Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(116,637)]
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([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.r (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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 116.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.116 |
Dual form | 637.2.r.c.324.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | + | 1.00000i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | 1.00000 | − | 1.73205i | 0.577350 | − | 1.00000i | −0.418432 | − | 0.908248i | \(-0.637420\pi\) |
0.995782 | − | 0.0917517i | \(-0.0292466\pi\) | |||||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | −0.680989 | − | 0.732294i | \(-0.738450\pi\) |
0.293691 | + | 0.955901i | \(0.405116\pi\) | |||||||
\(6\) | 4.00000i | 1.63299i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | 1.73205 | + | 1.00000i | 0.522233 | + | 0.301511i | 0.737848 | − | 0.674967i | \(-0.235842\pi\) |
−0.215615 | + | 0.976478i | \(0.569176\pi\) | |||||||
\(12\) | −2.00000 | − | 3.46410i | −0.577350 | − | 1.00000i | ||||
\(13\) | −2.00000 | + | 3.00000i | −0.554700 | + | 0.832050i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000i | 0.516398i | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | 1.73205 | + | 1.00000i | 0.408248 | + | 0.235702i | ||||
\(19\) | 2.59808 | − | 1.50000i | 0.596040 | − | 0.344124i | −0.171442 | − | 0.985194i | \(-0.554843\pi\) |
0.767482 | + | 0.641071i | \(0.221509\pi\) | |||||||
\(20\) | 2.00000i | 0.447214i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0.464102 | − | 7.19615i | 0.0910178 | − | 1.41128i | ||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | −2.00000 | − | 3.46410i | −0.365148 | − | 0.632456i | ||||
\(31\) | −2.59808 | − | 1.50000i | −0.466628 | − | 0.269408i | 0.248199 | − | 0.968709i | \(-0.420161\pi\) |
−0.714827 | + | 0.699301i | \(0.753495\pi\) | |||||||
\(32\) | −6.92820 | − | 4.00000i | −1.22474 | − | 0.707107i | ||||
\(33\) | 3.46410 | − | 2.00000i | 0.603023 | − | 0.348155i | ||||
\(34\) | 12.0000i | 2.05798i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 5.19615 | − | 3.00000i | 0.854242 | − | 0.493197i | −0.00783774 | − | 0.999969i | \(-0.502495\pi\) |
0.862080 | + | 0.506772i | \(0.169162\pi\) | |||||||
\(38\) | −3.00000 | + | 5.19615i | −0.486664 | + | 0.842927i | ||||
\(39\) | 3.19615 | + | 6.46410i | 0.511794 | + | 1.03508i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.0000i | − | 1.56174i | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||
0.624695 | − | 0.780869i | \(-0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 3.46410 | − | 2.00000i | 0.522233 | − | 0.301511i | ||||
\(45\) | 0.866025 | + | 0.500000i | 0.129099 | + | 0.0745356i | ||||
\(46\) | −5.19615 | − | 3.00000i | −0.766131 | − | 0.442326i | ||||
\(47\) | 9.52628 | − | 5.50000i | 1.38955 | − | 0.802257i | 0.396286 | − | 0.918127i | \(-0.370299\pi\) |
0.993264 | + | 0.115870i | \(0.0369655\pi\) | |||||||
\(48\) | 8.00000 | 1.15470 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 8.00000i | − | 1.13137i | ||||||
\(51\) | −6.00000 | − | 10.3923i | −0.840168 | − | 1.45521i | ||||
\(52\) | 3.19615 | + | 6.46410i | 0.443227 | + | 0.896410i | ||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | −6.92820 | + | 4.00000i | −0.942809 | + | 0.544331i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | −5.19615 | + | 3.00000i | −0.682288 | + | 0.393919i | ||||
\(59\) | 6.92820 | + | 4.00000i | 0.901975 | + | 0.520756i | 0.877841 | − | 0.478953i | \(-0.158984\pi\) |
0.0241347 | + | 0.999709i | \(0.492317\pi\) | |||||||
\(60\) | 3.46410 | + | 2.00000i | 0.447214 | + | 0.258199i | ||||
\(61\) | 4.00000 | + | 6.92820i | 0.512148 | + | 0.887066i | 0.999901 | + | 0.0140840i | \(0.00448323\pi\) |
−0.487753 | + | 0.872982i | \(0.662183\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0.232051 | − | 3.59808i | 0.0287824 | − | 0.446286i | ||||
\(66\) | −4.00000 | + | 6.92820i | −0.492366 | + | 0.852803i | ||||
\(67\) | −10.3923 | − | 6.00000i | −1.26962 | − | 0.733017i | −0.294706 | − | 0.955588i | \(-0.595222\pi\) |
−0.974916 | + | 0.222571i | \(0.928555\pi\) | |||||||
\(68\) | −6.00000 | − | 10.3923i | −0.727607 | − | 1.26025i | ||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0000i | 1.66149i | 0.556650 | + | 0.830747i | \(0.312086\pi\) | ||||
−0.556650 | + | 0.830747i | \(0.687914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.79423 | + | 4.50000i | 0.912245 | + | 0.526685i | 0.881153 | − | 0.472831i | \(-0.156768\pi\) |
0.0310925 | + | 0.999517i | \(0.490101\pi\) | |||||||
\(74\) | −6.00000 | + | 10.3923i | −0.697486 | + | 1.20808i | ||||
\(75\) | 4.00000 | + | 6.92820i | 0.461880 | + | 0.800000i | ||||
\(76\) | − | 6.00000i | − | 0.688247i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −12.0000 | − | 8.00000i | −1.35873 | − | 0.905822i | ||||
\(79\) | 4.50000 | + | 7.79423i | 0.506290 | + | 0.876919i | 0.999974 | + | 0.00727784i | \(0.00231663\pi\) |
−0.493684 | + | 0.869641i | \(0.664350\pi\) | |||||||
\(80\) | −3.46410 | − | 2.00000i | −0.387298 | − | 0.223607i | ||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 10.0000 | + | 17.3205i | 1.10432 | + | 1.91273i | ||||
\(83\) | − | 11.0000i | − | 1.20741i | −0.797209 | − | 0.603703i | \(-0.793691\pi\) | ||
0.797209 | − | 0.603703i | \(-0.206309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000i | 0.650791i | ||||||||
\(86\) | −1.73205 | + | 1.00000i | −0.186772 | + | 0.107833i | ||||
\(87\) | 3.00000 | − | 5.19615i | 0.321634 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.33013 | + | 2.50000i | −0.458993 | + | 0.264999i | −0.711621 | − | 0.702564i | \(-0.752038\pi\) |
0.252628 | + | 0.967563i | \(0.418705\pi\) | |||||||
\(90\) | −2.00000 | −0.210819 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | −5.19615 | + | 3.00000i | −0.538816 | + | 0.311086i | ||||
\(94\) | −11.0000 | + | 19.0526i | −1.13456 | + | 1.96512i | ||||
\(95\) | −1.50000 | + | 2.59808i | −0.153897 | + | 0.266557i | ||||
\(96\) | −13.8564 | + | 8.00000i | −1.41421 | + | 0.816497i | ||||
\(97\) | 9.00000i | 0.913812i | 0.889515 | + | 0.456906i | \(0.151042\pi\) | ||||
−0.889515 | + | 0.456906i | \(0.848958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.00000i | − | 0.201008i | ||||||
\(100\) | 4.00000 | + | 6.92820i | 0.400000 | + | 0.692820i | ||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | 20.7846 | + | 12.0000i | 2.05798 | + | 1.18818i | ||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.0000i | 1.74831i | ||||||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 4.00000 | − | 6.92820i | 0.384900 | − | 0.666667i | ||||
\(109\) | 15.5885 | + | 9.00000i | 1.49310 | + | 0.862044i | 0.999969 | − | 0.00790932i | \(-0.00251764\pi\) |
0.493135 | + | 0.869953i | \(0.335851\pi\) | |||||||
\(110\) | 3.46410 | − | 2.00000i | 0.330289 | − | 0.190693i | ||||
\(111\) | − | 12.0000i | − | 1.13899i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0000 | −1.41108 | −0.705541 | − | 0.708669i | \(-0.749296\pi\) | ||||
−0.705541 | + | 0.708669i | \(0.749296\pi\) | |||||||
\(114\) | 6.00000 | + | 10.3923i | 0.561951 | + | 0.973329i | ||||
\(115\) | −2.59808 | − | 1.50000i | −0.242272 | − | 0.139876i | ||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | 3.59808 | + | 0.232051i | 0.332642 | + | 0.0214531i | ||||
\(118\) | −16.0000 | −1.47292 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50000 | − | 6.06218i | −0.318182 | − | 0.551107i | ||||
\(122\) | −13.8564 | − | 8.00000i | −1.25450 | − | 0.724286i | ||||
\(123\) | −17.3205 | − | 10.0000i | −1.56174 | − | 0.901670i | ||||
\(124\) | −5.19615 | + | 3.00000i | −0.466628 | + | 0.269408i | ||||
\(125\) | − | 9.00000i | − | 0.804984i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.00000 | − | 1.73205i | 0.0880451 | − | 0.152499i | ||||
\(130\) | 3.19615 | + | 6.46410i | 0.280321 | + | 0.566939i | ||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | − | 8.00000i | − | 0.696311i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 24.0000 | 2.07328 | ||||||||
