Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (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: | \(5.08647060876\) |
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: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.361 |
Dual form | 637.2.u.a.30.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | − | 0.866025i | −1.06066 | − | 0.612372i | −0.135045 | − | 0.990839i | \(-0.543118\pi\) |
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | −1.50000 | − | 0.866025i | −0.612372 | − | 0.353553i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | −3.00000 | −0.948683 | ||||||||
\(11\) | 5.19615i | 1.56670i | 0.621582 | + | 0.783349i | \(0.286490\pi\) | ||||
−0.621582 | + | 0.783349i | \(0.713510\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 1.00000 | + | 3.46410i | 0.277350 | + | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 0.866025i | 0.387298 | − | 0.223607i | ||||
\(16\) | 2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | ||||
\(17\) | 3.00000 | + | 5.19615i | 0.727607 | + | 1.26025i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) |
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | 3.00000 | + | 1.73205i | 0.707107 | + | 0.408248i | ||||
\(19\) | 1.73205i | 0.397360i | 0.980064 | + | 0.198680i | \(0.0636654\pi\) | ||||
−0.980064 | + | 0.198680i | \(0.936335\pi\) | |||||||
\(20\) | 1.50000 | + | 0.866025i | 0.335410 | + | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.50000 | − | 7.79423i | 0.959403 | − | 1.66174i | ||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 1.73205i | 0.353553i | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 1.50000 | − | 6.06218i | 0.294174 | − | 1.18889i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | − | 2.59808i | −0.278543 | − | 0.482451i | 0.692480 | − | 0.721437i | \(-0.256518\pi\) |
−0.971023 | + | 0.238987i | \(0.923185\pi\) | |||||||
\(30\) | −3.00000 | −0.547723 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −4.50000 | + | 2.59808i | −0.795495 | + | 0.459279i | ||||
\(33\) | 5.19615i | 0.904534i | ||||||||
\(34\) | − | 10.3923i | − | 1.78227i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | − | 1.73205i | −0.166667 | − | 0.288675i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 1.50000 | − | 2.59808i | 0.243332 | − | 0.421464i | ||||
\(39\) | 1.00000 | + | 3.46410i | 0.160128 | + | 0.554700i | ||||
\(40\) | 1.50000 | + | 2.59808i | 0.237171 | + | 0.410792i | ||||
\(41\) | 4.50000 | − | 2.59808i | 0.702782 | − | 0.405751i | −0.105601 | − | 0.994409i | \(-0.533677\pi\) |
0.808383 | + | 0.588657i | \(0.200343\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.50000 | + | 9.52628i | −0.838742 | + | 1.45274i | 0.0522047 | + | 0.998636i | \(0.483375\pi\) |
−0.890947 | + | 0.454108i | \(0.849958\pi\) | |||||||
\(44\) | −4.50000 | + | 2.59808i | −0.678401 | + | 0.391675i | ||||
\(45\) | −3.00000 | + | 1.73205i | −0.447214 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.50000 | − | 4.33013i | 1.09399 | − | 0.631614i | 0.159352 | − | 0.987222i | \(-0.449059\pi\) |
0.934635 | + | 0.355608i | \(0.115726\pi\) | |||||||
\(48\) | 2.50000 | − | 4.33013i | 0.360844 | − | 0.625000i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.00000 | − | 1.73205i | 0.424264 | − | 0.244949i | ||||
\(51\) | 3.00000 | + | 5.19615i | 0.420084 | + | 0.727607i | ||||
\(52\) | −2.50000 | + | 2.59808i | −0.346688 | + | 0.360288i | ||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | 7.50000 | + | 4.33013i | 1.02062 | + | 0.589256i | ||||
\(55\) | 4.50000 | + | 7.79423i | 0.606780 | + | 1.05097i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.73205i | 0.229416i | ||||||||
\(58\) | 5.19615i | 0.682288i | ||||||||
\(59\) | 3.00000 | − | 1.73205i | 0.390567 | − | 0.225494i | −0.291839 | − | 0.956467i | \(-0.594267\pi\) |
0.682406 | + | 0.730974i | \(0.260934\pi\) | |||||||
\(60\) | 1.50000 | + | 0.866025i | 0.193649 | + | 0.111803i | ||||
\(61\) | −7.00000 | −0.896258 | −0.448129 | − | 0.893969i | \(-0.647910\pi\) | ||||
−0.448129 | + | 0.893969i | \(0.647910\pi\) | |||||||
\(62\) | 1.50000 | + | 2.59808i | 0.190500 | + | 0.329956i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.50000 | + | 4.33013i | 0.558156 | + | 0.537086i | ||||
\(66\) | 4.50000 | − | 7.79423i | 0.553912 | − | 0.959403i | ||||
\(67\) | − | 8.66025i | − | 1.05802i | −0.848616 | − | 0.529009i | \(-0.822564\pi\) | ||
0.848616 | − | 0.529009i | \(-0.177436\pi\) | |||||||
\(68\) | −3.00000 | + | 5.19615i | −0.363803 | + | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.50000 | + | 0.866025i | 0.178017 | + | 0.102778i | 0.586361 | − | 0.810050i | \(-0.300560\pi\) |
−0.408344 | + | 0.912828i | \(0.633893\pi\) | |||||||
\(72\) | − | 3.46410i | − | 0.408248i | ||||||
\(73\) | 7.50000 | + | 4.33013i | 0.877809 | + | 0.506803i | 0.869935 | − | 0.493166i | \(-0.164160\pi\) |
0.00787336 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | + | 1.73205i | −0.115470 | + | 0.200000i | ||||
\(76\) | −1.50000 | + | 0.866025i | −0.172062 | + | 0.0993399i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.50000 | − | 6.06218i | 0.169842 | − | 0.686406i | ||||
\(79\) | 2.50000 | + | 4.33013i | 0.281272 | + | 0.487177i | 0.971698 | − | 0.236225i | \(-0.0759104\pi\) |
−0.690426 | + | 0.723403i | \(0.742577\pi\) | |||||||
\(80\) | − | 8.66025i | − | 0.968246i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.00000 | −0.993884 | ||||||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | + | 5.19615i | 0.976187 | + | 0.563602i | ||||
\(86\) | 16.5000 | − | 9.52628i | 1.77924 | − | 1.02725i | ||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | −9.00000 | −0.959403 | ||||||||
\(89\) | 6.00000 | + | 3.46410i | 0.635999 | + | 0.367194i | 0.783072 | − | 0.621932i | \(-0.213652\pi\) |
−0.147073 | + | 0.989126i | \(0.546985\pi\) | |||||||
\(90\) | 6.00000 | 0.632456 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | − | 0.866025i | −0.155543 | − | 0.0898027i | ||||
\(94\) | −15.0000 | −1.54713 | ||||||||
\(95\) | 1.50000 | + | 2.59808i | 0.153897 | + | 0.266557i | ||||
\(96\) | −4.50000 | + | 2.59808i | −0.459279 | + | 0.265165i | ||||
\(97\) | 4.50000 | + | 2.59808i | 0.456906 | + | 0.263795i | 0.710742 | − | 0.703452i | \(-0.248359\pi\) |
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 10.3923i | − | 1.04447i | ||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 9.00000 | 0.895533 | 0.447767 | − | 0.894150i | \(-0.352219\pi\) | ||||
0.447767 | + | 0.894150i | \(0.352219\pi\) | |||||||
\(102\) | − | 10.3923i | − | 1.02899i | ||||||
\(103\) | −6.50000 | − | 11.2583i | −0.640464 | − | 1.10932i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) |
0.344865 | − | 0.938652i | \(-0.387925\pi\) | |||||||
\(104\) | −6.00000 | + | 1.73205i | −0.588348 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.5000 | + | 7.79423i | −1.31124 | + | 0.757042i | ||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | −2.50000 | − | 4.33013i | −0.240563 | − | 0.416667i | ||||
\(109\) | 4.50000 | + | 2.59808i | 0.431022 | + | 0.248851i | 0.699782 | − | 0.714357i | \(-0.253281\pi\) |
−0.268760 | + | 0.963207i | \(0.586614\pi\) | |||||||
\(110\) | − | 15.5885i | − | 1.48630i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.50000 | + | 12.9904i | −0.705541 | + | 1.22203i | 0.260955 | + | 0.965351i | \(0.415962\pi\) |
−0.966496 | + | 0.256681i | \(0.917371\pi\) | |||||||
\(114\) | 1.50000 | − | 2.59808i | 0.140488 | − | 0.243332i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.50000 | − | 2.59808i | 0.139272 | − | 0.241225i | ||||
\(117\) | −2.00000 | − | 6.92820i | −0.184900 | − | 0.640513i | ||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.50000 | + | 2.59808i | 0.136931 | + | 0.237171i | ||||
\(121\) | −16.0000 | −1.45455 | ||||||||
\(122\) | 10.5000 | + | 6.06218i | 0.950625 | + | 0.548844i | ||||
\(123\) | 4.50000 | − | 2.59808i | 0.405751 | − | 0.234261i | ||||
\(124\) | − | 1.73205i | − | 0.155543i | ||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.50000 | − | 11.2583i | −0.576782 | − | 0.999015i | −0.995846 | − | 0.0910585i | \(-0.970975\pi\) |
0.419064 | − | 0.907957i | \(-0.362358\pi\) | |||||||
\(128\) | 10.5000 | + | 6.06218i | 0.928078 | + | 0.535826i | ||||
\(129\) | −5.50000 | + | 9.52628i | −0.484248 | + | 0.838742i | ||||
\(130\) | −3.00000 | − | 10.3923i | −0.263117 | − | 0.911465i | ||||
