697757\pi\) | ||||
−0.582069 | + | 0.813139i | \(0.697757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.0000 | 0.410391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.0000 | − | 22.5167i | −0.444072 | − | 0.769154i | 0.553915 | − | 0.832573i | \(-0.313133\pi\) |
−0.997987 | + | 0.0634184i | \(0.979800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.0000 | − | 48.4974i | 0.955348 | − | 1.65471i | 0.221777 | − | 0.975097i | \(-0.428814\pi\) |
0.733571 | − | 0.679613i | \(-0.237852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.5000 | − | 37.2391i | 0.731869 | − | 1.26763i | −0.224215 | − | 0.974540i | \(-0.571982\pi\) |
0.956084 | − | 0.293094i | \(-0.0946848\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.00000 | − | 6.92820i | −0.136004 | − | 0.235566i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | −0.407072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.0000 | + | 38.1051i | 0.745442 | + | 1.29114i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.00000 | − | 3.46410i | 0.0676897 | − | 0.117242i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.0000 | − | 19.0526i | 0.371444 | − | 0.643359i | −0.618344 | − | 0.785907i | \(-0.712196\pi\) |
0.989788 | + | 0.142548i | \(0.0455296\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.00000 | − | 3.46410i | −0.0674583 | − | 0.116841i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.0000 | −1.38133 | −0.690663 | − | 0.723177i | \(-0.742681\pi\) | ||||
−0.690663 | + | 0.723177i | \(0.742681\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.00000 | − | 8.66025i | −0.168073 | − | 0.291111i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.5000 | − | 32.0429i | 0.621169 | − | 1.07590i | −0.368099 | − | 0.929787i | \(-0.619991\pi\) |
0.989268 | − | 0.146110i | \(-0.0466754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | −0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.50000 | + | 4.33013i | −0.0831028 | + | 0.143938i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.50000 | − | 7.79423i | −0.149420 | − | 0.258803i | 0.781593 | − | 0.623788i | \(-0.214407\pi\) |
−0.931013 | + | 0.364985i | \(0.881074\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.0000 | −1.12771 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.0000 | −1.12647 | −0.563235 | − | 0.826297i | \(-0.690443\pi\) | ||||
−0.563235 | + | 0.826297i | \(0.690443\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.00000 | + | 5.19615i | 0.0992855 | + | 0.171968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.50000 | − | 4.33013i | 0.0826475 | − | 0.143150i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.0000 | + | 29.4449i | −0.560778 | + | 0.971296i | 0.436650 | + | 0.899631i | \(0.356165\pi\) |
−0.997429 | + | 0.0716652i | \(0.977169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.5000 | − | 18.1865i | −0.345987 | − | 0.599267i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.0000 | 1.31662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | −0.394558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.0000 | + | 25.9808i | 0.492665 | + | 0.853320i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.5000 | − | 23.3827i | 0.442921 | − | 0.767161i | −0.554984 | − | 0.831861i | \(-0.687276\pi\) |
0.997905 | + | 0.0646999i | \(0.0206090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.00000 | − | 8.66025i | 0.163693 | − | 0.283524i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.00000 | −0.130674 | −0.0653372 | − | 0.997863i | \(-0.520812\pi\) | ||||
−0.0653372 | + | 0.997863i | \(0.520812\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.0000 | 0.522140 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.0000 | − | 32.9090i | −0.619382 | − | 1.07280i | −0.989599 | − | 0.143856i | \(-0.954050\pi\) |
0.370216 | − | 0.928946i | \(-0.379284\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.5000 | + | 18.1865i | −0.341927 | + | 0.592235i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.50000 | − | 11.2583i | 0.211222 | − | 0.365847i | −0.740875 | − | 0.671642i | \(-0.765589\pi\) |