\(135\) | −3.46410 | + | 2.00000i | −0.298142 | + | 0.172133i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.73205 | − | 1.00000i | −0.147979 | − | 0.0854358i | 0.424182 | − | 0.905577i | \(-0.360562\pi\) |
−0.572161 | + | 0.820141i | \(0.693895\pi\) | |||||||
\(138\) | −10.3923 | + | 6.00000i | −0.884652 | + | 0.510754i | ||||
\(139\) | −18.0000 | −1.52674 | −0.763370 | − | 0.645961i | \(-0.776457\pi\) | ||||
−0.763370 | + | 0.645961i | \(0.776457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 22.0000i | − | 1.85273i | ||||||
\(142\) | −14.0000 | − | 24.2487i | −1.17485 | − | 2.03491i | ||||
\(143\) | −6.46410 | + | 3.19615i | −0.540555 | + | 0.267276i | ||||
\(144\) | 2.00000 | − | 3.46410i | 0.166667 | − | 0.288675i | ||||
\(145\) | −2.59808 | + | 1.50000i | −0.215758 | + | 0.124568i | ||||
\(146\) | −18.0000 | −1.48969 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 12.0000i | − | 0.986394i | ||||||
\(149\) | −8.66025 | + | 5.00000i | −0.709476 | + | 0.409616i | −0.810867 | − | 0.585231i | \(-0.801004\pi\) |
0.101391 | + | 0.994847i | \(0.467671\pi\) | |||||||
\(150\) | −13.8564 | − | 8.00000i | −1.13137 | − | 0.653197i | ||||
\(151\) | −5.19615 | − | 3.00000i | −0.422857 | − | 0.244137i | 0.273442 | − | 0.961888i | \(-0.411838\pi\) |
−0.696299 | + | 0.717752i | \(0.745171\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.00000 | 0.240966 | ||||||||
\(156\) | 14.3923 | + | 0.928203i | 1.15231 | + | 0.0743157i | ||||
\(157\) | 9.00000 | − | 15.5885i | 0.718278 | − | 1.24409i | −0.243403 | − | 0.969925i | \(-0.578264\pi\) |
0.961681 | − | 0.274169i | \(-0.0884028\pi\) | |||||||
\(158\) | −15.5885 | − | 9.00000i | −1.24015 | − | 0.716002i | ||||
\(159\) | −9.00000 | − | 15.5885i | −0.713746 | − | 1.23625i | ||||
\(160\) | 8.00000 | 0.632456 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 22.0000i | 1.72848i | ||||||||
\(163\) | −10.3923 | + | 6.00000i | −0.813988 | + | 0.469956i | −0.848339 | − | 0.529454i | \(-0.822397\pi\) |
0.0343508 | + | 0.999410i | \(0.489064\pi\) | |||||||
\(164\) | −17.3205 | − | 10.0000i | −1.35250 | − | 0.780869i | ||||
\(165\) | −2.00000 | + | 3.46410i | −0.155700 | + | 0.269680i | ||||
\(166\) | 11.0000 | + | 19.0526i | 0.853766 | + | 1.47877i | ||||
\(167\) | 1.00000i | 0.0773823i | 0.999251 | + | 0.0386912i | \(0.0123189\pi\) | ||||
−0.999251 | + | 0.0386912i | \(0.987681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | − | 12.0000i | −0.384615 | − | 0.923077i | ||||
\(170\) | −6.00000 | − | 10.3923i | −0.460179 | − | 0.797053i | ||||
\(171\) | −2.59808 | − | 1.50000i | −0.198680 | − | 0.114708i | ||||
\(172\) | 1.00000 | − | 1.73205i | 0.0762493 | − | 0.132068i | ||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 12.0000i | 0.909718i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.00000i | 0.603023i | ||||||||
\(177\) | 13.8564 | − | 8.00000i | 1.04151 | − | 0.601317i | ||||
\(178\) | 5.00000 | − | 8.66025i | 0.374766 | − | 0.649113i | ||||
\(179\) | −4.50000 | + | 7.79423i | −0.336346 | + | 0.582568i | −0.983742 | − | 0.179585i | \(-0.942524\pi\) |
0.647397 | + | 0.762153i | \(0.275858\pi\) | |||||||
\(180\) | 1.73205 | − | 1.00000i | 0.129099 | − | 0.0745356i | ||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.0000 | 1.18275 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | + | 5.19615i | −0.220564 | + | 0.382029i | ||||
\(186\) | 6.00000 | − | 10.3923i | 0.439941 | − | 0.762001i | ||||
\(187\) | 10.3923 | − | 6.00000i | 0.759961 | − | 0.438763i | ||||
\(188\) | − | 22.0000i | − | 1.60451i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 6.00000i | − | 0.435286i | ||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 8.00000 | − | 13.8564i | 0.577350 | − | 1.00000i | ||||
\(193\) | 10.3923 | + | 6.00000i | 0.748054 | + | 0.431889i | 0.824991 | − | 0.565147i | \(-0.191180\pi\) |
−0.0769360 | + | 0.997036i | \(0.524514\pi\) | |||||||
\(194\) | −9.00000 | − | 15.5885i | −0.646162 | − | 1.11919i | ||||
\(195\) | −6.00000 | − | 4.00000i | −0.429669 | − | 0.286446i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000i | 0.284988i | 0.989796 | + | 0.142494i | \(0.0455122\pi\) | ||||
−0.989796 | + | 0.142494i | \(0.954488\pi\) | |||||||
\(198\) | 2.00000 | + | 3.46410i | 0.142134 | + | 0.246183i | ||||
\(199\) | −1.00000 | + | 1.73205i | −0.0708881 | + | 0.122782i | −0.899291 | − | 0.437351i | \(-0.855917\pi\) |
0.828403 | + | 0.560133i | \(0.189250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.7846 | + | 12.0000i | −1.46603 | + | 0.846415i | ||||
\(202\) | 12.0000i | 0.844317i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −24.0000 | −1.68034 | ||||||||
\(205\) | 5.00000 | + | 8.66025i | 0.349215 | + | 0.604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.50000 | − | 2.59808i | 0.104257 | − | 0.180579i | ||||
\(208\) | −14.3923 | − | 0.928203i | −0.997927 | − | 0.0643593i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | −0.619586 | −0.309793 | − | 0.950804i | \(-0.600260\pi\) | ||||
−0.309793 | + | 0.950804i | \(0.600260\pi\) | |||||||
\(212\) | −9.00000 | − | 15.5885i | −0.618123 | − | 1.07062i | ||||
\(213\) | 24.2487 | + | 14.0000i | 1.66149 | + | 0.959264i | ||||
\(214\) | −20.7846 | − | 12.0000i | −1.42081 | − | 0.820303i | ||||
\(215\) | −0.866025 | + | 0.500000i | −0.0590624 | + | 0.0340997i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −36.0000 | −2.43823 | ||||||||
\(219\) | 15.5885 | − | 9.00000i | 1.05337 | − | 0.608164i | ||||
\(220\) | −2.00000 | + | 3.46410i | −0.134840 | + | 0.233550i | ||||
\(221\) | 9.58846 | + | 19.3923i | 0.644989 | + | 1.30447i | ||||
\(222\) | 12.0000 | + | 20.7846i | 0.805387 | + | 1.39497i | ||||
\(223\) | 21.0000i | 1.40626i | 0.711059 | + | 0.703132i | \(0.248216\pi\) | ||||
−0.711059 | + | 0.703132i | \(0.751784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 25.9808 | − | 15.0000i | 1.72821 | − | 0.997785i | ||||
\(227\) | −17.3205 | − | 10.0000i | −1.14960 | − | 0.663723i | −0.200812 | − | 0.979630i | \(-0.564358\pi\) |
−0.948790 | + | 0.315906i | \(0.897691\pi\) | |||||||
\(228\) | −10.3923 | − | 6.00000i | −0.688247 | − | 0.397360i | ||||
\(229\) | −5.19615 | + | 3.00000i | −0.343371 | + | 0.198246i | −0.661762 | − | 0.749714i | \(-0.730191\pi\) |
0.318390 | + | 0.947960i | \(0.396858\pi\) | |||||||
\(230\) | 6.00000 | 0.395628 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.50000 | + | 2.59808i | 0.0982683 | + | 0.170206i | 0.910968 | − | 0.412477i | \(-0.135336\pi\) |
−0.812700 | + | 0.582683i | \(0.802003\pi\) | |||||||
\(234\) | −6.46410 | + | 3.19615i | −0.422572 | + | 0.208939i | ||||
\(235\) | −5.50000 | + | 9.52628i | −0.358780 | + | 0.621426i | ||||
\(236\) | 13.8564 | − | 8.00000i | 0.901975 | − | 0.520756i | ||||
\(237\) | 18.0000 | 1.16923 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.00000i | − | 0.517477i | −0.965947 | − | 0.258738i | \(-0.916693\pi\) | ||
0.965947 | − | 0.258738i | \(-0.0833068\pi\) | |||||||
\(240\) | −6.92820 | + | 4.00000i | −0.447214 | + | 0.258199i | ||||
\(241\) | 18.1865 | + | 10.5000i | 1.17150 | + | 0.676364i | 0.954032 | − | 0.299704i | \(-0.0968878\pi\) |
0.217465 | + | 0.976068i | \(0.430221\pi\) | |||||||
\(242\) | 12.1244 | + | 7.00000i | 0.779383 | + | 0.449977i | ||||
\(243\) | −5.00000 | − | 8.66025i | −0.320750 | − | 0.555556i | ||||
\(244\) | 16.0000 | 1.02430 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 40.0000 | 2.55031 | ||||||||
\(247\) | −0.696152 | + | 10.7942i | −0.0442951 | + | 0.686820i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.0526 | − | 11.0000i | −1.20741 | − | 0.697097i | ||||
\(250\) | 9.00000 | + | 15.5885i | 0.569210 | + | 0.985901i | ||||
\(251\) | −6.00000 | −0.378717 | −0.189358 | − | 0.981908i | \(-0.560641\pi\) | ||||
−0.189358 | + | 0.981908i | \(0.560641\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000i | 0.377217i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.3923 | + | 6.00000i | 0.650791 | + | 0.375735i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | 4.00000i | 0.249029i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.00000 | − | 4.00000i | −0.372104 | − | 0.248069i | ||||
\(261\) | −1.50000 | − | 2.59808i | −0.0928477 | − | 0.160817i | ||||
\(262\) | 20.7846 | + | 12.0000i | 1.28408 | + | 0.741362i | ||||