\(131\) | 7.50000 | + | 12.9904i | 0.655278 | + | 1.13497i | 0.981824 | + | 0.189794i | \(0.0607819\pi\) |
−0.326546 | + | 0.945181i | \(0.605885\pi\) | |||||||
\(132\) | −4.50000 | + | 2.59808i | −0.391675 | + | 0.226134i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.50000 | + | 12.9904i | −0.647901 | + | 1.12220i | ||||
\(135\) | −7.50000 | + | 4.33013i | −0.645497 | + | 0.372678i | ||||
\(136\) | −9.00000 | + | 5.19615i | −0.771744 | + | 0.445566i | ||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.50000 | + | 11.2583i | −0.551323 | + | 0.954919i | 0.446857 | + | 0.894606i | \(0.352543\pi\) |
−0.998179 | + | 0.0603135i | \(0.980790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.50000 | − | 4.33013i | 0.631614 | − | 0.364662i | ||||
\(142\) | −1.50000 | − | 2.59808i | −0.125877 | − | 0.218026i | ||||
\(143\) | −18.0000 | + | 5.19615i | −1.50524 | + | 0.434524i | ||||
\(144\) | −5.00000 | + | 8.66025i | −0.416667 | + | 0.721688i | ||||
\(145\) | −4.50000 | − | 2.59808i | −0.373705 | − | 0.215758i | ||||
\(146\) | −7.50000 | − | 12.9904i | −0.620704 | − | 1.07509i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 19.0526i | − | 1.56085i | −0.625252 | − | 0.780423i | \(-0.715004\pi\) | ||
0.625252 | − | 0.780423i | \(-0.284996\pi\) | |||||||
\(150\) | 3.00000 | − | 1.73205i | 0.244949 | − | 0.141421i | ||||
\(151\) | −10.5000 | − | 6.06218i | −0.854478 | − | 0.493333i | 0.00768132 | − | 0.999970i | \(-0.497555\pi\) |
−0.862159 | + | 0.506637i | \(0.830888\pi\) | |||||||
\(152\) | −3.00000 | −0.243332 | ||||||||
\(153\) | −6.00000 | − | 10.3923i | −0.485071 | − | 0.840168i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00000 | −0.240966 | ||||||||
\(156\) | −2.50000 | + | 2.59808i | −0.200160 | + | 0.208013i | ||||
\(157\) | 11.5000 | − | 19.9186i | 0.917800 | − | 1.58968i | 0.115050 | − | 0.993360i | \(-0.463297\pi\) |
0.802749 | − | 0.596316i | \(-0.203370\pi\) | |||||||
\(158\) | − | 8.66025i | − | 0.688973i | ||||||
\(159\) | 4.50000 | − | 7.79423i | 0.356873 | − | 0.618123i | ||||
\(160\) | −4.50000 | + | 7.79423i | −0.355756 | + | 0.616188i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.50000 | − | 0.866025i | −0.117851 | − | 0.0680414i | ||||
\(163\) | 12.1244i | 0.949653i | 0.880079 | + | 0.474826i | \(0.157489\pi\) | ||||
−0.880079 | + | 0.474826i | \(0.842511\pi\) | |||||||
\(164\) | 4.50000 | + | 2.59808i | 0.351391 | + | 0.202876i | ||||
\(165\) | 4.50000 | + | 7.79423i | 0.350325 | + | 0.606780i | ||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | 1.50000 | − | 0.866025i | 0.116073 | − | 0.0670151i | −0.440839 | − | 0.897586i | \(-0.645319\pi\) |
0.556913 | + | 0.830571i | \(0.311986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | −9.00000 | − | 15.5885i | −0.690268 | − | 1.19558i | ||||
\(171\) | − | 3.46410i | − | 0.264906i | ||||||
\(172\) | −11.0000 | −0.838742 | ||||||||
\(173\) | −15.0000 | −1.14043 | −0.570214 | − | 0.821496i | \(-0.693140\pi\) | ||||
−0.570214 | + | 0.821496i | \(0.693140\pi\) | |||||||
\(174\) | 5.19615i | 0.393919i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 22.5000 | + | 12.9904i | 1.69600 | + | 0.979187i | ||||
\(177\) | 3.00000 | − | 1.73205i | 0.225494 | − | 0.130189i | ||||
\(178\) | −6.00000 | − | 10.3923i | −0.449719 | − | 0.778936i | ||||
\(179\) | 3.00000 | 0.224231 | 0.112115 | − | 0.993695i | \(-0.464237\pi\) | ||||
0.112115 | + | 0.993695i | \(0.464237\pi\) | |||||||
\(180\) | −3.00000 | − | 1.73205i | −0.223607 | − | 0.129099i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50000 | + | 2.59808i | 0.109985 | + | 0.190500i | ||||
\(187\) | −27.0000 | + | 15.5885i | −1.97444 | + | 1.13994i | ||||
\(188\) | 7.50000 | + | 4.33013i | 0.546994 | + | 0.315807i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 5.19615i | − | 0.376969i | ||||||
\(191\) | −15.0000 | −1.08536 | −0.542681 | − | 0.839939i | \(-0.682591\pi\) | ||||
−0.542681 | + | 0.839939i | \(0.682591\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − | 1.73205i | − | 0.124676i | −0.998055 | − | 0.0623379i | \(-0.980144\pi\) | ||
0.998055 | − | 0.0623379i | \(-0.0198556\pi\) | |||||||
\(194\) | −4.50000 | − | 7.79423i | −0.323081 | − | 0.559593i | ||||
\(195\) | 4.50000 | + | 4.33013i | 0.322252 | + | 0.310087i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.5000 | − | 11.2583i | 1.38932 | − | 0.802123i | 0.396079 | − | 0.918216i | \(-0.370371\pi\) |
0.993238 | + | 0.116094i | \(0.0370372\pi\) | |||||||
\(198\) | −9.00000 | + | 15.5885i | −0.639602 | + | 1.10782i | ||||
\(199\) | 2.00000 | + | 3.46410i | 0.141776 | + | 0.245564i | 0.928166 | − | 0.372168i | \(-0.121385\pi\) |
−0.786389 | + | 0.617731i | \(0.788052\pi\) | |||||||
\(200\) | −3.00000 | − | 1.73205i | −0.212132 | − | 0.122474i | ||||
\(201\) | − | 8.66025i | − | 0.610847i | ||||||
\(202\) | −13.5000 | − | 7.79423i | −0.949857 | − | 0.548400i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.00000 | + | 5.19615i | −0.210042 | + | 0.363803i | ||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | 22.5167i | 1.56881i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.5000 | + | 4.33013i | 1.21341 | + | 0.300240i | ||||
\(209\) | −9.00000 | −0.622543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.50000 | − | 11.2583i | −0.447478 | − | 0.775055i | 0.550743 | − | 0.834675i | \(-0.314345\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | 9.00000 | 0.618123 | ||||||||
\(213\) | 1.50000 | + | 0.866025i | 0.102778 | + | 0.0593391i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.0526i | 1.29937i | ||||||||
\(216\) | − | 8.66025i | − | 0.589256i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.50000 | − | 7.79423i | −0.304778 | − | 0.527892i | ||||
\(219\) | 7.50000 | + | 4.33013i | 0.506803 | + | 0.292603i | ||||
\(220\) | −4.50000 | + | 7.79423i | −0.303390 | + | 0.525487i | ||||
\(221\) | −15.0000 | + | 15.5885i | −1.00901 | + | 1.04859i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.50000 | + | 2.59808i | −0.301342 | + | 0.173980i | −0.643046 | − | 0.765828i | \(-0.722329\pi\) |
0.341703 | + | 0.939808i | \(0.388996\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | − | 3.46410i | 0.133333 | − | 0.230940i | ||||
\(226\) | 22.5000 | − | 12.9904i | 1.49668 | − | 0.864107i | ||||
\(227\) | 15.0000 | − | 8.66025i | 0.995585 | − | 0.574801i | 0.0886460 | − | 0.996063i | \(-0.471746\pi\) |
0.906939 | + | 0.421262i | \(0.138413\pi\) | |||||||
\(228\) | −1.50000 | + | 0.866025i | −0.0993399 | + | 0.0573539i | ||||
\(229\) | −10.5000 | + | 6.06218i | −0.693860 | + | 0.400600i | −0.805056 | − | 0.593198i | \(-0.797865\pi\) |
0.111197 | + | 0.993798i | \(0.464532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.50000 | − | 2.59808i | 0.295439 | − | 0.170572i | ||||
\(233\) | −1.50000 | − | 2.59808i | −0.0982683 | − | 0.170206i | 0.812700 | − | 0.582683i | \(-0.197997\pi\) |
−0.910968 | + | 0.412477i | \(0.864664\pi\) | |||||||
\(234\) | −3.00000 | + | 12.1244i | −0.196116 | + | 0.792594i | ||||
\(235\) | 7.50000 | − | 12.9904i | 0.489246 | − | 0.847399i | ||||
\(236\) | 3.00000 | + | 1.73205i | 0.195283 | + | 0.112747i | ||||
\(237\) | 2.50000 | + | 4.33013i | 0.162392 | + | 0.281272i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3923i | 0.672222i | 0.941822 | + | 0.336111i | \(0.109112\pi\) | ||||
−0.941822 | + | 0.336111i | \(0.890888\pi\) | |||||||
\(240\) | − | 8.66025i | − | 0.559017i | ||||||
\(241\) | 6.00000 | − | 3.46410i | 0.386494 | − | 0.223142i | −0.294146 | − | 0.955761i | \(-0.595035\pi\) |
0.680640 | + | 0.732618i | \(0.261702\pi\) | |||||||
\(242\) | 24.0000 | + | 13.8564i | 1.54278 | + | 0.890724i | ||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | −3.50000 | − | 6.06218i | −0.224065 | − | 0.388091i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | −6.00000 | + | 1.73205i | −0.381771 | + | 0.110208i | ||||
\(248\) | 1.50000 | − | 2.59808i | 0.0952501 | − | 0.164978i | ||||
\(249\) | − | 3.46410i | − | 0.219529i | ||||||
\(250\) | 10.5000 | − | 18.1865i | 0.664078 | − | 1.15022i | ||||
\(251\) | 1.50000 | − | 2.59808i | 0.0946792 | − | 0.163989i | −0.814795 | − | 0.579748i | \(-0.803151\pi\) |
0.909475 | + | 0.415759i | \(0.136484\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 22.5167i | 1.41282i | ||||||||
