Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(55,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.82836056527\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.271 |
Dual form | 324.3.f.c.55.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(5\) | −3.50000 | + | 6.06218i | −0.700000 | + | 1.21244i | 0.268466 | + | 0.963289i | \(0.413483\pi\) |
−0.968466 | + | 0.249146i | \(0.919850\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.50000 | − | 4.33013i | 1.07143 | − | 0.618590i | 0.142857 | − | 0.989743i | \(-0.454371\pi\) |
0.928571 | + | 0.371154i | \(0.121038\pi\) | |||||||
\(8\) | 8.00000 | 1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.00000 | − | 12.1244i | −0.700000 | − | 1.21244i | ||||
\(11\) | −7.50000 | + | 4.33013i | −0.681818 | + | 0.393648i | −0.800540 | − | 0.599280i | \(-0.795454\pi\) |
0.118722 | + | 0.992928i | \(0.462120\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.0000 | + | 17.3205i | −0.769231 | + | 1.33235i | 0.168750 | + | 0.985659i | \(0.446027\pi\) |
−0.937981 | + | 0.346688i | \(0.887306\pi\) | |||||||
\(14\) | 17.3205i | 1.23718i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(17\) | −8.00000 | −0.470588 | −0.235294 | − | 0.971924i | \(-0.575605\pi\) | ||||
−0.235294 | + | 0.971924i | \(0.575605\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 10.3923i | − | 0.546963i | −0.961877 | − | 0.273482i | \(-0.911825\pi\) | ||
0.961877 | − | 0.273482i | \(-0.0881753\pi\) | |||||||
\(20\) | 28.0000 | 1.40000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 17.3205i | − | 0.787296i | ||||||
\(23\) | −3.00000 | − | 1.73205i | −0.130435 | − | 0.0753066i | 0.433363 | − | 0.901220i | \(-0.357327\pi\) |
−0.563798 | + | 0.825913i | \(0.690660\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.0000 | − | 20.7846i | −0.480000 | − | 0.831384i | ||||
\(26\) | −20.0000 | − | 34.6410i | −0.769231 | − | 1.33235i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −30.0000 | − | 17.3205i | −1.07143 | − | 0.618590i | ||||
\(29\) | −5.00000 | − | 8.66025i | −0.172414 | − | 0.298629i | 0.766849 | − | 0.641827i | \(-0.221823\pi\) |
−0.939263 | + | 0.343198i | \(0.888490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.5000 | − | 26.8468i | −1.50000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(32\) | −16.0000 | − | 27.7128i | −0.500000 | − | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.00000 | − | 13.8564i | 0.235294 | − | 0.407541i | ||||
\(35\) | 60.6218i | 1.73205i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0000 | −0.270270 | −0.135135 | − | 0.990827i | \(-0.543147\pi\) | ||||
−0.135135 | + | 0.990827i | \(0.543147\pi\) | |||||||
\(38\) | 18.0000 | + | 10.3923i | 0.473684 | + | 0.273482i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −28.0000 | + | 48.4974i | −0.700000 | + | 1.21244i | ||||
\(41\) | 25.0000 | − | 43.3013i | 0.609756 | − | 1.05613i | −0.381524 | − | 0.924359i | \(-0.624601\pi\) |
0.991280 | − | 0.131770i | \(-0.0420659\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15.0000 | + | 8.66025i | −0.348837 | + | 0.201401i | −0.664173 | − | 0.747579i | \(-0.731216\pi\) |
0.315336 | + | 0.948980i | \(0.397883\pi\) | |||||||
\(44\) | 30.0000 | + | 17.3205i | 0.681818 | + | 0.393648i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | − | 3.46410i | 0.130435 | − | 0.0753066i | ||||
\(47\) | −75.0000 | + | 43.3013i | −1.59574 | + | 0.921304i | −0.603450 | + | 0.797401i | \(0.706208\pi\) |
−0.992294 | + | 0.123903i | \(0.960459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.0000 | − | 22.5167i | 0.265306 | − | 0.459524i | ||||
\(50\) | 48.0000 | 0.960000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 80.0000 | 1.53846 | ||||||||
\(53\) | −47.0000 | −0.886792 | −0.443396 | − | 0.896326i | \(-0.646227\pi\) | ||||
−0.443396 | + | 0.896326i | \(0.646227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 60.6218i | − | 1.10221i | ||||||
\(56\) | 60.0000 | − | 34.6410i | 1.07143 | − | 0.618590i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 20.0000 | 0.344828 | ||||||||
\(59\) | −30.0000 | − | 17.3205i | −0.508475 | − | 0.293568i | 0.223732 | − | 0.974651i | \(-0.428176\pi\) |
−0.732206 | + | 0.681083i | \(0.761509\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32.0000 | + | 55.4256i | 0.524590 | + | 0.908617i | 0.999590 | + | 0.0286310i | \(0.00911476\pi\) |
−0.475000 | + | 0.879986i | \(0.657552\pi\) | |||||||
\(62\) | 93.0000 | − | 53.6936i | 1.50000 | − | 0.866025i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | −70.0000 | − | 121.244i | −1.07692 | − | 1.86529i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 75.0000 | + | 43.3013i | 1.11940 | + | 0.646288i | 0.941248 | − | 0.337715i | \(-0.109654\pi\) |
0.178155 | + | 0.984003i | \(0.442987\pi\) | |||||||
\(68\) | 16.0000 | + | 27.7128i | 0.235294 | + | 0.407541i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −105.000 | − | 60.6218i | −1.50000 | − | 0.866025i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55.0000 | −0.753425 | −0.376712 | − | 0.926330i | \(-0.622945\pi\) | ||||
−0.376712 | + | 0.926330i | \(0.622945\pi\) | |||||||
\(74\) | 10.0000 | − | 17.3205i | 0.135135 | − | 0.234061i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −36.0000 | + | 20.7846i | −0.473684 | + | 0.273482i | ||||
\(77\) | −37.5000 | + | 64.9519i | −0.487013 | + | 0.843531i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | + | 3.46410i | −0.0759494 | + | 0.0438494i | −0.537494 | − | 0.843268i | \(-0.680629\pi\) |
0.461544 | + | 0.887117i | \(0.347296\pi\) | |||||||
\(80\) | −56.0000 | − | 96.9948i | −0.700000 | − | 1.21244i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 50.0000 | + | 86.6025i | 0.609756 | + | 1.05613i | ||||
\(83\) | −25.5000 | + | 14.7224i | −0.307229 | + | 0.177379i | −0.645686 | − | 0.763603i | \(-0.723428\pi\) |
0.338457 | + | 0.940982i | \(0.390095\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.0000 | − | 48.4974i | 0.329412 | − | 0.570558i | ||||
\(86\) | − | 34.6410i | − | 0.402803i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −60.0000 | + | 34.6410i | −0.681818 | + | 0.393648i | ||||
\(89\) | 10.0000 | 0.112360 | 0.0561798 | − | 0.998421i | \(-0.482108\pi\) | ||||
0.0561798 | + | 0.998421i | \(0.482108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 173.205i | 1.90335i | ||||||||
\(92\) | 13.8564i | 0.150613i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 173.205i | − | 1.84261i | ||||||
\(95\) | 63.0000 | + | 36.3731i | 0.663158 | + | 0.382874i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.5000 | + | 21.6506i | 0.128866 | + | 0.223202i | 0.923237 | − | 0.384230i | \(-0.125533\pi\) |
−0.794372 | + | 0.607432i | \(0.792200\pi\) | |||||||
\(98\) | 26.0000 | + | 45.0333i | 0.265306 | + | 0.459524i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −48.0000 | + | 83.1384i | −0.480000 | + | 0.831384i | ||||
\(101\) | 77.5000 | + | 134.234i | 0.767327 | + | 1.32905i | 0.939008 | + | 0.343896i | \(0.111747\pi\) |
−0.171681 | + | 0.985153i | \(0.554920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 120.000 | + | 69.2820i | 1.16505 | + | 0.672641i | 0.952509 | − | 0.304511i | \(-0.0984931\pi\) |
0.212540 | + | 0.977152i | \(0.431826\pi\) | |||||||
\(104\) | −80.0000 | + | 138.564i | −0.769231 | + | 1.33235i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 47.0000 | − | 81.4064i | 0.443396 | − | 0.767985i | ||||
\(107\) | 129.904i | 1.21405i | 0.794681 | + | 0.607027i | \(0.207638\pi\) | ||||
−0.794681 | + | 0.607027i | \(0.792362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 134.000 | 1.22936 | 0.614679 | − | 0.788777i | \(-0.289286\pi\) | ||||
0.614679 | + | 0.788777i | \(0.289286\pi\) | |||||||
\(110\) | 105.000 | + | 60.6218i | 0.954545 | + | 0.551107i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 138.564i | 1.23718i | ||||||||
\(113\) | 37.0000 | − | 64.0859i | 0.327434 | − | 0.567132i | −0.654568 | − | 0.756003i | \(-0.727150\pi\) |
0.982002 | + | 0.188871i | \(0.0604829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.0000 | − | 12.1244i | 0.182609 | − | 0.105429i | ||||
\(116\) | −20.0000 | + | 34.6410i | −0.172414 | + | 0.298629i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 60.0000 | − | 34.6410i | 0.508475 | − | 0.293568i | ||||
