Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(373,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 445.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.445 |
Dual form | 546.2.k.a.373.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | 0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.00000 | − | 3.46410i | −0.485071 | − | 0.840168i | 0.514782 | − | 0.857321i | \(-0.327873\pi\) |
−0.999853 | + | 0.0171533i | \(0.994540\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | − | 0.866025i | 0.545545 | − | 0.188982i | ||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | −1.00000 | + | 3.46410i | −0.196116 | + | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 5.50000 | − | 9.52628i | 0.904194 | − | 1.56611i | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) |
0.821995 | − | 0.569495i | \(-0.192861\pi\) | |||||||
\(38\) | −0.500000 | + | 0.866025i | −0.0811107 | + | 0.140488i | ||||
\(39\) | −3.50000 | + | 0.866025i | −0.560449 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | + | 1.73205i | 0.156174 | + | 0.270501i | 0.933486 | − | 0.358614i | \(-0.116751\pi\) |
−0.777312 | + | 0.629115i | \(0.783417\pi\) | |||||||
\(42\) | −0.500000 | + | 2.59808i | −0.0771517 | + | 0.400892i | ||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | 1.00000 | + | 1.73205i | 0.150756 | + | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | + | 3.46410i | 0.294884 | + | 0.510754i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 2.50000 | + | 4.33013i | 0.353553 | + | 0.612372i | ||||
\(51\) | 2.00000 | + | 3.46410i | 0.280056 | + | 0.485071i | ||||
\(52\) | −2.50000 | − | 2.59808i | −0.346688 | − | 0.360288i | ||||
\(53\) | −2.00000 | + | 3.46410i | −0.274721 | + | 0.475831i | −0.970065 | − | 0.242846i | \(-0.921919\pi\) |
0.695344 | + | 0.718677i | \(0.255252\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.50000 | + | 0.866025i | −0.334077 | + | 0.115728i | ||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | −2.00000 | − | 3.46410i | −0.260378 | − | 0.450988i | 0.705965 | − | 0.708247i | \(-0.250514\pi\) |
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) | ||||
0.0640184 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.50000 | + | 0.866025i | −0.314970 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | + | 1.73205i | −0.123091 | + | 0.213201i | ||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | −2.00000 | + | 3.46410i | −0.242536 | + | 0.420084i | ||||
\(69\) | −2.00000 | + | 3.46410i | −0.240772 | + | 0.417029i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | + | 5.19615i | −0.356034 | + | 0.616670i | −0.987294 | − | 0.158901i | \(-0.949205\pi\) |
0.631260 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 3.50000 | − | 6.06218i | 0.409644 | − | 0.709524i | −0.585206 | − | 0.810885i | \(-0.698986\pi\) |
0.994850 | + | 0.101361i | \(0.0323196\pi\) | |||||||
\(74\) | 5.50000 | + | 9.52628i | 0.639362 | + | 1.10741i | ||||
\(75\) | −2.50000 | + | 4.33013i | −0.288675 | + | 0.500000i | ||||
\(76\) | −0.500000 | − | 0.866025i | −0.0573539 | − | 0.0993399i | ||||
\(77\) | 5.00000 | − | 1.73205i | 0.569803 | − | 0.197386i | ||||
\(78\) | 1.00000 | − | 3.46410i | 0.113228 | − | 0.392232i | ||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.00000 | −0.220863 | ||||||||
\(83\) | −14.0000 | −1.53670 | −0.768350 | − | 0.640030i | \(-0.778922\pi\) | ||||
−0.768350 | + | 0.640030i | \(0.778922\pi\) | |||||||
\(84\) | −2.00000 | − | 1.73205i | −0.218218 | − | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.500000 | + | 0.866025i | 0.0539164 | + | 0.0933859i | ||||
\(87\) | 3.00000 | + | 5.19615i | 0.321634 | + | 0.557086i | ||||
\(88\) | −2.00000 | −0.213201 | ||||||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | + | 5.19615i | −0.838628 | + | 0.544705i | ||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −4.50000 | + | 7.79423i | −0.456906 | + | 0.791384i | −0.998796 | − | 0.0490655i | \(-0.984376\pi\) |
0.541890 | + | 0.840450i | \(0.317709\pi\) | |||||||
\(98\) | 1.00000 | + | 6.92820i | 0.101015 | + | 0.699854i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | −18.0000 | −1.79107 | −0.895533 | − | 0.444994i | \(-0.853206\pi\) | ||||
−0.895533 | + | 0.444994i | \(0.853206\pi\) | |||||||
\(102\) | −4.00000 | −0.396059 | ||||||||
\(103\) | 3.50000 | + | 6.06218i | 0.344865 | + | 0.597324i | 0.985329 | − | 0.170664i | \(-0.0545913\pi\) |
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | 3.50000 | − | 0.866025i | 0.343203 | − | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | − | 3.46410i | −0.194257 | − | 0.336463i | ||||
\(107\) | 9.00000 | − | 15.5885i | 0.870063 | − | 1.50699i | 0.00813215 | − | 0.999967i | \(-0.497411\pi\) |
0.861931 | − | 0.507026i | \(-0.169255\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −5.50000 | + | 9.52628i | −0.526804 | + | 0.912452i | 0.472708 | + | 0.881219i | \(0.343277\pi\) |
−0.999512 | + | 0.0312328i | \(0.990057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.50000 | + | 9.52628i | −0.522037 | + | 0.904194i | ||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | 4.00000 | − | 6.92820i | 0.376288 | − | 0.651751i | −0.614231 | − | 0.789127i | \(-0.710534\pi\) |
0.990519 | + | 0.137376i | \(0.0438669\pi\) | |||||||
\(114\) | 0.500000 | − | 0.866025i | 0.0468293 | − | 0.0811107i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.00000 | + | 5.19615i | −0.278543 | + | 0.482451i | ||||
\(117\) | 3.50000 | − | 0.866025i | 0.323575 | − | 0.0800641i | ||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 8.00000 | + | 6.92820i | 0.733359 | + | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −0.500000 | + | 0.866025i | −0.0452679 | + | 0.0784063i | ||||
\(123\) | −1.00000 | − | 1.73205i | −0.0901670 | − | 0.156174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.500000 | − | 2.59808i | 0.0445435 | − | 0.231455i | ||||
\(127\) | −6.50000 | − | 11.2583i | −0.576782 | − | 0.999015i | −0.995846 | − | 0.0910585i | \(-0.970975\pi\) |
0.419064 | − | 0.907957i | \(-0.362358\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −0.500000 | + | 0.866025i | −0.0440225 | + | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | −1.00000 | − | 1.73205i | −0.0870388 | − | 0.150756i | ||||
\(133\) | −2.50000 | + | 0.866025i | −0.216777 | + | 0.0750939i | ||||
\(134\) | −6.00000 | + | 10.3923i | −0.518321 | + | 0.897758i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | − | 3.46410i | −0.171499 | − | 0.297044i | ||||
\(137\) | −6.00000 | − | 10.3923i | −0.512615 | − | 0.887875i | −0.999893 | − | 0.0146279i | \(-0.995344\pi\) |
0.487278 | − | 0.873247i | \(-0.337990\pi\) | |||||||
\(138\) | −2.00000 | − | 3.46410i | −0.170251 | − | 0.294884i | ||||
\(139\) | −8.00000 | + | 13.8564i | −0.678551 | + | 1.17529i | 0.296866 | + | 0.954919i | \(0.404058\pi\) |
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | −7.00000 | + | 1.73205i | −0.585369 | + | 0.144841i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.50000 | + | 6.06218i | 0.289662 | + | 0.501709i | ||||
\(147\) | −5.50000 | + | 4.33013i | −0.453632 | + | 0.357143i | ||||
\(148\) | −11.0000 | −0.904194 | ||||||||
\(149\) | 10.0000 | 0.819232 | 0.409616 | − | 0.912258i | \(-0.365663\pi\) | ||||
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(150\) | −2.50000 | − | 4.33013i | −0.204124 | − | 0.353553i | ||||
\(151\) | −2.00000 | + | 3.46410i | −0.162758 | + | 0.281905i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) |
0.773099 | + | 0.634285i | \(0.218706\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −2.00000 | − | 3.46410i | −0.161690 | − | 0.280056i | ||||
\(154\) | −1.00000 | + | 5.19615i | −0.0805823 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.50000 | + | 2.59808i | 0.200160 | + | 0.208013i | ||||