\(255\) | 9.00000 | + | 5.19615i | 0.563602 | + | 0.325396i | ||||
\(256\) | −9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | ||||
\(257\) | 15.0000 | − | 25.9808i | 0.935674 | − | 1.62064i | 0.162247 | − | 0.986750i | \(-0.448126\pi\) |
0.773427 | − | 0.633885i | \(-0.218541\pi\) | |||||||
\(258\) | 16.5000 | − | 9.52628i | 1.02725 | − | 0.593080i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.50000 | + | 6.06218i | −0.0930261 | + | 0.375960i | ||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | − | 25.9808i | − | 1.60510i | ||||||
\(263\) | 3.00000 | 0.184988 | 0.0924940 | − | 0.995713i | \(-0.470516\pi\) | ||||
0.0924940 | + | 0.995713i | \(0.470516\pi\) | |||||||
\(264\) | −9.00000 | −0.553912 | ||||||||
\(265\) | − | 15.5885i | − | 0.957591i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000 | + | 3.46410i | 0.367194 | + | 0.212000i | ||||
\(268\) | 7.50000 | − | 4.33013i | 0.458135 | − | 0.264505i | ||||
\(269\) | −3.00000 | − | 5.19615i | −0.182913 | − | 0.316815i | 0.759958 | − | 0.649972i | \(-0.225219\pi\) |
−0.942871 | + | 0.333157i | \(0.891886\pi\) | |||||||
\(270\) | 15.0000 | 0.912871 | ||||||||
\(271\) | 15.0000 | + | 8.66025i | 0.911185 | + | 0.526073i | 0.880812 | − | 0.473466i | \(-0.156997\pi\) |
0.0303728 | + | 0.999539i | \(0.490331\pi\) | |||||||
\(272\) | 30.0000 | 1.81902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.00000 | − | 5.19615i | −0.542720 | − | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | 19.5000 | − | 11.2583i | 1.16953 | − | 0.675230i | ||||
\(279\) | 3.00000 | + | 1.73205i | 0.179605 | + | 0.103695i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.92820i | − | 0.413302i | −0.978415 | − | 0.206651i | \(-0.933744\pi\) | ||
0.978415 | − | 0.206651i | \(-0.0662565\pi\) | |||||||
\(282\) | −15.0000 | −0.893237 | ||||||||
\(283\) | −19.0000 | −1.12943 | −0.564716 | − | 0.825285i | \(-0.691014\pi\) | ||||
−0.564716 | + | 0.825285i | \(0.691014\pi\) | |||||||
\(284\) | 1.73205i | 0.102778i | ||||||||
\(285\) | 1.50000 | + | 2.59808i | 0.0888523 | + | 0.153897i | ||||
\(286\) | 31.5000 | + | 7.79423i | 1.86263 | + | 0.460882i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.00000 | − | 5.19615i | 0.530330 | − | 0.306186i | ||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 4.50000 | + | 7.79423i | 0.264249 | + | 0.457693i | ||||
\(291\) | 4.50000 | + | 2.59808i | 0.263795 | + | 0.152302i | ||||
\(292\) | 8.66025i | 0.506803i | ||||||||
\(293\) | 22.5000 | + | 12.9904i | 1.31446 | + | 0.758906i | 0.982832 | − | 0.184503i | \(-0.0590674\pi\) |
0.331632 | + | 0.943409i | \(0.392401\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | − | 5.19615i | 0.174667 | − | 0.302532i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 25.9808i | − | 1.50756i | ||||||
\(298\) | −16.5000 | + | 28.5788i | −0.955819 | + | 1.65553i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.5000 | + | 18.1865i | 0.604207 | + | 1.04652i | ||||
\(303\) | 9.00000 | 0.517036 | ||||||||
\(304\) | 7.50000 | + | 4.33013i | 0.430155 | + | 0.248350i | ||||
\(305\) | −10.5000 | + | 6.06218i | −0.601228 | + | 0.347119i | ||||
\(306\) | 20.7846i | 1.18818i | ||||||||
\(307\) | − | 24.2487i | − | 1.38395i | −0.721923 | − | 0.691974i | \(-0.756741\pi\) | ||
0.721923 | − | 0.691974i | \(-0.243259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.50000 | − | 11.2583i | −0.369772 | − | 0.640464i | ||||
\(310\) | 4.50000 | + | 2.59808i | 0.255583 | + | 0.147561i | ||||
\(311\) | −7.50000 | + | 12.9904i | −0.425286 | + | 0.736617i | −0.996447 | − | 0.0842210i | \(-0.973160\pi\) |
0.571161 | + | 0.820838i | \(0.306493\pi\) | |||||||
\(312\) | −6.00000 | + | 1.73205i | −0.339683 | + | 0.0980581i | ||||
\(313\) | 9.50000 | + | 16.4545i | 0.536972 | + | 0.930062i | 0.999065 | + | 0.0432311i | \(0.0137652\pi\) |
−0.462093 | + | 0.886831i | \(0.652902\pi\) | |||||||
\(314\) | −34.5000 | + | 19.9186i | −1.94695 | + | 1.12407i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.50000 | + | 4.33013i | −0.140636 | + | 0.243589i | ||||
\(317\) | 4.50000 | − | 2.59808i | 0.252745 | − | 0.145922i | −0.368275 | − | 0.929717i | \(-0.620052\pi\) |
0.621021 | + | 0.783794i | \(0.286718\pi\) | |||||||
\(318\) | −13.5000 | + | 7.79423i | −0.757042 | + | 0.437079i | ||||
\(319\) | 13.5000 | − | 7.79423i | 0.755855 | − | 0.436393i | ||||
\(320\) | −1.50000 | + | 0.866025i | −0.0838525 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.00000 | + | 5.19615i | −0.500773 | + | 0.289122i | ||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | −7.00000 | − | 1.73205i | −0.388290 | − | 0.0960769i | ||||
\(326\) | 10.5000 | − | 18.1865i | 0.581541 | − | 1.00726i | ||||
\(327\) | 4.50000 | + | 2.59808i | 0.248851 | + | 0.143674i | ||||
\(328\) | 4.50000 | + | 7.79423i | 0.248471 | + | 0.430364i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 15.5885i | − | 0.858116i | ||||||
\(331\) | 32.9090i | 1.80884i | 0.426643 | + | 0.904420i | \(0.359696\pi\) | ||||
−0.426643 | + | 0.904420i | \(0.640304\pi\) | |||||||
\(332\) | 3.00000 | − | 1.73205i | 0.164646 | − | 0.0950586i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.00000 | −0.164153 | ||||||||
\(335\) | −7.50000 | − | 12.9904i | −0.409769 | − | 0.709740i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 22.5000 | − | 0.866025i | 1.22384 | − | 0.0471056i | ||||
\(339\) | −7.50000 | + | 12.9904i | −0.407344 | + | 0.705541i | ||||
\(340\) | 10.3923i | 0.563602i | ||||||||
\(341\) | 4.50000 | − | 7.79423i | 0.243689 | − | 0.422081i | ||||
\(342\) | −3.00000 | + | 5.19615i | −0.162221 | + | 0.280976i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −16.5000 | − | 9.52628i | −0.889620 | − | 0.513623i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.5000 | + | 12.9904i | 1.20961 | + | 0.698367i | ||||
\(347\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(348\) | 1.50000 | − | 2.59808i | 0.0804084 | − | 0.139272i | ||||
\(349\) | 4.50000 | − | 2.59808i | 0.240879 | − | 0.139072i | −0.374701 | − | 0.927146i | \(-0.622255\pi\) |
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | − | 17.3205i | −0.266880 | − | 0.924500i | ||||
\(352\) | −13.5000 | − | 23.3827i | −0.719552 | − | 1.24630i | ||||
\(353\) | 1.73205i | 0.0921878i | 0.998937 | + | 0.0460939i | \(0.0146773\pi\) | ||||
−0.998937 | + | 0.0460939i | \(0.985323\pi\) | |||||||
\(354\) | −6.00000 | −0.318896 | ||||||||
\(355\) | 3.00000 | 0.159223 | ||||||||
\(356\) | 6.92820i | 0.367194i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.50000 | − | 2.59808i | −0.237832 | − | 0.137313i | ||||
\(359\) | 16.5000 | − | 9.52628i | 0.870837 | − | 0.502778i | 0.00321050 | − | 0.999995i | \(-0.498978\pi\) |
0.867626 | + | 0.497217i | \(0.165645\pi\) | |||||||
\(360\) | −3.00000 | − | 5.19615i | −0.158114 | − | 0.273861i | ||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | 3.00000 | + | 1.73205i | 0.157676 | + | 0.0910346i | ||||
\(363\) | −16.0000 | −0.839782 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.0000 | 0.785136 | ||||||||
\(366\) | 10.5000 | + | 6.06218i | 0.548844 | + | 0.316875i | ||||
\(367\) | −23.0000 | −1.20059 | −0.600295 | − | 0.799779i | \(-0.704950\pi\) | ||||
−0.600295 | + | 0.799779i | \(0.704950\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.00000 | + | 5.19615i | −0.468521 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 1.73205i | − | 0.0898027i | ||||||
\(373\) | 19.0000 | 0.983783 | 0.491891 | − | 0.870657i | \(-0.336306\pi\) | ||||
0.491891 | + | 0.870657i | \(0.336306\pi\) | |||||||
\(374\) | 54.0000 | 2.79227 | ||||||||
\(375\) | 12.1244i | 0.626099i | ||||||||
\(376\) | 7.50000 | + | 12.9904i | 0.386783 | + | 0.669928i | ||||
\(377\) | 7.50000 | − | 7.79423i | 0.386270 | − | 0.401423i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.50000 | + | 0.866025i | −0.0770498 | + | 0.0444847i | −0.538030 | − | 0.842926i | \(-0.680831\pi\) |
0.460980 | + | 0.887410i | \(0.347498\pi\) | |||||||
\(380\) | −1.50000 | + | 2.59808i | −0.0769484 | + | 0.133278i | ||||
\(381\) | −6.50000 | − | 11.2583i | −0.333005 | − | 0.576782i | ||||
\(382\) | 22.5000 | + | 12.9904i | 1.15120 | + | 0.664646i | ||||
\(383\) | 15.5885i | 0.796533i | 0.917270 | + | 0.398266i | \(0.130388\pi\) | ||||
−0.917270 | + | 0.398266i | \(0.869612\pi\) | |||||||