\(119\) | −60.0000 | + | 34.6410i | −0.504202 | + | 0.291101i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −23.0000 | + | 39.8372i | −0.190083 | + | 0.329233i | ||||
\(122\) | −128.000 | −1.04918 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 214.774i | 1.73205i | ||||||||
\(125\) | −7.00000 | −0.0560000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 25.9808i | 0.204573i | 0.994755 | + | 0.102286i | \(0.0326158\pi\) | ||||
−0.994755 | + | 0.102286i | \(0.967384\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.500000 | + | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 280.000 | 2.15385 | ||||||||
\(131\) | −142.500 | − | 82.2724i | −1.08779 | − | 0.628034i | −0.154800 | − | 0.987946i | \(-0.549473\pi\) |
−0.932986 | + | 0.359912i | \(0.882807\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −45.0000 | − | 77.9423i | −0.338346 | − | 0.586032i | ||||
\(134\) | −150.000 | + | 86.6025i | −1.11940 | + | 0.646288i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −64.0000 | −0.470588 | ||||||||
\(137\) | 31.0000 | + | 53.6936i | 0.226277 | + | 0.391924i | 0.956702 | − | 0.291070i | \(-0.0940111\pi\) |
−0.730425 | + | 0.682993i | \(0.760678\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −150.000 | − | 86.6025i | −1.07914 | − | 0.623040i | −0.148473 | − | 0.988916i | \(-0.547436\pi\) |
−0.930663 | + | 0.365877i | \(0.880769\pi\) | |||||||
\(140\) | 210.000 | − | 121.244i | 1.50000 | − | 0.866025i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 173.205i | − | 1.21122i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 70.0000 | 0.482759 | ||||||||
\(146\) | 55.0000 | − | 95.2628i | 0.376712 | − | 0.652485i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.0000 | + | 34.6410i | 0.135135 | + | 0.234061i | ||||
\(149\) | −57.5000 | + | 99.5929i | −0.385906 | + | 0.668409i | −0.991894 | − | 0.127065i | \(-0.959444\pi\) |
0.605988 | + | 0.795473i | \(0.292778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −37.5000 | + | 21.6506i | −0.248344 | + | 0.143382i | −0.619006 | − | 0.785386i | \(-0.712464\pi\) |
0.370662 | + | 0.928768i | \(0.379131\pi\) | |||||||
\(152\) | − | 83.1384i | − | 0.546963i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −75.0000 | − | 129.904i | −0.487013 | − | 0.843531i | ||||
\(155\) | 325.500 | − | 187.928i | 2.10000 | − | 1.21244i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | + | 17.3205i | −0.0636943 | + | 0.110322i | −0.896114 | − | 0.443824i | \(-0.853622\pi\) |
0.832420 | + | 0.554146i | \(0.186955\pi\) | |||||||
\(158\) | − | 13.8564i | − | 0.0876988i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 224.000 | 1.40000 | ||||||||
\(161\) | −30.0000 | −0.186335 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 103.923i | − | 0.637565i | −0.947828 | − | 0.318782i | \(-0.896726\pi\) | ||
0.947828 | − | 0.318782i | \(-0.103274\pi\) | |||||||
\(164\) | −200.000 | −1.21951 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 58.8897i | − | 0.354757i | ||||||
\(167\) | 213.000 | + | 122.976i | 1.27545 | + | 0.736381i | 0.976008 | − | 0.217734i | \(-0.0698665\pi\) |
0.299441 | + | 0.954115i | \(0.403200\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −115.500 | − | 200.052i | −0.683432 | − | 1.18374i | ||||
\(170\) | 56.0000 | + | 96.9948i | 0.329412 | + | 0.570558i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 60.0000 | + | 34.6410i | 0.348837 | + | 0.201401i | ||||
\(173\) | −63.5000 | − | 109.985i | −0.367052 | − | 0.635753i | 0.622051 | − | 0.782977i | \(-0.286300\pi\) |
−0.989103 | + | 0.147224i | \(0.952966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −180.000 | − | 103.923i | −1.02857 | − | 0.593846i | ||||
\(176\) | − | 138.564i | − | 0.787296i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.0000 | + | 17.3205i | −0.0561798 | + | 0.0973062i | ||||
\(179\) | − | 233.827i | − | 1.30630i | −0.757231 | − | 0.653148i | \(-0.773448\pi\) | ||
0.757231 | − | 0.653148i | \(-0.226552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 56.0000 | 0.309392 | 0.154696 | − | 0.987962i | \(-0.450560\pi\) | ||||
0.154696 | + | 0.987962i | \(0.450560\pi\) | |||||||
\(182\) | −300.000 | − | 173.205i | −1.64835 | − | 0.951676i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −24.0000 | − | 13.8564i | −0.130435 | − | 0.0753066i | ||||
\(185\) | 35.0000 | − | 60.6218i | 0.189189 | − | 0.327685i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 60.0000 | − | 34.6410i | 0.320856 | − | 0.185246i | ||||
\(188\) | 300.000 | + | 173.205i | 1.59574 | + | 0.921304i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −126.000 | + | 72.7461i | −0.663158 | + | 0.382874i | ||||
\(191\) | −30.0000 | + | 17.3205i | −0.157068 | + | 0.0906833i | −0.576474 | − | 0.817116i | \(-0.695572\pi\) |
0.419406 | + | 0.907799i | \(0.362238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −32.5000 | + | 56.2917i | −0.168394 | + | 0.291667i | −0.937855 | − | 0.347027i | \(-0.887191\pi\) |
0.769462 | + | 0.638693i | \(0.220525\pi\) | |||||||
\(194\) | −50.0000 | −0.257732 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −104.000 | −0.530612 | ||||||||
\(197\) | 253.000 | 1.28426 | 0.642132 | − | 0.766594i | \(-0.278050\pi\) | ||||
0.642132 | + | 0.766594i | \(0.278050\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 129.904i | 0.652783i | 0.945235 | + | 0.326391i | \(0.105833\pi\) | ||||
−0.945235 | + | 0.326391i | \(0.894167\pi\) | |||||||
\(200\) | −96.0000 | − | 166.277i | −0.480000 | − | 0.831384i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −310.000 | −1.53465 | ||||||||
\(203\) | −75.0000 | − | 43.3013i | −0.369458 | − | 0.213307i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 175.000 | + | 303.109i | 0.853659 | + | 1.47858i | ||||
\(206\) | −240.000 | + | 138.564i | −1.16505 | + | 0.672641i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −160.000 | − | 277.128i | −0.769231 | − | 1.33235i | ||||
\(209\) | 45.0000 | + | 77.9423i | 0.215311 | + | 0.372930i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 129.000 | + | 74.4782i | 0.611374 | + | 0.352977i | 0.773503 | − | 0.633792i | \(-0.218503\pi\) |
−0.162129 | + | 0.986770i | \(0.551836\pi\) | |||||||
\(212\) | 94.0000 | + | 162.813i | 0.443396 | + | 0.767985i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −225.000 | − | 129.904i | −1.05140 | − | 0.607027i | ||||
\(215\) | − | 121.244i | − | 0.563924i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −465.000 | −2.14286 | ||||||||
\(218\) | −134.000 | + | 232.095i | −0.614679 | + | 1.06466i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −210.000 | + | 121.244i | −0.954545 | + | 0.551107i | ||||
\(221\) | 80.0000 | − | 138.564i | 0.361991 | − | 0.626987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 30.0000 | − | 17.3205i | 0.134529 | − | 0.0776704i | −0.431225 | − | 0.902244i | \(-0.641918\pi\) |
0.565754 | + | 0.824574i | \(0.308585\pi\) | |||||||
\(224\) | −240.000 | − | 138.564i | −1.07143 | − | 0.618590i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 74.0000 | + | 128.172i | 0.327434 | + | 0.567132i | ||||
\(227\) | 78.0000 | − | 45.0333i | 0.343612 | − | 0.198385i | −0.318256 | − | 0.948005i | \(-0.603097\pi\) |
0.661868 | + | 0.749620i | \(0.269764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −73.0000 | + | 126.440i | −0.318777 | + | 0.552138i | −0.980233 | − | 0.197846i | \(-0.936606\pi\) |
0.661456 | + | 0.749984i | \(0.269939\pi\) | |||||||
\(230\) | 48.4974i | 0.210858i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −40.0000 | − | 69.2820i | −0.172414 | − | 0.298629i | ||||
\(233\) | 334.000 | 1.43348 | 0.716738 | − | 0.697342i | \(-0.245634\pi\) | ||||
0.716738 | + | 0.697342i | \(0.245634\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 606.218i | − | 2.57965i | ||||||
\(236\) | 138.564i | 0.587136i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 138.564i | − | 0.582202i | ||||||
\(239\) | 15.0000 | + | 8.66025i | 0.0627615 | + | 0.0362354i | 0.531052 | − | 0.847339i | \(-0.321797\pi\) |
−0.468291 | + | 0.883574i | \(0.655130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −67.0000 | − | 116.047i | −0.278008 | − | 0.481524i | 0.692881 | − | 0.721052i | \(-0.256341\pi\) |
−0.970890 | + | 0.239527i | \(0.923008\pi\) | |||||||
\(242\) | −46.0000 | − | 79.6743i | −0.190083 | − | 0.329233i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 128.000 | − | 221.703i | 0.524590 | − | 0.908617i | ||||