\(157\) | 3.50000 | − | 6.06218i | 0.279330 | − | 0.483814i | −0.691888 | − | 0.722005i | \(-0.743221\pi\) |
0.971219 | + | 0.238190i | \(0.0765542\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | 2.00000 | − | 3.46410i | 0.158610 | − | 0.274721i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | + | 10.3923i | −0.157622 | + | 0.819028i | ||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −11.0000 | −0.861586 | −0.430793 | − | 0.902451i | \(-0.641766\pi\) | ||||
−0.430793 | + | 0.902451i | \(0.641766\pi\) | |||||||
\(164\) | 1.00000 | − | 1.73205i | 0.0780869 | − | 0.135250i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.00000 | − | 12.1244i | 0.543305 | − | 0.941033i | ||||
\(167\) | 1.00000 | + | 1.73205i | 0.0773823 | + | 0.134030i | 0.902120 | − | 0.431486i | \(-0.142010\pi\) |
−0.824737 | + | 0.565516i | \(0.808677\pi\) | |||||||
\(168\) | 2.50000 | − | 0.866025i | 0.192879 | − | 0.0668153i | ||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | 8.00000 | 0.608229 | 0.304114 | − | 0.952636i | \(-0.401639\pi\) | ||||
0.304114 | + | 0.952636i | \(0.401639\pi\) | |||||||
\(174\) | −6.00000 | −0.454859 | ||||||||
\(175\) | −2.50000 | + | 12.9904i | −0.188982 | + | 0.981981i | ||||
\(176\) | 1.00000 | − | 1.73205i | 0.0753778 | − | 0.130558i | ||||
\(177\) | 2.00000 | + | 3.46410i | 0.150329 | + | 0.260378i | ||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | −16.0000 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | −0.500000 | − | 9.52628i | −0.0370625 | − | 0.706135i | ||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | + | 6.92820i | 0.292509 | + | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.50000 | − | 0.866025i | 0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0000 | 1.73658 | 0.868290 | − | 0.496058i | \(-0.165220\pi\) | ||||
0.868290 | + | 0.496058i | \(0.165220\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 19.0000 | 1.36765 | 0.683825 | − | 0.729646i | \(-0.260315\pi\) | ||||
0.683825 | + | 0.729646i | \(0.260315\pi\) | |||||||
\(194\) | −4.50000 | − | 7.79423i | −0.323081 | − | 0.559593i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 4.00000 | + | 6.92820i | 0.284988 | + | 0.493614i | 0.972606 | − | 0.232458i | \(-0.0746770\pi\) |
−0.687618 | + | 0.726073i | \(0.741344\pi\) | |||||||
\(198\) | 1.00000 | − | 1.73205i | 0.0710669 | − | 0.123091i | ||||
\(199\) | 1.50000 | + | 2.59808i | 0.106332 | + | 0.184173i | 0.914282 | − | 0.405079i | \(-0.132756\pi\) |
−0.807950 | + | 0.589252i | \(0.799423\pi\) | |||||||
\(200\) | 2.50000 | − | 4.33013i | 0.176777 | − | 0.306186i | ||||
\(201\) | −12.0000 | −0.846415 | ||||||||
\(202\) | 9.00000 | − | 15.5885i | 0.633238 | − | 1.09680i | ||||
\(203\) | 12.0000 | + | 10.3923i | 0.842235 | + | 0.729397i | ||||
\(204\) | 2.00000 | − | 3.46410i | 0.140028 | − | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.00000 | −0.487713 | ||||||||
\(207\) | 2.00000 | − | 3.46410i | 0.139010 | − | 0.240772i | ||||
\(208\) | −1.00000 | + | 3.46410i | −0.0693375 | + | 0.240192i | ||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.50000 | − | 11.2583i | −0.447478 | − | 0.775055i | 0.550743 | − | 0.834675i | \(-0.314345\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | 4.00000 | 0.274721 | ||||||||
\(213\) | 3.00000 | − | 5.19615i | 0.205557 | − | 0.356034i | ||||
\(214\) | 9.00000 | + | 15.5885i | 0.615227 | + | 1.06561i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.50000 | − | 9.52628i | −0.372507 | − | 0.645201i | ||||
\(219\) | −3.50000 | + | 6.06218i | −0.236508 | + | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0000 | − | 10.3923i | −0.672673 | − | 0.699062i | ||||
\(222\) | −5.50000 | − | 9.52628i | −0.369136 | − | 0.639362i | ||||
\(223\) | 8.00000 | + | 13.8564i | 0.535720 | + | 0.927894i | 0.999128 | + | 0.0417488i | \(0.0132929\pi\) |
−0.463409 | + | 0.886145i | \(0.653374\pi\) | |||||||
\(224\) | 2.00000 | + | 1.73205i | 0.133631 | + | 0.115728i | ||||
\(225\) | 2.50000 | − | 4.33013i | 0.166667 | − | 0.288675i | ||||
\(226\) | 4.00000 | + | 6.92820i | 0.266076 | + | 0.460857i | ||||
\(227\) | −9.00000 | − | 15.5885i | −0.597351 | − | 1.03464i | −0.993210 | − | 0.116331i | \(-0.962887\pi\) |
0.395860 | − | 0.918311i | \(-0.370447\pi\) | |||||||
\(228\) | 0.500000 | + | 0.866025i | 0.0331133 | + | 0.0573539i | ||||
\(229\) | 10.5000 | + | 18.1865i | 0.693860 | + | 1.20180i | 0.970564 | + | 0.240845i | \(0.0774245\pi\) |
−0.276704 | + | 0.960955i | \(0.589242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.00000 | + | 1.73205i | −0.328976 | + | 0.113961i | ||||
\(232\) | −3.00000 | − | 5.19615i | −0.196960 | − | 0.341144i | ||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | −1.00000 | + | 3.46410i | −0.0653720 | + | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | + | 3.46410i | −0.130189 | + | 0.225494i | ||||
\(237\) | 4.00000 | + | 6.92820i | 0.259828 | + | 0.450035i | ||||
\(238\) | −10.0000 | + | 3.46410i | −0.648204 | + | 0.224544i | ||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.00000 | − | 15.5885i | −0.579741 | − | 1.00414i | −0.995509 | − | 0.0946700i | \(-0.969820\pi\) |
0.415768 | − | 0.909471i | \(-0.363513\pi\) | |||||||
\(242\) | 3.50000 | − | 6.06218i | 0.224989 | − | 0.389692i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.500000 | − | 0.866025i | −0.0320092 | − | 0.0554416i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 3.50000 | − | 0.866025i | 0.222700 | − | 0.0551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.0000 | 0.887214 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0000 | + | 25.9808i | −0.946792 | + | 1.63989i | −0.194668 | + | 0.980869i | \(0.562363\pi\) |
−0.752124 | + | 0.659022i | \(0.770970\pi\) | |||||||
\(252\) | 2.00000 | + | 1.73205i | 0.125988 | + | 0.109109i | ||||
\(253\) | −4.00000 | + | 6.92820i | −0.251478 | + | 0.435572i | ||||
\(254\) | 13.0000 | 0.815693 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.00000 | − | 6.92820i | 0.249513 | − | 0.432169i | −0.713878 | − | 0.700270i | \(-0.753063\pi\) |
0.963391 | + | 0.268101i | \(0.0863961\pi\) | |||||||
\(258\) | −0.500000 | − | 0.866025i | −0.0311286 | − | 0.0539164i | ||||
\(259\) | −5.50000 | + | 28.5788i | −0.341753 | + | 1.77580i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.0000 | 1.60323 | 0.801614 | − | 0.597841i | \(-0.203975\pi\) | ||||
0.801614 | + | 0.597841i | \(0.203975\pi\) | |||||||
\(264\) | 2.00000 | 0.123091 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.500000 | − | 2.59808i | 0.0306570 | − | 0.159298i | ||||
\(267\) | 3.00000 | − | 5.19615i | 0.183597 | − | 0.317999i | ||||
\(268\) | −6.00000 | − | 10.3923i | −0.366508 | − | 0.634811i | ||||
\(269\) | 5.00000 | + | 8.66025i | 0.304855 | + | 0.528025i | 0.977229 | − | 0.212187i | \(-0.0680585\pi\) |
−0.672374 | + | 0.740212i | \(0.734725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.50000 | − | 12.9904i | 0.455593 | − | 0.789109i | −0.543130 | − | 0.839649i | \(-0.682761\pi\) |
0.998722 | + | 0.0505395i | \(0.0160941\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 8.00000 | − | 5.19615i | 0.484182 | − | 0.314485i | ||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | −5.00000 | + | 8.66025i | −0.301511 | + | 0.522233i | ||||
\(276\) | 4.00000 | 0.240772 | ||||||||
\(277\) | −9.50000 | − | 16.4545i | −0.570800 | − | 0.988654i | −0.996484 | − | 0.0837823i | \(-0.973300\pi\) |
0.425684 | − | 0.904872i | \(-0.360033\pi\) | |||||||
\(278\) | −8.00000 | − | 13.8564i | −0.479808 | − | 0.831052i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.0000 | −1.48610 | −0.743048 | − | 0.669238i | \(-0.766621\pi\) | ||||
−0.743048 | + | 0.669238i | \(0.766621\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | − | 6.92820i | 0.118262 | − | 0.409673i | ||||
