Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(30,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, 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("91.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.u (of order \(6\), 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: | \(0.726638658394\) |
Analytic rank: | \(1\) |
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: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 30.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.30 |
Dual form | 91.2.u.a.88.1 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | + | 0.866025i | −1.06066 | + | 0.612372i | −0.925615 | − | 0.378467i | \(-0.876451\pi\) |
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | −0.288675 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288675 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.50000 | − | 0.866025i | −0.670820 | − | 0.387298i | 0.125567 | − | 0.992085i | \(-0.459925\pi\) |
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | 1.50000 | − | 0.866025i | 0.612372 | − | 0.353553i | ||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 3.00000 | 0.948683 | ||||||||
\(11\) | − | 5.19615i | − | 1.56670i | −0.621582 | − | 0.783349i | \(-0.713510\pi\) | ||
0.621582 | − | 0.783349i | \(-0.286490\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −1.00000 | + | 3.46410i | −0.277350 | + | 0.960769i | ||||
\(14\) | 3.00000 | − | 3.46410i | 0.801784 | − | 0.925820i | ||||
\(15\) | 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 | 0.230285 | + | 0.973123i | \(0.426034\pi\) |
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | 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 | ||||
\(21\) | 2.50000 | − | 0.866025i | 0.545545 | − | 0.188982i | ||||
\(22\) | 4.50000 | + | 7.79423i | 0.959403 | + | 1.66174i | ||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 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 | ||||||||
\(28\) | −0.500000 | + | 2.59808i | −0.0944911 | + | 0.490990i | ||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | −3.00000 | −0.547723 | ||||||||
\(31\) | 1.50000 | − | 0.866025i | 0.269408 | − | 0.155543i | −0.359211 | − | 0.933257i | \(-0.616954\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | −4.50000 | − | 2.59808i | −0.795495 | − | 0.459279i | ||||
\(33\) | 5.19615i | 0.904534i | ||||||||
\(34\) | − | 10.3923i | − | 1.78227i | ||||||
\(35\) | 4.50000 | + | 0.866025i | 0.760639 | + | 0.146385i | ||||
\(36\) | −1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | ||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | −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 | \(-0.466323\pi\) |
−0.808383 | + | 0.588657i | \(0.799657\pi\) | |||||||
\(42\) | −3.00000 | + | 3.46410i | −0.462910 | + | 0.534522i | ||||
\(43\) | −5.50000 | − | 9.52628i | −0.838742 | − | 1.45274i | −0.890947 | − | 0.454108i | \(-0.849958\pi\) |
0.0522047 | − | 0.998636i | \(-0.483375\pi\) | |||||||
\(44\) | −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 | \(-0.550941\pi\) |
−0.934635 | + | 0.355608i | \(0.884274\pi\) | |||||||
\(48\) | −2.50000 | − | 4.33013i | −0.360844 | − | 0.625000i | ||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 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 | 0.989828 | + | 0.142269i | \(0.0454398\pi\) |
−0.371706 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(54\) | −7.50000 | + | 4.33013i | −1.02062 | + | 0.589256i | ||||
\(55\) | −4.50000 | + | 7.79423i | −0.606780 | + | 1.05097i | ||||
\(56\) | 1.50000 | + | 4.33013i | 0.200446 | + | 0.578638i | ||||
\(57\) | − | 1.73205i | − | 0.229416i | ||||||
\(58\) | − | 5.19615i | − | 0.682288i | ||||||
\(59\) | −3.00000 | − | 1.73205i | −0.390567 | − | 0.225494i | 0.291839 | − | 0.956467i | \(-0.405733\pi\) |
−0.682406 | + | 0.730974i | \(0.739066\pi\) | |||||||
\(60\) | 1.50000 | − | 0.866025i | 0.193649 | − | 0.111803i | ||||
\(61\) | 7.00000 | 0.896258 | 0.448129 | − | 0.893969i | \(-0.352090\pi\) | ||||
0.448129 | + | 0.893969i | \(0.352090\pi\) | |||||||
\(62\) | −1.50000 | + | 2.59808i | −0.190500 | + | 0.329956i | ||||
\(63\) | 5.00000 | − | 1.73205i | 0.629941 | − | 0.218218i | ||||
\(64\) | −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 | \(0.177436\pi\) | ||||
−0.848616 | + | 0.529009i | \(0.822564\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.50000 | + | 2.59808i | −0.896421 | + | 0.310530i | ||||
\(71\) | 1.50000 | − | 0.866025i | 0.178017 | − | 0.102778i | −0.408344 | − | 0.912828i | \(-0.633893\pi\) |
0.586361 | + | 0.810050i | \(0.300560\pi\) | |||||||
\(72\) | 3.46410i | 0.408248i | ||||||||
\(73\) | −7.50000 | + | 4.33013i | −0.877809 | + | 0.506803i | −0.869935 | − | 0.493166i | \(-0.835840\pi\) |
−0.00787336 | + | 0.999969i | \(0.502506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | + | 1.73205i | 0.115470 | + | 0.200000i | ||||
\(76\) | 1.50000 | + | 0.866025i | 0.172062 | + | 0.0993399i | ||||
\(77\) | 4.50000 | + | 12.9904i | 0.512823 | + | 1.48039i | ||||
\(78\) | 1.50000 | + | 6.06218i | 0.169842 | + | 0.686406i | ||||
\(79\) | 2.50000 | − | 4.33013i | 0.281272 | − | 0.487177i | −0.690426 | − | 0.723403i | \(-0.742577\pi\) |
0.971698 | + | 0.236225i | \(0.0759104\pi\) | |||||||
\(80\) | − | 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 | \(-0.0608868\pi\) | |||||||
\(84\) | 0.500000 | − | 2.59808i | 0.0545545 | − | 0.283473i | ||||
\(85\) | 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 | \(-0.786348\pi\) |
0.147073 | + | 0.989126i | \(0.453015\pi\) | |||||||
\(90\) | −6.00000 | −0.632456 | ||||||||
\(91\) | −0.500000 | − | 9.52628i | −0.0524142 | − | 0.998625i | ||||