\(245\) | 91.0000 | + | 157.617i | 0.371429 | + | 0.643333i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 180.000 | + | 103.923i | 0.728745 | + | 0.420741i | ||||
\(248\) | −372.000 | − | 214.774i | −1.50000 | − | 0.866025i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.00000 | − | 12.1244i | 0.0280000 | − | 0.0484974i | ||||
\(251\) | 207.846i | 0.828072i | 0.910260 | + | 0.414036i | \(0.135881\pi\) | ||||
−0.910260 | + | 0.414036i | \(0.864119\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0000 | 0.118577 | ||||||||
\(254\) | −45.0000 | − | 25.9808i | −0.177165 | − | 0.102286i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.500000 | − | 0.866025i | ||||
\(257\) | −134.000 | + | 232.095i | −0.521401 | + | 0.903093i | 0.478289 | + | 0.878202i | \(0.341257\pi\) |
−0.999690 | + | 0.0248904i | \(0.992076\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −75.0000 | + | 43.3013i | −0.289575 | + | 0.167186i | ||||
\(260\) | −280.000 | + | 484.974i | −1.07692 | + | 1.86529i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 285.000 | − | 164.545i | 1.08779 | − | 0.628034i | ||||
\(263\) | 375.000 | − | 216.506i | 1.42586 | − | 0.823218i | 0.429065 | − | 0.903274i | \(-0.358843\pi\) |
0.996790 | + | 0.0800555i | \(0.0255098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 164.500 | − | 284.922i | 0.620755 | − | 1.07518i | ||||
\(266\) | 180.000 | 0.676692 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 346.410i | − | 1.29258i | ||||||
\(269\) | −350.000 | −1.30112 | −0.650558 | − | 0.759457i | \(-0.725465\pi\) | ||||
−0.650558 | + | 0.759457i | \(0.725465\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 36.3731i | 0.134218i | 0.997746 | + | 0.0671090i | \(0.0213775\pi\) | ||||
−0.997746 | + | 0.0671090i | \(0.978622\pi\) | |||||||
\(272\) | 64.0000 | − | 110.851i | 0.235294 | − | 0.407541i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −124.000 | −0.452555 | ||||||||
\(275\) | 180.000 | + | 103.923i | 0.654545 | + | 0.377902i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 260.000 | + | 450.333i | 0.938628 | + | 1.62575i | 0.768033 | + | 0.640410i | \(0.221236\pi\) |
0.170595 | + | 0.985341i | \(0.445431\pi\) | |||||||
\(278\) | 300.000 | − | 173.205i | 1.07914 | − | 0.623040i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 484.974i | 1.73205i | ||||||||
\(281\) | 220.000 | + | 381.051i | 0.782918 | + | 1.35605i | 0.930235 | + | 0.366965i | \(0.119603\pi\) |
−0.147317 | + | 0.989089i | \(0.547064\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −285.000 | − | 164.545i | −1.00707 | − | 0.581430i | −0.0967355 | − | 0.995310i | \(-0.530840\pi\) |
−0.910332 | + | 0.413880i | \(0.864173\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 300.000 | + | 173.205i | 1.04895 | + | 0.605612i | ||||
\(287\) | − | 433.013i | − | 1.50876i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −225.000 | −0.778547 | ||||||||
\(290\) | −70.0000 | + | 121.244i | −0.241379 | + | 0.418081i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 110.000 | + | 190.526i | 0.376712 | + | 0.652485i | ||||
\(293\) | 109.000 | − | 188.794i | 0.372014 | − | 0.644347i | −0.617862 | − | 0.786287i | \(-0.712001\pi\) |
0.989875 | + | 0.141940i | \(0.0453341\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 210.000 | − | 121.244i | 0.711864 | − | 0.410995i | ||||
\(296\) | −80.0000 | −0.270270 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −115.000 | − | 199.186i | −0.385906 | − | 0.668409i | ||||
\(299\) | 60.0000 | − | 34.6410i | 0.200669 | − | 0.115856i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −75.0000 | + | 129.904i | −0.249169 | + | 0.431574i | ||||
\(302\) | − | 86.6025i | − | 0.286763i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 144.000 | + | 83.1384i | 0.473684 | + | 0.273482i | ||||
\(305\) | −448.000 | −1.46885 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 207.846i | 0.677023i | 0.940962 | + | 0.338512i | \(0.109923\pi\) | ||||
−0.940962 | + | 0.338512i | \(0.890077\pi\) | |||||||
\(308\) | 300.000 | 0.974026 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 751.710i | 2.42487i | ||||||||
\(311\) | −255.000 | − | 147.224i | −0.819936 | − | 0.473390i | 0.0304586 | − | 0.999536i | \(-0.490303\pi\) |
−0.850394 | + | 0.526146i | \(0.823637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −242.500 | − | 420.022i | −0.774760 | − | 1.34192i | −0.934929 | − | 0.354835i | \(-0.884537\pi\) |
0.160169 | − | 0.987090i | \(-0.448796\pi\) | |||||||
\(314\) | −20.0000 | − | 34.6410i | −0.0636943 | − | 0.110322i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.0000 | + | 13.8564i | 0.0759494 | + | 0.0438494i | ||||
\(317\) | −108.500 | − | 187.928i | −0.342271 | − | 0.592831i | 0.642583 | − | 0.766216i | \(-0.277863\pi\) |
−0.984854 | + | 0.173385i | \(0.944530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 75.0000 | + | 43.3013i | 0.235110 | + | 0.135741i | ||||
\(320\) | −224.000 | + | 387.979i | −0.700000 | + | 1.21244i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 30.0000 | − | 51.9615i | 0.0931677 | − | 0.161371i | ||||
\(323\) | 83.1384i | 0.257395i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 480.000 | 1.47692 | ||||||||
\(326\) | 180.000 | + | 103.923i | 0.552147 | + | 0.318782i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 200.000 | − | 346.410i | 0.609756 | − | 1.05613i | ||||
\(329\) | −375.000 | + | 649.519i | −1.13982 | + | 1.97422i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −375.000 | + | 216.506i | −1.13293 | + | 0.654098i | −0.944670 | − | 0.328021i | \(-0.893618\pi\) |
−0.188260 | + | 0.982119i | \(0.560285\pi\) | |||||||
\(332\) | 102.000 | + | 58.8897i | 0.307229 | + | 0.177379i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −426.000 | + | 245.951i | −1.27545 | + | 0.736381i | ||||
\(335\) | −525.000 | + | 303.109i | −1.56716 | + | 0.904803i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 155.000 | − | 268.468i | 0.459941 | − | 0.796641i | −0.539017 | − | 0.842295i | \(-0.681204\pi\) |
0.998957 | + | 0.0456545i | \(0.0145373\pi\) | |||||||
\(338\) | 462.000 | 1.36686 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −224.000 | −0.658824 | ||||||||
\(341\) | 465.000 | 1.36364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 199.186i | 0.580717i | ||||||||
\(344\) | −120.000 | + | 69.2820i | −0.348837 | + | 0.201401i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 254.000 | 0.734104 | ||||||||
\(347\) | −187.500 | − | 108.253i | −0.540346 | − | 0.311969i | 0.204873 | − | 0.978789i | \(-0.434322\pi\) |
−0.745219 | + | 0.666820i | \(0.767655\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −37.0000 | − | 64.0859i | −0.106017 | − | 0.183627i | 0.808136 | − | 0.588996i | \(-0.200477\pi\) |
−0.914153 | + | 0.405369i | \(0.867143\pi\) | |||||||
\(350\) | 360.000 | − | 207.846i | 1.02857 | − | 0.593846i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 240.000 | + | 138.564i | 0.681818 | + | 0.393648i | ||||
\(353\) | −197.000 | − | 341.214i | −0.558074 | − | 0.966612i | −0.997657 | − | 0.0684103i | \(-0.978207\pi\) |
0.439584 | − | 0.898202i | \(-0.355126\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −20.0000 | − | 34.6410i | −0.0561798 | − | 0.0973062i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 405.000 | + | 233.827i | 1.13128 | + | 0.653148i | ||||
\(359\) | 571.577i | 1.59214i | 0.605207 | + | 0.796068i | \(0.293090\pi\) | ||||
−0.605207 | + | 0.796068i | \(0.706910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 253.000 | 0.700831 | ||||||||
\(362\) | −56.0000 | + | 96.9948i | −0.154696 | + | 0.267942i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 600.000 | − | 346.410i | 1.64835 | − | 0.951676i | ||||
\(365\) | 192.500 | − | 333.420i | 0.527397 | − | 0.913479i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −487.500 | + | 281.458i | −1.32834 | + | 0.766916i | −0.985043 | − | 0.172311i | \(-0.944877\pi\) |
−0.343295 | + | 0.939228i | \(0.611543\pi\) | |||||||
\(368\) | 48.0000 | − | 27.7128i | 0.130435 | − | 0.0753066i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 70.0000 | + | 121.244i | 0.189189 | + | 0.327685i | ||||
\(371\) | −352.500 | + | 203.516i | −0.950135 | + | 0.548561i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0000 | − | 34.6410i | 0.0536193 | − | 0.0928714i | −0.837970 | − | 0.545716i | \(-0.816258\pi\) |