\(384\) | 10.5000 | + | 6.06218i | 0.535826 | + | 0.309359i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.50000 | + | 2.59808i | −0.0763480 | + | 0.132239i | ||||
\(387\) | 11.0000 | − | 19.0526i | 0.559161 | − | 0.968496i | ||||
\(388\) | 5.19615i | 0.263795i | ||||||||
\(389\) | −1.50000 | + | 2.59808i | −0.0760530 | + | 0.131728i | −0.901544 | − | 0.432688i | \(-0.857565\pi\) |
0.825491 | + | 0.564416i | \(0.190898\pi\) | |||||||
\(390\) | −3.00000 | − | 10.3923i | −0.151911 | − | 0.526235i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.50000 | + | 12.9904i | 0.378325 | + | 0.655278i | ||||
\(394\) | −39.0000 | −1.96479 | ||||||||
\(395\) | 7.50000 | + | 4.33013i | 0.377366 | + | 0.217872i | ||||
\(396\) | 9.00000 | − | 5.19615i | 0.452267 | − | 0.261116i | ||||
\(397\) | − | 36.3731i | − | 1.82551i | −0.408505 | − | 0.912756i | \(-0.633950\pi\) | ||
0.408505 | − | 0.912756i | \(-0.366050\pi\) | |||||||
\(398\) | − | 6.92820i | − | 0.347279i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | + | 8.66025i | 0.250000 | + | 0.433013i | ||||
\(401\) | −6.00000 | − | 3.46410i | −0.299626 | − | 0.172989i | 0.342649 | − | 0.939463i | \(-0.388676\pi\) |
−0.642275 | + | 0.766475i | \(0.722009\pi\) | |||||||
\(402\) | −7.50000 | + | 12.9904i | −0.374066 | + | 0.647901i | ||||
\(403\) | 1.50000 | − | 6.06218i | 0.0747203 | − | 0.301979i | ||||
\(404\) | 4.50000 | + | 7.79423i | 0.223883 | + | 0.387777i | ||||
\(405\) | 1.50000 | − | 0.866025i | 0.0745356 | − | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.00000 | + | 5.19615i | −0.445566 | + | 0.257248i | ||||
\(409\) | −6.00000 | + | 3.46410i | −0.296681 | + | 0.171289i | −0.640951 | − | 0.767582i | \(-0.721460\pi\) |
0.344270 | + | 0.938871i | \(0.388126\pi\) | |||||||
\(410\) | −13.5000 | + | 7.79423i | −0.666717 | + | 0.384930i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.50000 | − | 11.2583i | 0.320232 | − | 0.554658i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.00000 | − | 5.19615i | −0.147264 | − | 0.255069i | ||||
\(416\) | −13.5000 | − | 12.9904i | −0.661892 | − | 0.636906i | ||||
\(417\) | −6.50000 | + | 11.2583i | −0.318306 | + | 0.551323i | ||||
\(418\) | 13.5000 | + | 7.79423i | 0.660307 | + | 0.381228i | ||||
\(419\) | 10.5000 | + | 18.1865i | 0.512959 | + | 0.888470i | 0.999887 | + | 0.0150285i | \(0.00478389\pi\) |
−0.486928 | + | 0.873442i | \(0.661883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 22.5167i | 1.09609i | ||||||||
\(423\) | −15.0000 | + | 8.66025i | −0.729325 | + | 0.421076i | ||||
\(424\) | 13.5000 | + | 7.79423i | 0.655618 | + | 0.378521i | ||||
\(425\) | −12.0000 | −0.582086 | ||||||||
\(426\) | −1.50000 | − | 2.59808i | −0.0726752 | − | 0.125877i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.0000 | + | 5.19615i | −0.869048 | + | 0.250873i | ||||
\(430\) | 16.5000 | − | 28.5788i | 0.795701 | − | 1.37819i | ||||
\(431\) | 32.9090i | 1.58517i | 0.609762 | + | 0.792585i | \(0.291265\pi\) | ||||
−0.609762 | + | 0.792585i | \(0.708735\pi\) | |||||||
\(432\) | −12.5000 | + | 21.6506i | −0.601407 | + | 1.04167i | ||||
\(433\) | 9.50000 | − | 16.4545i | 0.456541 | − | 0.790752i | −0.542234 | − | 0.840227i | \(-0.682422\pi\) |
0.998775 | + | 0.0494752i | \(0.0157549\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.50000 | − | 2.59808i | −0.215758 | − | 0.124568i | ||||
\(436\) | 5.19615i | 0.248851i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −7.50000 | − | 12.9904i | −0.358364 | − | 0.620704i | ||||
\(439\) | 4.00000 | − | 6.92820i | 0.190910 | − | 0.330665i | −0.754642 | − | 0.656136i | \(-0.772190\pi\) |
0.945552 | + | 0.325471i | \(0.105523\pi\) | |||||||
\(440\) | −13.5000 | + | 7.79423i | −0.643587 | + | 0.371575i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.0000 | − | 10.3923i | 1.71235 | − | 0.494312i | ||||
\(443\) | −7.50000 | − | 12.9904i | −0.356336 | − | 0.617192i | 0.631010 | − | 0.775775i | \(-0.282641\pi\) |
−0.987346 | + | 0.158583i | \(0.949307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | 9.00000 | 0.426162 | ||||||||
\(447\) | − | 19.0526i | − | 0.901155i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.50000 | + | 0.866025i | 0.0707894 | + | 0.0408703i | 0.534977 | − | 0.844867i | \(-0.320320\pi\) |
−0.464188 | + | 0.885737i | \(0.653654\pi\) | |||||||
\(450\) | −6.00000 | + | 3.46410i | −0.282843 | + | 0.163299i | ||||
\(451\) | 13.5000 | + | 23.3827i | 0.635690 | + | 1.10105i | ||||
\(452\) | −15.0000 | −0.705541 | ||||||||
\(453\) | −10.5000 | − | 6.06218i | −0.493333 | − | 0.284826i | ||||
\(454\) | −30.0000 | −1.40797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −30.0000 | − | 17.3205i | −1.40334 | − | 0.810219i | −0.408607 | − | 0.912710i | \(-0.633985\pi\) |
−0.994734 | + | 0.102491i | \(0.967319\pi\) | |||||||
\(458\) | 21.0000 | 0.981266 | ||||||||
\(459\) | −15.0000 | − | 25.9808i | −0.700140 | − | 1.21268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.5000 | − | 14.7224i | −1.18765 | − | 0.685692i | −0.229881 | − | 0.973219i | \(-0.573834\pi\) |
−0.957773 | + | 0.287527i | \(0.907167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.2487i | − | 1.12693i | −0.826139 | − | 0.563467i | \(-0.809467\pi\) | ||
0.826139 | − | 0.563467i | \(-0.190533\pi\) | |||||||
\(464\) | −15.0000 | −0.696358 | ||||||||
\(465\) | −3.00000 | −0.139122 | ||||||||
\(466\) | 5.19615i | 0.240707i | ||||||||
\(467\) | −10.5000 | − | 18.1865i | −0.485882 | − | 0.841572i | 0.513986 | − | 0.857798i | \(-0.328168\pi\) |
−0.999868 | + | 0.0162260i | \(0.994835\pi\) | |||||||
\(468\) | 5.00000 | − | 5.19615i | 0.231125 | − | 0.240192i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −22.5000 | + | 12.9904i | −1.03785 | + | 0.599202i | ||||
\(471\) | 11.5000 | − | 19.9186i | 0.529892 | − | 0.917800i | ||||
\(472\) | 3.00000 | + | 5.19615i | 0.138086 | + | 0.239172i | ||||
\(473\) | −49.5000 | − | 28.5788i | −2.27601 | − | 1.31406i | ||||
\(474\) | − | 8.66025i | − | 0.397779i | ||||||
\(475\) | −3.00000 | − | 1.73205i | −0.137649 | − | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | + | 15.5885i | −0.412082 | + | 0.713746i | ||||
\(478\) | 9.00000 | − | 15.5885i | 0.411650 | − | 0.712999i | ||||
\(479\) | 29.4449i | 1.34537i | 0.739929 | + | 0.672685i | \(0.234859\pi\) | ||||
−0.739929 | + | 0.672685i | \(0.765141\pi\) | |||||||
\(480\) | −4.50000 | + | 7.79423i | −0.205396 | + | 0.355756i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12.0000 | −0.546585 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.00000 | − | 13.8564i | −0.363636 | − | 0.629837i | ||||
\(485\) | 9.00000 | 0.408669 | ||||||||
\(486\) | −24.0000 | − | 13.8564i | −1.08866 | − | 0.628539i | ||||
\(487\) | −21.0000 | + | 12.1244i | −0.951601 | + | 0.549407i | −0.893578 | − | 0.448908i | \(-0.851813\pi\) |
−0.0580230 | + | 0.998315i | \(0.518480\pi\) | |||||||
\(488\) | − | 12.1244i | − | 0.548844i | ||||||
\(489\) | 12.1244i | 0.548282i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.5000 | + | 23.3827i | 0.609246 | + | 1.05525i | 0.991365 | + | 0.131132i | \(0.0418613\pi\) |
−0.382118 | + | 0.924113i | \(0.624805\pi\) | |||||||
\(492\) | 4.50000 | + | 2.59808i | 0.202876 | + | 0.117130i | ||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | 10.5000 | + | 2.59808i | 0.472417 | + | 0.116893i | ||||
\(495\) | −9.00000 | − | 15.5885i | −0.404520 | − | 0.700649i | ||||
\(496\) | −7.50000 | + | 4.33013i | −0.336760 | + | 0.194428i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.00000 | + | 5.19615i | −0.134433 | + | 0.232845i | ||||
\(499\) | −1.50000 | + | 0.866025i | −0.0671492 | + | 0.0387686i | −0.533199 | − | 0.845990i | \(-0.679010\pi\) |
0.466049 | + | 0.884759i | \(0.345677\pi\) | |||||||
\(500\) | −10.5000 | + | 6.06218i | −0.469574 | + | 0.271109i | ||||
\(501\) | 1.50000 | − | 0.866025i | 0.0670151 | − | 0.0386912i | ||||
\(502\) | −4.50000 | + | 2.59808i | −0.200845 | + | 0.115958i | ||||
\(503\) | −4.50000 | + | 7.79423i | −0.200645 | + | 0.347527i | −0.948736 | − | 0.316068i | \(-0.897637\pi\) |
0.748091 | + | 0.663596i | \(0.230970\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5000 | − | 7.79423i | 0.600742 | − | 0.346839i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.0000 | + | 6.92820i | −0.488527 | + | 0.307692i | ||||
\(508\) | 6.50000 | − | 11.2583i | 0.288391 | − | 0.499508i | ||||
\(509\) | 6.00000 | + | 3.46410i | 0.265945 | + | 0.153544i | 0.627044 | − | 0.778984i | \(-0.284265\pi\) |