\(263\) | −4.50000 | + | 7.79423i | −0.277482 | + | 0.480613i | −0.970758 | − | 0.240059i | \(-0.922833\pi\) |
0.693276 | + | 0.720672i | \(0.256167\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000i | 0.552866i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | −20.7846 | + | 12.0000i | −1.26962 | + | 0.733017i | ||||
\(269\) | −12.0000 | + | 20.7846i | −0.731653 | + | 1.26726i | 0.224523 | + | 0.974469i | \(0.427917\pi\) |
−0.956176 | + | 0.292791i | \(0.905416\pi\) | |||||||
\(270\) | 4.00000 | − | 6.92820i | 0.243432 | − | 0.421637i | ||||
\(271\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(272\) | 24.0000 | 1.45521 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.00000 | 0.241649 | ||||||||
\(275\) | −6.92820 | + | 4.00000i | −0.417786 | + | 0.241209i | ||||
\(276\) | 6.00000 | − | 10.3923i | 0.361158 | − | 0.625543i | ||||
\(277\) | 8.50000 | − | 14.7224i | 0.510716 | − | 0.884585i | −0.489207 | − | 0.872167i | \(-0.662714\pi\) |
0.999923 | − | 0.0124177i | \(-0.00395278\pi\) | |||||||
\(278\) | 31.1769 | − | 18.0000i | 1.86987 | − | 1.07957i | ||||
\(279\) | 3.00000i | 0.179605i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000i | 0.119310i | 0.998219 | + | 0.0596550i | \(0.0190001\pi\) | ||||
−0.998219 | + | 0.0596550i | \(0.981000\pi\) | |||||||
\(282\) | 22.0000 | + | 38.1051i | 1.31008 | + | 2.26913i | ||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 24.2487 | + | 14.0000i | 1.43890 | + | 0.830747i | ||||
\(285\) | 3.00000 | + | 5.19615i | 0.177705 | + | 0.307794i | ||||
\(286\) | 8.00000 | − | 12.0000i | 0.473050 | − | 0.709575i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.00000i | 0.471405i | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 3.00000 | − | 5.19615i | 0.176166 | − | 0.305129i | ||||
\(291\) | 15.5885 | + | 9.00000i | 0.913812 | + | 0.527589i | ||||
\(292\) | 15.5885 | − | 9.00000i | 0.912245 | − | 0.526685i | ||||
\(293\) | 1.00000i | 0.0584206i | 0.999573 | + | 0.0292103i | \(0.00929925\pi\) | ||||
−0.999573 | + | 0.0292103i | \(0.990701\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.92820 | + | 4.00000i | 0.402015 | + | 0.232104i | ||||
\(298\) | 10.0000 | − | 17.3205i | 0.579284 | − | 1.00335i | ||||
\(299\) | −10.7942 | − | 0.696152i | −0.624246 | − | 0.0402595i | ||||
\(300\) | 16.0000 | 0.923760 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | −6.00000 | − | 10.3923i | −0.344691 | − | 0.597022i | ||||
\(304\) | 10.3923 | + | 6.00000i | 0.596040 | + | 0.344124i | ||||
\(305\) | −6.92820 | − | 4.00000i | −0.396708 | − | 0.229039i | ||||
\(306\) | 10.3923 | − | 6.00000i | 0.594089 | − | 0.342997i | ||||
\(307\) | − | 33.0000i | − | 1.88341i | −0.336440 | − | 0.941705i | \(-0.609223\pi\) | ||
0.336440 | − | 0.941705i | \(-0.390777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.19615 | + | 3.00000i | −0.295122 | + | 0.170389i | ||||
\(311\) | −15.0000 | + | 25.9808i | −0.850572 | + | 1.47323i | 0.0301210 | + | 0.999546i | \(0.490411\pi\) |
−0.880693 | + | 0.473688i | \(0.842923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | − | 8.66025i | −0.282617 | − | 0.489506i | 0.689412 | − | 0.724370i | \(-0.257869\pi\) |
−0.972028 | + | 0.234863i | \(0.924536\pi\) | |||||||
\(314\) | 36.0000i | 2.03160i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.0000 | 1.01258 | ||||||||
\(317\) | −17.3205 | + | 10.0000i | −0.972817 | + | 0.561656i | −0.900094 | − | 0.435696i | \(-0.856502\pi\) |
−0.0727229 | + | 0.997352i | \(0.523169\pi\) | |||||||
\(318\) | 31.1769 | + | 18.0000i | 1.74831 | + | 1.00939i | ||||
\(319\) | 5.19615 | + | 3.00000i | 0.290929 | + | 0.167968i | ||||
\(320\) | −6.92820 | + | 4.00000i | −0.387298 | + | 0.223607i | ||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18.0000i | − | 1.00155i | ||||||
\(324\) | −11.0000 | − | 19.0526i | −0.611111 | − | 1.05848i | ||||
\(325\) | −6.39230 | − | 12.9282i | −0.354581 | − | 0.717128i | ||||
\(326\) | 12.0000 | − | 20.7846i | 0.664619 | − | 1.15115i | ||||
\(327\) | 31.1769 | − | 18.0000i | 1.72409 | − | 0.995402i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 8.00000i | − | 0.440386i | ||||||
\(331\) | −10.3923 | + | 6.00000i | −0.571213 | + | 0.329790i | −0.757634 | − | 0.652680i | \(-0.773645\pi\) |
0.186421 | + | 0.982470i | \(0.440311\pi\) | |||||||
\(332\) | −19.0526 | − | 11.0000i | −1.04565 | − | 0.603703i | ||||
\(333\) | −5.19615 | − | 3.00000i | −0.284747 | − | 0.164399i | ||||
\(334\) | −1.00000 | − | 1.73205i | −0.0547176 | − | 0.0947736i | ||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.0000 | 1.47078 | 0.735392 | − | 0.677642i | \(-0.236998\pi\) | ||||
0.735392 | + | 0.677642i | \(0.236998\pi\) | |||||||
\(338\) | 20.6603 | + | 15.7846i | 1.12377 | + | 0.858570i | ||||
\(339\) | −15.0000 | + | 25.9808i | −0.814688 | + | 1.41108i | ||||
\(340\) | 10.3923 | + | 6.00000i | 0.563602 | + | 0.325396i | ||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | 6.00000 | 0.324443 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.19615 | + | 3.00000i | −0.279751 | + | 0.161515i | ||||
\(346\) | −10.3923 | − | 6.00000i | −0.558694 | − | 0.322562i | ||||
\(347\) | 12.0000 | − | 20.7846i | 0.644194 | − | 1.11578i | −0.340293 | − | 0.940319i | \(-0.610526\pi\) |
0.984487 | − | 0.175457i | \(-0.0561403\pi\) | |||||||
\(348\) | −6.00000 | − | 10.3923i | −0.321634 | − | 0.557086i | ||||
\(349\) | 27.0000i | 1.44528i | 0.691226 | + | 0.722638i | \(0.257071\pi\) | ||||
−0.691226 | + | 0.722638i | \(0.742929\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | + | 12.0000i | −0.427008 | + | 0.640513i | ||||
\(352\) | −8.00000 | − | 13.8564i | −0.426401 | − | 0.738549i | ||||
\(353\) | 1.73205 | + | 1.00000i | 0.0921878 | + | 0.0532246i | 0.545385 | − | 0.838186i | \(-0.316383\pi\) |
−0.453197 | + | 0.891410i | \(0.649717\pi\) | |||||||
\(354\) | −16.0000 | + | 27.7128i | −0.850390 | + | 1.47292i | ||||
\(355\) | −7.00000 | − | 12.1244i | −0.371521 | − | 0.643494i | ||||
\(356\) | 10.0000i | 0.529999i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 18.0000i | − | 0.951330i | ||||||
\(359\) | 19.0526 | − | 11.0000i | 1.00556 | − | 0.580558i | 0.0956683 | − | 0.995413i | \(-0.469501\pi\) |
0.909887 | + | 0.414855i | \(0.136168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | + | 8.66025i | −0.263158 | + | 0.455803i | ||||
\(362\) | 31.1769 | − | 18.0000i | 1.63862 | − | 0.946059i | ||||
\(363\) | −14.0000 | −0.734809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.00000 | −0.471082 | ||||||||
\(366\) | −27.7128 | + | 16.0000i | −1.44857 | + | 0.836333i | ||||
\(367\) | 9.00000 | − | 15.5885i | 0.469796 | − | 0.813711i | −0.529607 | − | 0.848243i | \(-0.677661\pi\) |
0.999404 | + | 0.0345320i | \(0.0109941\pi\) | |||||||
\(368\) | −6.00000 | + | 10.3923i | −0.312772 | + | 0.541736i | ||||
\(369\) | −8.66025 | + | 5.00000i | −0.450835 | + | 0.260290i | ||||
\(370\) | − | 12.0000i | − | 0.623850i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.0000i | 0.622171i | ||||||||
\(373\) | 9.00000 | + | 15.5885i | 0.466002 | + | 0.807140i | 0.999246 | − | 0.0388219i | \(-0.0123605\pi\) |
−0.533244 | + | 0.845962i | \(0.679027\pi\) | |||||||
\(374\) | −12.0000 | + | 20.7846i | −0.620505 | + | 1.07475i | ||||
\(375\) | −15.5885 | − | 9.00000i | −0.804984 | − | 0.464758i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00000 | + | 9.00000i | −0.309016 | + | 0.463524i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0000i | 0.924598i | 0.886724 | + | 0.462299i | \(0.152975\pi\) | ||||
−0.886724 | + | 0.462299i | \(0.847025\pi\) | |||||||
\(380\) | 3.00000 | + | 5.19615i | 0.153897 | + | 0.266557i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.92820 | − | 4.00000i | 0.354015 | − | 0.204390i | −0.312437 | − | 0.949938i | \(-0.601145\pi\) |
0.666452 | + | 0.745548i | \(0.267812\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.0000 | −1.22157 | ||||||||
\(387\) | −0.500000 | − | 0.866025i | −0.0254164 | − | 0.0440225i | ||||
\(388\) | 15.5885 | + | 9.00000i | 0.791384 | + | 0.456906i | ||||
\(389\) | 15.0000 | − | 25.9808i | 0.760530 | − | 1.31728i | −0.182047 | − | 0.983290i | \(-0.558272\pi\) |