0.891589 | + | 0.452845i | \(0.149591\pi\) | |||||||
\(374\) | 138.564i | 0.370492i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −600.000 | + | 346.410i | −1.59574 | + | 0.921304i | ||||
\(377\) | 200.000 | 0.530504 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 685.892i | 1.80974i | 0.425686 | + | 0.904871i | \(0.360033\pi\) | ||||
−0.425686 | + | 0.904871i | \(0.639967\pi\) | |||||||
\(380\) | − | 290.985i | − | 0.765749i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 69.2820i | − | 0.181367i | ||||||
\(383\) | 312.000 | + | 180.133i | 0.814621 | + | 0.470322i | 0.848558 | − | 0.529102i | \(-0.177471\pi\) |
−0.0339368 | + | 0.999424i | \(0.510804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −262.500 | − | 454.663i | −0.681818 | − | 1.18094i | ||||
\(386\) | −65.0000 | − | 112.583i | −0.168394 | − | 0.291667i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 50.0000 | − | 86.6025i | 0.128866 | − | 0.223202i | ||||
\(389\) | −237.500 | − | 411.362i | −0.610540 | − | 1.05749i | −0.991150 | − | 0.132750i | \(-0.957619\pi\) |
0.380610 | − | 0.924736i | \(-0.375714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | + | 13.8564i | 0.0613811 | + | 0.0354384i | ||||
\(392\) | 104.000 | − | 180.133i | 0.265306 | − | 0.459524i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −253.000 | + | 438.209i | −0.642132 | + | 1.11221i | ||||
\(395\) | − | 48.4974i | − | 0.122778i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 260.000 | 0.654912 | 0.327456 | − | 0.944866i | \(-0.393809\pi\) | ||||
0.327456 | + | 0.944866i | \(0.393809\pi\) | |||||||
\(398\) | −225.000 | − | 129.904i | −0.565327 | − | 0.326391i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 384.000 | 0.960000 | ||||||||
\(401\) | 370.000 | − | 640.859i | 0.922693 | − | 1.59815i | 0.127464 | − | 0.991843i | \(-0.459316\pi\) |
0.795230 | − | 0.606308i | \(-0.207350\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 930.000 | − | 536.936i | 2.30769 | − | 1.33235i | ||||
\(404\) | 310.000 | − | 536.936i | 0.767327 | − | 1.32905i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 150.000 | − | 86.6025i | 0.369458 | − | 0.213307i | ||||
\(407\) | 75.0000 | − | 43.3013i | 0.184275 | − | 0.106391i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −329.500 | + | 570.711i | −0.805623 | + | 1.39538i | 0.110246 | + | 0.993904i | \(0.464836\pi\) |
−0.915869 | + | 0.401476i | \(0.868497\pi\) | |||||||
\(410\) | −700.000 | −1.70732 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 554.256i | − | 1.34528i | ||||||
\(413\) | −300.000 | −0.726392 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 206.114i | − | 0.496660i | ||||||
\(416\) | 640.000 | 1.53846 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −180.000 | −0.430622 | ||||||||
\(419\) | 510.000 | + | 294.449i | 1.21718 | + | 0.702741i | 0.964315 | − | 0.264759i | \(-0.0852924\pi\) |
0.252869 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 248.000 | + | 429.549i | 0.589074 | + | 1.02031i | 0.994354 | + | 0.106113i | \(0.0338405\pi\) |
−0.405280 | + | 0.914192i | \(0.632826\pi\) | |||||||
\(422\) | −258.000 | + | 148.956i | −0.611374 | + | 0.352977i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −376.000 | −0.886792 | ||||||||
\(425\) | 96.0000 | + | 166.277i | 0.225882 | + | 0.391240i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 480.000 | + | 277.128i | 1.12412 | + | 0.649012i | ||||
\(428\) | 450.000 | − | 259.808i | 1.05140 | − | 0.607027i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 210.000 | + | 121.244i | 0.488372 | + | 0.281962i | ||||
\(431\) | 571.577i | 1.32616i | 0.748547 | + | 0.663082i | \(0.230752\pi\) | ||||
−0.748547 | + | 0.663082i | \(0.769248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −235.000 | −0.542725 | −0.271363 | − | 0.962477i | \(-0.587474\pi\) | ||||
−0.271363 | + | 0.962477i | \(0.587474\pi\) | |||||||
\(434\) | 465.000 | − | 805.404i | 1.07143 | − | 1.85577i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −268.000 | − | 464.190i | −0.614679 | − | 1.06466i | ||||
\(437\) | −18.0000 | + | 31.1769i | −0.0411899 | + | 0.0713431i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 358.500 | − | 206.980i | 0.816629 | − | 0.471481i | −0.0326238 | − | 0.999468i | \(-0.510386\pi\) |
0.849253 | + | 0.527987i | \(0.177053\pi\) | |||||||
\(440\) | − | 484.974i | − | 1.10221i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 160.000 | + | 277.128i | 0.361991 | + | 0.626987i | ||||
\(443\) | −498.000 | + | 287.520i | −1.12415 | + | 0.649030i | −0.942458 | − | 0.334325i | \(-0.891492\pi\) |
−0.181695 | + | 0.983355i | \(0.558159\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.0000 | + | 60.6218i | −0.0786517 | + | 0.136229i | ||||
\(446\) | 69.2820i | 0.155341i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 480.000 | − | 277.128i | 1.07143 | − | 0.618590i | ||||
\(449\) | −470.000 | −1.04677 | −0.523385 | − | 0.852096i | \(-0.675331\pi\) | ||||
−0.523385 | + | 0.852096i | \(0.675331\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 433.013i | 0.960117i | ||||||||
\(452\) | −296.000 | −0.654867 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 180.133i | 0.396769i | ||||||||
\(455\) | −1050.00 | − | 606.218i | −2.30769 | − | 1.33235i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 162.500 | + | 281.458i | 0.355580 | + | 0.615882i | 0.987217 | − | 0.159382i | \(-0.0509501\pi\) |
−0.631637 | + | 0.775264i | \(0.717617\pi\) | |||||||
\(458\) | −146.000 | − | 252.879i | −0.318777 | − | 0.552138i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −84.0000 | − | 48.4974i | −0.182609 | − | 0.105429i | ||||
\(461\) | −327.500 | − | 567.247i | −0.710412 | − | 1.23047i | −0.964703 | − | 0.263342i | \(-0.915175\pi\) |
0.254290 | − | 0.967128i | \(-0.418158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 142.500 | + | 82.2724i | 0.307775 | + | 0.177694i | 0.645931 | − | 0.763396i | \(-0.276470\pi\) |
−0.338155 | + | 0.941090i | \(0.609803\pi\) | |||||||
\(464\) | 160.000 | 0.344828 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −334.000 | + | 578.505i | −0.716738 | + | 1.24143i | ||||
\(467\) | − | 57.1577i | − | 0.122393i | −0.998126 | − | 0.0611967i | \(-0.980508\pi\) | ||
0.998126 | − | 0.0611967i | \(-0.0194917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 750.000 | 1.59915 | ||||||||
\(470\) | 1050.00 | + | 606.218i | 2.23404 | + | 1.28983i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −240.000 | − | 138.564i | −0.508475 | − | 0.293568i | ||||
\(473\) | 75.0000 | − | 129.904i | 0.158562 | − | 0.274638i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −216.000 | + | 124.708i | −0.454737 | + | 0.262542i | ||||
\(476\) | 240.000 | + | 138.564i | 0.504202 | + | 0.291101i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −30.0000 | + | 17.3205i | −0.0627615 | + | 0.0362354i | ||||
\(479\) | 285.000 | − | 164.545i | 0.594990 | − | 0.343517i | −0.172078 | − | 0.985083i | \(-0.555048\pi\) |
0.767068 | + | 0.641566i | \(0.221715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 100.000 | − | 173.205i | 0.207900 | − | 0.360094i | ||||
\(482\) | 268.000 | 0.556017 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 184.000 | 0.380165 | ||||||||
\(485\) | −175.000 | −0.360825 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 519.615i | − | 1.06697i | −0.845809 | − | 0.533486i | \(-0.820882\pi\) | ||
0.845809 | − | 0.533486i | \(-0.179118\pi\) | |||||||
\(488\) | 256.000 | + | 443.405i | 0.524590 | + | 0.908617i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −364.000 | −0.742857 | ||||||||
\(491\) | −187.500 | − | 108.253i | −0.381874 | − | 0.220475i | 0.296759 | − | 0.954952i | \(-0.404094\pi\) |
−0.678633 | + | 0.734477i | \(0.737427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.0000 | + | 69.2820i | 0.0811359 | + | 0.140532i | ||||
\(494\) | −360.000 | + | 207.846i | −0.728745 | + | 0.420741i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 744.000 | − | 429.549i | 1.50000 | − | 0.866025i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.0000 | + | 22.5167i | 0.0781563 | + | 0.0451236i | 0.538569 | − | 0.842581i | \(-0.318965\pi\) |
−0.460413 | + | 0.887705i | \(0.652299\pi\) | |||||||