−0.361098 | + | 0.932528i | \(0.617598\pi\) | |||||||
\(510\) | −9.00000 | − | 15.5885i | −0.398527 | − | 0.690268i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | − | 8.66025i | − | 0.382360i | ||||||
\(514\) | −45.0000 | + | 25.9808i | −1.98486 | + | 1.14596i | ||||
\(515\) | −19.5000 | − | 11.2583i | −0.859273 | − | 0.496101i | ||||
\(516\) | −11.0000 | −0.484248 | ||||||||
\(517\) | 22.5000 | + | 38.9711i | 0.989549 | + | 1.71395i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.0000 | −0.658427 | ||||||||
\(520\) | −7.50000 | + | 7.79423i | −0.328897 | + | 0.341800i | ||||
\(521\) | 19.5000 | − | 33.7750i | 0.854311 | − | 1.47971i | −0.0229727 | − | 0.999736i | \(-0.507313\pi\) |
0.877283 | − | 0.479973i | \(-0.159354\pi\) | |||||||
\(522\) | − | 10.3923i | − | 0.454859i | ||||||
\(523\) | −2.00000 | + | 3.46410i | −0.0874539 | + | 0.151475i | −0.906434 | − | 0.422347i | \(-0.861206\pi\) |
0.818980 | + | 0.573822i | \(0.194540\pi\) | |||||||
\(524\) | −7.50000 | + | 12.9904i | −0.327639 | + | 0.567487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.50000 | − | 2.59808i | −0.196209 | − | 0.113282i | ||||
\(527\) | − | 10.3923i | − | 0.452696i | ||||||
\(528\) | 22.5000 | + | 12.9904i | 0.979187 | + | 0.565334i | ||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | −13.5000 | + | 23.3827i | −0.586403 | + | 1.01568i | ||||
\(531\) | −6.00000 | + | 3.46410i | −0.260378 | + | 0.150329i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.5000 | + | 12.9904i | 0.584750 | + | 0.562676i | ||||
\(534\) | −6.00000 | − | 10.3923i | −0.259645 | − | 0.449719i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.0000 | 0.647901 | ||||||||
\(537\) | 3.00000 | 0.129460 | ||||||||
\(538\) | 10.3923i | 0.448044i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.50000 | − | 4.33013i | −0.322749 | − | 0.186339i | ||||
\(541\) | 10.5000 | − | 6.06218i | 0.451430 | − | 0.260633i | −0.257004 | − | 0.966410i | \(-0.582735\pi\) |
0.708434 | + | 0.705777i | \(0.249402\pi\) | |||||||
\(542\) | −15.0000 | − | 25.9808i | −0.644305 | − | 1.11597i | ||||
\(543\) | −2.00000 | −0.0858282 | ||||||||
\(544\) | −27.0000 | − | 15.5885i | −1.15762 | − | 0.668350i | ||||
\(545\) | 9.00000 | 0.385518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.0000 | 0.597505 | ||||||||
\(550\) | 9.00000 | + | 15.5885i | 0.383761 | + | 0.664694i | ||||
\(551\) | 4.50000 | − | 2.59808i | 0.191706 | − | 0.110682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 17.3205i | − | 0.735878i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.0000 | −0.551323 | ||||||||
\(557\) | − | 15.5885i | − | 0.660504i | −0.943893 | − | 0.330252i | \(-0.892866\pi\) | ||
0.943893 | − | 0.330252i | \(-0.107134\pi\) | |||||||
\(558\) | −3.00000 | − | 5.19615i | −0.127000 | − | 0.219971i | ||||
\(559\) | −38.5000 | − | 9.52628i | −1.62838 | − | 0.402919i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.0000 | + | 15.5885i | −1.13994 | + | 0.658145i | ||||
\(562\) | −6.00000 | + | 10.3923i | −0.253095 | + | 0.438373i | ||||
\(563\) | −18.0000 | − | 31.1769i | −0.758610 | − | 1.31395i | −0.943560 | − | 0.331202i | \(-0.892546\pi\) |
0.184950 | − | 0.982748i | \(-0.440788\pi\) | |||||||
\(564\) | 7.50000 | + | 4.33013i | 0.315807 | + | 0.182331i | ||||
\(565\) | 25.9808i | 1.09302i | ||||||||
\(566\) | 28.5000 | + | 16.4545i | 1.19794 | + | 0.691633i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.50000 | + | 2.59808i | −0.0629386 | + | 0.109013i | ||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | − | 5.19615i | − | 0.217643i | ||||||
\(571\) | 11.5000 | − | 19.9186i | 0.481260 | − | 0.833567i | −0.518509 | − | 0.855072i | \(-0.673513\pi\) |
0.999769 | + | 0.0215055i | \(0.00684595\pi\) | |||||||
\(572\) | −13.5000 | − | 12.9904i | −0.564463 | − | 0.543155i | ||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.00000 | 0.0833333 | ||||||||
\(577\) | 13.5000 | + | 7.79423i | 0.562012 | + | 0.324478i | 0.753953 | − | 0.656929i | \(-0.228145\pi\) |
−0.191940 | + | 0.981407i | \(0.561478\pi\) | |||||||
\(578\) | 28.5000 | − | 16.4545i | 1.18544 | − | 0.684416i | ||||
\(579\) | − | 1.73205i | − | 0.0719816i | ||||||
\(580\) | − | 5.19615i | − | 0.215758i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.50000 | − | 7.79423i | −0.186531 | − | 0.323081i | ||||
\(583\) | 40.5000 | + | 23.3827i | 1.67734 | + | 0.968412i | ||||
\(584\) | −7.50000 | + | 12.9904i | −0.310352 | + | 0.537546i | ||||
\(585\) | −9.00000 | − | 8.66025i | −0.372104 | − | 0.358057i | ||||
\(586\) | −22.5000 | − | 38.9711i | −0.929466 | − | 1.60988i | ||||
\(587\) | 13.5000 | − | 7.79423i | 0.557205 | − | 0.321702i | −0.194818 | − | 0.980839i | \(-0.562412\pi\) |
0.752023 | + | 0.659137i | \(0.229078\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50000 | − | 2.59808i | 0.0618064 | − | 0.107052i | ||||
\(590\) | −9.00000 | + | 5.19615i | −0.370524 | + | 0.213922i | ||||
\(591\) | 19.5000 | − | 11.2583i | 0.802123 | − | 0.463106i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.50000 | + | 2.59808i | −0.184793 | + | 0.106690i | −0.589543 | − | 0.807737i | \(-0.700692\pi\) |
0.404750 | + | 0.914428i | \(0.367359\pi\) | |||||||
\(594\) | −22.5000 | + | 38.9711i | −0.923186 | + | 1.59901i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.5000 | − | 9.52628i | 0.675866 | − | 0.390212i | ||||
\(597\) | 2.00000 | + | 3.46410i | 0.0818546 | + | 0.141776i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.50000 | + | 7.79423i | −0.183865 | + | 0.318464i | −0.943193 | − | 0.332244i | \(-0.892194\pi\) |
0.759328 | + | 0.650708i | \(0.225528\pi\) | |||||||
\(600\) | −3.00000 | − | 1.73205i | −0.122474 | − | 0.0707107i | ||||
\(601\) | 9.50000 | + | 16.4545i | 0.387513 | + | 0.671192i | 0.992114 | − | 0.125336i | \(-0.0400009\pi\) |
−0.604601 | + | 0.796528i | \(0.706668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.3205i | 0.705346i | ||||||||
\(604\) | − | 12.1244i | − | 0.493333i | ||||||
\(605\) | −24.0000 | + | 13.8564i | −0.975739 | + | 0.563343i | ||||
\(606\) | −13.5000 | − | 7.79423i | −0.548400 | − | 0.316619i | ||||
\(607\) | 43.0000 | 1.74532 | 0.872658 | − | 0.488332i | \(-0.162394\pi\) | ||||
0.872658 | + | 0.488332i | \(0.162394\pi\) | |||||||
\(608\) | −4.50000 | − | 7.79423i | −0.182499 | − | 0.316098i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.0000 | 0.850265 | ||||||||
\(611\) | 22.5000 | + | 21.6506i | 0.910253 | + | 0.875891i | ||||
\(612\) | 6.00000 | − | 10.3923i | 0.242536 | − | 0.420084i | ||||
\(613\) | − | 36.3731i | − | 1.46909i | −0.678558 | − | 0.734547i | \(-0.737395\pi\) | ||
0.678558 | − | 0.734547i | \(-0.262605\pi\) | |||||||
\(614\) | −21.0000 | + | 36.3731i | −0.847491 | + | 1.46790i | ||||
\(615\) | 4.50000 | − | 7.79423i | 0.181458 | − | 0.314294i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.5000 | + | 21.6506i | 1.50969 | + | 0.871622i | 0.999936 | + | 0.0113033i | \(0.00359804\pi\) |
0.509757 | + | 0.860318i | \(0.329735\pi\) | |||||||
\(618\) | 22.5167i | 0.905753i | ||||||||
\(619\) | 16.5000 | + | 9.52628i | 0.663191 | + | 0.382893i | 0.793492 | − | 0.608581i | \(-0.208261\pi\) |
−0.130301 | + | 0.991475i | \(0.541594\pi\) | |||||||
\(620\) | −1.50000 | − | 2.59808i | −0.0602414 | − | 0.104341i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.5000 | − | 12.9904i | 0.902168 | − | 0.520867i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.5000 | + | 4.33013i | 0.700561 | + | 0.173344i | ||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | − | 32.9090i | − | 1.31531i | ||||||
\(627\) | −9.00000 | −0.359425 | ||||||||
\(628\) | 23.0000 | 0.917800 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.5000 | − | 23.3827i | −1.61228 | − | 0.930850i | −0.988841 | − | 0.148978i | \(-0.952402\pi\) |
−0.623439 | − | 0.781872i | \(-0.714265\pi\) | |||||||
\(632\) | −7.50000 | + | 4.33013i | −0.298334 | + | 0.172243i | ||||
\(633\) | −6.50000 | − | 11.2583i | −0.258352 | − | 0.447478i | ||||
\(634\) | −9.00000 | −0.357436 | ||||||||
\(635\) | −19.5000 | − | 11.2583i | −0.773834 | − | 0.446773i | ||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −27.0000 | −1.06894 | ||||||||
\(639\) | −3.00000 | − | 1.73205i | −0.118678 | − | 0.0685189i | ||||
\(640\) | 21.0000 | 0.830098 | ||||||||