\(287\) | −4.00000 | − | 3.46410i | −0.236113 | − | 0.204479i | ||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.50000 | − | 7.79423i | 0.263795 | − | 0.456906i | ||||
\(292\) | −7.00000 | −0.409644 | ||||||||
\(293\) | 6.00000 | − | 10.3923i | 0.350524 | − | 0.607125i | −0.635818 | − | 0.771839i | \(-0.719337\pi\) |
0.986341 | + | 0.164714i | \(0.0526703\pi\) | |||||||
\(294\) | −1.00000 | − | 6.92820i | −0.0583212 | − | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.50000 | − | 9.52628i | 0.319681 | − | 0.553704i | ||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | −5.00000 | + | 8.66025i | −0.289642 | + | 0.501675i | ||||
\(299\) | 4.00000 | − | 13.8564i | 0.231326 | − | 0.801337i | ||||
\(300\) | 5.00000 | 0.288675 | ||||||||
\(301\) | −0.500000 | + | 2.59808i | −0.0288195 | + | 0.149751i | ||||
\(302\) | −2.00000 | − | 3.46410i | −0.115087 | − | 0.199337i | ||||
\(303\) | 18.0000 | 1.03407 | ||||||||
\(304\) | −0.500000 | + | 0.866025i | −0.0286770 | + | 0.0496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.00000 | 0.228665 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | −4.00000 | − | 3.46410i | −0.227921 | − | 0.197386i | ||||
\(309\) | −3.50000 | − | 6.06218i | −0.199108 | − | 0.344865i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.0000 | − | 24.2487i | 0.793867 | − | 1.37502i | −0.129689 | − | 0.991555i | \(-0.541398\pi\) |
0.923556 | − | 0.383464i | \(-0.125269\pi\) | |||||||
\(312\) | −3.50000 | + | 0.866025i | −0.198148 | + | 0.0490290i | ||||
\(313\) | 10.5000 | + | 18.1865i | 0.593495 | + | 1.02796i | 0.993757 | + | 0.111563i | \(0.0355857\pi\) |
−0.400262 | + | 0.916401i | \(0.631081\pi\) | |||||||
\(314\) | 3.50000 | + | 6.06218i | 0.197516 | + | 0.342108i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | + | 6.92820i | −0.225018 | + | 0.389742i | ||||
\(317\) | −4.00000 | − | 6.92820i | −0.224662 | − | 0.389127i | 0.731556 | − | 0.681782i | \(-0.238795\pi\) |
−0.956218 | + | 0.292655i | \(0.905461\pi\) | |||||||
\(318\) | 2.00000 | + | 3.46410i | 0.112154 | + | 0.194257i | ||||
\(319\) | 6.00000 | + | 10.3923i | 0.335936 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | + | 15.5885i | −0.502331 | + | 0.870063i | ||||
\(322\) | −8.00000 | − | 6.92820i | −0.445823 | − | 0.386094i | ||||
\(323\) | −2.00000 | − | 3.46410i | −0.111283 | − | 0.192748i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 5.00000 | − | 17.3205i | 0.277350 | − | 0.960769i | ||||
\(326\) | 5.50000 | − | 9.52628i | 0.304617 | − | 0.527612i | ||||
\(327\) | 5.50000 | − | 9.52628i | 0.304151 | − | 0.526804i | ||||
\(328\) | 1.00000 | + | 1.73205i | 0.0552158 | + | 0.0956365i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0000 | −0.604615 | −0.302307 | − | 0.953211i | \(-0.597757\pi\) | ||||
−0.302307 | + | 0.953211i | \(0.597757\pi\) | |||||||
\(332\) | 7.00000 | + | 12.1244i | 0.384175 | + | 0.665410i | ||||
\(333\) | 5.50000 | − | 9.52628i | 0.301398 | − | 0.522037i | ||||
\(334\) | −2.00000 | −0.109435 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.500000 | + | 2.59808i | −0.0272772 | + | 0.141737i | ||||
\(337\) | 9.00000 | 0.490261 | 0.245131 | − | 0.969490i | \(-0.421169\pi\) | ||||
0.245131 | + | 0.969490i | \(0.421169\pi\) | |||||||
\(338\) | −0.500000 | + | 12.9904i | −0.0271964 | + | 0.706584i | ||||
\(339\) | −4.00000 | + | 6.92820i | −0.217250 | + | 0.376288i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.500000 | + | 0.866025i | −0.0270369 | + | 0.0468293i | ||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0.500000 | − | 0.866025i | 0.0269582 | − | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.00000 | + | 6.92820i | −0.215041 | + | 0.372463i | ||||
\(347\) | −13.0000 | − | 22.5167i | −0.697877 | − | 1.20876i | −0.969201 | − | 0.246270i | \(-0.920795\pi\) |
0.271325 | − | 0.962488i | \(-0.412538\pi\) | |||||||
\(348\) | 3.00000 | − | 5.19615i | 0.160817 | − | 0.278543i | ||||
\(349\) | −2.50000 | − | 4.33013i | −0.133822 | − | 0.231786i | 0.791325 | − | 0.611396i | \(-0.209392\pi\) |
−0.925147 | + | 0.379610i | \(0.876058\pi\) | |||||||
\(350\) | −10.0000 | − | 8.66025i | −0.534522 | − | 0.462910i | ||||
\(351\) | −3.50000 | + | 0.866025i | −0.186816 | + | 0.0462250i | ||||
\(352\) | 1.00000 | + | 1.73205i | 0.0533002 | + | 0.0923186i | ||||
\(353\) | −4.00000 | −0.212899 | −0.106449 | − | 0.994318i | \(-0.533948\pi\) | ||||
−0.106449 | + | 0.994318i | \(0.533948\pi\) | |||||||
\(354\) | −4.00000 | −0.212598 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −8.00000 | − | 6.92820i | −0.423405 | − | 0.366679i | ||||
\(358\) | 8.00000 | − | 13.8564i | 0.422813 | − | 0.732334i | ||||
\(359\) | 3.00000 | + | 5.19615i | 0.158334 | + | 0.274242i | 0.934268 | − | 0.356572i | \(-0.116054\pi\) |
−0.775934 | + | 0.630814i | \(0.782721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | −3.50000 | + | 6.06218i | −0.183956 | + | 0.318621i | ||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 8.50000 | + | 4.33013i | 0.445521 | + | 0.226960i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.500000 | − | 0.866025i | 0.0261354 | − | 0.0452679i | ||||
\(367\) | −25.0000 | −1.30499 | −0.652495 | − | 0.757793i | \(-0.726278\pi\) | ||||
−0.652495 | + | 0.757793i | \(0.726278\pi\) | |||||||
\(368\) | 2.00000 | + | 3.46410i | 0.104257 | + | 0.180579i | ||||
\(369\) | 1.00000 | + | 1.73205i | 0.0520579 | + | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | − | 10.3923i | 0.103835 | − | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0000 | −0.932005 | −0.466002 | − | 0.884783i | \(-0.654306\pi\) | ||||
−0.466002 | + | 0.884783i | \(0.654306\pi\) | |||||||
\(374\) | −8.00000 | −0.413670 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0000 | − | 15.5885i | −0.772539 | − | 0.802846i | ||||
\(378\) | −0.500000 | + | 2.59808i | −0.0257172 | + | 0.133631i | ||||
\(379\) | −10.0000 | − | 17.3205i | −0.513665 | − | 0.889695i | −0.999874 | − | 0.0158521i | \(-0.994954\pi\) |
0.486209 | − | 0.873843i | \(-0.338379\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.50000 | + | 11.2583i | 0.333005 | + | 0.576782i | ||||
\(382\) | −12.0000 | + | 20.7846i | −0.613973 | + | 1.06343i | ||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.50000 | + | 16.4545i | −0.483537 | + | 0.837511i | ||||
\(387\) | 0.500000 | − | 0.866025i | 0.0254164 | − | 0.0440225i | ||||
\(388\) | 9.00000 | 0.456906 | ||||||||
\(389\) | −2.00000 | + | 3.46410i | −0.101404 | + | 0.175637i | −0.912263 | − | 0.409604i | \(-0.865667\pi\) |
0.810859 | + | 0.585241i | \(0.199000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 5.50000 | − | 4.33013i | 0.277792 | − | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.00000 | −0.403034 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000 | + | 1.73205i | 0.0502519 | + | 0.0870388i | ||||
\(397\) | 1.00000 | 0.0501886 | 0.0250943 | − | 0.999685i | \(-0.492011\pi\) | ||||
0.0250943 | + | 0.999685i | \(0.492011\pi\) | |||||||
\(398\) | −3.00000 | −0.150376 | ||||||||
\(399\) | 2.50000 | − | 0.866025i | 0.125157 | − | 0.0433555i | ||||
\(400\) | 2.50000 | + | 4.33013i | 0.125000 | + | 0.216506i | ||||
\(401\) | −5.00000 | + | 8.66025i | −0.249688 | + | 0.432472i | −0.963439 | − | 0.267927i | \(-0.913661\pi\) |
0.713751 | + | 0.700399i | \(0.246995\pi\) | |||||||
\(402\) | 6.00000 | − | 10.3923i | 0.299253 | − | 0.518321i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 9.00000 | + | 15.5885i | 0.447767 | + | 0.775555i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | + | 5.19615i | −0.744438 | + | 0.257881i | ||||
\(407\) | −11.0000 | + | 19.0526i | −0.545250 | + | 0.944400i | ||||
\(408\) | 2.00000 | + | 3.46410i | 0.0990148 | + | 0.171499i | ||||