0.942578 | − | 0.333987i | \(-0.108394\pi\) | |||||||
\(390\) | 14.3923 | + | 0.928203i | 0.728783 | + | 0.0470014i | ||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.0000 | −1.21064 | ||||||||
\(394\) | −4.00000 | − | 6.92820i | −0.201517 | − | 0.349038i | ||||
\(395\) | −7.79423 | − | 4.50000i | −0.392170 | − | 0.226420i | ||||
\(396\) | −3.46410 | − | 2.00000i | −0.174078 | − | 0.100504i | ||||
\(397\) | −18.1865 | + | 10.5000i | −0.912756 | + | 0.526980i | −0.881317 | − | 0.472526i | \(-0.843342\pi\) |
−0.0314391 | + | 0.999506i | \(0.510009\pi\) | |||||||
\(398\) | − | 4.00000i | − | 0.200502i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.0000 | −0.800000 | ||||||||
\(401\) | 24.2487 | − | 14.0000i | 1.21092 | − | 0.699127i | 0.247962 | − | 0.968770i | \(-0.420239\pi\) |
0.962960 | + | 0.269643i | \(0.0869057\pi\) | |||||||
\(402\) | 24.0000 | − | 41.5692i | 1.19701 | − | 2.07328i | ||||
\(403\) | 9.69615 | − | 4.79423i | 0.483000 | − | 0.238818i | ||||
\(404\) | −6.00000 | − | 10.3923i | −0.298511 | − | 0.517036i | ||||
\(405\) | 11.0000i | 0.546594i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | 0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.79423 | − | 4.50000i | −0.385400 | − | 0.222511i | 0.294765 | − | 0.955570i | \(-0.404759\pi\) |
−0.680165 | + | 0.733059i | \(0.738092\pi\) | |||||||
\(410\) | −17.3205 | − | 10.0000i | −0.855399 | − | 0.493865i | ||||
\(411\) | −3.46410 | + | 2.00000i | −0.170872 | + | 0.0986527i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.00000i | 0.294884i | ||||||||
\(415\) | 5.50000 | + | 9.52628i | 0.269984 | + | 0.467627i | ||||
\(416\) | 25.8564 | − | 12.7846i | 1.26771 | − | 0.626817i | ||||
\(417\) | −18.0000 | + | 31.1769i | −0.881464 | + | 1.52674i | ||||
\(418\) | −10.3923 | + | 6.00000i | −0.508304 | + | 0.293470i | ||||
\(419\) | 6.00000 | 0.293119 | 0.146560 | − | 0.989202i | \(-0.453180\pi\) | ||||
0.146560 | + | 0.989202i | \(0.453180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000i | 1.46211i | 0.682318 | + | 0.731055i | \(0.260972\pi\) | ||||
−0.682318 | + | 0.731055i | \(0.739028\pi\) | |||||||
\(422\) | 15.5885 | − | 9.00000i | 0.758834 | − | 0.438113i | ||||
\(423\) | −9.52628 | − | 5.50000i | −0.463184 | − | 0.267419i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | + | 20.7846i | 0.582086 | + | 1.00820i | ||||
\(426\) | −56.0000 | −2.71321 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.0000 | 1.16008 | ||||||||
\(429\) | −0.928203 | + | 14.3923i | −0.0448141 | + | 0.694867i | ||||
\(430\) | 1.00000 | − | 1.73205i | 0.0482243 | − | 0.0835269i | ||||
\(431\) | 3.46410 | + | 2.00000i | 0.166860 | + | 0.0963366i | 0.581104 | − | 0.813829i | \(-0.302621\pi\) |
−0.414244 | + | 0.910166i | \(0.635954\pi\) | |||||||
\(432\) | 8.00000 | + | 13.8564i | 0.384900 | + | 0.666667i | ||||
\(433\) | −20.0000 | −0.961139 | −0.480569 | − | 0.876957i | \(-0.659570\pi\) | ||||
−0.480569 | + | 0.876957i | \(0.659570\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.00000i | 0.287678i | ||||||||
\(436\) | 31.1769 | − | 18.0000i | 1.49310 | − | 0.862044i | ||||
\(437\) | 7.79423 | + | 4.50000i | 0.372849 | + | 0.215264i | ||||
\(438\) | −18.0000 | + | 31.1769i | −0.860073 | + | 1.48969i | ||||
\(439\) | −18.0000 | − | 31.1769i | −0.859093 | − | 1.48799i | −0.872795 | − | 0.488087i | \(-0.837695\pi\) |
0.0137020 | − | 0.999906i | \(-0.495638\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.0000 | − | 24.0000i | −1.71235 | − | 1.14156i | ||||
\(443\) | −13.5000 | − | 23.3827i | −0.641404 | − | 1.11094i | −0.985119 | − | 0.171871i | \(-0.945019\pi\) |
0.343715 | − | 0.939074i | \(-0.388315\pi\) | |||||||
\(444\) | −20.7846 | − | 12.0000i | −0.986394 | − | 0.569495i | ||||
\(445\) | 2.50000 | − | 4.33013i | 0.118511 | − | 0.205268i | ||||
\(446\) | −21.0000 | − | 36.3731i | −0.994379 | − | 1.72231i | ||||
\(447\) | 20.0000i | 0.945968i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.00000i | 0.188772i | 0.995536 | + | 0.0943858i | \(0.0300887\pi\) | ||||
−0.995536 | + | 0.0943858i | \(0.969911\pi\) | |||||||
\(450\) | −6.92820 | + | 4.00000i | −0.326599 | + | 0.188562i | ||||
\(451\) | 10.0000 | − | 17.3205i | 0.470882 | − | 0.815591i | ||||
\(452\) | −15.0000 | + | 25.9808i | −0.705541 | + | 1.22203i | ||||
\(453\) | −10.3923 | + | 6.00000i | −0.488273 | + | 0.281905i | ||||
\(454\) | 40.0000 | 1.87729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.3731 | − | 21.0000i | 1.70146 | − | 0.982339i | 0.757174 | − | 0.653213i | \(-0.226579\pi\) |
0.944286 | − | 0.329125i | \(-0.106754\pi\) | |||||||
\(458\) | 6.00000 | − | 10.3923i | 0.280362 | − | 0.485601i | ||||
\(459\) | 12.0000 | − | 20.7846i | 0.560112 | − | 0.970143i | ||||
\(460\) | −5.19615 | + | 3.00000i | −0.242272 | + | 0.139876i | ||||
\(461\) | − | 2.00000i | − | 0.0931493i | −0.998915 | − | 0.0465746i | \(-0.985169\pi\) | ||
0.998915 | − | 0.0465746i | \(-0.0148305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.0000i | − | 1.39422i | −0.716965 | − | 0.697109i | \(-0.754469\pi\) | ||
0.716965 | − | 0.697109i | \(-0.245531\pi\) | |||||||
\(464\) | 6.00000 | + | 10.3923i | 0.278543 | + | 0.482451i | ||||
\(465\) | 3.00000 | − | 5.19615i | 0.139122 | − | 0.240966i | ||||
\(466\) | −5.19615 | − | 3.00000i | −0.240707 | − | 0.138972i | ||||
\(467\) | 21.0000 | + | 36.3731i | 0.971764 | + | 1.68314i | 0.690225 | + | 0.723595i | \(0.257512\pi\) |
0.281539 | + | 0.959550i | \(0.409155\pi\) | |||||||
\(468\) | 4.00000 | − | 6.00000i | 0.184900 | − | 0.277350i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 22.0000i | − | 1.01478i | ||||||
\(471\) | −18.0000 | − | 31.1769i | −0.829396 | − | 1.43656i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.73205 | + | 1.00000i | 0.0796398 | + | 0.0459800i | ||||
\(474\) | −31.1769 | + | 18.0000i | −1.43200 | + | 0.826767i | ||||
\(475\) | 12.0000i | 0.550598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | −0.412082 | ||||||||
\(478\) | 8.00000 | + | 13.8564i | 0.365911 | + | 0.633777i | ||||
\(479\) | −25.1147 | − | 14.5000i | −1.14752 | − | 0.662522i | −0.199240 | − | 0.979951i | \(-0.563847\pi\) |
−0.948282 | + | 0.317429i | \(0.897181\pi\) | |||||||
\(480\) | 8.00000 | − | 13.8564i | 0.365148 | − | 0.632456i | ||||
\(481\) | −1.39230 | + | 21.5885i | −0.0634836 | + | 0.984349i | ||||
\(482\) | −42.0000 | −1.91305 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.0000 | −0.636364 | ||||||||
\(485\) | −4.50000 | − | 7.79423i | −0.204334 | − | 0.353918i | ||||
\(486\) | 17.3205 | + | 10.0000i | 0.785674 | + | 0.453609i | ||||
\(487\) | 10.3923 | + | 6.00000i | 0.470920 | + | 0.271886i | 0.716625 | − | 0.697459i | \(-0.245686\pi\) |
−0.245705 | + | 0.969345i | \(0.579019\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0000i | 1.08532i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | −34.6410 | + | 20.0000i | −1.56174 | + | 0.901670i | ||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | −9.58846 | − | 19.3923i | −0.431405 | − | 0.872501i | ||||
\(495\) | 1.00000 | + | 1.73205i | 0.0449467 | + | 0.0778499i | ||||
\(496\) | − | 12.0000i | − | 0.538816i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 44.0000 | 1.97169 | ||||||||
\(499\) | −5.19615 | + | 3.00000i | −0.232612 | + | 0.134298i | −0.611776 | − | 0.791031i | \(-0.709545\pi\) |
0.379165 | + | 0.925329i | \(0.376211\pi\) | |||||||
\(500\) | −15.5885 | − | 9.00000i | −0.697137 | − | 0.402492i | ||||
\(501\) | 1.73205 | + | 1.00000i | 0.0773823 | + | 0.0446767i | ||||
\(502\) | 10.3923 | − | 6.00000i | 0.463831 | − | 0.267793i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000i | 0.266996i | ||||||||
\(506\) | −6.00000 | − | 10.3923i | −0.266733 | − | 0.461994i | ||||
\(507\) | −25.7846 | − | 3.33975i | −1.14513 | − | 0.148323i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.0429 | + | 18.5000i | −1.42028 | + | 0.819998i | −0.996322 | − | 0.0856847i | \(-0.972692\pi\) |
−0.423956 | + | 0.905683i | \(0.639359\pi\) | |||||||
\(510\) | −24.0000 | −1.06274 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 32.0000i | − | 1.41421i | ||||||
\(513\) | 10.3923 | − | 6.00000i | 0.458831 | − | 0.264906i | ||||