\(641\) | −15.0000 | − | 25.9808i | −0.592464 | − | 1.02618i | −0.993899 | − | 0.110291i | \(-0.964822\pi\) |
0.401435 | − | 0.915888i | \(-0.368512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.50000 | + | 2.59808i | 0.177463 | + | 0.102458i | 0.586100 | − | 0.810239i | \(-0.300663\pi\) |
−0.408637 | + | 0.912697i | \(0.633996\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.0526i | 0.750194i | ||||||||
\(646\) | 18.0000 | 0.708201 | ||||||||
\(647\) | 9.00000 | 0.353827 | 0.176913 | − | 0.984226i | \(-0.443389\pi\) | ||||
0.176913 | + | 0.984226i | \(0.443389\pi\) | |||||||
\(648\) | 1.73205i | 0.0680414i | ||||||||
\(649\) | 9.00000 | + | 15.5885i | 0.353281 | + | 0.611900i | ||||
\(650\) | 9.00000 | + | 8.66025i | 0.353009 | + | 0.339683i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.5000 | + | 6.06218i | −0.411212 | + | 0.237413i | ||||
\(653\) | 15.0000 | − | 25.9808i | 0.586995 | − | 1.01671i | −0.407628 | − | 0.913148i | \(-0.633644\pi\) |
0.994623 | − | 0.103558i | \(-0.0330227\pi\) | |||||||
\(654\) | −4.50000 | − | 7.79423i | −0.175964 | − | 0.304778i | ||||
\(655\) | 22.5000 | + | 12.9904i | 0.879148 | + | 0.507576i | ||||
\(656\) | − | 25.9808i | − | 1.01438i | ||||||
\(657\) | −15.0000 | − | 8.66025i | −0.585206 | − | 0.337869i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.50000 | + | 12.9904i | −0.292159 | + | 0.506033i | −0.974320 | − | 0.225168i | \(-0.927707\pi\) |
0.682161 | + | 0.731202i | \(0.261040\pi\) | |||||||
\(660\) | −4.50000 | + | 7.79423i | −0.175162 | + | 0.303390i | ||||
\(661\) | 36.3731i | 1.41475i | 0.706839 | + | 0.707374i | \(0.250120\pi\) | ||||
−0.706839 | + | 0.707374i | \(0.749880\pi\) | |||||||
\(662\) | 28.5000 | − | 49.3634i | 1.10768 | − | 1.91856i | ||||
\(663\) | −15.0000 | + | 15.5885i | −0.582552 | + | 0.605406i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.50000 | + | 0.866025i | 0.0580367 | + | 0.0335075i | ||||
\(669\) | −4.50000 | + | 2.59808i | −0.173980 | + | 0.100447i | ||||
\(670\) | 25.9808i | 1.00372i | ||||||||
\(671\) | − | 36.3731i | − | 1.40417i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.500000 | + | 0.866025i | 0.0192736 | + | 0.0333828i | 0.875501 | − | 0.483216i | \(-0.160531\pi\) |
−0.856228 | + | 0.516599i | \(0.827198\pi\) | |||||||
\(674\) | −33.0000 | − | 19.0526i | −1.27111 | − | 0.733877i | ||||
\(675\) | 5.00000 | − | 8.66025i | 0.192450 | − | 0.333333i | ||||
\(676\) | −11.5000 | − | 6.06218i | −0.442308 | − | 0.233161i | ||||
\(677\) | 13.5000 | + | 23.3827i | 0.518847 | + | 0.898670i | 0.999760 | + | 0.0219013i | \(0.00697196\pi\) |
−0.480913 | + | 0.876768i | \(0.659695\pi\) | |||||||
\(678\) | 22.5000 | − | 12.9904i | 0.864107 | − | 0.498893i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.00000 | + | 15.5885i | −0.345134 | + | 0.597790i | ||||
\(681\) | 15.0000 | − | 8.66025i | 0.574801 | − | 0.331862i | ||||
\(682\) | −13.5000 | + | 7.79423i | −0.516942 | + | 0.298456i | ||||
\(683\) | 21.0000 | − | 12.1244i | 0.803543 | − | 0.463926i | −0.0411658 | − | 0.999152i | \(-0.513107\pi\) |
0.844708 | + | 0.535227i | \(0.179774\pi\) | |||||||
\(684\) | 3.00000 | − | 1.73205i | 0.114708 | − | 0.0662266i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.5000 | + | 6.06218i | −0.400600 | + | 0.231287i | ||||
\(688\) | 27.5000 | + | 47.6314i | 1.04843 | + | 1.81593i | ||||
\(689\) | 31.5000 | + | 7.79423i | 1.20005 | + | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0000 | − | 15.5885i | −1.02713 | − | 0.593013i | −0.110968 | − | 0.993824i | \(-0.535395\pi\) |
−0.916161 | + | 0.400811i | \(0.868728\pi\) | |||||||
\(692\) | −7.50000 | − | 12.9904i | −0.285107 | − | 0.493820i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.5167i | 0.854106i | ||||||||
\(696\) | 4.50000 | − | 2.59808i | 0.170572 | − | 0.0984798i | ||||
\(697\) | 27.0000 | + | 15.5885i | 1.02270 | + | 0.590455i | ||||
\(698\) | −9.00000 | −0.340655 | ||||||||
\(699\) | −1.50000 | − | 2.59808i | −0.0567352 | − | 0.0982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | −7.50000 | + | 30.3109i | −0.283069 | + | 1.14401i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 5.19615i | − | 0.195837i | ||||||
\(705\) | 7.50000 | − | 12.9904i | 0.282466 | − | 0.489246i | ||||
\(706\) | 1.50000 | − | 2.59808i | 0.0564532 | − | 0.0977799i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.00000 | + | 1.73205i | 0.112747 | + | 0.0650945i | ||||
\(709\) | − | 12.1244i | − | 0.455340i | −0.973738 | − | 0.227670i | \(-0.926889\pi\) | ||
0.973738 | − | 0.227670i | \(-0.0731107\pi\) | |||||||
\(710\) | −4.50000 | − | 2.59808i | −0.168882 | − | 0.0975041i | ||||
\(711\) | −5.00000 | − | 8.66025i | −0.187515 | − | 0.324785i | ||||
\(712\) | −6.00000 | + | 10.3923i | −0.224860 | + | 0.389468i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.5000 | + | 23.3827i | −0.841452 | + | 0.874463i | ||||
\(716\) | 1.50000 | + | 2.59808i | 0.0560576 | + | 0.0970947i | ||||
\(717\) | 10.3923i | 0.388108i | ||||||||
\(718\) | −33.0000 | −1.23155 | ||||||||
\(719\) | 15.0000 | 0.559406 | 0.279703 | − | 0.960087i | \(-0.409764\pi\) | ||||
0.279703 | + | 0.960087i | \(0.409764\pi\) | |||||||
\(720\) | 17.3205i | 0.645497i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.0000 | − | 13.8564i | −0.893188 | − | 0.515682i | ||||
\(723\) | 6.00000 | − | 3.46410i | 0.223142 | − | 0.128831i | ||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 24.0000 | + | 13.8564i | 0.890724 | + | 0.514259i | ||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −22.5000 | − | 12.9904i | −0.832762 | − | 0.480796i | ||||
\(731\) | −66.0000 | −2.44110 | ||||||||
\(732\) | −3.50000 | − | 6.06218i | −0.129364 | − | 0.224065i | ||||
\(733\) | 43.5000 | − | 25.1147i | 1.60671 | − | 0.927634i | 0.616609 | − | 0.787269i | \(-0.288506\pi\) |
0.990100 | − | 0.140365i | \(-0.0448275\pi\) | |||||||
\(734\) | 34.5000 | + | 19.9186i | 1.27342 | + | 0.735208i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.0000 | 1.65760 | ||||||||
\(738\) | 18.0000 | 0.662589 | ||||||||
\(739\) | 39.8372i | 1.46543i | 0.680534 | + | 0.732717i | \(0.261748\pi\) | ||||
−0.680534 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | + | 1.73205i | −0.220416 | + | 0.0636285i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.50000 | + | 0.866025i | −0.0550297 | + | 0.0317714i | −0.527262 | − | 0.849703i | \(-0.676782\pi\) |
0.472233 | + | 0.881474i | \(0.343448\pi\) | |||||||
\(744\) | 1.50000 | − | 2.59808i | 0.0549927 | − | 0.0952501i | ||||
\(745\) | −16.5000 | − | 28.5788i | −0.604513 | − | 1.04705i | ||||
\(746\) | −28.5000 | − | 16.4545i | −1.04346 | − | 0.602441i | ||||
\(747\) | 6.92820i | 0.253490i | ||||||||
\(748\) | −27.0000 | − | 15.5885i | −0.987218 | − | 0.569970i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.5000 | − | 18.1865i | 0.383406 | − | 0.664078i | ||||
\(751\) | −10.0000 | + | 17.3205i | −0.364905 | + | 0.632034i | −0.988761 | − | 0.149505i | \(-0.952232\pi\) |
0.623856 | + | 0.781540i | \(0.285565\pi\) | |||||||
\(752\) | − | 43.3013i | − | 1.57903i | ||||||
\(753\) | 1.50000 | − | 2.59808i | 0.0546630 | − | 0.0946792i | ||||
\(754\) | −18.0000 | + | 5.19615i | −0.655521 | + | 0.189233i | ||||
\(755\) | −21.0000 | −0.764268 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.50000 | + | 14.7224i | 0.308938 | + | 0.535096i | 0.978130 | − | 0.207993i | \(-0.0666932\pi\) |
−0.669193 | + | 0.743089i | \(0.733360\pi\) | |||||||
\(758\) | 3.00000 | 0.108965 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.50000 | + | 2.59808i | −0.163232 | + | 0.0942421i | ||||
\(761\) | − | 29.4449i | − | 1.06738i | −0.845682 | − | 0.533688i | \(-0.820806\pi\) | ||
0.845682 | − | 0.533688i | \(-0.179194\pi\) | |||||||
\(762\) | 22.5167i | 0.815693i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.50000 | − | 12.9904i | −0.271340 | − | 0.469975i | ||||
\(765\) | −18.0000 | − | 10.3923i | −0.650791 | − | 0.375735i | ||||
\(766\) | 13.5000 | − | 23.3827i | 0.487775 | − | 0.844851i | ||||
\(767\) | 9.00000 | + | 8.66025i | 0.324971 | + | 0.312704i | ||||
\(768\) | −9.50000 | − | 16.4545i | −0.342802 | − | 0.593750i | ||||
\(769\) | 16.5000 | − | 9.52628i | 0.595005 | − | 0.343526i | −0.172069 | − | 0.985085i | \(-0.555045\pi\) |
0.767074 | + | 0.641558i | \(0.221712\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0000 | − | 25.9808i | 0.540212 | − | 0.935674i | ||||