\(409\) | 15.5000 | + | 26.8468i | 0.766426 | + | 1.32749i | 0.939490 | + | 0.342578i | \(0.111300\pi\) |
−0.173064 | + | 0.984911i | \(0.555367\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | + | 10.3923i | 0.295958 | + | 0.512615i | ||||
\(412\) | 3.50000 | − | 6.06218i | 0.172433 | − | 0.298662i | ||||
\(413\) | 8.00000 | + | 6.92820i | 0.393654 | + | 0.340915i | ||||
\(414\) | 2.00000 | + | 3.46410i | 0.0982946 | + | 0.170251i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.50000 | − | 2.59808i | −0.122573 | − | 0.127381i | ||||
\(417\) | 8.00000 | − | 13.8564i | 0.391762 | − | 0.678551i | ||||
\(418\) | 1.00000 | − | 1.73205i | 0.0489116 | − | 0.0847174i | ||||
\(419\) | −13.0000 | − | 22.5167i | −0.635092 | − | 1.10001i | −0.986496 | − | 0.163787i | \(-0.947629\pi\) |
0.351404 | − | 0.936224i | \(-0.385704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 13.0000 | 0.632830 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | + | 3.46410i | −0.0971286 | + | 0.168232i | ||||
\(425\) | −20.0000 | −0.970143 | ||||||||
\(426\) | 3.00000 | + | 5.19615i | 0.145350 | + | 0.251754i | ||||
\(427\) | −2.50000 | + | 0.866025i | −0.120983 | + | 0.0419099i | ||||
\(428\) | −18.0000 | −0.870063 | ||||||||
\(429\) | 7.00000 | − | 1.73205i | 0.337963 | − | 0.0836242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.0000 | 1.25238 | 0.626188 | − | 0.779672i | \(-0.284614\pi\) | ||||
0.626188 | + | 0.779672i | \(0.284614\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 13.0000 | − | 22.5167i | 0.624740 | − | 1.08208i | −0.363851 | − | 0.931457i | \(-0.618538\pi\) |
0.988591 | − | 0.150624i | \(-0.0481284\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.0000 | 0.526804 | ||||||||
\(437\) | 2.00000 | − | 3.46410i | 0.0956730 | − | 0.165710i | ||||
\(438\) | −3.50000 | − | 6.06218i | −0.167236 | − | 0.289662i | ||||
\(439\) | 0.500000 | − | 0.866025i | 0.0238637 | − | 0.0413331i | −0.853847 | − | 0.520524i | \(-0.825737\pi\) |
0.877711 | + | 0.479191i | \(0.159070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | 14.0000 | − | 3.46410i | 0.665912 | − | 0.164771i | ||||
\(443\) | −4.00000 | − | 6.92820i | −0.190046 | − | 0.329169i | 0.755219 | − | 0.655472i | \(-0.227530\pi\) |
−0.945265 | + | 0.326303i | \(0.894197\pi\) | |||||||
\(444\) | 11.0000 | 0.522037 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.0000 | −0.757622 | ||||||||
\(447\) | −10.0000 | −0.472984 | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | −17.0000 | + | 29.4449i | −0.802280 | + | 1.38959i | 0.115833 | + | 0.993269i | \(0.463046\pi\) |
−0.918112 | + | 0.396320i | \(0.870287\pi\) | |||||||
\(450\) | 2.50000 | + | 4.33013i | 0.117851 | + | 0.204124i | ||||
\(451\) | −2.00000 | − | 3.46410i | −0.0941763 | − | 0.163118i | ||||
\(452\) | −8.00000 | −0.376288 | ||||||||
\(453\) | 2.00000 | − | 3.46410i | 0.0939682 | − | 0.162758i | ||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −19.0000 | + | 32.9090i | −0.888783 | + | 1.53942i | −0.0474665 | + | 0.998873i | \(0.515115\pi\) |
−0.841316 | + | 0.540544i | \(0.818219\pi\) | |||||||
\(458\) | −21.0000 | −0.981266 | ||||||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.00000 | + | 13.8564i | −0.372597 | + | 0.645357i | −0.989964 | − | 0.141318i | \(-0.954866\pi\) |
0.617367 | + | 0.786675i | \(0.288199\pi\) | |||||||
\(462\) | 1.00000 | − | 5.19615i | 0.0465242 | − | 0.241747i | ||||
\(463\) | 23.0000 | 1.06890 | 0.534450 | − | 0.845200i | \(-0.320519\pi\) | ||||
0.534450 | + | 0.845200i | \(0.320519\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | −0.277945 | ||||||||
\(467\) | −21.0000 | − | 36.3731i | −0.971764 | − | 1.68314i | −0.690225 | − | 0.723595i | \(-0.742488\pi\) |
−0.281539 | − | 0.959550i | \(-0.590845\pi\) | |||||||
\(468\) | −2.50000 | − | 2.59808i | −0.115563 | − | 0.120096i | ||||
\(469\) | −30.0000 | + | 10.3923i | −1.38527 | + | 0.479872i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.50000 | + | 6.06218i | −0.161271 | + | 0.279330i | ||||
\(472\) | −2.00000 | − | 3.46410i | −0.0920575 | − | 0.159448i | ||||
\(473\) | −1.00000 | + | 1.73205i | −0.0459800 | + | 0.0796398i | ||||
\(474\) | −8.00000 | −0.367452 | ||||||||
\(475\) | 2.50000 | − | 4.33013i | 0.114708 | − | 0.198680i | ||||
\(476\) | 2.00000 | − | 10.3923i | 0.0916698 | − | 0.476331i | ||||
\(477\) | −2.00000 | + | 3.46410i | −0.0915737 | + | 0.158610i | ||||
\(478\) | −1.00000 | + | 1.73205i | −0.0457389 | + | 0.0792222i | ||||
\(479\) | 10.0000 | 0.456912 | 0.228456 | − | 0.973554i | \(-0.426632\pi\) | ||||
0.228456 | + | 0.973554i | \(0.426632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.0000 | − | 38.1051i | 0.501557 | − | 1.73744i | ||||
\(482\) | 18.0000 | 0.819878 | ||||||||
\(483\) | 2.00000 | − | 10.3923i | 0.0910032 | − | 0.472866i | ||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 11.5000 | + | 19.9186i | 0.521115 | + | 0.902597i | 0.999698 | + | 0.0245553i | \(0.00781698\pi\) |
−0.478584 | + | 0.878042i | \(0.658850\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | 11.0000 | 0.497437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0000 | + | 19.0526i | 0.496423 | + | 0.859830i | 0.999991 | − | 0.00412539i | \(-0.00131316\pi\) |
−0.503568 | + | 0.863955i | \(0.667980\pi\) | |||||||
\(492\) | −1.00000 | + | 1.73205i | −0.0450835 | + | 0.0780869i | ||||
\(493\) | −12.0000 | + | 20.7846i | −0.540453 | + | 0.936092i | ||||
\(494\) | −1.00000 | + | 3.46410i | −0.0449921 | + | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.00000 | − | 15.5885i | 0.134568 | − | 0.699238i | ||||
\(498\) | −7.00000 | + | 12.1244i | −0.313678 | + | 0.543305i | ||||
\(499\) | −0.500000 | − | 0.866025i | −0.0223831 | − | 0.0387686i | 0.854617 | − | 0.519259i | \(-0.173792\pi\) |
−0.877000 | + | 0.480490i | \(0.840459\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | − | 1.73205i | −0.0446767 | − | 0.0773823i | ||||
\(502\) | −15.0000 | − | 25.9808i | −0.669483 | − | 1.15958i | ||||
\(503\) | −15.0000 | + | 25.9808i | −0.668817 | + | 1.15842i | 0.309418 | + | 0.950926i | \(0.399866\pi\) |
−0.978235 | + | 0.207499i | \(0.933468\pi\) | |||||||
\(504\) | −2.50000 | + | 0.866025i | −0.111359 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.00000 | − | 6.92820i | −0.177822 | − | 0.307996i | ||||
\(507\) | −11.5000 | + | 6.06218i | −0.510733 | + | 0.269231i | ||||
\(508\) | −6.50000 | + | 11.2583i | −0.288391 | + | 0.499508i | ||||
\(509\) | −3.00000 | + | 5.19615i | −0.132973 | + | 0.230315i | −0.924821 | − | 0.380402i | \(-0.875786\pi\) |
0.791849 | + | 0.610718i | \(0.209119\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.50000 | + | 18.1865i | −0.154831 | + | 0.804525i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 4.00000 | + | 6.92820i | 0.176432 | + | 0.305590i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.00000 | 0.0440225 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −22.0000 | − | 19.0526i | −0.966625 | − | 0.837121i | ||||
\(519\) | −8.00000 | −0.351161 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.0000 | + | 24.2487i | −0.613351 | + | 1.06236i | 0.377320 | + | 0.926083i | \(0.376846\pi\) |
−0.990671 | + | 0.136272i | \(0.956488\pi\) | |||||||
\(522\) | 6.00000 | 0.262613 | ||||||||
\(523\) | 0.500000 | − | 0.866025i | 0.0218635 | − | 0.0378686i | −0.854887 | − | 0.518815i | \(-0.826373\pi\) |
0.876750 | + | 0.480946i | \(0.159707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.50000 | − | 12.9904i | 0.109109 | − | 0.566947i | ||||
\(526\) | −13.0000 | + | 22.5167i | −0.566827 | + | 0.981773i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.00000 | + | 1.73205i | −0.0435194 | + | 0.0753778i | ||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.00000 | − | 3.46410i | −0.0867926 | − | 0.150329i | ||||