\(514\) | 10.3923 | + | 6.00000i | 0.458385 | + | 0.264649i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.00000 | − | 3.46410i | −0.0880451 | − | 0.152499i | ||||
\(517\) | 22.0000 | 0.967559 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.0000 | 0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | − | 20.7846i | 0.525730 | − | 0.910590i | −0.473821 | − | 0.880621i | \(-0.657126\pi\) |
0.999551 | − | 0.0299693i | \(-0.00954094\pi\) | |||||||
\(522\) | 5.19615 | + | 3.00000i | 0.227429 | + | 0.131306i | ||||
\(523\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(524\) | −24.0000 | −1.04844 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 18.0000i | − | 0.784837i | ||||||
\(527\) | −15.5885 | + | 9.00000i | −0.679044 | + | 0.392046i | ||||
\(528\) | 13.8564 | + | 8.00000i | 0.603023 | + | 0.348155i | ||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | −9.00000 | − | 15.5885i | −0.390935 | − | 0.677119i | ||||
\(531\) | − | 8.00000i | − | 0.347170i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.0000 | + | 20.0000i | 1.29944 | + | 0.866296i | ||||
\(534\) | −10.0000 | − | 17.3205i | −0.432742 | − | 0.749532i | ||||
\(535\) | −10.3923 | − | 6.00000i | −0.449299 | − | 0.259403i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.00000 | + | 15.5885i | 0.388379 | + | 0.672692i | ||||
\(538\) | − | 48.0000i | − | 2.06943i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.00000i | 0.344265i | ||||||||
\(541\) | −15.5885 | + | 9.00000i | −0.670200 | + | 0.386940i | −0.796152 | − | 0.605096i | \(-0.793135\pi\) |
0.125952 | + | 0.992036i | \(0.459801\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.0000 | + | 31.1769i | −0.772454 | + | 1.33793i | ||||
\(544\) | −41.5692 | + | 24.0000i | −1.78227 | + | 1.02899i | ||||
\(545\) | −18.0000 | −0.771035 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0000 | 0.726868 | 0.363434 | − | 0.931620i | \(-0.381604\pi\) | ||||
0.363434 | + | 0.931620i | \(0.381604\pi\) | |||||||
\(548\) | −3.46410 | + | 2.00000i | −0.147979 | + | 0.0854358i | ||||
\(549\) | 4.00000 | − | 6.92820i | 0.170716 | − | 0.295689i | ||||
\(550\) | 8.00000 | − | 13.8564i | 0.341121 | − | 0.590839i | ||||
\(551\) | 7.79423 | − | 4.50000i | 0.332045 | − | 0.191706i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 34.0000i | 1.44452i | ||||||||
\(555\) | 6.00000 | + | 10.3923i | 0.254686 | + | 0.441129i | ||||
\(556\) | −18.0000 | + | 31.1769i | −0.763370 | + | 1.32220i | ||||
\(557\) | −27.7128 | − | 16.0000i | −1.17423 | − | 0.677942i | −0.219557 | − | 0.975600i | \(-0.570461\pi\) |
−0.954673 | + | 0.297658i | \(0.903795\pi\) | |||||||
\(558\) | −3.00000 | − | 5.19615i | −0.127000 | − | 0.219971i | ||||
\(559\) | −2.00000 | + | 3.00000i | −0.0845910 | + | 0.126886i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 24.0000i | − | 1.01328i | ||||||
\(562\) | −2.00000 | − | 3.46410i | −0.0843649 | − | 0.146124i | ||||
\(563\) | −18.0000 | + | 31.1769i | −0.758610 | + | 1.31395i | 0.184950 | + | 0.982748i | \(0.440788\pi\) |
−0.943560 | + | 0.331202i | \(0.892546\pi\) | |||||||
\(564\) | −38.1051 | − | 22.0000i | −1.60451 | − | 0.926367i | ||||
\(565\) | 12.9904 | − | 7.50000i | 0.546509 | − | 0.315527i | ||||
\(566\) | − | 8.00000i | − | 0.336265i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.50000 | + | 12.9904i | 0.314416 | + | 0.544585i | 0.979313 | − | 0.202350i | \(-0.0648579\pi\) |
−0.664897 | + | 0.746935i | \(0.731525\pi\) | |||||||
\(570\) | −10.3923 | − | 6.00000i | −0.435286 | − | 0.251312i | ||||
\(571\) | −4.50000 | + | 7.79423i | −0.188319 | + | 0.326178i | −0.944690 | − | 0.327965i | \(-0.893637\pi\) |
0.756371 | + | 0.654143i | \(0.226971\pi\) | |||||||
\(572\) | −0.928203 | + | 14.3923i | −0.0388101 | + | 0.601772i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | −0.500435 | ||||||||
\(576\) | −4.00000 | − | 6.92820i | −0.166667 | − | 0.288675i | ||||
\(577\) | −36.3731 | − | 21.0000i | −1.51423 | − | 0.874241i | −0.999861 | − | 0.0166728i | \(-0.994693\pi\) |
−0.514370 | − | 0.857569i | \(-0.671974\pi\) | |||||||
\(578\) | 32.9090 | + | 19.0000i | 1.36883 | + | 0.790296i | ||||
\(579\) | 20.7846 | − | 12.0000i | 0.863779 | − | 0.498703i | ||||
\(580\) | 6.00000i | 0.249136i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −36.0000 | −1.49225 | ||||||||
\(583\) | 15.5885 | − | 9.00000i | 0.645608 | − | 0.372742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.23205 | + | 1.59808i | −0.133629 | + | 0.0660723i | ||||
\(586\) | −1.00000 | − | 1.73205i | −0.0413096 | − | 0.0715504i | ||||
\(587\) | − | 43.0000i | − | 1.77480i | −0.461000 | − | 0.887400i | \(-0.652509\pi\) | ||
0.461000 | − | 0.887400i | \(-0.347491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | −0.370839 | ||||||||
\(590\) | 13.8564 | − | 8.00000i | 0.570459 | − | 0.329355i | ||||
\(591\) | 6.92820 | + | 4.00000i | 0.284988 | + | 0.164538i | ||||
\(592\) | 20.7846 | + | 12.0000i | 0.854242 | + | 0.493197i | ||||
\(593\) | 11.2583 | − | 6.50000i | 0.462324 | − | 0.266923i | −0.250697 | − | 0.968066i | \(-0.580660\pi\) |
0.713021 | + | 0.701143i | \(0.247326\pi\) | |||||||
\(594\) | −16.0000 | −0.656488 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.0000i | 0.819232i | ||||||||
\(597\) | 2.00000 | + | 3.46410i | 0.0818546 | + | 0.141776i | ||||
\(598\) | 19.3923 | − | 9.58846i | 0.793010 | − | 0.392101i | ||||
\(599\) | 10.5000 | − | 18.1865i | 0.429018 | − | 0.743082i | −0.567768 | − | 0.823189i | \(-0.692193\pi\) |
0.996786 | + | 0.0801071i | \(0.0255262\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.0000 | 1.79480 | 0.897399 | − | 0.441221i | \(-0.145454\pi\) | ||||
0.897399 | + | 0.441221i | \(0.145454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | −10.3923 | + | 6.00000i | −0.422857 | + | 0.244137i | ||||
\(605\) | 6.06218 | + | 3.50000i | 0.246463 | + | 0.142295i | ||||
\(606\) | 20.7846 | + | 12.0000i | 0.844317 | + | 0.487467i | ||||
\(607\) | −9.00000 | − | 15.5885i | −0.365299 | − | 0.632716i | 0.623525 | − | 0.781803i | \(-0.285700\pi\) |
−0.988824 | + | 0.149087i | \(0.952366\pi\) | |||||||
\(608\) | −24.0000 | −0.973329 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.0000 | 0.647821 | ||||||||
\(611\) | −2.55256 | + | 39.5788i | −0.103265 | + | 1.60119i | ||||
\(612\) | −6.00000 | + | 10.3923i | −0.242536 | + | 0.420084i | ||||
\(613\) | 20.7846 | + | 12.0000i | 0.839482 | + | 0.484675i | 0.857088 | − | 0.515170i | \(-0.172271\pi\) |
−0.0176058 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(614\) | 33.0000 | + | 57.1577i | 1.33177 | + | 2.30670i | ||||
\(615\) | 20.0000 | 0.806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8.00000i | − | 0.322068i | −0.986949 | − | 0.161034i | \(-0.948517\pi\) | ||
0.986949 | − | 0.161034i | \(-0.0514829\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.1769 | − | 18.0000i | −1.25311 | − | 0.723481i | −0.281381 | − | 0.959596i | \(-0.590792\pi\) |
−0.971725 | + | 0.236115i | \(0.924126\pi\) | |||||||
\(620\) | 3.00000 | − | 5.19615i | 0.120483 | − | 0.208683i | ||||
\(621\) | 6.00000 | + | 10.3923i | 0.240772 | + | 0.417029i | ||||
\(622\) | − | 60.0000i | − | 2.40578i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −16.0000 | + | 24.0000i | −0.640513 | + | 0.960769i | ||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 17.3205 | + | 10.0000i | 0.692267 | + | 0.399680i | ||||
\(627\) | 6.00000 | − | 10.3923i | 0.239617 | − | 0.415029i | ||||
\(628\) | −18.0000 | − | 31.1769i | −0.718278 | − | 1.24409i | ||||
\(629\) | − | 36.0000i | − | 1.43541i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.0000i | − | 0.477712i | −0.971055 | − | 0.238856i | \(-0.923228\pi\) | ||
0.971055 | − | 0.238856i | \(-0.0767725\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.00000 | + | 15.5885i | −0.357718 | + | 0.619586i | ||||
\(634\) | 20.0000 | − | 34.6410i | 0.794301 | − | 1.37577i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −36.0000 | −1.42749 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −12.0000 | −0.475085 | ||||||||
\(639\) | 12.1244 | − | 7.00000i | 0.479632 | − | 0.276916i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.5000 | + | 33.7750i | −0.770204 | + | 1.33403i | 0.167247 | + | 0.985915i | \(0.446512\pi\) |