\(500\) | 14.0000 | + | 24.2487i | 0.0280000 | + | 0.0484974i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −360.000 | − | 207.846i | −0.717131 | − | 0.414036i | ||||
\(503\) | 384.515i | 0.764444i | 0.924071 | + | 0.382222i | \(0.124841\pi\) | ||||
−0.924071 | + | 0.382222i | \(0.875159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1085.00 | −2.14851 | ||||||||
\(506\) | −30.0000 | + | 51.9615i | −0.0592885 | + | 0.102691i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 90.0000 | − | 51.9615i | 0.177165 | − | 0.102286i | ||||
\(509\) | −132.500 | + | 229.497i | −0.260314 | + | 0.450878i | −0.966325 | − | 0.257323i | \(-0.917160\pi\) |
0.706011 | + | 0.708201i | \(0.250493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −412.500 | + | 238.157i | −0.807241 | + | 0.466061i | ||||
\(512\) | 512.000 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −268.000 | − | 464.190i | −0.521401 | − | 0.903093i | ||||
\(515\) | −840.000 | + | 484.974i | −1.63107 | + | 0.941698i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 375.000 | − | 649.519i | 0.725338 | − | 1.25632i | ||||
\(518\) | − | 173.205i | − | 0.334373i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −560.000 | − | 969.948i | −1.07692 | − | 1.86529i | ||||
\(521\) | −380.000 | −0.729367 | −0.364683 | − | 0.931132i | \(-0.618823\pi\) | ||||
−0.364683 | + | 0.931132i | \(0.618823\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 623.538i | − | 1.19223i | −0.802898 | − | 0.596117i | \(-0.796709\pi\) | ||
0.802898 | − | 0.596117i | \(-0.203291\pi\) | |||||||
\(524\) | 658.179i | 1.25607i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 866.025i | 1.64644i | ||||||||
\(527\) | 372.000 | + | 214.774i | 0.705882 | + | 0.407541i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −258.500 | − | 447.735i | −0.488658 | − | 0.846380i | ||||
\(530\) | 329.000 | + | 569.845i | 0.620755 | + | 1.07518i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −180.000 | + | 311.769i | −0.338346 | + | 0.586032i | ||||
\(533\) | 500.000 | + | 866.025i | 0.938086 | + | 1.62481i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −787.500 | − | 454.663i | −1.47196 | − | 0.849838i | ||||
\(536\) | 600.000 | + | 346.410i | 1.11940 | + | 0.646288i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 350.000 | − | 606.218i | 0.650558 | − | 1.12680i | ||||
\(539\) | 225.167i | 0.417749i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −532.000 | −0.983364 | −0.491682 | − | 0.870775i | \(-0.663618\pi\) | ||||
−0.491682 | + | 0.870775i | \(0.663618\pi\) | |||||||
\(542\) | −63.0000 | − | 36.3731i | −0.116236 | − | 0.0671090i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 128.000 | + | 221.703i | 0.235294 | + | 0.407541i | ||||
\(545\) | −469.000 | + | 812.332i | −0.860550 | + | 1.49052i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −780.000 | + | 450.333i | −1.42596 | + | 0.823278i | −0.996799 | − | 0.0799498i | \(-0.974524\pi\) |
−0.429161 | + | 0.903228i | \(0.641191\pi\) | |||||||
\(548\) | 124.000 | − | 214.774i | 0.226277 | − | 0.391924i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −360.000 | + | 207.846i | −0.654545 | + | 0.377902i | ||||
\(551\) | −90.0000 | + | 51.9615i | −0.163339 | + | 0.0943040i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.0000 | + | 51.9615i | −0.0542495 | + | 0.0939630i | ||||
\(554\) | −1040.00 | −1.87726 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 692.820i | 1.24608i | ||||||||
\(557\) | −89.0000 | −0.159785 | −0.0798923 | − | 0.996804i | \(-0.525458\pi\) | ||||
−0.0798923 | + | 0.996804i | \(0.525458\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 346.410i | − | 0.619696i | ||||||
\(560\) | −840.000 | − | 484.974i | −1.50000 | − | 0.866025i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −880.000 | −1.56584 | ||||||||
\(563\) | 262.500 | + | 151.554i | 0.466252 | + | 0.269191i | 0.714670 | − | 0.699462i | \(-0.246577\pi\) |
−0.248417 | + | 0.968653i | \(0.579910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 259.000 | + | 448.601i | 0.458407 | + | 0.793984i | ||||
\(566\) | 570.000 | − | 329.090i | 1.00707 | − | 0.581430i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −50.0000 | − | 86.6025i | −0.0878735 | − | 0.152201i | 0.818739 | − | 0.574166i | \(-0.194674\pi\) |
−0.906612 | + | 0.421965i | \(0.861340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −294.000 | − | 169.741i | −0.514886 | − | 0.297270i | 0.219954 | − | 0.975510i | \(-0.429409\pi\) |
−0.734840 | + | 0.678241i | \(0.762743\pi\) | |||||||
\(572\) | −600.000 | + | 346.410i | −1.04895 | + | 0.605612i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 750.000 | + | 433.013i | 1.30662 | + | 0.754378i | ||||
\(575\) | 83.1384i | 0.144589i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −730.000 | −1.26516 | −0.632582 | − | 0.774493i | \(-0.718005\pi\) | ||||
−0.632582 | + | 0.774493i | \(0.718005\pi\) | |||||||
\(578\) | 225.000 | − | 389.711i | 0.389273 | − | 0.674241i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −140.000 | − | 242.487i | −0.241379 | − | 0.418081i | ||||
\(581\) | −127.500 | + | 220.836i | −0.219449 | + | 0.380097i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 352.500 | − | 203.516i | 0.604631 | − | 0.349084i | ||||
\(584\) | −440.000 | −0.753425 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 218.000 | + | 377.587i | 0.372014 | + | 0.644347i | ||||
\(587\) | 694.500 | − | 400.970i | 1.18313 | − | 0.683083i | 0.226397 | − | 0.974035i | \(-0.427305\pi\) |
0.956738 | + | 0.290952i | \(0.0939720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −279.000 | + | 483.242i | −0.473684 | + | 0.820445i | ||||
\(590\) | 484.974i | 0.821990i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 80.0000 | − | 138.564i | 0.135135 | − | 0.234061i | ||||
\(593\) | 982.000 | 1.65599 | 0.827993 | − | 0.560738i | \(-0.189483\pi\) | ||||
0.827993 | + | 0.560738i | \(0.189483\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 484.974i | − | 0.815083i | ||||||
\(596\) | 460.000 | 0.771812 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 138.564i | 0.231712i | ||||||||
\(599\) | 195.000 | + | 112.583i | 0.325543 | + | 0.187952i | 0.653860 | − | 0.756615i | \(-0.273148\pi\) |
−0.328318 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −125.500 | − | 217.372i | −0.208819 | − | 0.361684i | 0.742524 | − | 0.669819i | \(-0.233629\pi\) |
−0.951343 | + | 0.308135i | \(0.900295\pi\) | |||||||
\(602\) | −150.000 | − | 259.808i | −0.249169 | − | 0.431574i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 150.000 | + | 86.6025i | 0.248344 | + | 0.143382i | ||||
\(605\) | −161.000 | − | 278.860i | −0.266116 | − | 0.460926i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −330.000 | − | 190.526i | −0.543657 | − | 0.313881i | 0.202903 | − | 0.979199i | \(-0.434963\pi\) |
−0.746560 | + | 0.665318i | \(0.768296\pi\) | |||||||
\(608\) | −288.000 | + | 166.277i | −0.473684 | + | 0.273482i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 448.000 | − | 775.959i | 0.734426 | − | 1.27206i | ||||
\(611\) | − | 1732.05i | − | 2.83478i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 650.000 | 1.06036 | 0.530179 | − | 0.847885i | \(-0.322125\pi\) | ||||
0.530179 | + | 0.847885i | \(0.322125\pi\) | |||||||
\(614\) | −360.000 | − | 207.846i | −0.586319 | − | 0.338512i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −300.000 | + | 519.615i | −0.487013 | + | 0.843531i | ||||
\(617\) | 379.000 | − | 656.447i | 0.614263 | − | 1.06393i | −0.376251 | − | 0.926518i | \(-0.622787\pi\) |
0.990513 | − | 0.137416i | \(-0.0438798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −150.000 | + | 86.6025i | −0.242326 | + | 0.139907i | −0.616245 | − | 0.787554i | \(-0.711347\pi\) |
0.373919 | + | 0.927461i | \(0.378014\pi\) | |||||||
\(620\) | −1302.00 | − | 751.710i | −2.10000 | − | 1.21244i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 510.000 | − | 294.449i | 0.819936 | − | 0.473390i | ||||
\(623\) | 75.0000 | − | 43.3013i | 0.120385 | − | 0.0695044i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 324.500 | − | 562.050i | 0.519200 | − | 0.899281i | ||||
\(626\) | 970.000 | 1.54952 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 80.0000 | 0.127389 | ||||||||
\(629\) | 80.0000 | 0.127186 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 119.512i | 0.189400i | 0.995506 | + | 0.0947001i | \(0.0301892\pi\) | ||||