\(532\) | 2.00000 | + | 1.73205i | 0.0867110 | + | 0.0750939i | ||||
\(533\) | 5.00000 | + | 5.19615i | 0.216574 | + | 0.225070i | ||||
\(534\) | 3.00000 | + | 5.19615i | 0.129823 | + | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.0000 | 0.518321 | ||||||||
\(537\) | 16.0000 | 0.690451 | ||||||||
\(538\) | −10.0000 | −0.431131 | ||||||||
\(539\) | −11.0000 | + | 8.66025i | −0.473804 | + | 0.373024i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.5000 | − | 37.2391i | −0.924357 | − | 1.60103i | −0.792592 | − | 0.609753i | \(-0.791269\pi\) |
−0.131765 | − | 0.991281i | \(-0.542065\pi\) | |||||||
\(542\) | 7.50000 | + | 12.9904i | 0.322153 | + | 0.557985i | ||||
\(543\) | −7.00000 | −0.300399 | ||||||||
\(544\) | −2.00000 | + | 3.46410i | −0.0857493 | + | 0.148522i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.500000 | + | 9.52628i | 0.0213980 | + | 0.407687i | ||||
\(547\) | −5.00000 | −0.213785 | −0.106892 | − | 0.994271i | \(-0.534090\pi\) | ||||
−0.106892 | + | 0.994271i | \(0.534090\pi\) | |||||||
\(548\) | −6.00000 | + | 10.3923i | −0.256307 | + | 0.443937i | ||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −5.00000 | − | 8.66025i | −0.213201 | − | 0.369274i | ||||
\(551\) | −3.00000 | − | 5.19615i | −0.127804 | − | 0.221364i | ||||
\(552\) | −2.00000 | + | 3.46410i | −0.0851257 | + | 0.147442i | ||||
\(553\) | 16.0000 | + | 13.8564i | 0.680389 | + | 0.589234i | ||||
\(554\) | 19.0000 | 0.807233 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.0000 | 0.678551 | ||||||||
\(557\) | −30.0000 | −1.27114 | −0.635570 | − | 0.772043i | \(-0.719235\pi\) | ||||
−0.635570 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00000 | − | 3.46410i | 0.0422955 | − | 0.146516i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | − | 6.92820i | −0.168880 | − | 0.292509i | ||||
\(562\) | −15.0000 | + | 25.9808i | −0.632737 | + | 1.09593i | ||||
\(563\) | 12.0000 | + | 20.7846i | 0.505740 | + | 0.875967i | 0.999978 | + | 0.00664037i | \(0.00211371\pi\) |
−0.494238 | + | 0.869326i | \(0.664553\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.5000 | − | 21.6506i | 0.525414 | − | 0.910044i | ||||
\(567\) | −2.50000 | + | 0.866025i | −0.104990 | + | 0.0363696i | ||||
\(568\) | −3.00000 | + | 5.19615i | −0.125877 | + | 0.218026i | ||||
\(569\) | 2.00000 | − | 3.46410i | 0.0838444 | − | 0.145223i | −0.821054 | − | 0.570851i | \(-0.806613\pi\) |
0.904898 | + | 0.425628i | \(0.139947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.5000 | + | 21.6506i | −0.523109 | + | 0.906051i | 0.476530 | + | 0.879158i | \(0.341895\pi\) |
−0.999638 | + | 0.0268925i | \(0.991439\pi\) | |||||||
\(572\) | 5.00000 | + | 5.19615i | 0.209061 | + | 0.217262i | ||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | 5.00000 | − | 1.73205i | 0.208696 | − | 0.0722944i | ||||
\(575\) | −10.0000 | − | 17.3205i | −0.417029 | − | 0.722315i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −3.50000 | + | 6.06218i | −0.145707 | + | 0.252372i | −0.929636 | − | 0.368478i | \(-0.879879\pi\) |
0.783930 | + | 0.620850i | \(0.213212\pi\) | |||||||
\(578\) | 0.500000 | + | 0.866025i | 0.0207973 | + | 0.0360219i | ||||
\(579\) | −19.0000 | −0.789613 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.0000 | − | 12.1244i | 1.45204 | − | 0.503003i | ||||
\(582\) | 4.50000 | + | 7.79423i | 0.186531 | + | 0.323081i | ||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | 3.50000 | − | 6.06218i | 0.144831 | − | 0.250855i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | + | 10.3923i | 0.247858 | + | 0.429302i | ||||
\(587\) | 15.0000 | + | 25.9808i | 0.619116 | + | 1.07234i | 0.989647 | + | 0.143521i | \(0.0458424\pi\) |
−0.370531 | + | 0.928820i | \(0.620824\pi\) | |||||||
\(588\) | 6.50000 | + | 2.59808i | 0.268055 | + | 0.107143i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.00000 | − | 6.92820i | −0.164538 | − | 0.284988i | ||||
\(592\) | 5.50000 | + | 9.52628i | 0.226049 | + | 0.391528i | ||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | −1.00000 | + | 1.73205i | −0.0410305 | + | 0.0710669i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.00000 | − | 8.66025i | −0.204808 | − | 0.354738i | ||||
\(597\) | −1.50000 | − | 2.59808i | −0.0613909 | − | 0.106332i | ||||
\(598\) | 10.0000 | + | 10.3923i | 0.408930 | + | 0.424973i | ||||
\(599\) | 5.00000 | − | 8.66025i | 0.204294 | − | 0.353848i | −0.745613 | − | 0.666379i | \(-0.767843\pi\) |
0.949908 | + | 0.312531i | \(0.101177\pi\) | |||||||
\(600\) | −2.50000 | + | 4.33013i | −0.102062 | + | 0.176777i | ||||
\(601\) | −9.50000 | − | 16.4545i | −0.387513 | − | 0.671192i | 0.604601 | − | 0.796528i | \(-0.293332\pi\) |
−0.992114 | + | 0.125336i | \(0.959999\pi\) | |||||||
\(602\) | −2.00000 | − | 1.73205i | −0.0815139 | − | 0.0705931i | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.00000 | + | 15.5885i | −0.365600 | + | 0.633238i | ||||
\(607\) | 1.00000 | 0.0405887 | 0.0202944 | − | 0.999794i | \(-0.493540\pi\) | ||||
0.0202944 | + | 0.999794i | \(0.493540\pi\) | |||||||
\(608\) | −0.500000 | − | 0.866025i | −0.0202777 | − | 0.0351220i | ||||
\(609\) | −12.0000 | − | 10.3923i | −0.486265 | − | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.00000 | + | 3.46410i | −0.0808452 | + | 0.140028i | ||||
\(613\) | 5.00000 | 0.201948 | 0.100974 | − | 0.994889i | \(-0.467804\pi\) | ||||
0.100974 | + | 0.994889i | \(0.467804\pi\) | |||||||
\(614\) | −14.0000 | + | 24.2487i | −0.564994 | + | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.00000 | − | 1.73205i | 0.201456 | − | 0.0697863i | ||||
\(617\) | −3.00000 | + | 5.19615i | −0.120775 | + | 0.209189i | −0.920074 | − | 0.391745i | \(-0.871871\pi\) |
0.799298 | + | 0.600935i | \(0.205205\pi\) | |||||||
\(618\) | 7.00000 | 0.281581 | ||||||||
\(619\) | 17.5000 | − | 30.3109i | 0.703384 | − | 1.21830i | −0.263887 | − | 0.964554i | \(-0.585005\pi\) |
0.967271 | − | 0.253744i | \(-0.0816620\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | + | 3.46410i | −0.0802572 | + | 0.139010i | ||||
\(622\) | 14.0000 | + | 24.2487i | 0.561349 | + | 0.972285i | ||||
\(623\) | 3.00000 | − | 15.5885i | 0.120192 | − | 0.624538i | ||||
\(624\) | 1.00000 | − | 3.46410i | 0.0400320 | − | 0.138675i | ||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −21.0000 | −0.839329 | ||||||||
\(627\) | 2.00000 | 0.0798723 | ||||||||
\(628\) | −7.00000 | −0.279330 | ||||||||
\(629\) | −44.0000 | −1.75439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.500000 | − | 0.866025i | 0.0199047 | − | 0.0344759i | −0.855901 | − | 0.517139i | \(-0.826997\pi\) |
0.875806 | + | 0.482663i | \(0.160330\pi\) | |||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | 6.50000 | + | 11.2583i | 0.258352 | + | 0.447478i | ||||
\(634\) | 8.00000 | 0.317721 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | 15.5000 | − | 19.9186i | 0.614132 | − | 0.789203i | ||||
\(638\) | −12.0000 | −0.475085 | ||||||||
\(639\) | −3.00000 | + | 5.19615i | −0.118678 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | + | 25.9808i | 0.592464 | + | 1.02618i | 0.993899 | + | 0.110291i | \(0.0351782\pi\) |
−0.401435 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(642\) | −9.00000 | − | 15.5885i | −0.355202 | − | 0.615227i | ||||
\(643\) | 16.5000 | − | 28.5788i | 0.650696 | − | 1.12704i | −0.332258 | − | 0.943189i | \(-0.607810\pi\) |
0.982954 | − | 0.183851i | \(-0.0588563\pi\) | |||||||
\(644\) | 10.0000 | − | 3.46410i | 0.394055 | − | 0.136505i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.00000 | 0.157378 | ||||||||
\(647\) | 24.0000 | 0.943537 | 0.471769 | − | 0.881722i | \(-0.343616\pi\) | ||||
0.471769 | + | 0.881722i | \(0.343616\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 4.00000 | + | 6.92820i | 0.157014 | + | 0.271956i | ||||