−0.937451 | + | 0.348117i | \(0.886821\pi\) | |||||||
\(642\) | −41.5692 | + | 24.0000i | −1.64061 | + | 0.947204i | ||||
\(643\) | 12.0000i | 0.473234i | 0.971603 | + | 0.236617i | \(0.0760386\pi\) | ||||
−0.971603 | + | 0.236617i | \(0.923961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.00000i | 0.0787499i | ||||||||
\(646\) | 18.0000 | + | 31.1769i | 0.708201 | + | 1.22664i | ||||
\(647\) | −9.00000 | + | 15.5885i | −0.353827 | + | 0.612845i | −0.986916 | − | 0.161233i | \(-0.948453\pi\) |
0.633090 | + | 0.774078i | \(0.281786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | + | 13.8564i | 0.314027 | + | 0.543912i | ||||
\(650\) | 24.0000 | + | 16.0000i | 0.941357 | + | 0.627572i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.0000i | 0.939913i | ||||||||
\(653\) | 9.00000 | + | 15.5885i | 0.352197 | + | 0.610023i | 0.986634 | − | 0.162951i | \(-0.0521013\pi\) |
−0.634437 | + | 0.772975i | \(0.718768\pi\) | |||||||
\(654\) | −36.0000 | + | 62.3538i | −1.40771 | + | 2.43823i | ||||
\(655\) | 10.3923 | + | 6.00000i | 0.406061 | + | 0.234439i | ||||
\(656\) | 34.6410 | − | 20.0000i | 1.35250 | − | 0.780869i | ||||
\(657\) | − | 9.00000i | − | 0.351123i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.0000 | −1.51922 | −0.759612 | − | 0.650376i | \(-0.774611\pi\) | ||||
−0.759612 | + | 0.650376i | \(0.774611\pi\) | |||||||
\(660\) | 4.00000 | + | 6.92820i | 0.155700 | + | 0.269680i | ||||
\(661\) | −2.59808 | − | 1.50000i | −0.101053 | − | 0.0583432i | 0.448622 | − | 0.893722i | \(-0.351915\pi\) |
−0.549675 | + | 0.835379i | \(0.685248\pi\) | |||||||
\(662\) | 12.0000 | − | 20.7846i | 0.466393 | − | 0.807817i | ||||
\(663\) | 43.1769 | + | 2.78461i | 1.67685 | + | 0.108145i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.0000 | 0.464991 | ||||||||
\(667\) | 4.50000 | + | 7.79423i | 0.174241 | + | 0.301794i | ||||
\(668\) | 1.73205 | + | 1.00000i | 0.0670151 | + | 0.0386912i | ||||
\(669\) | 36.3731 | + | 21.0000i | 1.40626 | + | 0.811907i | ||||
\(670\) | −20.7846 | + | 12.0000i | −0.802980 | + | 0.463600i | ||||
\(671\) | 16.0000i | 0.617673i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | −0.0385472 | −0.0192736 | − | 0.999814i | \(-0.506135\pi\) | ||||
−0.0192736 | + | 0.999814i | \(0.506135\pi\) | |||||||
\(674\) | −46.7654 | + | 27.0000i | −1.80133 | + | 1.04000i | ||||
\(675\) | −8.00000 | + | 13.8564i | −0.307920 | + | 0.533333i | ||||
\(676\) | −25.7846 | − | 3.33975i | −0.991716 | − | 0.128452i | ||||
\(677\) | 9.00000 | + | 15.5885i | 0.345898 | + | 0.599113i | 0.985517 | − | 0.169580i | \(-0.0542410\pi\) |
−0.639618 | + | 0.768693i | \(0.720908\pi\) | |||||||
\(678\) | − | 60.0000i | − | 2.30429i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.6410 | + | 20.0000i | −1.32745 | + | 0.766402i | ||||
\(682\) | 10.3923 | + | 6.00000i | 0.397942 | + | 0.229752i | ||||
\(683\) | 34.6410 | + | 20.0000i | 1.32550 | + | 0.765279i | 0.984600 | − | 0.174820i | \(-0.0559345\pi\) |
0.340901 | + | 0.940099i | \(0.389268\pi\) | |||||||
\(684\) | −5.19615 | + | 3.00000i | −0.198680 | + | 0.114708i | ||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.0000i | 0.457829i | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | 14.3827 | + | 29.0885i | 0.547937 | + | 1.10818i | ||||
\(690\) | 6.00000 | − | 10.3923i | 0.228416 | − | 0.395628i | ||||
\(691\) | −12.9904 | + | 7.50000i | −0.494177 | + | 0.285313i | −0.726306 | − | 0.687372i | \(-0.758764\pi\) |
0.232128 | + | 0.972685i | \(0.425431\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 48.0000i | 1.82206i | ||||||||
\(695\) | 15.5885 | − | 9.00000i | 0.591304 | − | 0.341389i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.9615 | − | 30.0000i | −1.96818 | − | 1.13633i | ||||
\(698\) | −27.0000 | − | 46.7654i | −1.02197 | − | 1.77010i | ||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.0000 | 0.566542 | 0.283271 | − | 0.959040i | \(-0.408580\pi\) | ||||
0.283271 | + | 0.959040i | \(0.408580\pi\) | |||||||
\(702\) | 1.85641 | − | 28.7846i | 0.0700655 | − | 1.08641i | ||||
\(703\) | 9.00000 | − | 15.5885i | 0.339441 | − | 0.587930i | ||||
\(704\) | 13.8564 | + | 8.00000i | 0.522233 | + | 0.301511i | ||||
\(705\) | 11.0000 | + | 19.0526i | 0.414284 | + | 0.717561i | ||||
\(706\) | −4.00000 | −0.150542 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 32.0000i | − | 1.20263i | ||||||
\(709\) | −25.9808 | + | 15.0000i | −0.975728 | + | 0.563337i | −0.900978 | − | 0.433865i | \(-0.857149\pi\) |
−0.0747503 | + | 0.997202i | \(0.523816\pi\) | |||||||
\(710\) | 24.2487 | + | 14.0000i | 0.910038 | + | 0.525411i | ||||
\(711\) | 4.50000 | − | 7.79423i | 0.168763 | − | 0.292306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 9.00000i | − | 0.337053i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | − | 6.00000i | 0.149592 | − | 0.224387i | ||||
\(716\) | 9.00000 | + | 15.5885i | 0.336346 | + | 0.582568i | ||||
\(717\) | −13.8564 | − | 8.00000i | −0.517477 | − | 0.298765i | ||||
\(718\) | −22.0000 | + | 38.1051i | −0.821033 | + | 1.42207i | ||||
\(719\) | 9.00000 | + | 15.5885i | 0.335643 | + | 0.581351i | 0.983608 | − | 0.180319i | \(-0.0577130\pi\) |
−0.647965 | + | 0.761670i | \(0.724380\pi\) | |||||||
\(720\) | 4.00000i | 0.149071i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 20.0000i | − | 0.744323i | ||||||
\(723\) | 36.3731 | − | 21.0000i | 1.35273 | − | 0.780998i | ||||
\(724\) | −18.0000 | + | 31.1769i | −0.668965 | + | 1.15868i | ||||
\(725\) | −6.00000 | + | 10.3923i | −0.222834 | + | 0.385961i | ||||
\(726\) | 24.2487 | − | 14.0000i | 0.899954 | − | 0.519589i | ||||
\(727\) | 28.0000 | 1.03846 | 0.519231 | − | 0.854634i | \(-0.326218\pi\) | ||||
0.519231 | + | 0.854634i | \(0.326218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 15.5885 | − | 9.00000i | 0.576955 | − | 0.333105i | ||||
\(731\) | 3.00000 | − | 5.19615i | 0.110959 | − | 0.192187i | ||||
\(732\) | 16.0000 | − | 27.7128i | 0.591377 | − | 1.02430i | ||||
\(733\) | −12.9904 | + | 7.50000i | −0.479811 | + | 0.277019i | −0.720338 | − | 0.693624i | \(-0.756013\pi\) |
0.240527 | + | 0.970642i | \(0.422680\pi\) | |||||||
\(734\) | 36.0000i | 1.32878i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 24.0000i | − | 0.884652i | ||||||
\(737\) | −12.0000 | − | 20.7846i | −0.442026 | − | 0.765611i | ||||
\(738\) | 10.0000 | − | 17.3205i | 0.368105 | − | 0.637577i | ||||
\(739\) | −25.9808 | − | 15.0000i | −0.955718 | − | 0.551784i | −0.0608653 | − | 0.998146i | \(-0.519386\pi\) |
−0.894852 | + | 0.446362i | \(0.852719\pi\) | |||||||
\(740\) | 6.00000 | + | 10.3923i | 0.220564 | + | 0.382029i | ||||
\(741\) | 18.0000 | + | 12.0000i | 0.661247 | + | 0.440831i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.0000i | − | 1.61420i | −0.590412 | − | 0.807102i | \(-0.701035\pi\) | ||
0.590412 | − | 0.807102i | \(-0.298965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00000 | − | 8.66025i | 0.183186 | − | 0.317287i | ||||
\(746\) | −31.1769 | − | 18.0000i | −1.14147 | − | 0.659027i | ||||
\(747\) | −9.52628 | + | 5.50000i | −0.348548 | + | 0.201234i | ||||
\(748\) | − | 24.0000i | − | 0.877527i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 36.0000 | 1.31453 | ||||||||
\(751\) | −6.50000 | − | 11.2583i | −0.237188 | − | 0.410822i | 0.722718 | − | 0.691143i | \(-0.242893\pi\) |
−0.959906 | + | 0.280321i | \(0.909559\pi\) | |||||||
\(752\) | 38.1051 | + | 22.0000i | 1.38955 | + | 0.802257i | ||||
\(753\) | −6.00000 | + | 10.3923i | −0.218652 | + | 0.378717i | ||||
\(754\) | 1.39230 | − | 21.5885i | 0.0507048 | − | 0.786205i | ||||
\(755\) | 6.00000 | 0.218362 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | 0.327111 | 0.163555 | − | 0.986534i | \(-0.447704\pi\) | ||||
0.163555 | + | 0.986534i | \(0.447704\pi\) | |||||||
\(758\) | −18.0000 | − | 31.1769i | −0.653789 | − | 1.13240i | ||||
\(759\) | 10.3923 | + | 6.00000i | 0.377217 | + | 0.217786i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.4545 | + | 9.50000i | −0.596475 | + | 0.344375i | −0.767653 | − | 0.640865i | \(-0.778576\pi\) |