\(92\) | 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 | \(-0.751641\pi\) |
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | −4.50000 | + | 11.2583i | −0.454569 | + | 1.13726i | ||||
\(99\) | 10.3923i | 1.04447i | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −9.00000 | −0.895533 | −0.447767 | − | 0.894150i | \(-0.647781\pi\) | ||||
−0.447767 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(102\) | 10.3923i | 1.02899i | ||||||||
\(103\) | 6.50000 | − | 11.2583i | 0.640464 | − | 1.10932i | −0.344865 | − | 0.938652i | \(-0.612075\pi\) |
0.985329 | − | 0.170664i | \(-0.0545913\pi\) | |||||||
\(104\) | 6.00000 | + | 1.73205i | 0.588348 | + | 0.169842i | ||||
\(105\) | −4.50000 | − | 0.866025i | −0.439155 | − | 0.0845154i | ||||
\(106\) | −13.5000 | − | 7.79423i | −1.31124 | − | 0.757042i | ||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | 2.50000 | − | 4.33013i | 0.240563 | − | 0.416667i | ||||
\(109\) | 4.50000 | − | 2.59808i | 0.431022 | − | 0.248851i | −0.268760 | − | 0.963207i | \(-0.586614\pi\) |
0.699782 | + | 0.714357i | \(0.253281\pi\) | |||||||
\(110\) | − | 15.5885i | − | 1.48630i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.0000 | − | 8.66025i | −0.944911 | − | 0.818317i | ||||
\(113\) | −7.50000 | − | 12.9904i | −0.705541 | − | 1.22203i | −0.966496 | − | 0.256681i | \(-0.917371\pi\) |
0.260955 | − | 0.965351i | \(-0.415962\pi\) | |||||||
\(114\) | 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 | ||||||||
\(119\) | 3.00000 | − | 15.5885i | 0.275010 | − | 1.42899i | ||||
\(120\) | 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 | ||||||||
\(126\) | −6.00000 | + | 6.92820i | −0.534522 | + | 0.617213i | ||||
\(127\) | −6.50000 | + | 11.2583i | −0.576782 | + | 0.999015i | 0.419064 | + | 0.907957i | \(0.362358\pi\) |
−0.995846 | + | 0.0910585i | \(0.970975\pi\) | |||||||
\(128\) | 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 | 0.326546 | + | 0.945181i | \(0.394115\pi\) |
−0.981824 | + | 0.189794i | \(0.939218\pi\) | |||||||
\(132\) | 4.50000 | + | 2.59808i | 0.391675 | + | 0.226134i | ||||
\(133\) | −1.50000 | − | 4.33013i | −0.130066 | − | 0.375470i | ||||
\(134\) | −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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50000 | + | 11.2583i | 0.551323 | + | 0.954919i | 0.998179 | + | 0.0603135i | \(0.0192101\pi\) |
−0.446857 | + | 0.894606i | \(0.647457\pi\) | |||||||
\(140\) | 3.00000 | − | 3.46410i | 0.253546 | − | 0.292770i | ||||
\(141\) | 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 | ||||
\(147\) | −5.50000 | + | 4.33013i | −0.453632 | + | 0.357143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.0526i | 1.56085i | 0.625252 | + | 0.780423i | \(0.284996\pi\) | ||||
−0.625252 | + | 0.780423i | \(0.715004\pi\) | |||||||
\(150\) | −3.00000 | − | 1.73205i | −0.244949 | − | 0.141421i | ||||
\(151\) | −10.5000 | + | 6.06218i | −0.854478 | + | 0.493333i | −0.862159 | − | 0.506637i | \(-0.830888\pi\) |
0.00768132 | + | 0.999970i | \(0.497555\pi\) | |||||||
\(152\) | 3.00000 | 0.243332 | ||||||||
\(153\) | 6.00000 | − | 10.3923i | 0.485071 | − | 0.840168i | ||||
\(154\) | −18.0000 | − | 15.5885i | −1.45048 | − | 1.25615i | ||||
\(155\) | −3.00000 | −0.240966 | ||||||||
\(156\) | −2.50000 | − | 2.59808i | −0.200160 | − | 0.208013i | ||||
\(157\) | −11.5000 | − | 19.9186i | −0.917800 | − | 1.58968i | −0.802749 | − | 0.596316i | \(-0.796630\pi\) |
−0.115050 | − | 0.993360i | \(-0.536703\pi\) | |||||||
\(158\) | 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 | \(-0.842511\pi\) | ||
0.880079 | − | 0.474826i | \(-0.157489\pi\) | |||||||
\(164\) | −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 | \(-0.354681\pi\) |
−0.556913 | + | 0.830571i | \(0.688014\pi\) | |||||||
\(168\) | −1.50000 | − | 4.33013i | −0.115728 | − | 0.334077i | ||||
\(169\) | −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 | \(-0.306860\pi\) | ||||
0.570214 | + | 0.821496i | \(0.306860\pi\) | |||||||
\(174\) | 5.19615i | 0.393919i | ||||||||
\(175\) | 4.00000 | + | 3.46410i | 0.302372 | + | 0.261861i | ||||
\(176\) | 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 | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 9.00000 | + | 13.8564i | 0.667124 | + | 1.02711i | ||||
\(183\) | −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 | ||||
\(189\) | −12.5000 | + | 4.33013i | −0.909241 | + | 0.314970i | ||||
\(190\) | 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 | \(0.0198556\pi\) | ||||
−0.998055 | + | 0.0623379i | \(0.980144\pi\) | |||||||
\(194\) | 4.50000 | − | 7.79423i | 0.323081 | − | 0.559593i | ||||
\(195\) | −4.50000 | + | 4.33013i | −0.322252 | + | 0.310087i | ||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | 19.5000 | + | 11.2583i | 1.38932 | + | 0.802123i | 0.993238 | − | 0.116094i | \(-0.0370372\pi\) |
0.396079 | + | 0.918216i | \(0.370371\pi\) | |||||||
\(198\) | −9.00000 | − | 15.5885i | −0.639602 | − | 1.10782i | ||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | −3.00000 | + | 1.73205i | −0.212132 | + | 0.122474i | ||||
\(201\) | − | 8.66025i | − | 0.610847i | ||||||
\(202\) | 13.5000 | − | 7.79423i | 0.949857 | − | 0.548400i | ||||
\(203\) | 1.50000 | − | 7.79423i | 0.105279 | − | 0.547048i | ||||
\(204\) | −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 | ||||||||
\(210\) | 7.50000 | − | 2.59808i | 0.517549 | − | 0.179284i | ||||
\(211\) | −6.50000 | + | 11.2583i | −0.447478 | + | 0.775055i | −0.998221 | − | 0.0596196i | \(-0.981011\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 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 | ||||||
\(217\) | −3.00000 | + | 3.46410i | −0.203653 | + | 0.235159i | ||||