−0.995506 | + | 0.0947001i | \(0.969811\pi\) | |||||||
\(632\) | −48.0000 | + | 27.7128i | −0.0759494 | + | 0.0438494i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 434.000 | 0.684543 | ||||||||
\(635\) | −157.500 | − | 90.9327i | −0.248031 | − | 0.143201i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 260.000 | + | 450.333i | 0.408163 | + | 0.706960i | ||||
\(638\) | −150.000 | + | 86.6025i | −0.235110 | + | 0.135741i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −448.000 | − | 775.959i | −0.700000 | − | 1.21244i | ||||
\(641\) | −455.000 | − | 788.083i | −0.709828 | − | 1.22946i | −0.964921 | − | 0.262542i | \(-0.915439\pi\) |
0.255092 | − | 0.966917i | \(-0.417894\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.0000 | + | 17.3205i | 0.0466563 | + | 0.0269370i | 0.523147 | − | 0.852243i | \(-0.324758\pi\) |
−0.476490 | + | 0.879180i | \(0.658091\pi\) | |||||||
\(644\) | 60.0000 | + | 103.923i | 0.0931677 | + | 0.161371i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −144.000 | − | 83.1384i | −0.222910 | − | 0.128697i | ||||
\(647\) | 914.523i | 1.41348i | 0.707472 | + | 0.706741i | \(0.249835\pi\) | ||||
−0.707472 | + | 0.706741i | \(0.750165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 300.000 | 0.462250 | ||||||||
\(650\) | −480.000 | + | 831.384i | −0.738462 | + | 1.27905i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −360.000 | + | 207.846i | −0.552147 | + | 0.318782i | ||||
\(653\) | −51.5000 | + | 89.2006i | −0.0788668 | + | 0.136601i | −0.902761 | − | 0.430142i | \(-0.858464\pi\) |
0.823894 | + | 0.566743i | \(0.191797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 997.500 | − | 575.907i | 1.52290 | − | 0.879247i | ||||
\(656\) | 400.000 | + | 692.820i | 0.609756 | + | 1.05613i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −750.000 | − | 1299.04i | −1.13982 | − | 1.97422i | ||||
\(659\) | −52.5000 | + | 30.3109i | −0.0796662 | + | 0.0459953i | −0.539304 | − | 0.842111i | \(-0.681313\pi\) |
0.459638 | + | 0.888106i | \(0.347979\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −289.000 | + | 500.563i | −0.437216 | + | 0.757281i | −0.997474 | − | 0.0710377i | \(-0.977369\pi\) |
0.560257 | + | 0.828319i | \(0.310702\pi\) | |||||||
\(662\) | − | 866.025i | − | 1.30820i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −204.000 | + | 117.779i | −0.307229 | + | 0.177379i | ||||
\(665\) | 630.000 | 0.947368 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.6410i | 0.0519356i | ||||||||
\(668\) | − | 983.805i | − | 1.47276i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 1212.44i | − | 1.80961i | ||||||
\(671\) | −480.000 | − | 277.128i | −0.715350 | − | 0.413008i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −422.500 | − | 731.791i | −0.627786 | − | 1.08736i | −0.987995 | − | 0.154486i | \(-0.950628\pi\) |
0.360209 | − | 0.932872i | \(-0.382705\pi\) | |||||||
\(674\) | 310.000 | + | 536.936i | 0.459941 | + | 0.796641i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −462.000 | + | 800.207i | −0.683432 | + | 1.18374i | ||||
\(677\) | 577.000 | + | 999.393i | 0.852290 | + | 1.47621i | 0.879137 | + | 0.476569i | \(0.158120\pi\) |
−0.0268475 | + | 0.999640i | \(0.508547\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 187.500 | + | 108.253i | 0.276141 | + | 0.159430i | ||||
\(680\) | 224.000 | − | 387.979i | 0.329412 | − | 0.570558i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −465.000 | + | 805.404i | −0.681818 | + | 1.18094i | ||||
\(683\) | 187.061i | 0.273882i | 0.990579 | + | 0.136941i | \(0.0437271\pi\) | ||||
−0.990579 | + | 0.136941i | \(0.956273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −434.000 | −0.633577 | ||||||||
\(686\) | −345.000 | − | 199.186i | −0.502915 | − | 0.290358i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 277.128i | − | 0.402803i | ||||||
\(689\) | 470.000 | − | 814.064i | 0.682148 | − | 1.18152i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 426.000 | − | 245.951i | 0.616498 | − | 0.355935i | −0.159006 | − | 0.987278i | \(-0.550829\pi\) |
0.775504 | + | 0.631342i | \(0.217496\pi\) | |||||||
\(692\) | −254.000 | + | 439.941i | −0.367052 | + | 0.635753i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 375.000 | − | 216.506i | 0.540346 | − | 0.311969i | ||||
\(695\) | 1050.00 | − | 606.218i | 1.51079 | − | 0.872256i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −200.000 | + | 346.410i | −0.286944 | + | 0.497002i | ||||
\(698\) | 148.000 | 0.212034 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 831.384i | 1.18769i | ||||||||
\(701\) | −215.000 | −0.306705 | −0.153352 | − | 0.988172i | \(-0.549007\pi\) | ||||
−0.153352 | + | 0.988172i | \(0.549007\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 103.923i | 0.147828i | ||||||||
\(704\) | −480.000 | + | 277.128i | −0.681818 | + | 0.393648i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 788.000 | 1.11615 | ||||||||
\(707\) | 1162.50 | + | 671.170i | 1.64427 | + | 0.949321i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 266.000 | + | 460.726i | 0.375176 | + | 0.649824i | 0.990353 | − | 0.138565i | \(-0.0442488\pi\) |
−0.615177 | + | 0.788389i | \(0.710916\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 80.0000 | 0.112360 | ||||||||
\(713\) | 93.0000 | + | 161.081i | 0.130435 | + | 0.225920i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1050.00 | + | 606.218i | 1.46853 | + | 0.847857i | ||||
\(716\) | −810.000 | + | 467.654i | −1.13128 | + | 0.653148i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −990.000 | − | 571.577i | −1.37883 | − | 0.796068i | ||||
\(719\) | − | 1143.15i | − | 1.58992i | −0.606661 | − | 0.794961i | \(-0.707491\pi\) | ||
0.606661 | − | 0.794961i | \(-0.292509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1200.00 | 1.66436 | ||||||||
\(722\) | −253.000 | + | 438.209i | −0.350416 | + | 0.606937i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −112.000 | − | 193.990i | −0.154696 | − | 0.267942i | ||||
\(725\) | −120.000 | + | 207.846i | −0.165517 | + | 0.286684i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1072.50 | + | 619.208i | −1.47524 | + | 0.851731i | −0.999610 | − | 0.0279146i | \(-0.991113\pi\) |
−0.475630 | + | 0.879645i | \(0.657780\pi\) | |||||||
\(728\) | 1385.64i | 1.90335i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 385.000 | + | 666.840i | 0.527397 | + | 0.913479i | ||||
\(731\) | 120.000 | − | 69.2820i | 0.164159 | − | 0.0947771i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −475.000 | + | 822.724i | −0.648022 | + | 1.12241i | 0.335573 | + | 0.942014i | \(0.391070\pi\) |
−0.983595 | + | 0.180392i | \(0.942263\pi\) | |||||||
\(734\) | − | 1125.83i | − | 1.53383i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 110.851i | 0.150613i | ||||||||
\(737\) | −750.000 | −1.01764 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 581.969i | 0.787509i | 0.919216 | + | 0.393754i | \(0.128824\pi\) | ||||
−0.919216 | + | 0.393754i | \(0.871176\pi\) | |||||||
\(740\) | −280.000 | −0.378378 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 814.064i | − | 1.09712i | ||||||
\(743\) | −750.000 | − | 433.013i | −1.00942 | − | 0.582790i | −0.0983991 | − | 0.995147i | \(-0.531372\pi\) |
−0.911022 | + | 0.412357i | \(0.864706\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −402.500 | − | 697.150i | −0.540268 | − | 0.935772i | ||||
\(746\) | 40.0000 | + | 69.2820i | 0.0536193 | + | 0.0928714i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −240.000 | − | 138.564i | −0.320856 | − | 0.185246i | ||||
\(749\) | 562.500 | + | 974.279i | 0.751001 | + | 1.30077i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 151.500 | + | 87.4686i | 0.201731 | + | 0.116469i | 0.597463 | − | 0.801897i | \(-0.296176\pi\) |
−0.395732 | + | 0.918366i | \(0.629509\pi\) | |||||||
\(752\) | − | 1385.64i | − | 1.84261i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −200.000 | + | 346.410i | −0.265252 | + | 0.459430i | ||||
\(755\) | − | 303.109i | − | 0.401469i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 830.000 | 1.09643 | 0.548217 | − | 0.836336i | \(-0.315307\pi\) | ||||
0.548217 | + | 0.836336i | \(0.315307\pi\) | |||||||
\(758\) | −1188.00 | − | 685.892i | −1.56728 | − | 0.904871i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 504.000 | + | 290.985i | 0.663158 | + | 0.382874i | ||||