\(650\) | 12.5000 | + | 12.9904i | 0.490290 | + | 0.509525i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.50000 | + | 9.52628i | 0.215397 | + | 0.373078i | ||||
\(653\) | 2.00000 | − | 3.46410i | 0.0782660 | − | 0.135561i | −0.824236 | − | 0.566247i | \(-0.808395\pi\) |
0.902502 | + | 0.430686i | \(0.141728\pi\) | |||||||
\(654\) | 5.50000 | + | 9.52628i | 0.215067 | + | 0.372507i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.00000 | −0.0780869 | ||||||||
\(657\) | 3.50000 | − | 6.06218i | 0.136548 | − | 0.236508i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0000 | − | 31.1769i | 0.701180 | − | 1.21448i | −0.266872 | − | 0.963732i | \(-0.585990\pi\) |
0.968052 | − | 0.250748i | \(-0.0806766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.0000 | 1.47803 | 0.739014 | − | 0.673690i | \(-0.235292\pi\) | ||||
0.739014 | + | 0.673690i | \(0.235292\pi\) | |||||||
\(662\) | 5.50000 | − | 9.52628i | 0.213764 | − | 0.370249i | ||||
\(663\) | 10.0000 | + | 10.3923i | 0.388368 | + | 0.403604i | ||||
\(664\) | −14.0000 | −0.543305 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.50000 | + | 9.52628i | 0.213121 | + | 0.369136i | ||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | 1.00000 | − | 1.73205i | 0.0386912 | − | 0.0670151i | ||||
\(669\) | −8.00000 | − | 13.8564i | −0.309298 | − | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | −2.00000 | − | 1.73205i | −0.0771517 | − | 0.0668153i | ||||
\(673\) | 14.5000 | + | 25.1147i | 0.558934 | + | 0.968102i | 0.997586 | + | 0.0694449i | \(0.0221228\pi\) |
−0.438652 | + | 0.898657i | \(0.644544\pi\) | |||||||
\(674\) | −4.50000 | + | 7.79423i | −0.173334 | + | 0.300222i | ||||
\(675\) | −2.50000 | + | 4.33013i | −0.0962250 | + | 0.166667i | ||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | 7.00000 | + | 12.1244i | 0.269032 | + | 0.465977i | 0.968612 | − | 0.248577i | \(-0.0799630\pi\) |
−0.699580 | + | 0.714554i | \(0.746630\pi\) | |||||||
\(678\) | −4.00000 | − | 6.92820i | −0.153619 | − | 0.266076i | ||||
\(679\) | 4.50000 | − | 23.3827i | 0.172694 | − | 0.897345i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00000 | + | 15.5885i | 0.344881 | + | 0.597351i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.00000 | + | 13.8564i | 0.306111 | + | 0.530201i | 0.977508 | − | 0.210898i | \(-0.0676386\pi\) |
−0.671397 | + | 0.741098i | \(0.734305\pi\) | |||||||
\(684\) | −0.500000 | − | 0.866025i | −0.0191180 | − | 0.0331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | −10.5000 | − | 18.1865i | −0.400600 | − | 0.693860i | ||||
\(688\) | 0.500000 | + | 0.866025i | 0.0190623 | + | 0.0330169i | ||||
\(689\) | −4.00000 | + | 13.8564i | −0.152388 | + | 0.527887i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5000 | + | 35.5070i | −0.779857 | + | 1.35075i | 0.152167 | + | 0.988355i | \(0.451375\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | −4.00000 | − | 6.92820i | −0.152057 | − | 0.263371i | ||||
\(693\) | 5.00000 | − | 1.73205i | 0.189934 | − | 0.0657952i | ||||
\(694\) | 26.0000 | 0.986947 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.00000 | + | 5.19615i | 0.113715 | + | 0.196960i | ||||
\(697\) | 4.00000 | − | 6.92820i | 0.151511 | − | 0.262424i | ||||
\(698\) | 5.00000 | 0.189253 | ||||||||
\(699\) | −3.00000 | − | 5.19615i | −0.113470 | − | 0.196537i | ||||
\(700\) | 12.5000 | − | 4.33013i | 0.472456 | − | 0.163663i | ||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 1.00000 | − | 3.46410i | 0.0377426 | − | 0.130744i | ||||
\(703\) | 5.50000 | − | 9.52628i | 0.207436 | − | 0.359290i | ||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.00000 | − | 3.46410i | 0.0752710 | − | 0.130373i | ||||
\(707\) | 45.0000 | − | 15.5885i | 1.69240 | − | 0.586264i | ||||
\(708\) | 2.00000 | − | 3.46410i | 0.0751646 | − | 0.130189i | ||||
\(709\) | −25.0000 | −0.938895 | −0.469447 | − | 0.882960i | \(-0.655547\pi\) | ||||
−0.469447 | + | 0.882960i | \(0.655547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | − | 6.92820i | −0.150012 | − | 0.259828i | ||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 10.0000 | − | 3.46410i | 0.374241 | − | 0.129641i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.00000 | + | 13.8564i | 0.298974 | + | 0.517838i | ||||
\(717\) | −2.00000 | −0.0746914 | ||||||||
\(718\) | −6.00000 | −0.223918 | ||||||||
\(719\) | 36.0000 | 1.34257 | 0.671287 | − | 0.741198i | \(-0.265742\pi\) | ||||
0.671287 | + | 0.741198i | \(0.265742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | − | 12.1244i | −0.521387 | − | 0.451535i | ||||
\(722\) | 9.00000 | − | 15.5885i | 0.334945 | − | 0.580142i | ||||
\(723\) | 9.00000 | + | 15.5885i | 0.334714 | + | 0.579741i | ||||
\(724\) | −3.50000 | − | 6.06218i | −0.130076 | − | 0.225299i | ||||
\(725\) | −30.0000 | −1.11417 | ||||||||
\(726\) | −3.50000 | + | 6.06218i | −0.129897 | + | 0.224989i | ||||
\(727\) | 28.0000 | 1.03846 | 0.519231 | − | 0.854634i | \(-0.326218\pi\) | ||||
0.519231 | + | 0.854634i | \(0.326218\pi\) | |||||||
\(728\) | −8.00000 | + | 5.19615i | −0.296500 | + | 0.192582i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | −0.147945 | ||||||||
\(732\) | 0.500000 | + | 0.866025i | 0.0184805 | + | 0.0320092i | ||||
\(733\) | −7.00000 | − | 12.1244i | −0.258551 | − | 0.447823i | 0.707303 | − | 0.706910i | \(-0.249912\pi\) |
−0.965854 | + | 0.259087i | \(0.916578\pi\) | |||||||
\(734\) | 12.5000 | − | 21.6506i | 0.461383 | − | 0.799140i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | −24.0000 | −0.884051 | ||||||||
\(738\) | −2.00000 | −0.0736210 | ||||||||
\(739\) | 5.00000 | 0.183928 | 0.0919640 | − | 0.995762i | \(-0.470686\pi\) | ||||
0.0919640 | + | 0.995762i | \(0.470686\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.50000 | + | 0.866025i | −0.128576 | + | 0.0318142i | ||||
\(742\) | 8.00000 | + | 6.92820i | 0.293689 | + | 0.254342i | ||||
\(743\) | 4.00000 | + | 6.92820i | 0.146746 | + | 0.254171i | 0.930023 | − | 0.367502i | \(-0.119787\pi\) |
−0.783277 | + | 0.621673i | \(0.786453\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.00000 | − | 15.5885i | 0.329513 | − | 0.570734i | ||||
\(747\) | −14.0000 | −0.512233 | ||||||||
\(748\) | 4.00000 | − | 6.92820i | 0.146254 | − | 0.253320i | ||||
\(749\) | −9.00000 | + | 46.7654i | −0.328853 | + | 1.70877i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5000 | − | 21.6506i | 0.456131 | − | 0.790043i | −0.542621 | − | 0.839978i | \(-0.682568\pi\) |
0.998752 | + | 0.0499348i | \(0.0159013\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.0000 | − | 25.9808i | 0.546630 | − | 0.946792i | ||||
\(754\) | 21.0000 | − | 5.19615i | 0.764775 | − | 0.189233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | − | 1.73205i | −0.0727393 | − | 0.0629941i | ||||
\(757\) | 11.0000 | + | 19.0526i | 0.399802 | + | 0.692477i | 0.993701 | − | 0.112062i | \(-0.0357456\pi\) |
−0.593899 | + | 0.804539i | \(0.702412\pi\) | |||||||
\(758\) | 20.0000 | 0.726433 | ||||||||
\(759\) | 4.00000 | − | 6.92820i | 0.145191 | − | 0.251478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.0000 | −0.724999 | −0.362500 | − | 0.931984i | \(-0.618077\pi\) | ||||
−0.362500 | + | 0.931984i | \(0.618077\pi\) | |||||||
\(762\) | −13.0000 | −0.470940 | ||||||||
\(763\) | 5.50000 | − | 28.5788i | 0.199113 | − | 1.03462i | ||||
\(764\) | −12.0000 | − | 20.7846i | −0.434145 | − | 0.751961i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.00000 | + | 6.92820i | −0.144526 | + | 0.250326i | ||||
\(767\) | −10.0000 | − | 10.3923i | −0.361079 | − | 0.375244i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −23.5000 | − | 40.7032i | −0.847432 | − | 1.46779i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