\(218\) | −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 | \(-0.277671\pi\) |
−0.341703 | + | 0.939808i | \(0.611004\pi\) | |||||||
\(224\) | 13.5000 | + | 2.59808i | 0.902007 | + | 0.173591i | ||||
\(225\) | 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 | \(-0.528254\pi\) |
−0.906939 | + | 0.421262i | \(0.861587\pi\) | |||||||
\(228\) | −1.50000 | − | 0.866025i | −0.0993399 | − | 0.0573539i | ||||
\(229\) | 10.5000 | + | 6.06218i | 0.693860 | + | 0.400600i | 0.805056 | − | 0.593198i | \(-0.202135\pi\) |
−0.111197 | + | 0.993798i | \(0.535468\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.50000 | − | 12.9904i | −0.296078 | − | 0.854704i | ||||
\(232\) | 4.50000 | + | 2.59808i | 0.295439 | + | 0.170572i | ||||
\(233\) | −1.50000 | + | 2.59808i | −0.0982683 | + | 0.170206i | −0.910968 | − | 0.412477i | \(-0.864664\pi\) |
0.812700 | + | 0.582683i | \(0.197997\pi\) | |||||||
\(234\) | 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 | ||||
\(238\) | 9.00000 | + | 25.9808i | 0.583383 | + | 1.68408i | ||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 8.66025i | 0.559017i | ||||||||
\(241\) | −6.00000 | − | 3.46410i | −0.386494 | − | 0.223142i | 0.294146 | − | 0.955761i | \(-0.404965\pi\) |
−0.680640 | + | 0.732618i | \(0.738298\pi\) | |||||||
\(242\) | 24.0000 | − | 13.8564i | 1.54278 | − | 0.890724i | ||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 3.50000 | − | 6.06218i | 0.224065 | − | 0.388091i | ||||
\(245\) | −12.0000 | + | 1.73205i | −0.766652 | + | 0.110657i | ||||
\(246\) | −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 | \(-0.196849\pi\) |
−0.909475 | + | 0.415759i | \(0.863516\pi\) | |||||||
\(252\) | 1.00000 | − | 5.19615i | 0.0629941 | − | 0.327327i | ||||
\(253\) | 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 | −0.773427 | − | 0.633885i | \(-0.781459\pi\) |
−0.162247 | − | 0.986750i | \(-0.551874\pi\) | |||||||
\(258\) | −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 | ||||||
\(266\) | 6.00000 | + | 5.19615i | 0.367884 | + | 0.318597i | ||||
\(267\) | 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 | \(-0.774781\pi\) |
0.942871 | + | 0.333157i | \(0.108114\pi\) | |||||||
\(270\) | 15.0000 | 0.912871 | ||||||||
\(271\) | −15.0000 | + | 8.66025i | −0.911185 | + | 0.526073i | −0.880812 | − | 0.473466i | \(-0.843003\pi\) |
−0.0303728 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(272\) | −30.0000 | −1.81902 | ||||||||
\(273\) | 0.500000 | + | 9.52628i | 0.0302614 | + | 0.576557i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.00000 | + | 5.19615i | −0.542720 | + | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | − | 8.66025i | 0.300421 | − | 0.520344i | −0.675810 | − | 0.737075i | \(-0.736206\pi\) |
0.976231 | + | 0.216731i | \(0.0695395\pi\) | |||||||
\(278\) | −19.5000 | − | 11.2583i | −1.16953 | − | 0.675230i | ||||
\(279\) | −3.00000 | + | 1.73205i | −0.179605 | + | 0.103695i | ||||
\(280\) | 1.50000 | − | 7.79423i | 0.0896421 | − | 0.465794i | ||||
\(281\) | 6.92820i | 0.413302i | 0.978415 | + | 0.206651i | \(0.0662565\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(282\) | −15.0000 | −0.893237 | ||||||||
\(283\) | 19.0000 | 1.12943 | 0.564716 | − | 0.825285i | \(-0.308986\pi\) | ||||
0.564716 | + | 0.825285i | \(0.308986\pi\) | |||||||
\(284\) | − | 1.73205i | − | 0.102778i | ||||||
\(285\) | −1.50000 | + | 2.59808i | −0.0888523 | + | 0.153897i | ||||
\(286\) | −31.5000 | + | 7.79423i | −1.86263 | + | 0.460882i | ||||
\(287\) | 13.5000 | + | 2.59808i | 0.796880 | + | 0.153360i | ||||
\(288\) | 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 | \(-0.940933\pi\) |
−0.331632 | + | 0.943409i | \(0.607599\pi\) | |||||||
\(294\) | 4.50000 | − | 11.2583i | 0.262445 | − | 0.656599i | ||||
\(295\) | 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 | ||||||||
\(301\) | 22.0000 | + | 19.0526i | 1.26806 | + | 1.09817i | ||||
\(302\) | 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 | \(-0.243259\pi\) | |||||||
\(308\) | 13.5000 | + | 2.59808i | 0.769234 | + | 0.148039i | ||||
\(309\) | −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 | \(-0.0268402\pi\) |
−0.571161 | + | 0.820838i | \(0.693507\pi\) | |||||||
\(312\) | −6.00000 | − | 1.73205i | −0.339683 | − | 0.0980581i | ||||
\(313\) | −9.50000 | + | 16.4545i | −0.536972 | + | 0.930062i | 0.462093 | + | 0.886831i | \(0.347098\pi\) |
−0.999065 | + | 0.0432311i | \(0.986235\pi\) | |||||||
\(314\) | 34.5000 | + | 19.9186i | 1.94695 | + | 1.12407i | ||||
\(315\) | −9.00000 | − | 1.73205i | −0.507093 | − | 0.0975900i | ||||
\(316\) | −2.50000 | − | 4.33013i | −0.140636 | − | 0.243589i | ||||
\(317\) | 4.50000 | + | 2.59808i | 0.252745 | + | 0.145922i | 0.621021 | − | 0.783794i | \(-0.286718\pi\) |
−0.368275 | + | 0.929717i | \(0.620052\pi\) | |||||||
\(318\) | 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 | ||||
\(329\) | 22.5000 | + | 4.33013i | 1.24047 | + | 0.238728i | ||||
\(330\) | 15.5885i | 0.858116i | ||||||||
\(331\) | − | 32.9090i | − | 1.80884i | −0.426643 | − | 0.904420i | \(-0.640304\pi\) | ||
0.426643 | − | 0.904420i | \(-0.359696\pi\) | |||||||
\(332\) | −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 | ||||
\(336\) | 10.0000 | + | 8.66025i | 0.545545 | + | 0.472456i | ||||
\(337\) | 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 | ||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | −1.50000 | − | 2.59808i | −0.0804084 | − | 0.139272i | ||||
\(349\) | −4.50000 | − | 2.59808i | −0.240879 | − | 0.139072i | 0.374701 | − | 0.927146i | \(-0.377745\pi\) |
−0.615581 | + | 0.788074i | \(0.711079\pi\) | |||||||