\(761\) | 280.000 | − | 484.974i | 0.367937 | − | 0.637285i | −0.621306 | − | 0.783568i | \(-0.713398\pi\) |
0.989243 | + | 0.146283i | \(0.0467309\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1005.00 | − | 580.237i | 1.31717 | − | 0.760468i | ||||
\(764\) | 120.000 | + | 69.2820i | 0.157068 | + | 0.0906833i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −624.000 | + | 360.267i | −0.814621 | + | 0.470322i | ||||
\(767\) | 600.000 | − | 346.410i | 0.782269 | − | 0.451643i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 165.500 | − | 286.654i | 0.215215 | − | 0.372763i | −0.738124 | − | 0.674665i | \(-0.764288\pi\) |
0.953339 | + | 0.301902i | \(0.0976216\pi\) | |||||||
\(770\) | 1050.00 | 1.36364 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 260.000 | 0.336788 | ||||||||
\(773\) | 298.000 | 0.385511 | 0.192755 | − | 0.981247i | \(-0.438258\pi\) | ||||
0.192755 | + | 0.981247i | \(0.438258\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1288.65i | 1.66277i | ||||||||
\(776\) | 100.000 | + | 173.205i | 0.128866 | + | 0.223202i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 950.000 | 1.22108 | ||||||||
\(779\) | −450.000 | − | 259.808i | −0.577664 | − | 0.333514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −48.0000 | + | 27.7128i | −0.0613811 | + | 0.0354384i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 208.000 | + | 360.267i | 0.265306 | + | 0.459524i | ||||
\(785\) | −70.0000 | − | 121.244i | −0.0891720 | − | 0.154450i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −960.000 | − | 554.256i | −1.21982 | − | 0.704265i | −0.254942 | − | 0.966956i | \(-0.582056\pi\) |
−0.964880 | + | 0.262692i | \(0.915390\pi\) | |||||||
\(788\) | −506.000 | − | 876.418i | −0.642132 | − | 1.11221i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 84.0000 | + | 48.4974i | 0.106329 | + | 0.0613891i | ||||
\(791\) | − | 640.859i | − | 0.810188i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1280.00 | −1.61412 | ||||||||
\(794\) | −260.000 | + | 450.333i | −0.327456 | + | 0.567170i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 450.000 | − | 259.808i | 0.565327 | − | 0.326391i | ||||
\(797\) | −651.500 | + | 1128.43i | −0.817440 | + | 1.41585i | 0.0901219 | + | 0.995931i | \(0.471274\pi\) |
−0.907562 | + | 0.419918i | \(0.862059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 600.000 | − | 346.410i | 0.750939 | − | 0.433555i | ||||
\(800\) | −384.000 | + | 665.108i | −0.480000 | + | 0.831384i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 740.000 | + | 1281.72i | 0.922693 | + | 1.59815i | ||||
\(803\) | 412.500 | − | 238.157i | 0.513699 | − | 0.296584i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 105.000 | − | 181.865i | 0.130435 | − | 0.225920i | ||||
\(806\) | 2147.74i | 2.66469i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 620.000 | + | 1073.87i | 0.767327 | + | 1.32905i | ||||
\(809\) | −170.000 | −0.210136 | −0.105068 | − | 0.994465i | \(-0.533506\pi\) | ||||
−0.105068 | + | 0.994465i | \(0.533506\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 779.423i | 0.961064i | 0.876977 | + | 0.480532i | \(0.159556\pi\) | ||||
−0.876977 | + | 0.480532i | \(0.840444\pi\) | |||||||
\(812\) | 346.410i | 0.426613i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 173.205i | 0.212783i | ||||||||
\(815\) | 630.000 | + | 363.731i | 0.773006 | + | 0.446295i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 90.0000 | + | 155.885i | 0.110159 | + | 0.190801i | ||||
\(818\) | −659.000 | − | 1141.42i | −0.805623 | − | 1.39538i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 700.000 | − | 1212.44i | 0.853659 | − | 1.47858i | ||||
\(821\) | −545.000 | − | 943.968i | −0.663825 | − | 1.14978i | −0.979603 | − | 0.200945i | \(-0.935599\pi\) |
0.315778 | − | 0.948833i | \(-0.397735\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 817.500 | + | 471.984i | 0.993317 | + | 0.573492i | 0.906264 | − | 0.422712i | \(-0.138922\pi\) |
0.0870530 | + | 0.996204i | \(0.472255\pi\) | |||||||
\(824\) | 960.000 | + | 554.256i | 1.16505 | + | 0.672641i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 300.000 | − | 519.615i | 0.363196 | − | 0.629074i | ||||
\(827\) | 83.1384i | 0.100530i | 0.998736 | + | 0.0502651i | \(0.0160066\pi\) | ||||
−0.998736 | + | 0.0502651i | \(0.983993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 542.000 | 0.653800 | 0.326900 | − | 0.945059i | \(-0.393996\pi\) | ||||
0.326900 | + | 0.945059i | \(0.393996\pi\) | |||||||
\(830\) | 357.000 | + | 206.114i | 0.430120 | + | 0.248330i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −640.000 | + | 1108.51i | −0.769231 | + | 1.33235i | ||||
\(833\) | −104.000 | + | 180.133i | −0.124850 | + | 0.216246i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1491.00 | + | 860.829i | −1.78563 | + | 1.03093i | ||||
\(836\) | 180.000 | − | 311.769i | 0.215311 | − | 0.372930i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1020.00 | + | 588.897i | −1.21718 | + | 0.702741i | ||||
\(839\) | 600.000 | − | 346.410i | 0.715137 | − | 0.412885i | −0.0978231 | − | 0.995204i | \(-0.531188\pi\) |
0.812960 | + | 0.582319i | \(0.197855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 370.500 | − | 641.725i | 0.440547 | − | 0.763050i | ||||
\(842\) | −992.000 | −1.17815 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 595.825i | − | 0.705954i | ||||||
\(845\) | 1617.00 | 1.91361 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 398.372i | 0.470333i | ||||||||
\(848\) | 376.000 | − | 651.251i | 0.443396 | − | 0.767985i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −384.000 | −0.451765 | ||||||||
\(851\) | 30.0000 | + | 17.3205i | 0.0352526 | + | 0.0203531i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −145.000 | − | 251.147i | −0.169988 | − | 0.294428i | 0.768427 | − | 0.639937i | \(-0.221040\pi\) |
−0.938415 | + | 0.345509i | \(0.887706\pi\) | |||||||
\(854\) | −960.000 | + | 554.256i | −1.12412 | + | 0.649012i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1039.23i | 1.21405i | ||||||||
\(857\) | 184.000 | + | 318.697i | 0.214702 | + | 0.371876i | 0.953180 | − | 0.302402i | \(-0.0977885\pi\) |
−0.738478 | + | 0.674278i | \(0.764455\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −924.000 | − | 533.472i | −1.07567 | − | 0.621038i | −0.145944 | − | 0.989293i | \(-0.546622\pi\) |
−0.929725 | + | 0.368255i | \(0.879955\pi\) | |||||||
\(860\) | −420.000 | + | 242.487i | −0.488372 | + | 0.281962i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −990.000 | − | 571.577i | −1.14849 | − | 0.663082i | ||||
\(863\) | − | 1018.45i | − | 1.18012i | −0.807358 | − | 0.590061i | \(-0.799104\pi\) | ||
0.807358 | − | 0.590061i | \(-0.200896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 889.000 | 1.02775 | ||||||||
\(866\) | 235.000 | − | 407.032i | 0.271363 | − | 0.470014i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 930.000 | + | 1610.81i | 1.07143 | + | 1.85577i | ||||
\(869\) | 30.0000 | − | 51.9615i | 0.0345224 | − | 0.0597946i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1500.00 | + | 866.025i | −1.72216 | + | 0.994289i | ||||
\(872\) | 1072.00 | 1.22936 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −36.0000 | − | 62.3538i | −0.0411899 | − | 0.0713431i | ||||
\(875\) | −52.5000 | + | 30.3109i | −0.0600000 | + | 0.0346410i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 665.000 | − | 1151.81i | 0.758267 | − | 1.31336i | −0.185467 | − | 0.982651i | \(-0.559380\pi\) |
0.943734 | − | 0.330706i | \(-0.107287\pi\) | |||||||
\(878\) | 827.920i | 0.942962i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 840.000 | + | 484.974i | 0.954545 | + | 0.551107i | ||||
\(881\) | 1060.00 | 1.20318 | 0.601589 | − | 0.798806i | \(-0.294534\pi\) | ||||
0.601589 | + | 0.798806i | \(0.294534\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1506.88i | − | 1.70655i | −0.521461 | − | 0.853275i | \(-0.674613\pi\) | ||
0.521461 | − | 0.853275i | \(-0.325387\pi\) | |||||||
\(884\) | −640.000 | −0.723982 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 1150.08i | − | 1.29806i | ||||||
\(887\) | 618.000 | + | 356.802i | 0.696731 | + | 0.402258i | 0.806129 | − | 0.591740i | \(-0.201559\pi\) |
−0.109398 | + | 0.993998i | \(0.534892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 112.500 | + | 194.856i | 0.126547 | + | 0.219185i | ||||