0.171179 | + | 0.985240i | \(0.445242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.19615 | − | 3.00000i | 0.187867 | − | 0.108465i | ||||
\(766\) | −8.00000 | + | 13.8564i | −0.289052 | + | 0.500652i | ||||
\(767\) | −25.8564 | + | 12.7846i | −0.933621 | + | 0.461626i | ||||
\(768\) | 16.0000 | + | 27.7128i | 0.577350 | + | 1.00000i | ||||
\(769\) | − | 9.00000i | − | 0.324548i | −0.986746 | − | 0.162274i | \(-0.948117\pi\) | ||
0.986746 | − | 0.162274i | \(-0.0518829\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 20.7846 | − | 12.0000i | 0.748054 | − | 0.431889i | ||||
\(773\) | 12.1244 | + | 7.00000i | 0.436083 | + | 0.251773i | 0.701935 | − | 0.712241i | \(-0.252320\pi\) |
−0.265852 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(774\) | 1.73205 | + | 1.00000i | 0.0622573 | + | 0.0359443i | ||||
\(775\) | 10.3923 | − | 6.00000i | 0.373303 | − | 0.215526i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 60.0000i | 2.15110i | ||||||||
\(779\) | −15.0000 | − | 25.9808i | −0.537431 | − | 0.930857i | ||||
\(780\) | −12.9282 | + | 6.39230i | −0.462904 | + | 0.228881i | ||||
\(781\) | −14.0000 | + | 24.2487i | −0.500959 | + | 0.867687i | ||||
\(782\) | −31.1769 | + | 18.0000i | −1.11488 | + | 0.643679i | ||||
\(783\) | 12.0000 | 0.428845 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.0000i | 0.642448i | ||||||||
\(786\) | 41.5692 | − | 24.0000i | 1.48272 | − | 0.856052i | ||||
\(787\) | −18.1865 | − | 10.5000i | −0.648280 | − | 0.374285i | 0.139517 | − | 0.990220i | \(-0.455445\pi\) |
−0.787797 | + | 0.615935i | \(0.788778\pi\) | |||||||
\(788\) | 6.92820 | + | 4.00000i | 0.246807 | + | 0.142494i | ||||
\(789\) | 9.00000 | + | 15.5885i | 0.320408 | + | 0.554964i | ||||
\(790\) | 18.0000 | 0.640411 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.7846 | − | 1.85641i | −1.02217 | − | 0.0659229i | ||||
\(794\) | 21.0000 | − | 36.3731i | 0.745262 | − | 1.29083i | ||||
\(795\) | 15.5885 | + | 9.00000i | 0.552866 | + | 0.319197i | ||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | −12.0000 | −0.425062 | −0.212531 | − | 0.977154i | \(-0.568171\pi\) | ||||
−0.212531 | + | 0.977154i | \(0.568171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 66.0000i | − | 2.33491i | ||||||
\(800\) | 27.7128 | − | 16.0000i | 0.979796 | − | 0.565685i | ||||
\(801\) | 4.33013 | + | 2.50000i | 0.152998 | + | 0.0883332i | ||||
\(802\) | −28.0000 | + | 48.4974i | −0.988714 | + | 1.71250i | ||||
\(803\) | 9.00000 | + | 15.5885i | 0.317603 | + | 0.550105i | ||||
\(804\) | 48.0000i | 1.69283i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.0000 | + | 18.0000i | −0.422682 | + | 0.634023i | ||||
\(807\) | 24.0000 | + | 41.5692i | 0.844840 | + | 1.46331i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.50000 | − | 12.9904i | 0.263686 | − | 0.456717i | −0.703533 | − | 0.710663i | \(-0.748395\pi\) |
0.967219 | + | 0.253946i | \(0.0817284\pi\) | |||||||
\(810\) | −11.0000 | − | 19.0526i | −0.386501 | − | 0.669439i | ||||
\(811\) | − | 12.0000i | − | 0.421377i | −0.977553 | − | 0.210688i | \(-0.932429\pi\) | ||
0.977553 | − | 0.210688i | \(-0.0675706\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.7846 | + | 12.0000i | −0.728500 | + | 0.420600i | ||||
\(815\) | 6.00000 | − | 10.3923i | 0.210171 | − | 0.364027i | ||||
\(816\) | 24.0000 | − | 41.5692i | 0.840168 | − | 1.45521i | ||||
\(817\) | 2.59808 | − | 1.50000i | 0.0908952 | − | 0.0524784i | ||||
\(818\) | 18.0000 | 0.629355 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.0000 | 0.698430 | ||||||||
\(821\) | −13.8564 | + | 8.00000i | −0.483592 | + | 0.279202i | −0.721912 | − | 0.691985i | \(-0.756737\pi\) |
0.238320 | + | 0.971187i | \(0.423403\pi\) | |||||||
\(822\) | 4.00000 | − | 6.92820i | 0.139516 | − | 0.241649i | ||||
\(823\) | 20.0000 | − | 34.6410i | 0.697156 | − | 1.20751i | −0.272292 | − | 0.962215i | \(-0.587782\pi\) |
0.969448 | − | 0.245295i | \(-0.0788849\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.0000i | 0.557048i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 4.00000i | − | 0.139094i | −0.997579 | − | 0.0695468i | \(-0.977845\pi\) | ||
0.997579 | − | 0.0695468i | \(-0.0221553\pi\) | |||||||
\(828\) | −3.00000 | − | 5.19615i | −0.104257 | − | 0.180579i | ||||
\(829\) | −1.00000 | + | 1.73205i | −0.0347314 | + | 0.0601566i | −0.882869 | − | 0.469620i | \(-0.844391\pi\) |
0.848137 | + | 0.529777i | \(0.177724\pi\) | |||||||
\(830\) | −19.0526 | − | 11.0000i | −0.661324 | − | 0.381816i | ||||
\(831\) | −17.0000 | − | 29.4449i | −0.589723 | − | 1.02143i | ||||
\(832\) | −16.0000 | + | 24.0000i | −0.554700 | + | 0.832050i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 72.0000i | − | 2.49316i | ||||||
\(835\) | −0.500000 | − | 0.866025i | −0.0173032 | − | 0.0299700i | ||||
\(836\) | 6.00000 | − | 10.3923i | 0.207514 | − | 0.359425i | ||||
\(837\) | −10.3923 | − | 6.00000i | −0.359211 | − | 0.207390i | ||||
\(838\) | −10.3923 | + | 6.00000i | −0.358996 | + | 0.207267i | ||||
\(839\) | 16.0000i | 0.552381i | 0.961103 | + | 0.276191i | \(0.0890721\pi\) | ||||
−0.961103 | + | 0.276191i | \(0.910928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −30.0000 | − | 51.9615i | −1.03387 | − | 1.79071i | ||||
\(843\) | 3.46410 | + | 2.00000i | 0.119310 | + | 0.0688837i | ||||
\(844\) | −9.00000 | + | 15.5885i | −0.309793 | + | 0.536577i | ||||
\(845\) | 10.3301 | + | 7.89230i | 0.355367 | + | 0.271504i | ||||
\(846\) | 22.0000 | 0.756376 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 36.0000 | 1.23625 | ||||||||
\(849\) | 4.00000 | + | 6.92820i | 0.137280 | + | 0.237775i | ||||
\(850\) | −41.5692 | − | 24.0000i | −1.42581 | − | 0.823193i | ||||
\(851\) | 15.5885 | + | 9.00000i | 0.534365 | + | 0.308516i | ||||
\(852\) | 48.4974 | − | 28.0000i | 1.66149 | − | 0.959264i | ||||
\(853\) | 45.0000i | 1.54077i | 0.637579 | + | 0.770385i | \(0.279936\pi\) | ||||
−0.637579 | + | 0.770385i | \(0.720064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | 0.102598 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000 | − | 31.1769i | 0.614868 | − | 1.06498i | −0.375539 | − | 0.926806i | \(-0.622542\pi\) |
0.990408 | − | 0.138177i | \(-0.0441242\pi\) | |||||||
\(858\) | −12.7846 | − | 25.8564i | −0.436459 | − | 0.882723i | ||||
\(859\) | −2.00000 | − | 3.46410i | −0.0682391 | − | 0.118194i | 0.829887 | − | 0.557931i | \(-0.188405\pi\) |
−0.898126 | + | 0.439738i | \(0.855071\pi\) | |||||||
\(860\) | 2.00000i | 0.0681994i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.00000 | −0.272481 | ||||||||
\(863\) | −27.7128 | + | 16.0000i | −0.943355 | + | 0.544646i | −0.891010 | − | 0.453983i | \(-0.850003\pi\) |
−0.0523446 | + | 0.998629i | \(0.516669\pi\) | |||||||
\(864\) | −27.7128 | − | 16.0000i | −0.942809 | − | 0.544331i | ||||
\(865\) | −5.19615 | − | 3.00000i | −0.176674 | − | 0.102003i | ||||
\(866\) | 34.6410 | − | 20.0000i | 1.17715 | − | 0.679628i | ||||
\(867\) | −38.0000 | −1.29055 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.0000i | 0.610608i | ||||||||
\(870\) | −6.00000 | − | 10.3923i | −0.203419 | − | 0.352332i | ||||
\(871\) | 38.7846 | − | 19.1769i | 1.31417 | − | 0.649785i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.79423 | − | 4.50000i | 0.263795 | − | 0.152302i | ||||
\(874\) | −18.0000 | −0.608859 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 36.0000i | − | 1.21633i | ||||||
\(877\) | −15.5885 | + | 9.00000i | −0.526385 | + | 0.303908i | −0.739543 | − | 0.673109i | \(-0.764958\pi\) |
0.213158 | + | 0.977018i | \(0.431625\pi\) | |||||||
\(878\) | 62.3538 | + | 36.0000i | 2.10434 | + | 1.21494i | ||||
\(879\) | 1.73205 | + | 1.00000i | 0.0584206 | + | 0.0337292i | ||||
\(880\) | −4.00000 | − | 6.92820i | −0.134840 | − | 0.233550i | ||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0000 | −1.21150 | −0.605748 | − | 0.795656i | \(-0.707126\pi\) | ||||
−0.605748 | + | 0.795656i | \(0.707126\pi\) | |||||||
\(884\) | 43.1769 | + | 2.78461i | 1.45220 | + | 0.0936566i | ||||
\(885\) | −8.00000 | + | 13.8564i | −0.268917 | + | 0.465778i | ||||
\(886\) | 46.7654 | + | 27.0000i | 1.57111 | + | 0.907083i | ||||
\(887\) | −18.0000 | − | 31.1769i | −0.604381 | − | 1.04682i | −0.992149 | − | 0.125061i | \(-0.960087\pi\) |