\(350\) | −9.00000 | − | 1.73205i | −0.481070 | − | 0.0925820i | ||||
\(351\) | −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 | ||||||||
\(357\) | −3.00000 | + | 15.5885i | −0.158777 | + | 0.825029i | ||||
\(358\) | −4.50000 | + | 2.59808i | −0.237832 | + | 0.137313i | ||||
\(359\) | 16.5000 | + | 9.52628i | 0.870837 | + | 0.502778i | 0.867626 | − | 0.497217i | \(-0.165645\pi\) |
0.00321050 | + | 0.999995i | \(0.498978\pi\) | |||||||
\(360\) | 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 | ||||||||
\(364\) | −8.50000 | − | 4.33013i | −0.445521 | − | 0.226960i | ||||
\(365\) | 15.0000 | 0.785136 | ||||||||
\(366\) | 10.5000 | − | 6.06218i | 0.548844 | − | 0.316875i | ||||
\(367\) | 23.0000 | 1.20059 | 0.600295 | − | 0.799779i | \(-0.295050\pi\) | ||||
0.600295 | + | 0.799779i | \(0.295050\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.00000 | + | 5.19615i | 0.468521 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.0000 | − | 15.5885i | −0.934513 | − | 0.809312i | ||||
\(372\) | 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 | ||||
\(378\) | 15.0000 | − | 17.3205i | 0.771517 | − | 0.890871i | ||||
\(379\) | −1.50000 | − | 0.866025i | −0.0770498 | − | 0.0444847i | 0.460980 | − | 0.887410i | \(-0.347498\pi\) |
−0.538030 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(380\) | −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 | ||||
\(385\) | 4.50000 | − | 23.3827i | 0.229341 | − | 1.19169i | ||||
\(386\) | −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 | 0.825491 | − | 0.564416i | \(-0.190898\pi\) |
−0.901544 | + | 0.432688i | \(0.857565\pi\) | |||||||
\(390\) | 3.00000 | − | 10.3923i | 0.151911 | − | 0.526235i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −7.50000 | − | 9.52628i | −0.378807 | − | 0.481150i | ||||
\(393\) | 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 | ||||||
\(399\) | 1.50000 | + | 4.33013i | 0.0750939 | + | 0.216777i | ||||
\(400\) | 5.00000 | − | 8.66025i | 0.250000 | − | 0.433013i | ||||
\(401\) | −6.00000 | + | 3.46410i | −0.299626 | + | 0.172989i | −0.642275 | − | 0.766475i | \(-0.722009\pi\) |
0.342649 | + | 0.939463i | \(0.388676\pi\) | |||||||
\(402\) | 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 | ||||
\(406\) | 4.50000 | + | 12.9904i | 0.223331 | + | 0.644702i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.00000 | − | 5.19615i | −0.445566 | − | 0.257248i | ||||
\(409\) | 6.00000 | + | 3.46410i | 0.296681 | + | 0.171289i | 0.640951 | − | 0.767582i | \(-0.278540\pi\) |
−0.344270 | + | 0.938871i | \(0.611874\pi\) | |||||||
\(410\) | −13.5000 | − | 7.79423i | −0.666717 | − | 0.384930i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.50000 | − | 11.2583i | −0.320232 | − | 0.554658i | ||||
\(413\) | 9.00000 | + | 1.73205i | 0.442861 | + | 0.0852286i | ||||
\(414\) | 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 | 0.486928 | + | 0.873442i | \(0.338117\pi\) |
−0.999887 | + | 0.0150285i | \(0.995216\pi\) | |||||||
\(420\) | −3.00000 | + | 3.46410i | −0.146385 | + | 0.169031i | ||||
\(421\) | 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 | ||||
\(427\) | −17.5000 | + | 6.06218i | −0.846884 | + | 0.293369i | ||||
\(428\) | 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 | \(-0.708735\pi\) | ||
0.609762 | − | 0.792585i | \(-0.291265\pi\) | |||||||
\(432\) | 12.5000 | + | 21.6506i | 0.601407 | + | 1.04167i | ||||
\(433\) | −9.50000 | − | 16.4545i | −0.456541 | − | 0.790752i | 0.542234 | − | 0.840227i | \(-0.317578\pi\) |
−0.998775 | + | 0.0494752i | \(0.984245\pi\) | |||||||
\(434\) | 1.50000 | − | 7.79423i | 0.0720023 | − | 0.374135i | ||||
\(435\) | −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 | \(-0.227810\pi\) |
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(440\) | 13.5000 | + | 7.79423i | 0.643587 | + | 0.371575i | ||||
\(441\) | −11.0000 | + | 8.66025i | −0.523810 | + | 0.412393i | ||||
\(442\) | 36.0000 | + | 10.3923i | 1.71235 | + | 0.494312i | ||||
\(443\) | −7.50000 | + | 12.9904i | −0.356336 | + | 0.617192i | −0.987346 | − | 0.158583i | \(-0.949307\pi\) |
0.631010 | + | 0.775775i | \(0.282641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | −9.00000 | −0.426162 | ||||||||
\(447\) | − | 19.0526i | − | 0.901155i | ||||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | 1.50000 | − | 0.866025i | 0.0707894 | − | 0.0408703i | −0.464188 | − | 0.885737i | \(-0.653654\pi\) |
0.534977 | + | 0.844867i | \(0.320320\pi\) | |||||||
\(450\) | −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 | ||||||||
\(455\) | −7.50000 | + | 14.7224i | −0.351605 | + | 0.690198i | ||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −30.0000 | + | 17.3205i | −1.40334 | + | 0.810219i | −0.994734 | − | 0.102491i | \(-0.967319\pi\) |
−0.408607 | + | 0.912710i | \(0.633985\pi\) | |||||||
\(458\) | −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 | \(-0.426166\pi\) |
0.957773 | + | 0.287527i | \(0.0928330\pi\) | |||||||
\(462\) | 18.0000 | + | 15.5885i | 0.837436 | + | 0.725241i | ||||
\(463\) | 24.2487i | 1.12693i | 0.826139 | + | 0.563467i | \(0.190533\pi\) | ||||
−0.826139 | + | 0.563467i | \(0.809467\pi\) | |||||||
\(464\) | −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 | \(-0.671832\pi\) |
0.999868 | + | 0.0162260i | \(0.00516512\pi\) | |||||||
\(468\) | −5.00000 | − | 5.19615i | −0.231125 | − | 0.240192i | ||||
\(469\) | −7.50000 | − | 21.6506i | −0.346318 | − | 0.999733i | ||||
\(470\) | −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 | ||||
\(476\) | −12.0000 | − | 10.3923i | −0.550019 | − | 0.476331i | ||||
\(477\) | −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 | −0.0580230 | − | 0.998315i | \(-0.518480\pi\) |