0.0360609 | − | 0.999350i | \(-0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.00000 | + | 6.92820i | −0.144056 | + | 0.249513i | ||||
\(772\) | −9.50000 | − | 16.4545i | −0.341912 | − | 0.592210i | ||||
\(773\) | 26.0000 | + | 45.0333i | 0.935155 | + | 1.61974i | 0.774357 | + | 0.632749i | \(0.218073\pi\) |
0.160798 | + | 0.986987i | \(0.448593\pi\) | |||||||
\(774\) | 0.500000 | + | 0.866025i | 0.0179721 | + | 0.0311286i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.50000 | + | 7.79423i | −0.161541 | + | 0.279797i | ||||
\(777\) | 5.50000 | − | 28.5788i | 0.197311 | − | 1.02526i | ||||
\(778\) | −2.00000 | − | 3.46410i | −0.0717035 | − | 0.124194i | ||||
\(779\) | 1.00000 | + | 1.73205i | 0.0358287 | + | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | − | 10.3923i | 0.214697 | − | 0.371866i | ||||
\(782\) | 8.00000 | − | 13.8564i | 0.286079 | − | 0.495504i | ||||
\(783\) | 3.00000 | + | 5.19615i | 0.107211 | + | 0.185695i | ||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.5000 | − | 45.8993i | −0.944623 | − | 1.63614i | −0.756504 | − | 0.653989i | \(-0.773094\pi\) |
−0.188119 | − | 0.982146i | \(-0.560239\pi\) | |||||||
\(788\) | 4.00000 | − | 6.92820i | 0.142494 | − | 0.246807i | ||||
\(789\) | −26.0000 | −0.925625 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.00000 | + | 20.7846i | −0.142224 | + | 0.739016i | ||||
\(792\) | −2.00000 | −0.0710669 | ||||||||
\(793\) | 3.50000 | − | 0.866025i | 0.124289 | − | 0.0307535i | ||||
\(794\) | −0.500000 | + | 0.866025i | −0.0177443 | + | 0.0307341i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.50000 | − | 2.59808i | 0.0531661 | − | 0.0920864i | ||||
\(797\) | 27.0000 | − | 46.7654i | 0.956389 | − | 1.65651i | 0.225232 | − | 0.974305i | \(-0.427686\pi\) |
0.731157 | − | 0.682209i | \(-0.238981\pi\) | |||||||
\(798\) | −0.500000 | + | 2.59808i | −0.0176998 | + | 0.0919709i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.00000 | −0.176777 | ||||||||
\(801\) | −3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | ||||
\(802\) | −5.00000 | − | 8.66025i | −0.176556 | − | 0.305804i | ||||
\(803\) | −7.00000 | + | 12.1244i | −0.247025 | + | 0.427859i | ||||
\(804\) | 6.00000 | + | 10.3923i | 0.211604 | + | 0.366508i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.00000 | − | 8.66025i | −0.176008 | − | 0.304855i | ||||
\(808\) | −18.0000 | −0.633238 | ||||||||
\(809\) | −2.00000 | −0.0703163 | −0.0351581 | − | 0.999382i | \(-0.511193\pi\) | ||||
−0.0351581 | + | 0.999382i | \(0.511193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.0000 | −0.737410 | −0.368705 | − | 0.929547i | \(-0.620199\pi\) | ||||
−0.368705 | + | 0.929547i | \(0.620199\pi\) | |||||||
\(812\) | 3.00000 | − | 15.5885i | 0.105279 | − | 0.547048i | ||||
\(813\) | −7.50000 | + | 12.9904i | −0.263036 | + | 0.455593i | ||||
\(814\) | −11.0000 | − | 19.0526i | −0.385550 | − | 0.667792i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 0.500000 | − | 0.866025i | 0.0174928 | − | 0.0302984i | ||||
\(818\) | −31.0000 | −1.08389 | ||||||||
\(819\) | −8.00000 | + | 5.19615i | −0.279543 | + | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.0000 | + | 45.0333i | −0.907406 | + | 1.57167i | −0.0897520 | + | 0.995964i | \(0.528607\pi\) |
−0.817654 | + | 0.575710i | \(0.804726\pi\) | |||||||
\(822\) | −12.0000 | −0.418548 | ||||||||
\(823\) | −20.0000 | − | 34.6410i | −0.697156 | − | 1.20751i | −0.969448 | − | 0.245295i | \(-0.921115\pi\) |
0.272292 | − | 0.962215i | \(-0.412218\pi\) | |||||||
\(824\) | 3.50000 | + | 6.06218i | 0.121928 | + | 0.211186i | ||||
\(825\) | 5.00000 | − | 8.66025i | 0.174078 | − | 0.301511i | ||||
\(826\) | −10.0000 | + | 3.46410i | −0.347945 | + | 0.120532i | ||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | −4.00000 | −0.139010 | ||||||||
\(829\) | 31.0000 | 1.07667 | 0.538337 | − | 0.842729i | \(-0.319053\pi\) | ||||
0.538337 | + | 0.842729i | \(0.319053\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.50000 | + | 16.4545i | 0.329551 | + | 0.570800i | ||||
\(832\) | 3.50000 | − | 0.866025i | 0.121341 | − | 0.0300240i | ||||
\(833\) | −26.0000 | − | 10.3923i | −0.900847 | − | 0.360072i | ||||
\(834\) | 8.00000 | + | 13.8564i | 0.277017 | + | 0.479808i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.00000 | + | 1.73205i | 0.0345857 | + | 0.0599042i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.0000 | 0.898155 | ||||||||
\(839\) | 20.0000 | − | 34.6410i | 0.690477 | − | 1.19594i | −0.281205 | − | 0.959648i | \(-0.590734\pi\) |
0.971682 | − | 0.236293i | \(-0.0759325\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −1.00000 | + | 1.73205i | −0.0344623 | + | 0.0596904i | ||||
\(843\) | −30.0000 | −1.03325 | ||||||||
\(844\) | −6.50000 | + | 11.2583i | −0.223739 | + | 0.387528i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.5000 | − | 6.06218i | 0.601307 | − | 0.208299i | ||||
\(848\) | −2.00000 | − | 3.46410i | −0.0686803 | − | 0.118958i | ||||
\(849\) | 25.0000 | 0.857998 | ||||||||
\(850\) | 10.0000 | − | 17.3205i | 0.342997 | − | 0.594089i | ||||
\(851\) | −22.0000 | − | 38.1051i | −0.754150 | − | 1.30623i | ||||
\(852\) | −6.00000 | −0.205557 | ||||||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 0.500000 | − | 2.59808i | 0.0171096 | − | 0.0889043i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | − | 15.5885i | 0.307614 | − | 0.532803i | ||||
\(857\) | 7.00000 | − | 12.1244i | 0.239115 | − | 0.414160i | −0.721345 | − | 0.692576i | \(-0.756476\pi\) |
0.960461 | + | 0.278416i | \(0.0898092\pi\) | |||||||
\(858\) | −2.00000 | + | 6.92820i | −0.0682789 | + | 0.236525i | ||||
\(859\) | 17.5000 | + | 30.3109i | 0.597092 | + | 1.03419i | 0.993248 | + | 0.116011i | \(0.0370107\pi\) |
−0.396156 | + | 0.918183i | \(0.629656\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.00000 | + | 3.46410i | 0.136320 | + | 0.118056i | ||||
\(862\) | −13.0000 | + | 22.5167i | −0.442782 | + | 0.766921i | ||||
\(863\) | 3.00000 | + | 5.19615i | 0.102121 | + | 0.176879i | 0.912558 | − | 0.408946i | \(-0.134104\pi\) |
−0.810437 | + | 0.585826i | \(0.800770\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.0000 | + | 22.5167i | 0.441758 | + | 0.765147i | ||||
\(867\) | −0.500000 | + | 0.866025i | −0.0169809 | + | 0.0294118i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | + | 13.8564i | 0.271381 | + | 0.470046i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.0000 | − | 10.3923i | 1.42312 | − | 0.352130i | ||||
\(872\) | −5.50000 | + | 9.52628i | −0.186254 | + | 0.322601i | ||||
\(873\) | −4.50000 | + | 7.79423i | −0.152302 | + | 0.263795i | ||||
\(874\) | 2.00000 | + | 3.46410i | 0.0676510 | + | 0.117175i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.00000 | 0.236508 | ||||||||
\(877\) | −18.0000 | −0.607817 | −0.303908 | − | 0.952701i | \(-0.598292\pi\) | ||||
−0.303908 | + | 0.952701i | \(0.598292\pi\) | |||||||
\(878\) | 0.500000 | + | 0.866025i | 0.0168742 | + | 0.0292269i | ||||
\(879\) | −6.00000 | + | 10.3923i | −0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.00000 | + | 1.73205i | 0.0336909 | + | 0.0583543i | 0.882379 | − | 0.470539i | \(-0.155941\pi\) |
−0.848688 | + | 0.528893i | \(0.822607\pi\) | |||||||
\(882\) | 1.00000 | + | 6.92820i | 0.0336718 | + | 0.233285i | ||||
\(883\) | −19.0000 | −0.639401 | −0.319700 | − | 0.947519i | \(-0.603582\pi\) | ||||
−0.319700 | + | 0.947519i | \(0.603582\pi\) | |||||||
\(884\) | −4.00000 | + | 13.8564i | −0.134535 | + | 0.466041i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.00000 | 0.268765 | ||||||||
\(887\) | −3.00000 | + | 5.19615i | −0.100730 | + | 0.174470i | −0.911986 | − | 0.410222i | \(-0.865451\pi\) |
0.811256 | + | 0.584692i | \(0.198785\pi\) | |||||||
\(888\) | −5.50000 | + | 9.52628i | −0.184568 | + | 0.319681i | ||||