\(890\) | −70.0000 | − | 121.244i | −0.0786517 | − | 0.136229i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −120.000 | − | 69.2820i | −0.134529 | − | 0.0776704i | ||||
\(893\) | 450.000 | + | 779.423i | 0.503919 | + | 0.872814i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1417.50 | + | 818.394i | 1.58380 | + | 0.914407i | ||||
\(896\) | 1108.51i | 1.23718i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 470.000 | − | 814.064i | 0.523385 | − | 0.906530i | ||||
\(899\) | 536.936i | 0.597259i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 376.000 | 0.417314 | ||||||||
\(902\) | −750.000 | − | 433.013i | −0.831486 | − | 0.480058i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 296.000 | − | 512.687i | 0.327434 | − | 0.567132i | ||||
\(905\) | −196.000 | + | 339.482i | −0.216575 | + | 0.375118i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1155.00 | − | 666.840i | 1.27343 | − | 0.735215i | 0.297797 | − | 0.954629i | \(-0.403748\pi\) |
0.975632 | + | 0.219415i | \(0.0704147\pi\) | |||||||
\(908\) | −312.000 | − | 180.133i | −0.343612 | − | 0.198385i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2100.00 | − | 1212.44i | 2.30769 | − | 1.33235i | ||||
\(911\) | −1335.00 | + | 770.763i | −1.46542 | + | 0.846062i | −0.999253 | − | 0.0386335i | \(-0.987700\pi\) |
−0.466169 | + | 0.884696i | \(0.654366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 127.500 | − | 220.836i | 0.139650 | − | 0.241880i | ||||
\(914\) | −650.000 | −0.711160 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 584.000 | 0.637555 | ||||||||
\(917\) | −1425.00 | −1.55398 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 909.327i | − | 0.989474i | −0.869043 | − | 0.494737i | \(-0.835264\pi\) | ||
0.869043 | − | 0.494737i | \(-0.164736\pi\) | |||||||
\(920\) | 168.000 | − | 96.9948i | 0.182609 | − | 0.105429i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1310.00 | 1.42082 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 120.000 | + | 207.846i | 0.129730 | + | 0.224698i | ||||
\(926\) | −285.000 | + | 164.545i | −0.307775 | + | 0.177694i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −160.000 | + | 277.128i | −0.172414 | + | 0.298629i | ||||
\(929\) | 670.000 | + | 1160.47i | 0.721206 | + | 1.24916i | 0.960517 | + | 0.278222i | \(0.0897450\pi\) |
−0.239311 | + | 0.970943i | \(0.576922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −234.000 | − | 135.100i | −0.251343 | − | 0.145113i | ||||
\(932\) | −668.000 | − | 1157.01i | −0.716738 | − | 1.24143i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 99.0000 | + | 57.1577i | 0.105996 | + | 0.0611967i | ||||
\(935\) | 484.974i | 0.518689i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1225.00 | −1.30736 | −0.653682 | − | 0.756769i | \(-0.726777\pi\) | ||||
−0.653682 | + | 0.756769i | \(0.726777\pi\) | |||||||
\(938\) | −750.000 | + | 1299.04i | −0.799574 | + | 1.38490i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2100.00 | + | 1212.44i | −2.23404 | + | 1.28983i | ||||
\(941\) | −57.5000 | + | 99.5929i | −0.0611052 | + | 0.105837i | −0.894960 | − | 0.446147i | \(-0.852796\pi\) |
0.833854 | + | 0.551984i | \(0.186129\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −150.000 | + | 86.6025i | −0.159067 | + | 0.0918373i | ||||
\(944\) | 480.000 | − | 277.128i | 0.508475 | − | 0.293568i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 150.000 | + | 259.808i | 0.158562 | + | 0.274638i | ||||
\(947\) | 595.500 | − | 343.812i | 0.628828 | − | 0.363054i | −0.151470 | − | 0.988462i | \(-0.548401\pi\) |
0.780298 | + | 0.625408i | \(0.215067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 550.000 | − | 952.628i | 0.579557 | − | 1.00382i | ||||
\(950\) | − | 498.831i | − | 0.525085i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −480.000 | + | 277.128i | −0.504202 | + | 0.291101i | ||||
\(953\) | −44.0000 | −0.0461700 | −0.0230850 | − | 0.999734i | \(-0.507349\pi\) | ||||
−0.0230850 | + | 0.999734i | \(0.507349\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 242.487i | − | 0.253913i | ||||||
\(956\) | − | 69.2820i | − | 0.0724707i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 658.179i | 0.687035i | ||||||||
\(959\) | 465.000 | + | 268.468i | 0.484880 | + | 0.279946i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 961.000 | + | 1664.50i | 1.00000 | + | 1.73205i | ||||
\(962\) | 200.000 | + | 346.410i | 0.207900 | + | 0.360094i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −268.000 | + | 464.190i | −0.278008 | + | 0.481524i | ||||
\(965\) | −227.500 | − | 394.042i | −0.235751 | − | 0.408333i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −217.500 | − | 125.574i | −0.224922 | − | 0.129859i | 0.383305 | − | 0.923622i | \(-0.374786\pi\) |
−0.608227 | + | 0.793763i | \(0.708119\pi\) | |||||||
\(968\) | −184.000 | + | 318.697i | −0.190083 | + | 0.329233i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 175.000 | − | 303.109i | 0.180412 | − | 0.312483i | ||||
\(971\) | 337.750i | 0.347837i | 0.984760 | + | 0.173919i | \(0.0556430\pi\) | ||||
−0.984760 | + | 0.173919i | \(0.944357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1500.00 | −1.54162 | ||||||||
\(974\) | 900.000 | + | 519.615i | 0.924025 | + | 0.533486i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1024.00 | −1.04918 | ||||||||
\(977\) | −173.000 | + | 299.645i | −0.177073 | + | 0.306699i | −0.940877 | − | 0.338749i | \(-0.889996\pi\) |
0.763804 | + | 0.645448i | \(0.223329\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −75.0000 | + | 43.3013i | −0.0766088 | + | 0.0442301i | ||||
\(980\) | 364.000 | − | 630.466i | 0.371429 | − | 0.643333i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 375.000 | − | 216.506i | 0.381874 | − | 0.220475i | ||||
\(983\) | −687.000 | + | 396.640i | −0.698881 | + | 0.403499i | −0.806931 | − | 0.590646i | \(-0.798873\pi\) |
0.108050 | + | 0.994146i | \(0.465539\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −885.500 | + | 1533.73i | −0.898985 | + | 1.55709i | ||||
\(986\) | −160.000 | −0.162272 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 831.384i | − | 0.841482i | ||||||
\(989\) | 60.0000 | 0.0606673 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1054.82i | 1.06440i | 0.846619 | + | 0.532199i | \(0.178634\pi\) | ||||
−0.846619 | + | 0.532199i | \(0.821366\pi\) | |||||||
\(992\) | 1718.19i | 1.73205i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −787.500 | − | 454.663i | −0.791457 | − | 0.456948i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −130.000 | − | 225.167i | −0.130391 | − | 0.225844i | 0.793436 | − | 0.608653i | \(-0.208290\pi\) |
−0.923827 | + | 0.382809i | \(0.874957\pi\) | |||||||
\(998\) | −78.0000 | + | 45.0333i | −0.0781563 | + | 0.0451236i | ||||
\(999\) | 0 | 0 |
(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 | 324.3.f.c.271.1 | 2 | ||
3.2 | odd | 2 | 324.3.f.h.271.1 | 2 | |||
4.3 | odd | 2 | 324.3.f.i.271.1 | 2 | |||
9.2 | odd | 6 | 324.3.f.b.55.1 | 2 | |||
9.4 | even | 3 | 108.3.d.a.55.1 | ✓ | 2 | ||
9.5 | odd | 6 | 108.3.d.b.55.2 | yes | 2 | ||
9.7 | even | 3 | 324.3.f.i.55.1 | 2 | |||
12.11 | even | 2 | 324.3.f.b.271.1 | 2 | |||
36.7 | odd | 6 | inner | 324.3.f.c.55.1 | 2 | ||
36.11 | even | 6 | 324.3.f.h.55.1 | 2 | |||
36.23 | even | 6 | 108.3.d.b.55.1 | yes | 2 | ||
36.31 | odd | 6 | 108.3.d.a.55.2 | yes | 2 | ||
72.5 | odd | 6 | 1728.3.g.f.703.2 | 2 | |||
72.13 | even | 6 | 1728.3.g.a.703.2 | 2 | |||
72.59 | even | 6 | 1728.3.g.f.703.1 | 2 | |||
72.67 | odd | 6 | 1728.3.g.a.703.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.d.a.55.1 | ✓ | 2 | 9.4 | even | 3 | ||
108.3.d.a.55.2 | yes | 2 | 36.31 | odd | 6 | ||
108.3.d.b.55.1 | yes | 2 | 36.23 | even | 6 | ||
108.3.d.b.55.2 | yes | 2 | 9.5 | odd | 6 | ||
324.3.f.b.55.1 | 2 | 9.2 | odd | 6 | |||
324.3.f.b.271.1 | 2 | 12.11 | even | 2 | |||
324.3.f.c.55.1 | 2 | 36.7 | odd | 6 | inner | ||
324.3.f.c.271.1 | 2 | 1.1 | even | 1 | trivial | ||
324.3.f.h.55.1 | 2 | 36.11 | even | 6 | |||
324.3.f.h.271.1 | 2 | 3.2 | odd | 2 | |||
324.3.f.i.55.1 | 2 | 9.7 | even | 3 | |||
324.3.f.i.271.1 | 2 | 4.3 | odd | 2 | |||
1728.3.g.a.703.1 | 2 | 72.67 | odd | 6 | |||
1728.3.g.a.703.2 | 2 | 72.13 | even | 6 | |||
1728.3.g.f.703.1 | 2 | 72.59 | even | 6 | |||
1728.3.g.f.703.2 | 2 | 72.5 | odd | 6 |