−0.893578 | + | 0.448908i | \(0.851813\pi\) | |||||||
\(488\) | − | 12.1244i | − | 0.548844i | ||||||
\(489\) | 12.1244i | 0.548282i | ||||||||
\(490\) | 16.5000 | − | 12.9904i | 0.745394 | − | 0.586846i | ||||
\(491\) | 13.5000 | − | 23.3827i | 0.609246 | − | 1.05525i | −0.382118 | − | 0.924113i | \(-0.624805\pi\) |
0.991365 | − | 0.131132i | \(-0.0418613\pi\) | |||||||
\(492\) | 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 | ||||
\(497\) | −3.00000 | + | 3.46410i | −0.134568 | + | 0.155386i | ||||
\(498\) | −3.00000 | − | 5.19615i | −0.134433 | − | 0.232845i | ||||
\(499\) | −1.50000 | − | 0.866025i | −0.0671492 | − | 0.0387686i | 0.466049 | − | 0.884759i | \(-0.345677\pi\) |
−0.533199 | + | 0.845990i | \(0.679010\pi\) | |||||||
\(500\) | 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 | \(-0.102363\pi\) |
−0.748091 | + | 0.663596i | \(0.769030\pi\) | |||||||
\(504\) | −3.00000 | − | 8.66025i | −0.133631 | − | 0.385758i | ||||
\(505\) | 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 | \(-0.715735\pi\) |
0.361098 | + | 0.932528i | \(0.382402\pi\) | |||||||
\(510\) | 9.00000 | − | 15.5885i | 0.398527 | − | 0.690268i | ||||
\(511\) | 15.0000 | − | 17.3205i | 0.663561 | − | 0.766214i | ||||
\(512\) | − | 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 | −0.877283 | − | 0.479973i | \(-0.840646\pi\) |
0.0229727 | − | 0.999736i | \(-0.492687\pi\) | |||||||
\(522\) | 10.3923i | 0.454859i | ||||||||
\(523\) | 2.00000 | + | 3.46410i | 0.0874539 | + | 0.151475i | 0.906434 | − | 0.422347i | \(-0.138794\pi\) |
−0.818980 | + | 0.573822i | \(0.805460\pi\) | |||||||
\(524\) | 7.50000 | + | 12.9904i | 0.327639 | + | 0.567487i | ||||
\(525\) | −4.00000 | − | 3.46410i | −0.174574 | − | 0.151186i | ||||
\(526\) | −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 | ||||
\(532\) | −4.50000 | − | 0.866025i | −0.195100 | − | 0.0375470i | ||||
\(533\) | 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 | ||||||||
\(539\) | −22.5000 | − | 28.5788i | −0.969144 | − | 1.23098i | ||||
\(540\) | −7.50000 | + | 4.33013i | −0.322749 | + | 0.186339i | ||||
\(541\) | 10.5000 | + | 6.06218i | 0.451430 | + | 0.260633i | 0.708434 | − | 0.705777i | \(-0.249402\pi\) |
−0.257004 | + | 0.966410i | \(0.582735\pi\) | |||||||
\(542\) | 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 | ||||||||
\(546\) | −9.00000 | − | 13.8564i | −0.385164 | − | 0.592999i | ||||
\(547\) | −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 | ||||||||
\(553\) | −2.50000 | + | 12.9904i | −0.106311 | + | 0.552407i | ||||
\(554\) | 17.3205i | 0.735878i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.0000 | 0.551323 | ||||||||
\(557\) | 15.5885i | 0.660504i | 0.943893 | + | 0.330252i | \(0.107134\pi\) | ||||
−0.943893 | + | 0.330252i | \(0.892866\pi\) | |||||||
\(558\) | 3.00000 | − | 5.19615i | 0.127000 | − | 0.219971i | ||||
\(559\) | 38.5000 | − | 9.52628i | 1.62838 | − | 0.402919i | ||||
\(560\) | 7.50000 | + | 21.6506i | 0.316933 | + | 0.914906i | ||||
\(561\) | −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 | −0.184950 | − | 0.982748i | \(-0.559212\pi\) |
0.943560 | − | 0.331202i | \(-0.107454\pi\) | |||||||
\(564\) | 7.50000 | − | 4.33013i | 0.315807 | − | 0.182331i | ||||
\(565\) | 25.9808i | 1.09302i | ||||||||
\(566\) | −28.5000 | + | 16.4545i | −1.19794 | + | 0.691633i | ||||
\(567\) | −2.50000 | + | 0.866025i | −0.104990 | + | 0.0363696i | ||||
\(568\) | −1.50000 | − | 2.59808i | −0.0629386 | − | 0.109013i | ||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | − | 5.19615i | − | 0.217643i | ||||||
\(571\) | 11.5000 | + | 19.9186i | 0.481260 | + | 0.833567i | 0.999769 | − | 0.0215055i | \(-0.00684595\pi\) |
−0.518509 | + | 0.855072i | \(0.673513\pi\) | |||||||
\(572\) | 13.5000 | − | 12.9904i | 0.564463 | − | 0.543155i | ||||
\(573\) | 15.0000 | 0.626634 | ||||||||
\(574\) | −22.5000 | + | 7.79423i | −0.939132 | + | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.00000 | 0.0833333 | ||||||||
\(577\) | −13.5000 | + | 7.79423i | −0.562012 | + | 0.324478i | −0.753953 | − | 0.656929i | \(-0.771855\pi\) |
0.191940 | + | 0.981407i | \(0.438522\pi\) | |||||||
\(578\) | 28.5000 | + | 16.4545i | 1.18544 | + | 0.684416i | ||||
\(579\) | − | 1.73205i | − | 0.0719816i | ||||||
\(580\) | − | 5.19615i | − | 0.215758i | ||||||
\(581\) | 3.00000 | + | 8.66025i | 0.124461 | + | 0.359288i | ||||
\(582\) | −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 | \(-0.437588\pi\) |
−0.752023 | + | 0.659137i | \(0.770922\pi\) | |||||||
\(588\) | 1.00000 | + | 6.92820i | 0.0412393 | + | 0.285714i | ||||
\(589\) | 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 | \(-0.299308\pi\) |
−0.404750 | + | 0.914428i | \(0.632641\pi\) | |||||||
\(594\) | 22.5000 | + | 38.9711i | 0.923186 | + | 1.59901i | ||||
\(595\) | −18.0000 | + | 20.7846i | −0.737928 | + | 0.852086i | ||||
\(596\) | 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 | 0.759328 | − | 0.650708i | \(-0.225528\pi\) |
−0.943193 | + | 0.332244i | \(0.892194\pi\) | |||||||
\(600\) | 3.00000 | − | 1.73205i | 0.122474 | − | 0.0707107i | ||||
\(601\) | −9.50000 | + | 16.4545i | −0.387513 | + | 0.671192i | −0.992114 | − | 0.125336i | \(-0.959999\pi\) |
0.604601 | + | 0.796528i | \(0.293332\pi\) | |||||||
\(602\) | −49.5000 | − | 9.52628i | −2.01747 | − | 0.388262i | ||||
\(603\) | − | 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 | \(-0.837606\pi\) | ||||
−0.872658 | + | 0.488332i | \(0.837606\pi\) | |||||||
\(608\) | 4.50000 | − | 7.79423i | 0.182499 | − | 0.316098i | ||||
\(609\) | −1.50000 | + | 7.79423i | −0.0607831 | + | 0.315838i | ||||