0.952097 | + | 0.305796i | \(0.0989225\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.0000 | + | 27.7128i | 0.519382 | + | 0.899596i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.0000 | −0.907009 | −0.453504 | − | 0.891254i | \(-0.649826\pi\) | ||||
−0.453504 | + | 0.891254i | \(0.649826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.00000 | − | 12.1244i | −0.226515 | − | 0.392335i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.00000 | + | 5.19615i | −0.0969762 | + | 0.167968i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.00000 | − | 1.73205i | −0.0322245 | − | 0.0558146i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.0000 | −0.708205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0000 | 0.418052 | 0.209026 | − | 0.977910i | \(-0.432971\pi\) | ||||
0.209026 | + | 0.977910i | \(0.432971\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | − | 34.6410i | 0.641831 | − | 1.11168i | −0.343193 | − | 0.939265i | \(-0.611509\pi\) |
0.985024 | − | 0.172418i | \(-0.0551581\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00000 | − | 3.46410i | 0.0640513 | − | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.0000 | 1.08664 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.50000 | + | 7.79423i | 0.143528 | + | 0.248597i | 0.928823 | − | 0.370525i | \(-0.120822\pi\) |
−0.785295 | + | 0.619122i | \(0.787489\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | − | 5.19615i | 0.0955879 | − | 0.165563i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.5000 | − | 23.3827i | 0.429275 | − | 0.743526i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.0000 | − | 17.3205i | −0.317660 | − | 0.550204i | 0.662339 | − | 0.749204i | \(-0.269564\pi\) |
−0.979999 | + | 0.199000i | \(0.936231\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.0000 | −0.380426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.00000 | + | 12.1244i | 0.221692 | + | 0.383982i | 0.955322 | − | 0.295567i | \(-0.0955086\pi\) |
−0.733630 | + | 0.679549i | \(0.762175\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.0000 | + | 51.9615i | −0.949158 | + | 1.64399i |
(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 | 1960.2.q.d.961.1 | 2 | ||
7.2 | even | 3 | 1960.2.a.l.1.1 | 1 | |||
7.3 | odd | 6 | 280.2.q.b.81.1 | ✓ | 2 | ||
7.4 | even | 3 | inner | 1960.2.q.d.361.1 | 2 | ||
7.5 | odd | 6 | 1960.2.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 280.2.q.b.121.1 | yes | 2 | ||
21.17 | even | 6 | 2520.2.bi.d.361.1 | 2 | |||
21.20 | even | 2 | 2520.2.bi.d.1801.1 | 2 | |||
28.3 | even | 6 | 560.2.q.e.81.1 | 2 | |||
28.19 | even | 6 | 3920.2.a.v.1.1 | 1 | |||
28.23 | odd | 6 | 3920.2.a.q.1.1 | 1 | |||
28.27 | even | 2 | 560.2.q.e.401.1 | 2 | |||
35.3 | even | 12 | 1400.2.bh.c.249.2 | 4 | |||
35.9 | even | 6 | 9800.2.a.o.1.1 | 1 | |||
35.13 | even | 4 | 1400.2.bh.c.849.1 | 4 | |||
35.17 | even | 12 | 1400.2.bh.c.249.1 | 4 | |||
35.19 | odd | 6 | 9800.2.a.z.1.1 | 1 | |||
35.24 | odd | 6 | 1400.2.q.c.1201.1 | 2 | |||
35.27 | even | 4 | 1400.2.bh.c.849.2 | 4 | |||
35.34 | odd | 2 | 1400.2.q.c.401.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.b.81.1 | ✓ | 2 | 7.3 | odd | 6 | ||
280.2.q.b.121.1 | yes | 2 | 7.6 | odd | 2 | ||
560.2.q.e.81.1 | 2 | 28.3 | even | 6 | |||
560.2.q.e.401.1 | 2 | 28.27 | even | 2 | |||
1400.2.q.c.401.1 | 2 | 35.34 | odd | 2 | |||
1400.2.q.c.1201.1 | 2 | 35.24 | odd | 6 | |||
1400.2.bh.c.249.1 | 4 | 35.17 | even | 12 | |||
1400.2.bh.c.249.2 | 4 | 35.3 | even | 12 | |||
1400.2.bh.c.849.1 | 4 | 35.13 | even | 4 | |||
1400.2.bh.c.849.2 | 4 | 35.27 | even | 4 | |||
1960.2.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
1960.2.a.l.1.1 | 1 | 7.2 | even | 3 | |||
1960.2.q.d.361.1 | 2 | 7.4 | even | 3 | inner | ||
1960.2.q.d.961.1 | 2 | 1.1 | even | 1 | trivial | ||
2520.2.bi.d.361.1 | 2 | 21.17 | even | 6 | |||
2520.2.bi.d.1801.1 | 2 | 21.20 | even | 2 | |||
3920.2.a.q.1.1 | 1 | 28.23 | odd | 6 | |||
3920.2.a.v.1.1 | 1 | 28.19 | even | 6 | |||
9800.2.a.o.1.1 | 1 | 35.9 | even | 6 | |||
9800.2.a.z.1.1 | 1 | 35.19 | odd | 6 |