\(772\) | 1.50000 | − | 0.866025i | 0.0539862 | − | 0.0311689i | ||||
\(773\) | 12.0000 | − | 6.92820i | 0.431610 | − | 0.249190i | −0.268422 | − | 0.963301i | \(-0.586502\pi\) |
0.700032 | + | 0.714111i | \(0.253169\pi\) | |||||||
\(774\) | −33.0000 | + | 19.0526i | −1.18616 | + | 0.684830i | ||||
\(775\) | 3.00000 | − | 1.73205i | 0.107763 | − | 0.0622171i | ||||
\(776\) | −4.50000 | + | 7.79423i | −0.161541 | + | 0.279797i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.50000 | − | 2.59808i | 0.161333 | − | 0.0931455i | ||||
\(779\) | 4.50000 | + | 7.79423i | 0.161229 | + | 0.279257i | ||||
\(780\) | −1.50000 | + | 6.06218i | −0.0537086 | + | 0.217061i | ||||
\(781\) | −4.50000 | + | 7.79423i | −0.161023 | + | 0.278899i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.50000 | + | 12.9904i | 0.268028 | + | 0.464238i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 39.8372i | − | 1.42185i | ||||||
\(786\) | − | 25.9808i | − | 0.926703i | ||||||
\(787\) | 27.0000 | − | 15.5885i | 0.962446 | − | 0.555668i | 0.0655211 | − | 0.997851i | \(-0.479129\pi\) |
0.896925 | + | 0.442183i | \(0.145796\pi\) | |||||||
\(788\) | 19.5000 | + | 11.2583i | 0.694659 | + | 0.401061i | ||||
\(789\) | 3.00000 | 0.106803 | ||||||||
\(790\) | −7.50000 | − | 12.9904i | −0.266838 | − | 0.462177i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 18.0000 | 0.639602 | ||||||||
\(793\) | −7.00000 | − | 24.2487i | −0.248577 | − | 0.861097i | ||||
\(794\) | −31.5000 | + | 54.5596i | −1.11789 | + | 1.93625i | ||||
\(795\) | − | 15.5885i | − | 0.552866i | ||||||
\(796\) | −2.00000 | + | 3.46410i | −0.0708881 | + | 0.122782i | ||||
\(797\) | −16.5000 | + | 28.5788i | −0.584460 | + | 1.01231i | 0.410483 | + | 0.911868i | \(0.365360\pi\) |
−0.994943 | + | 0.100446i | \(0.967973\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.0000 | + | 25.9808i | 1.59199 | + | 0.919133i | ||||
\(800\) | − | 10.3923i | − | 0.367423i | ||||||
\(801\) | −12.0000 | − | 6.92820i | −0.423999 | − | 0.244796i | ||||
\(802\) | 6.00000 | + | 10.3923i | 0.211867 | + | 0.366965i | ||||
\(803\) | −22.5000 | + | 38.9711i | −0.794008 | + | 1.37526i | ||||
\(804\) | 7.50000 | − | 4.33013i | 0.264505 | − | 0.152712i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.50000 | + | 7.79423i | −0.264176 | + | 0.274540i | ||||
\(807\) | −3.00000 | − | 5.19615i | −0.105605 | − | 0.182913i | ||||
\(808\) | 15.5885i | 0.548400i | ||||||||
\(809\) | −21.0000 | −0.738321 | −0.369160 | − | 0.929366i | \(-0.620355\pi\) | ||||
−0.369160 | + | 0.929366i | \(0.620355\pi\) | |||||||
\(810\) | −3.00000 | −0.105409 | ||||||||
\(811\) | 3.46410i | 0.121641i | 0.998149 | + | 0.0608205i | \(0.0193717\pi\) | ||||
−0.998149 | + | 0.0608205i | \(0.980628\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.0000 | + | 8.66025i | 0.526073 | + | 0.303728i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.5000 | + | 18.1865i | 0.367799 | + | 0.637046i | ||||
\(816\) | 30.0000 | 1.05021 | ||||||||
\(817\) | −16.5000 | − | 9.52628i | −0.577262 | − | 0.333282i | ||||
\(818\) | 12.0000 | 0.419570 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | − | 27.7128i | −0.557725 | − | 0.966008i | −0.997686 | − | 0.0679910i | \(-0.978341\pi\) |
0.439961 | − | 0.898017i | \(-0.354992\pi\) | |||||||
\(824\) | 19.5000 | − | 11.2583i | 0.679315 | − | 0.392203i | ||||
\(825\) | −9.00000 | − | 5.19615i | −0.313340 | − | 0.180907i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.3923i | 0.361376i | 0.983540 | + | 0.180688i | \(0.0578324\pi\) | ||||
−0.983540 | + | 0.180688i | \(0.942168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00000 | −0.243120 | −0.121560 | − | 0.992584i | \(-0.538790\pi\) | ||||
−0.121560 | + | 0.992584i | \(0.538790\pi\) | |||||||
\(830\) | 10.3923i | 0.360722i | ||||||||
\(831\) | 5.00000 | + | 8.66025i | 0.173448 | + | 0.300421i | ||||
\(832\) | −1.00000 | − | 3.46410i | −0.0346688 | − | 0.120096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.5000 | − | 11.2583i | 0.675230 | − | 0.389844i | ||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | −4.50000 | − | 7.79423i | −0.155636 | − | 0.269569i | ||||
\(837\) | 7.50000 | + | 4.33013i | 0.259238 | + | 0.149671i | ||||
\(838\) | − | 36.3731i | − | 1.25649i | ||||||
\(839\) | −1.50000 | − | 0.866025i | −0.0517858 | − | 0.0298985i | 0.473884 | − | 0.880587i | \(-0.342852\pi\) |
−0.525669 | + | 0.850689i | \(0.676185\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 6.92820i | − | 0.238620i | ||||||
\(844\) | 6.50000 | − | 11.2583i | 0.223739 | − | 0.387528i | ||||
\(845\) | −10.5000 | + | 19.9186i | −0.361211 | + | 0.685220i | ||||
\(846\) | 30.0000 | 1.03142 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −22.5000 | − | 38.9711i | −0.772653 | − | 1.33827i | ||||
\(849\) | −19.0000 | −0.652078 | ||||||||
\(850\) | 18.0000 | + | 10.3923i | 0.617395 | + | 0.356453i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 1.73205i | 0.0593391i | ||||||||
\(853\) | − | 41.5692i | − | 1.42330i | −0.702533 | − | 0.711651i | \(-0.747948\pi\) | ||
0.702533 | − | 0.711651i | \(-0.252052\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.00000 | − | 5.19615i | −0.102598 | − | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.5000 | + | 28.5788i | −0.563629 | + | 0.976235i | 0.433546 | + | 0.901131i | \(0.357262\pi\) |
−0.997176 | + | 0.0751033i | \(0.976071\pi\) | |||||||
\(858\) | 31.5000 | + | 7.79423i | 1.07539 | + | 0.266091i | ||||
\(859\) | −14.5000 | − | 25.1147i | −0.494734 | − | 0.856904i | 0.505248 | − | 0.862974i | \(-0.331401\pi\) |
−0.999982 | + | 0.00607046i | \(0.998068\pi\) | |||||||
\(860\) | −16.5000 | + | 9.52628i | −0.562645 | + | 0.324843i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.5000 | − | 49.3634i | 0.970714 | − | 1.68133i | ||||
\(863\) | −1.50000 | + | 0.866025i | −0.0510606 | + | 0.0294798i | −0.525313 | − | 0.850909i | \(-0.676052\pi\) |
0.474252 | + | 0.880389i | \(0.342718\pi\) | |||||||
\(864\) | 22.5000 | − | 12.9904i | 0.765466 | − | 0.441942i | ||||
\(865\) | −22.5000 | + | 12.9904i | −0.765023 | + | 0.441686i | ||||
\(866\) | −28.5000 | + | 16.4545i | −0.968469 | + | 0.559146i | ||||
\(867\) | −9.50000 | + | 16.4545i | −0.322637 | + | 0.558824i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.5000 | + | 12.9904i | −0.763260 | + | 0.440668i | ||||
\(870\) | 4.50000 | + | 7.79423i | 0.152564 | + | 0.264249i | ||||
\(871\) | 30.0000 | − | 8.66025i | 1.01651 | − | 0.293442i | ||||
\(872\) | −4.50000 | + | 7.79423i | −0.152389 | + | 0.263946i | ||||
\(873\) | −9.00000 | − | 5.19615i | −0.304604 | − | 0.175863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.66025i | 0.292603i | ||||||||
\(877\) | 1.73205i | 0.0584872i | 0.999572 | + | 0.0292436i | \(0.00930985\pi\) | ||||
−0.999572 | + | 0.0292436i | \(0.990690\pi\) | |||||||
\(878\) | −12.0000 | + | 6.92820i | −0.404980 | + | 0.233816i | ||||
\(879\) | 22.5000 | + | 12.9904i | 0.758906 | + | 0.438155i | ||||
\(880\) | 45.0000 | 1.51695 | ||||||||
\(881\) | −16.5000 | − | 28.5788i | −0.555899 | − | 0.962846i | −0.997833 | − | 0.0657979i | \(-0.979041\pi\) |
0.441934 | − | 0.897048i | \(-0.354293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | −21.0000 | − | 5.19615i | −0.706306 | − | 0.174766i | ||||
\(885\) | 3.00000 | − | 5.19615i | 0.100844 | − | 0.174667i | ||||
\(886\) | 25.9808i | 0.872841i | ||||||||
\(887\) | 12.0000 | − | 20.7846i | 0.402921 | − | 0.697879i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.994077 | + | 0.108678i | \(0.0346618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −18.0000 | − | 10.3923i | −0.603361 | − | 0.348351i | ||||
\(891\) | 5.19615i | 0.174078i | ||||||||
\(892\) | −4.50000 | − | 2.59808i | −0.150671 | − | 0.0869900i | ||||
\(893\) | 7.50000 | + | 12.9904i | 0.250978 | + | 0.434707i | ||||
\(894\) | −16.5000 | + | 28.5788i | −0.551843 | + | 0.955819i | ||||
\(895\) | 4.50000 | − | 2.59808i | 0.150418 | − | 0.0868441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.50000 | − | 2.59808i | −0.0500556 | − | 0.0866989i | ||||
\(899\) | 5.19615i | 0.173301i | ||||||||
\(900\) | 4.00000 | 0.133333 | ||||||||
\(901\) | 54.0000 | 1.79900 | ||||||||
\(902\) | − | 46.7654i | − | 1.55712i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.5000 | − | 12.9904i | −0.748339 | − | 0.432054i | ||||