\(610\) | 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 | \(0.262605\pi\) | ||||
−0.678558 | + | 0.734547i | \(0.737395\pi\) | |||||||
\(614\) | 21.0000 | + | 36.3731i | 0.847491 | + | 1.46790i | ||||
\(615\) | −4.50000 | − | 7.79423i | −0.181458 | − | 0.314294i | ||||
\(616\) | 22.5000 | − | 7.79423i | 0.906551 | − | 0.314038i | ||||
\(617\) | 37.5000 | − | 21.6506i | 1.50969 | − | 0.871622i | 0.509757 | − | 0.860318i | \(-0.329735\pi\) |
0.999936 | − | 0.0113033i | \(-0.00359804\pi\) | |||||||
\(618\) | − | 22.5167i | − | 0.905753i | ||||||
\(619\) | −16.5000 | + | 9.52628i | −0.663191 | + | 0.382893i | −0.793492 | − | 0.608581i | \(-0.791739\pi\) |
0.130301 | + | 0.991475i | \(0.458406\pi\) | |||||||
\(620\) | −1.50000 | + | 2.59808i | −0.0602414 | + | 0.104341i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.5000 | − | 12.9904i | −0.902168 | − | 0.520867i | ||||
\(623\) | 12.0000 | − | 13.8564i | 0.480770 | − | 0.555145i | ||||
\(624\) | 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 | ||||||||
\(630\) | 15.0000 | − | 5.19615i | 0.597614 | − | 0.207020i | ||||
\(631\) | −40.5000 | + | 23.3827i | −1.61228 | + | 0.930850i | −0.623439 | + | 0.781872i | \(0.714265\pi\) |
−0.988841 | + | 0.148978i | \(0.952402\pi\) | |||||||
\(632\) | −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 | ||||||||
\(637\) | 9.50000 | + | 23.3827i | 0.376404 | + | 0.926456i | ||||
\(638\) | −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 | 0.401435 | + | 0.915888i | \(0.368512\pi\) |
−0.993899 | + | 0.110291i | \(0.964822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.50000 | + | 2.59808i | −0.177463 | + | 0.102458i | −0.586100 | − | 0.810239i | \(-0.699337\pi\) |
0.408637 | + | 0.912697i | \(0.366004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 19.0526i | − | 0.750194i | ||||||
\(646\) | 18.0000 | 0.708201 | ||||||||
\(647\) | −9.00000 | −0.353827 | −0.176913 | − | 0.984226i | \(-0.556611\pi\) | ||||
−0.176913 | + | 0.984226i | \(0.556611\pi\) | |||||||
\(648\) | − | 1.73205i | − | 0.0680414i | ||||||
\(649\) | −9.00000 | + | 15.5885i | −0.353281 | + | 0.611900i | ||||
\(650\) | −9.00000 | + | 8.66025i | −0.353009 | + | 0.339683i | ||||
\(651\) | 3.00000 | − | 3.46410i | 0.117579 | − | 0.135769i | ||||
\(652\) | −10.5000 | − | 6.06218i | −0.411212 | − | 0.237413i | ||||
\(653\) | 15.0000 | + | 25.9808i | 0.586995 | + | 1.01671i | 0.994623 | + | 0.103558i | \(0.0330227\pi\) |
−0.407628 | + | 0.913148i | \(0.633644\pi\) | |||||||
\(654\) | 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 | ||||
\(658\) | −37.5000 | + | 12.9904i | −1.46190 | + | 0.506418i | ||||
\(659\) | −7.50000 | − | 12.9904i | −0.292159 | − | 0.506033i | 0.682161 | − | 0.731202i | \(-0.261040\pi\) |
−0.974320 | + | 0.225168i | \(0.927707\pi\) | |||||||
\(660\) | −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 | ||||||||
\(665\) | −1.50000 | + | 7.79423i | −0.0581675 | + | 0.302247i | ||||
\(666\) | 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 | ||||||
\(672\) | −13.5000 | − | 2.59808i | −0.520774 | − | 0.100223i | ||||
\(673\) | 0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | \(-0.827198\pi\) |
0.875501 | + | 0.483216i | \(0.160531\pi\) | |||||||
\(674\) | −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 | 0.480913 | + | 0.876768i | \(0.340305\pi\) |
−0.999760 | + | 0.0219013i | \(0.993028\pi\) | |||||||
\(678\) | −22.5000 | − | 12.9904i | −0.864107 | − | 0.498893i | ||||
\(679\) | 9.00000 | − | 10.3923i | 0.345388 | − | 0.398820i | ||||
\(680\) | −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 | 0.844708 | − | 0.535227i | \(-0.179774\pi\) |
−0.0411658 | + | 0.999152i | \(0.513107\pi\) | |||||||
\(684\) | −3.00000 | − | 1.73205i | −0.114708 | − | 0.0662266i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.50000 | − | 32.0429i | 0.0572703 | − | 1.22341i | ||||
\(687\) | −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 | \(-0.464605\pi\) |
0.916161 | + | 0.400811i | \(0.131272\pi\) | |||||||
\(692\) | 7.50000 | − | 12.9904i | 0.285107 | − | 0.493820i | ||||
\(693\) | −9.00000 | − | 25.9808i | −0.341882 | − | 0.986928i | ||||
\(694\) | 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 | ||||
\(700\) | 5.00000 | − | 1.73205i | 0.188982 | − | 0.0654654i | ||||
\(701\) | −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 | ||||
\(707\) | 22.5000 | − | 7.79423i | 0.846200 | − | 0.293132i | ||||
\(708\) | 3.00000 | − | 1.73205i | 0.112747 | − | 0.0650945i | ||||
\(709\) | 12.1244i | 0.455340i | 0.973738 | + | 0.227670i | \(0.0731107\pi\) | ||||
−0.973738 | + | 0.227670i | \(0.926889\pi\) | |||||||
\(710\) | 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 | ||||||||
\(714\) | −9.00000 | − | 25.9808i | −0.336817 | − | 0.972306i | ||||
\(715\) | −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 | \(-0.590236\pi\) | ||||
−0.279703 | + | 0.960087i | \(0.590236\pi\) | |||||||
\(720\) | 17.3205i | 0.645497i | ||||||||
\(721\) | −6.50000 | + | 33.7750i | −0.242073 | + | 1.25785i | ||||
\(722\) | −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 | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | −16.5000 | + | 0.866025i | −0.611531 | + | 0.0320970i | ||||
\(729\) | 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 | −0.990100 | − | 0.140365i | \(-0.955173\pi\) |
−0.616609 | − | 0.787269i | \(-0.711494\pi\) | |||||||
\(734\) | −34.5000 | + | 19.9186i | −1.27342 | + | 0.735208i | ||||
\(735\) | 12.0000 | − | 1.73205i | 0.442627 | − | 0.0638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.0000 | 1.65760 | ||||||||
\(738\) | −18.0000 | −0.662589 | ||||||||