\(889\) | 26.0000 | + | 22.5167i | 0.872012 | + | 0.755185i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 8.00000 | − | 13.8564i | 0.267860 | − | 0.463947i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 5.00000 | − | 8.66025i | 0.167225 | − | 0.289642i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | − | 2.59808i | 0.0167038 | − | 0.0867956i | ||||
\(897\) | −4.00000 | + | 13.8564i | −0.133556 | + | 0.462652i | ||||
\(898\) | −17.0000 | − | 29.4449i | −0.567297 | − | 0.982588i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −5.00000 | −0.166667 | ||||||||
\(901\) | 16.0000 | 0.533037 | ||||||||
\(902\) | 4.00000 | 0.133185 | ||||||||
\(903\) | 0.500000 | − | 2.59808i | 0.0166390 | − | 0.0864586i | ||||
\(904\) | 4.00000 | − | 6.92820i | 0.133038 | − | 0.230429i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.00000 | + | 3.46410i | 0.0664455 | + | 0.115087i | ||||
\(907\) | −9.00000 | −0.298840 | −0.149420 | − | 0.988774i | \(-0.547741\pi\) | ||||
−0.149420 | + | 0.988774i | \(0.547741\pi\) | |||||||
\(908\) | −9.00000 | + | 15.5885i | −0.298675 | + | 0.517321i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 0.500000 | − | 0.866025i | 0.0165567 | − | 0.0286770i | ||||
\(913\) | 28.0000 | 0.926665 | ||||||||
\(914\) | −19.0000 | − | 32.9090i | −0.628464 | − | 1.08853i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.5000 | − | 18.1865i | 0.346930 | − | 0.600900i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.00000 | −0.132020 | ||||||||
\(919\) | −11.0000 | −0.362857 | −0.181428 | − | 0.983404i | \(-0.558072\pi\) | ||||
−0.181428 | + | 0.983404i | \(0.558072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.0000 | −0.922631 | ||||||||
\(922\) | −8.00000 | − | 13.8564i | −0.263466 | − | 0.456336i | ||||
\(923\) | −6.00000 | + | 20.7846i | −0.197492 | + | 0.684134i | ||||
\(924\) | 4.00000 | + | 3.46410i | 0.131590 | + | 0.113961i | ||||
\(925\) | −27.5000 | − | 47.6314i | −0.904194 | − | 1.56611i | ||||
\(926\) | −11.5000 | + | 19.9186i | −0.377913 | + | 0.654565i | ||||
\(927\) | 3.50000 | + | 6.06218i | 0.114955 | + | 0.199108i | ||||
\(928\) | −3.00000 | + | 5.19615i | −0.0984798 | + | 0.170572i | ||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.50000 | − | 4.33013i | 0.180255 | − | 0.141914i | ||||
\(932\) | 3.00000 | − | 5.19615i | 0.0982683 | − | 0.170206i | ||||
\(933\) | −14.0000 | + | 24.2487i | −0.458339 | + | 0.793867i | ||||
\(934\) | 42.0000 | 1.37428 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.50000 | − | 0.866025i | 0.114401 | − | 0.0283069i | ||||
\(937\) | 35.0000 | 1.14340 | 0.571700 | − | 0.820463i | \(-0.306284\pi\) | ||||
0.571700 | + | 0.820463i | \(0.306284\pi\) | |||||||
\(938\) | 6.00000 | − | 31.1769i | 0.195907 | − | 1.01796i | ||||
\(939\) | −10.5000 | − | 18.1865i | −0.342655 | − | 0.593495i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.0000 | − | 48.4974i | 0.912774 | − | 1.58097i | 0.102646 | − | 0.994718i | \(-0.467269\pi\) |
0.810128 | − | 0.586253i | \(-0.199397\pi\) | |||||||
\(942\) | −3.50000 | − | 6.06218i | −0.114036 | − | 0.197516i | ||||
\(943\) | 8.00000 | 0.260516 | ||||||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.00000 | − | 1.73205i | −0.0325128 | − | 0.0563138i | ||||
\(947\) | −5.00000 | + | 8.66025i | −0.162478 | + | 0.281420i | −0.935757 | − | 0.352646i | \(-0.885282\pi\) |
0.773279 | + | 0.634066i | \(0.218615\pi\) | |||||||
\(948\) | 4.00000 | − | 6.92820i | 0.129914 | − | 0.225018i | ||||
\(949\) | 7.00000 | − | 24.2487i | 0.227230 | − | 0.787146i | ||||
\(950\) | 2.50000 | + | 4.33013i | 0.0811107 | + | 0.140488i | ||||
\(951\) | 4.00000 | + | 6.92820i | 0.129709 | + | 0.224662i | ||||
\(952\) | 8.00000 | + | 6.92820i | 0.259281 | + | 0.224544i | ||||
\(953\) | −24.0000 | + | 41.5692i | −0.777436 | + | 1.34656i | 0.155979 | + | 0.987760i | \(0.450147\pi\) |
−0.933415 | + | 0.358799i | \(0.883186\pi\) | |||||||
\(954\) | −2.00000 | − | 3.46410i | −0.0647524 | − | 0.112154i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.00000 | − | 1.73205i | −0.0323423 | − | 0.0560185i | ||||
\(957\) | −6.00000 | − | 10.3923i | −0.193952 | − | 0.335936i | ||||
\(958\) | −5.00000 | + | 8.66025i | −0.161543 | + | 0.279800i | ||||
\(959\) | 24.0000 | + | 20.7846i | 0.775000 | + | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 27.5000 | + | 28.5788i | 0.886636 | + | 0.921419i | ||||
\(963\) | 9.00000 | − | 15.5885i | 0.290021 | − | 0.502331i | ||||
\(964\) | −9.00000 | + | 15.5885i | −0.289870 | + | 0.502070i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.00000 | + | 6.92820i | 0.257396 | + | 0.222911i | ||||
\(967\) | 37.0000 | 1.18984 | 0.594920 | − | 0.803785i | \(-0.297184\pi\) | ||||
0.594920 | + | 0.803785i | \(0.297184\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 2.00000 | + | 3.46410i | 0.0642493 | + | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.0000 | 1.15529 | 0.577647 | − | 0.816286i | \(-0.303971\pi\) | ||||
0.577647 | + | 0.816286i | \(0.303971\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 8.00000 | − | 41.5692i | 0.256468 | − | 1.33265i | ||||
\(974\) | −23.0000 | −0.736968 | ||||||||
\(975\) | −5.00000 | + | 17.3205i | −0.160128 | + | 0.554700i | ||||
\(976\) | −0.500000 | + | 0.866025i | −0.0160046 | + | 0.0277208i | ||||
\(977\) | −16.0000 | −0.511885 | −0.255943 | − | 0.966692i | \(-0.582386\pi\) | ||||
−0.255943 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(978\) | −5.50000 | + | 9.52628i | −0.175871 | + | 0.304617i | ||||
\(979\) | 6.00000 | − | 10.3923i | 0.191761 | − | 0.332140i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.50000 | + | 9.52628i | −0.175601 | + | 0.304151i | ||||
\(982\) | −22.0000 | −0.702048 | ||||||||
\(983\) | −7.00000 | + | 12.1244i | −0.223265 | + | 0.386707i | −0.955798 | − | 0.294025i | \(-0.905005\pi\) |
0.732532 | + | 0.680732i | \(0.238338\pi\) | |||||||
\(984\) | −1.00000 | − | 1.73205i | −0.0318788 | − | 0.0552158i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.0000 | − | 20.7846i | −0.382158 | − | 0.661917i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.50000 | − | 2.59808i | −0.0795356 | − | 0.0826558i | ||||
\(989\) | −2.00000 | − | 3.46410i | −0.0635963 | − | 0.110152i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0000 | 0.603555 | 0.301777 | − | 0.953378i | \(-0.402420\pi\) | ||||
0.301777 | + | 0.953378i | \(0.402420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.0000 | 0.349074 | ||||||||
\(994\) | 12.0000 | + | 10.3923i | 0.380617 | + | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.00000 | − | 12.1244i | −0.221803 | − | 0.384175i | ||||
\(997\) | 1.50000 | + | 2.59808i | 0.0475055 | + | 0.0822819i | 0.888800 | − | 0.458295i | \(-0.151540\pi\) |
−0.841295 | + | 0.540576i | \(0.818206\pi\) | |||||||
\(998\) | 1.00000 | 0.0316544 | ||||||||
\(999\) | −5.50000 | + | 9.52628i | −0.174012 | + | 0.301398i |
(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 | 546.2.k.a.445.1 | yes | 2 | |
3.2 | odd | 2 | 1638.2.p.d.991.1 | 2 | |||
7.2 | even | 3 | 546.2.j.a.289.1 | ✓ | 2 | ||
13.9 | even | 3 | 546.2.j.a.529.1 | yes | 2 | ||
21.2 | odd | 6 | 1638.2.m.a.289.1 | 2 | |||
39.35 | odd | 6 | 1638.2.m.a.1621.1 | 2 | |||
91.9 | even | 3 | inner | 546.2.k.a.373.1 | yes | 2 | |
273.191 | odd | 6 | 1638.2.p.d.919.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.a.289.1 | ✓ | 2 | 7.2 | even | 3 | ||
546.2.j.a.529.1 | yes | 2 | 13.9 | even | 3 | ||
546.2.k.a.373.1 | yes | 2 | 91.9 | even | 3 | inner | |
546.2.k.a.445.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1638.2.m.a.289.1 | 2 | 21.2 | odd | 6 | |||
1638.2.m.a.1621.1 | 2 | 39.35 | odd | 6 | |||
1638.2.p.d.919.1 | 2 | 273.191 | odd | 6 | |||
1638.2.p.d.991.1 | 2 | 3.2 | odd | 2 |