\(905\) | −3.00000 | + | 1.73205i | −0.0997234 | + | 0.0575753i | ||||
\(906\) | 10.5000 | + | 18.1865i | 0.348839 | + | 0.604207i | ||||
\(907\) | −29.0000 | −0.962929 | −0.481465 | − | 0.876466i | \(-0.659895\pi\) | ||||
−0.481465 | + | 0.876466i | \(0.659895\pi\) | |||||||
\(908\) | 15.0000 | + | 8.66025i | 0.497792 | + | 0.287401i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 7.50000 | + | 4.33013i | 0.248350 | + | 0.143385i | ||||
\(913\) | 18.0000 | 0.595713 | ||||||||
\(914\) | 30.0000 | + | 51.9615i | 0.992312 | + | 1.71873i | ||||
\(915\) | −10.5000 | + | 6.06218i | −0.347119 | + | 0.200409i | ||||
\(916\) | −10.5000 | − | 6.06218i | −0.346930 | − | 0.200300i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 51.9615i | 1.71499i | ||||||||
\(919\) | −47.0000 | −1.55039 | −0.775193 | − | 0.631724i | \(-0.782348\pi\) | ||||
−0.775193 | + | 0.631724i | \(0.782348\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 24.2487i | − | 0.799022i | ||||||
\(922\) | 25.5000 | + | 44.1673i | 0.839798 | + | 1.45457i | ||||
\(923\) | −1.50000 | + | 6.06218i | −0.0493731 | + | 0.199539i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.0000 | + | 36.3731i | −0.690103 | + | 1.19529i | ||||
\(927\) | 13.0000 | + | 22.5167i | 0.426976 | + | 0.739544i | ||||
\(928\) | 13.5000 | + | 7.79423i | 0.443159 | + | 0.255858i | ||||
\(929\) | 46.7654i | 1.53432i | 0.641455 | + | 0.767161i | \(0.278331\pi\) | ||||
−0.641455 | + | 0.767161i | \(0.721669\pi\) | |||||||
\(930\) | 4.50000 | + | 2.59808i | 0.147561 | + | 0.0851943i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.50000 | − | 2.59808i | 0.0491341 | − | 0.0851028i | ||||
\(933\) | −7.50000 | + | 12.9904i | −0.245539 | + | 0.425286i | ||||
\(934\) | 36.3731i | 1.19016i | ||||||||
\(935\) | −27.0000 | + | 46.7654i | −0.882994 | + | 1.52939i | ||||
\(936\) | 12.0000 | − | 3.46410i | 0.392232 | − | 0.113228i | ||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.50000 | + | 16.4545i | 0.310021 | + | 0.536972i | ||||
\(940\) | 15.0000 | 0.489246 | ||||||||
\(941\) | −4.50000 | − | 2.59808i | −0.146696 | − | 0.0846949i | 0.424856 | − | 0.905261i | \(-0.360325\pi\) |
−0.571551 | + | 0.820566i | \(0.693658\pi\) | |||||||
\(942\) | −34.5000 | + | 19.9186i | −1.12407 | + | 0.648983i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 17.3205i | − | 0.563735i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 49.5000 | + | 85.7365i | 1.60938 | + | 2.78753i | ||||
\(947\) | −33.0000 | − | 19.0526i | −1.07236 | − | 0.619125i | −0.143532 | − | 0.989646i | \(-0.545846\pi\) |
−0.928824 | + | 0.370521i | \(0.879179\pi\) | |||||||
\(948\) | −2.50000 | + | 4.33013i | −0.0811962 | + | 0.140636i | ||||
\(949\) | −7.50000 | + | 30.3109i | −0.243460 | + | 0.983933i | ||||
\(950\) | 3.00000 | + | 5.19615i | 0.0973329 | + | 0.168585i | ||||
\(951\) | 4.50000 | − | 2.59808i | 0.145922 | − | 0.0842484i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.5000 | − | 49.3634i | 0.923206 | − | 1.59904i | 0.128784 | − | 0.991673i | \(-0.458893\pi\) |
0.794422 | − | 0.607366i | \(-0.207774\pi\) | |||||||
\(954\) | 27.0000 | − | 15.5885i | 0.874157 | − | 0.504695i | ||||
\(955\) | −22.5000 | + | 12.9904i | −0.728083 | + | 0.420359i | ||||
\(956\) | −9.00000 | + | 5.19615i | −0.291081 | + | 0.168056i | ||||
\(957\) | 13.5000 | − | 7.79423i | 0.436393 | − | 0.251952i | ||||
\(958\) | 25.5000 | − | 44.1673i | 0.823868 | − | 1.42698i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.50000 | + | 0.866025i | −0.0484123 | + | 0.0279508i | ||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.00000 | + | 3.46410i | 0.193247 | + | 0.111571i | ||||
\(965\) | −1.50000 | − | 2.59808i | −0.0482867 | − | 0.0836350i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 10.3923i | − | 0.334194i | −0.985940 | − | 0.167097i | \(-0.946561\pi\) | ||
0.985940 | − | 0.167097i | \(-0.0534393\pi\) | |||||||
\(968\) | − | 27.7128i | − | 0.890724i | ||||||
\(969\) | −9.00000 | + | 5.19615i | −0.289122 | + | 0.166924i | ||||
\(970\) | −13.5000 | − | 7.79423i | −0.433459 | − | 0.250258i | ||||
\(971\) | −21.0000 | −0.673922 | −0.336961 | − | 0.941519i | \(-0.609399\pi\) | ||||
−0.336961 | + | 0.941519i | \(0.609399\pi\) | |||||||
\(972\) | 8.00000 | + | 13.8564i | 0.256600 | + | 0.444444i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 42.0000 | 1.34577 | ||||||||
\(975\) | −7.00000 | − | 1.73205i | −0.224179 | − | 0.0554700i | ||||
\(976\) | −17.5000 | + | 30.3109i | −0.560161 | + | 0.970228i | ||||
\(977\) | 19.0526i | 0.609545i | 0.952425 | + | 0.304773i | \(0.0985805\pi\) | ||||
−0.952425 | + | 0.304773i | \(0.901420\pi\) | |||||||
\(978\) | 10.5000 | − | 18.1865i | 0.335753 | − | 0.581541i | ||||
\(979\) | −18.0000 | + | 31.1769i | −0.575282 | + | 0.996419i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.00000 | − | 5.19615i | −0.287348 | − | 0.165900i | ||||
\(982\) | − | 46.7654i | − | 1.49234i | ||||||
\(983\) | −31.5000 | − | 18.1865i | −1.00469 | − | 0.580060i | −0.0950602 | − | 0.995472i | \(-0.530304\pi\) |
−0.909634 | + | 0.415411i | \(0.863638\pi\) | |||||||
\(984\) | 4.50000 | + | 7.79423i | 0.143455 | + | 0.248471i | ||||
\(985\) | 19.5000 | − | 33.7750i | 0.621322 | − | 1.07616i | ||||
\(986\) | −27.0000 | + | 15.5885i | −0.859855 | + | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.50000 | − | 4.33013i | −0.143164 | − | 0.137760i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 31.1769i | 0.990867i | ||||||||
\(991\) | 59.0000 | 1.87420 | 0.937098 | − | 0.349065i | \(-0.113501\pi\) | ||||
0.937098 | + | 0.349065i | \(0.113501\pi\) | |||||||
\(992\) | 9.00000 | 0.285750 | ||||||||
\(993\) | 32.9090i | 1.04433i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.00000 | + | 3.46410i | 0.190213 | + | 0.109819i | ||||
\(996\) | 3.00000 | − | 1.73205i | 0.0950586 | − | 0.0548821i | ||||
\(997\) | 1.00000 | + | 1.73205i | 0.0316703 | + | 0.0548546i | 0.881426 | − | 0.472322i | \(-0.156584\pi\) |
−0.849756 | + | 0.527176i | \(0.823251\pi\) | |||||||
\(998\) | 3.00000 | 0.0949633 | ||||||||
\(999\) | 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 | 637.2.u.a.361.1 | 2 | ||
7.2 | even | 3 | 637.2.k.b.569.1 | 2 | |||
7.3 | odd | 6 | 637.2.q.c.491.1 | 2 | |||
7.4 | even | 3 | 637.2.q.b.491.1 | 2 | |||
7.5 | odd | 6 | 91.2.k.a.23.1 | yes | 2 | ||
7.6 | odd | 2 | 91.2.u.a.88.1 | yes | 2 | ||
13.4 | even | 6 | 637.2.k.b.459.1 | 2 | |||
21.5 | even | 6 | 819.2.bm.a.478.1 | 2 | |||
21.20 | even | 2 | 819.2.do.c.361.1 | 2 | |||
91.4 | even | 6 | 637.2.q.b.589.1 | 2 | |||
91.11 | odd | 12 | 8281.2.a.w.1.1 | 2 | |||
91.17 | odd | 6 | 637.2.q.c.589.1 | 2 | |||
91.24 | even | 12 | 8281.2.a.s.1.1 | 2 | |||
91.30 | even | 6 | inner | 637.2.u.a.30.1 | 2 | ||
91.41 | even | 12 | 1183.2.e.e.508.1 | 4 | |||
91.54 | even | 12 | 1183.2.e.e.170.1 | 4 | |||
91.67 | odd | 12 | 8281.2.a.w.1.2 | 2 | |||
91.69 | odd | 6 | 91.2.k.a.4.1 | ✓ | 2 | ||
91.76 | even | 12 | 1183.2.e.e.508.2 | 4 | |||
91.80 | even | 12 | 8281.2.a.s.1.2 | 2 | |||
91.82 | odd | 6 | 91.2.u.a.30.1 | yes | 2 | ||
91.89 | even | 12 | 1183.2.e.e.170.2 | 4 | |||
273.173 | even | 6 | 819.2.do.c.667.1 | 2 | |||
273.251 | even | 6 | 819.2.bm.a.550.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.a.4.1 | ✓ | 2 | 91.69 | odd | 6 | ||
91.2.k.a.23.1 | yes | 2 | 7.5 | odd | 6 | ||
91.2.u.a.30.1 | yes | 2 | 91.82 | odd | 6 | ||
91.2.u.a.88.1 | yes | 2 | 7.6 | odd | 2 | ||
637.2.k.b.459.1 | 2 | 13.4 | even | 6 | |||
637.2.k.b.569.1 | 2 | 7.2 | even | 3 | |||
637.2.q.b.491.1 | 2 | 7.4 | even | 3 | |||
637.2.q.b.589.1 | 2 | 91.4 | even | 6 | |||
637.2.q.c.491.1 | 2 | 7.3 | odd | 6 | |||
637.2.q.c.589.1 | 2 | 91.17 | odd | 6 | |||
637.2.u.a.30.1 | 2 | 91.30 | even | 6 | inner | ||
637.2.u.a.361.1 | 2 | 1.1 | even | 1 | trivial | ||
819.2.bm.a.478.1 | 2 | 21.5 | even | 6 | |||
819.2.bm.a.550.1 | 2 | 273.251 | even | 6 | |||
819.2.do.c.361.1 | 2 | 21.20 | even | 2 | |||
819.2.do.c.667.1 | 2 | 273.173 | even | 6 | |||
1183.2.e.e.170.1 | 4 | 91.54 | even | 12 | |||
1183.2.e.e.170.2 | 4 | 91.89 | even | 12 | |||
1183.2.e.e.508.1 | 4 | 91.41 | even | 12 | |||
1183.2.e.e.508.2 | 4 | 91.76 | even | 12 | |||
8281.2.a.s.1.1 | 2 | 91.24 | even | 12 | |||
8281.2.a.s.1.2 | 2 | 91.80 | even | 12 | |||
8281.2.a.w.1.1 | 2 | 91.11 | odd | 12 | |||
8281.2.a.w.1.2 | 2 | 91.67 | odd | 12 |