\(739\) | − | 39.8372i | − | 1.46543i | −0.680534 | − | 0.732717i | \(-0.738252\pi\) | ||
0.680534 | − | 0.732717i | \(-0.261748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00000 | + | 1.73205i | 0.220416 | + | 0.0636285i | ||||
\(742\) | 40.5000 | + | 7.79423i | 1.48680 | + | 0.286135i | ||||
\(743\) | −1.50000 | − | 0.866025i | −0.0550297 | − | 0.0317714i | 0.472233 | − | 0.881474i | \(-0.343448\pi\) |
−0.527262 | + | 0.849703i | \(0.676782\pi\) | |||||||
\(744\) | 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 | 0.623856 | − | 0.781540i | \(-0.285565\pi\) |
−0.988761 | + | 0.149505i | \(0.952232\pi\) | |||||||
\(752\) | − | 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 | ||||||||
\(756\) | −2.50000 | + | 12.9904i | −0.0909241 | + | 0.472456i | ||||
\(757\) | 8.50000 | − | 14.7224i | 0.308938 | − | 0.535096i | −0.669193 | − | 0.743089i | \(-0.733360\pi\) |
0.978130 | + | 0.207993i | \(0.0666932\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −9.00000 | + | 10.3923i | −0.325822 | + | 0.376227i | ||||
\(764\) | −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 | \(-0.444955\pi\) |
−0.767074 | + | 0.641558i | \(0.778288\pi\) | |||||||
\(770\) | 13.5000 | + | 38.9711i | 0.486506 | + | 1.40442i | ||||
\(771\) | 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 | \(-0.413498\pi\) |
−0.700032 | + | 0.714111i | \(0.746831\pi\) | |||||||
\(774\) | −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 | ||||
\(784\) | 32.5000 | + | 12.9904i | 1.16071 | + | 0.463942i | ||||
\(785\) | 39.8372i | 1.42185i | ||||||||
\(786\) | 25.9808i | 0.926703i | ||||||||
\(787\) | −27.0000 | − | 15.5885i | −0.962446 | − | 0.555668i | −0.0655211 | − | 0.997851i | \(-0.520871\pi\) |
−0.896925 | + | 0.442183i | \(0.854204\pi\) | |||||||
\(788\) | 19.5000 | − | 11.2583i | 0.694659 | − | 0.401061i | ||||
\(789\) | −3.00000 | −0.106803 | ||||||||
\(790\) | 7.50000 | − | 12.9904i | 0.266838 | − | 0.462177i | ||||
\(791\) | 30.0000 | + | 25.9808i | 1.06668 | + | 0.923770i | ||||
\(792\) | 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 | 0.994943 | + | 0.100446i | \(0.0320269\pi\) |
−0.410483 | + | 0.911868i | \(0.634640\pi\) | |||||||
\(798\) | −6.00000 | − | 5.19615i | −0.212398 | − | 0.183942i | ||||
\(799\) | 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 | \(0.980628\pi\) | |||||||
\(812\) | −6.00000 | − | 5.19615i | −0.210559 | − | 0.182349i | ||||
\(813\) | 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 | ||||||||
\(819\) | 1.00000 | + | 19.0526i | 0.0349428 | + | 0.665750i | ||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | + | 27.7128i | −0.557725 | + | 0.966008i | 0.439961 | + | 0.898017i | \(0.354992\pi\) |
−0.997686 | + | 0.0679910i | \(0.978341\pi\) | |||||||
\(824\) | −19.5000 | − | 11.2583i | −0.679315 | − | 0.392203i | ||||
\(825\) | 9.00000 | − | 5.19615i | 0.313340 | − | 0.180907i | ||||
\(826\) | −15.0000 | + | 5.19615i | −0.521917 | + | 0.180797i | ||||
\(827\) | − | 10.3923i | − | 0.361376i | −0.983540 | − | 0.180688i | \(-0.942168\pi\) | ||
0.983540 | − | 0.180688i | \(-0.0578324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.00000 | 0.243120 | 0.121560 | − | 0.992584i | \(-0.461210\pi\) | ||||
0.121560 | + | 0.992584i | \(0.461210\pi\) | |||||||
\(830\) | − | 10.3923i | − | 0.360722i | ||||||
\(831\) | −5.00000 | + | 8.66025i | −0.173448 | + | 0.300421i | ||||
\(832\) | 1.00000 | − | 3.46410i | 0.0346688 | − | 0.120096i | ||||
\(833\) | 6.00000 | + | 41.5692i | 0.207888 | + | 1.44029i | ||||
\(834\) | 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 | \(-0.657148\pi\) |
0.525669 | + | 0.850689i | \(0.323815\pi\) | |||||||
\(840\) | −1.50000 | + | 7.79423i | −0.0517549 | + | 0.268926i | ||||
\(841\) | 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 | ||||||||
\(847\) | 40.0000 | − | 13.8564i | 1.37442 | − | 0.476112i | ||||
\(848\) | −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 | \(-0.252052\pi\) | |||||||
\(854\) | 21.0000 | − | 24.2487i | 0.718605 | − | 0.829774i | ||||
\(855\) | −3.00000 | + | 5.19615i | −0.102598 | + | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5000 | + | 28.5788i | 0.563629 | + | 0.976235i | 0.997176 | + | 0.0751033i | \(0.0239287\pi\) |
−0.433546 | + | 0.901131i | \(0.642738\pi\) | |||||||
\(858\) | 31.5000 | − | 7.79423i | 1.07539 | − | 0.266091i | ||||
\(859\) | 14.5000 | − | 25.1147i | 0.494734 | − | 0.856904i | −0.505248 | − | 0.862974i | \(-0.668599\pi\) |
0.999982 | + | 0.00607046i | \(0.00193230\pi\) | |||||||
\(860\) | 16.5000 | + | 9.52628i | 0.562645 | + | 0.324843i | ||||
\(861\) | −13.5000 | − | 2.59808i | −0.460079 | − | 0.0885422i | ||||
\(862\) | 28.5000 | + | 49.3634i | 0.970714 | + | 1.68133i | ||||
\(863\) | −1.50000 | − | 0.866025i | −0.0510606 | − | 0.0294798i | 0.474252 | − | 0.880389i | \(-0.342718\pi\) |
−0.525313 | + | 0.850909i | \(0.676052\pi\) | |||||||
\(864\) | −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 | ||||
\(868\) | 1.50000 | + | 4.33013i | 0.0509133 | + | 0.146974i | ||||
\(869\) | −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 | ||||||||
\(875\) | −10.5000 | − | 30.3109i | −0.354965 | − | 1.02470i | ||||
\(876\) | − | 8.66025i | − | 0.292603i | ||||||
\(877\) | − | 1.73205i | − | 0.0584872i | −0.999572 | − | 0.0292436i | \(-0.990690\pi\) | ||
0.999572 | − | 0.0292436i | \(-0.00930985\pi\) | |||||||
\(878\) | 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 | −0.441934 | − | 0.897048i | \(-0.645707\pi\) |
0.997833 | − | 0.0657979i | \(-0.0209593\pi\) | |||||||
\(882\) | 9.00000 | − | 22.5167i | 0.303046 | − | 0.758175i | ||||
\(883\) | −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 | \(-0.298672\pi\) |
−0.994077 | + | 0.108678i | \(0.965338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.50000 | − | 33.7750i | 0.218003 | − | 1.13278i | ||||
\(890\) | −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 | ||||
\(896\) | −21.0000 | + | 24.2487i | −0.701561 | + | 0.810093i | ||||
\(897\) | 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 | ||||||
\(903\) | −22.0000 | − | 19.0526i | −0.732114 | − | 0.634029i | ||||
\(904\) | −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 | ||||||||
\(910\) | −1.50000 | − | 28.5788i | −0.0497245 | − | 0.947379i | ||||
\(911\) | 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 | ||||
\(917\) | 7.50000 | − | 38.9711i | 0.247672 | − | 1.28694i | ||||
\(918\) | − | 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 | ||||
\(924\) | −13.5000 | − | 2.59808i | −0.444117 | − | 0.0854704i | ||||
\(925\) | 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 | ||||
\(931\) | 7.50000 | + | 9.52628i | 0.245803 | + | 0.312211i | ||||
\(932\) | 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 | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 30.0000 | + | 25.9808i | 0.979535 | + | 0.848302i | ||||
\(939\) | 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 | \(-0.639675\pi\) |
0.571551 | + | 0.820566i | \(0.306342\pi\) | |||||||
\(942\) | −34.5000 | − | 19.9186i | −1.12407 | − | 0.648983i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 17.3205i | − | 0.563735i | ||||||
\(945\) | 22.5000 | + | 4.33013i | 0.731925 | + | 0.140859i | ||||
\(946\) | 49.5000 | − | 85.7365i | 1.60938 | − | 2.78753i | ||||
\(947\) | −33.0000 | + | 19.0526i | −1.07236 | + | 0.619125i | −0.928824 | − | 0.370521i | \(-0.879179\pi\) |
−0.143532 | + | 0.989646i | \(0.545846\pi\) | |||||||
\(948\) | 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 | ||||
\(952\) | −27.0000 | − | 5.19615i | −0.875075 | − | 0.168408i | ||||
\(953\) | 28.5000 | + | 49.3634i | 0.923206 | + | 1.59904i | 0.794422 | + | 0.607366i | \(0.207774\pi\) |
0.128784 | + | 0.991673i | \(0.458893\pi\) | |||||||
\(954\) | 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 | \(0.0534393\pi\) | ||||
−0.985940 | + | 0.167097i | \(0.946561\pi\) | |||||||
\(968\) | 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 | \(-0.390601\pi\) | ||||
0.336961 | + | 0.941519i | \(0.390601\pi\) | |||||||
\(972\) | −8.00000 | + | 13.8564i | −0.256600 | + | 0.444444i | ||||
\(973\) | −26.0000 | − | 22.5167i | −0.833522 | − | 0.721851i | ||||
\(974\) | 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 | \(-0.901420\pi\) | ||
0.952425 | − | 0.304773i | \(-0.0985805\pi\) | |||||||
\(978\) | −10.5000 | − | 18.1865i | −0.335753 | − | 0.581541i | ||||
\(979\) | 18.0000 | + | 31.1769i | 0.575282 | + | 0.996419i | ||||
\(980\) | −4.50000 | + | 11.2583i | −0.143747 | + | 0.359634i | ||||
\(981\) | −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 | \(-0.469696\pi\) |
0.909634 | + | 0.415411i | \(0.136362\pi\) | |||||||
\(984\) | 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 | ||||
\(987\) | −22.5000 | − | 4.33013i | −0.716183 | − | 0.137829i | ||||
\(988\) | −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 | ||||||||
\(994\) | 1.50000 | − | 7.79423i | 0.0475771 | − | 0.247218i | ||||
\(995\) | 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 | \(-0.843416\pi\) |
0.849756 | + | 0.527176i | \(0.176749\pi\) | |||||||
\(998\) | 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 | 91.2.u.a.30.1 | yes | 2 | |
3.2 | odd | 2 | 819.2.do.c.667.1 | 2 | |||
7.2 | even | 3 | 637.2.q.c.589.1 | 2 | |||
7.3 | odd | 6 | 637.2.k.b.459.1 | 2 | |||
7.4 | even | 3 | 91.2.k.a.4.1 | ✓ | 2 | ||
7.5 | odd | 6 | 637.2.q.b.589.1 | 2 | |||
7.6 | odd | 2 | 637.2.u.a.30.1 | 2 | |||
13.6 | odd | 12 | 1183.2.e.e.170.2 | 4 | |||
13.7 | odd | 12 | 1183.2.e.e.170.1 | 4 | |||
13.10 | even | 6 | 91.2.k.a.23.1 | yes | 2 | ||
21.11 | odd | 6 | 819.2.bm.a.550.1 | 2 | |||
39.23 | odd | 6 | 819.2.bm.a.478.1 | 2 | |||
91.10 | odd | 6 | 637.2.u.a.361.1 | 2 | |||
91.19 | even | 12 | 8281.2.a.w.1.1 | 2 | |||
91.23 | even | 6 | 637.2.q.c.491.1 | 2 | |||
91.32 | odd | 12 | 1183.2.e.e.508.2 | 4 | |||
91.33 | even | 12 | 8281.2.a.w.1.2 | 2 | |||
91.46 | odd | 12 | 1183.2.e.e.508.1 | 4 | |||
91.58 | odd | 12 | 8281.2.a.s.1.1 | 2 | |||
91.62 | odd | 6 | 637.2.k.b.569.1 | 2 | |||
91.72 | odd | 12 | 8281.2.a.s.1.2 | 2 | |||
91.75 | odd | 6 | 637.2.q.b.491.1 | 2 | |||
91.88 | even | 6 | inner | 91.2.u.a.88.1 | yes | 2 | |
273.179 | odd | 6 | 819.2.do.c.361.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.a.4.1 | ✓ | 2 | 7.4 | even | 3 | ||
91.2.k.a.23.1 | yes | 2 | 13.10 | even | 6 | ||
91.2.u.a.30.1 | yes | 2 | 1.1 | even | 1 | trivial | |
91.2.u.a.88.1 | yes | 2 | 91.88 | even | 6 | inner | |
637.2.k.b.459.1 | 2 | 7.3 | odd | 6 | |||
637.2.k.b.569.1 | 2 | 91.62 | odd | 6 | |||
637.2.q.b.491.1 | 2 | 91.75 | odd | 6 | |||
637.2.q.b.589.1 | 2 | 7.5 | odd | 6 | |||
637.2.q.c.491.1 | 2 | 91.23 | even | 6 | |||
637.2.q.c.589.1 | 2 | 7.2 | even | 3 | |||
637.2.u.a.30.1 | 2 | 7.6 | odd | 2 | |||
637.2.u.a.361.1 | 2 | 91.10 | odd | 6 | |||
819.2.bm.a.478.1 | 2 | 39.23 | odd | 6 | |||
819.2.bm.a.550.1 | 2 | 21.11 | odd | 6 | |||
819.2.do.c.361.1 | 2 | 273.179 | odd | 6 | |||
819.2.do.c.667.1 | 2 | 3.2 | odd | 2 | |||
1183.2.e.e.170.1 | 4 | 13.7 | odd | 12 | |||
1183.2.e.e.170.2 | 4 | 13.6 | odd | 12 | |||
1183.2.e.e.508.1 | 4 | 91.46 | odd | 12 | |||
1183.2.e.e.508.2 | 4 | 91.32 | odd | 12 | |||
8281.2.a.s.1.1 | 2 | 91.58 | odd | 12 | |||
8281.2.a.s.1.2 | 2 | 91.72 | odd | 12 | |||
8281.2.a.w.1.1 | 2 | 91.19 | even | 12 | |||
8281.2.a.w.1.2 | 2 | 91.33 | even | 12 |