0.387768 | − | 0.921757i | \(-0.373246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.0000i | 0.335201i | ||||||||
\(891\) | 19.0526 | − | 11.0000i | 0.638285 | − | 0.368514i | ||||
\(892\) | 36.3731 | + | 21.0000i | 1.21786 | + | 0.703132i | ||||
\(893\) | 16.5000 | − | 28.5788i | 0.552151 | − | 0.956354i | ||||
\(894\) | −20.0000 | − | 34.6410i | −0.668900 | − | 1.15857i | ||||
\(895\) | − | 9.00000i | − | 0.300837i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.0000 | + | 18.0000i | −0.400668 | + | 0.601003i | ||||
\(898\) | −4.00000 | − | 6.92820i | −0.133482 | − | 0.231197i | ||||
\(899\) | −7.79423 | − | 4.50000i | −0.259952 | − | 0.150083i | ||||
\(900\) | 4.00000 | − | 6.92820i | 0.133333 | − | 0.230940i | ||||
\(901\) | −27.0000 | − | 46.7654i | −0.899500 | − | 1.55798i | ||||
\(902\) | 40.0000i | 1.33185i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.5885 | − | 9.00000i | 0.518178 | − | 0.299170i | ||||
\(906\) | 12.0000 | − | 20.7846i | 0.398673 | − | 0.690522i | ||||
\(907\) | −4.50000 | + | 7.79423i | −0.149420 | + | 0.258803i | −0.931013 | − | 0.364985i | \(-0.881074\pi\) |
0.781593 | + | 0.623788i | \(0.214407\pi\) | |||||||
\(908\) | −34.6410 | + | 20.0000i | −1.14960 | + | 0.663723i | ||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.0000 | −0.894550 | −0.447275 | − | 0.894397i | \(-0.647605\pi\) | ||||
−0.447275 | + | 0.894397i | \(0.647605\pi\) | |||||||
\(912\) | 20.7846 | − | 12.0000i | 0.688247 | − | 0.397360i | ||||
\(913\) | 11.0000 | − | 19.0526i | 0.364047 | − | 0.630548i | ||||
\(914\) | −42.0000 | + | 72.7461i | −1.38924 | + | 2.40623i | ||||
\(915\) | −13.8564 | + | 8.00000i | −0.458079 | + | 0.264472i | ||||
\(916\) | 12.0000i | 0.396491i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 48.0000i | 1.58424i | ||||||||
\(919\) | −18.0000 | − | 31.1769i | −0.593765 | − | 1.02843i | −0.993720 | − | 0.111897i | \(-0.964307\pi\) |
0.399955 | − | 0.916535i | \(-0.369026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −57.1577 | − | 33.0000i | −1.88341 | − | 1.08739i | ||||
\(922\) | 2.00000 | + | 3.46410i | 0.0658665 | + | 0.114084i | ||||
\(923\) | −42.0000 | − | 28.0000i | −1.38245 | − | 0.921631i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.0000i | 0.789115i | ||||||||
\(926\) | 30.0000 | + | 51.9615i | 0.985861 | + | 1.70756i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.7846 | − | 12.0000i | −0.682288 | − | 0.393919i | ||||
\(929\) | 6.06218 | − | 3.50000i | 0.198894 | − | 0.114831i | −0.397246 | − | 0.917712i | \(-0.630034\pi\) |
0.596139 | + | 0.802881i | \(0.296701\pi\) | |||||||
\(930\) | 12.0000i | 0.393496i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | 30.0000 | + | 51.9615i | 0.982156 | + | 1.70114i | ||||
\(934\) | −72.7461 | − | 42.0000i | −2.38033 | − | 1.37428i | ||||
\(935\) | −6.00000 | + | 10.3923i | −0.196221 | + | 0.339865i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.0000 | −0.652675 | ||||||||
\(940\) | 11.0000 | + | 19.0526i | 0.358780 | + | 0.621426i | ||||
\(941\) | −0.866025 | − | 0.500000i | −0.0282316 | − | 0.0162995i | 0.485818 | − | 0.874060i | \(-0.338522\pi\) |
−0.514049 | + | 0.857761i | \(0.671855\pi\) | |||||||
\(942\) | 62.3538 | + | 36.0000i | 2.03160 | + | 1.17294i | ||||
\(943\) | 25.9808 | − | 15.0000i | 0.846050 | − | 0.488467i | ||||
\(944\) | 32.0000i | 1.04151i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | −13.8564 | + | 8.00000i | −0.450273 | + | 0.259965i | −0.707945 | − | 0.706267i | \(-0.750378\pi\) |
0.257673 | + | 0.966232i | \(0.417044\pi\) | |||||||
\(948\) | 18.0000 | − | 31.1769i | 0.584613 | − | 1.01258i | ||||
\(949\) | −29.0885 | + | 14.3827i | −0.944251 | + | 0.466882i | ||||
\(950\) | −12.0000 | − | 20.7846i | −0.389331 | − | 0.674342i | ||||
\(951\) | 40.0000i | 1.29709i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.00000 | 0.0971795 | 0.0485898 | − | 0.998819i | \(-0.484527\pi\) | ||||
0.0485898 | + | 0.998819i | \(0.484527\pi\) | |||||||
\(954\) | 15.5885 | − | 9.00000i | 0.504695 | − | 0.291386i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.8564 | − | 8.00000i | −0.448148 | − | 0.258738i | ||||
\(957\) | 10.3923 | − | 6.00000i | 0.335936 | − | 0.193952i | ||||
\(958\) | 58.0000 | 1.87389 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 16.0000i | 0.516398i | ||||||||
\(961\) | −11.0000 | − | 19.0526i | −0.354839 | − | 0.614599i | ||||
\(962\) | −19.1769 | − | 38.7846i | −0.618289 | − | 1.25047i | ||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | 36.3731 | − | 21.0000i | 1.17150 | − | 0.676364i | ||||
\(965\) | −12.0000 | −0.386294 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.0000i | 1.73652i | 0.496107 | + | 0.868261i | \(0.334762\pi\) | ||||
−0.496107 | + | 0.868261i | \(0.665238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31.1769 | − | 18.0000i | −1.00155 | − | 0.578243i | ||||
\(970\) | 15.5885 | + | 9.00000i | 0.500515 | + | 0.288973i | ||||
\(971\) | 6.00000 | + | 10.3923i | 0.192549 | + | 0.333505i | 0.946094 | − | 0.323891i | \(-0.104991\pi\) |
−0.753545 | + | 0.657396i | \(0.771658\pi\) | |||||||
\(972\) | −20.0000 | −0.641500 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −24.0000 | −0.769010 | ||||||||
\(975\) | −28.7846 | − | 1.85641i | −0.921845 | − | 0.0594526i | ||||
\(976\) | −16.0000 | + | 27.7128i | −0.512148 | + | 0.887066i | ||||
\(977\) | −8.66025 | − | 5.00000i | −0.277066 | − | 0.159964i | 0.355028 | − | 0.934856i | \(-0.384471\pi\) |
−0.632094 | + | 0.774891i | \(0.717805\pi\) | |||||||
\(978\) | −24.0000 | − | 41.5692i | −0.767435 | − | 1.32924i | ||||
\(979\) | −10.0000 | −0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 18.0000i | − | 0.574696i | ||||||
\(982\) | −20.7846 | + | 12.0000i | −0.663264 | + | 0.382935i | ||||
\(983\) | −25.1147 | − | 14.5000i | −0.801036 | − | 0.462478i | 0.0427975 | − | 0.999084i | \(-0.486373\pi\) |
−0.843833 | + | 0.536606i | \(0.819706\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00000 | − | 3.46410i | −0.0637253 | − | 0.110375i | ||||
\(986\) | 36.0000i | 1.14647i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.0000 | + | 12.0000i | 0.572656 | + | 0.381771i | ||||
\(989\) | 1.50000 | + | 2.59808i | 0.0476972 | + | 0.0826140i | ||||
\(990\) | −3.46410 | − | 2.00000i | −0.110096 | − | 0.0635642i | ||||
\(991\) | 28.0000 | − | 48.4974i | 0.889449 | − | 1.54057i | 0.0489218 | − | 0.998803i | \(-0.484422\pi\) |
0.840528 | − | 0.541769i | \(-0.182245\pi\) | |||||||
\(992\) | 12.0000 | + | 20.7846i | 0.381000 | + | 0.659912i | ||||
\(993\) | 24.0000i | 0.761617i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.00000i | − | 0.0634043i | ||||||
\(996\) | −38.1051 | + | 22.0000i | −1.20741 | + | 0.697097i | ||||
\(997\) | −18.0000 | + | 31.1769i | −0.570066 | + | 0.987383i | 0.426493 | + | 0.904491i | \(0.359749\pi\) |
−0.996559 | + | 0.0828918i | \(0.973584\pi\) | |||||||
\(998\) | 6.00000 | − | 10.3923i | 0.189927 | − | 0.328963i | ||||
\(999\) | 20.7846 | − | 12.0000i | 0.657596 | − | 0.379663i |
(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.r.c.116.1 | 4 | ||
7.2 | even | 3 | inner | 637.2.r.c.324.2 | 4 | ||
7.3 | odd | 6 | 637.2.c.c.246.1 | yes | 2 | ||
7.4 | even | 3 | 637.2.c.a.246.1 | ✓ | 2 | ||
7.5 | odd | 6 | 637.2.r.a.324.2 | 4 | |||
7.6 | odd | 2 | 637.2.r.a.116.1 | 4 | |||
13.12 | even | 2 | inner | 637.2.r.c.116.2 | 4 | ||
91.12 | odd | 6 | 637.2.r.a.324.1 | 4 | |||
91.18 | odd | 12 | 8281.2.a.a.1.1 | 1 | |||
91.25 | even | 6 | 637.2.c.a.246.2 | yes | 2 | ||
91.31 | even | 12 | 8281.2.a.b.1.1 | 1 | |||
91.38 | odd | 6 | 637.2.c.c.246.2 | yes | 2 | ||
91.51 | even | 6 | inner | 637.2.r.c.324.1 | 4 | ||
91.60 | odd | 12 | 8281.2.a.k.1.1 | 1 | |||
91.73 | even | 12 | 8281.2.a.m.1.1 | 1 | |||
91.90 | odd | 2 | 637.2.r.a.116.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.a.246.1 | ✓ | 2 | 7.4 | even | 3 | ||
637.2.c.a.246.2 | yes | 2 | 91.25 | even | 6 | ||
637.2.c.c.246.1 | yes | 2 | 7.3 | odd | 6 | ||
637.2.c.c.246.2 | yes | 2 | 91.38 | odd | 6 | ||
637.2.r.a.116.1 | 4 | 7.6 | odd | 2 | |||
637.2.r.a.116.2 | 4 | 91.90 | odd | 2 | |||
637.2.r.a.324.1 | 4 | 91.12 | odd | 6 | |||
637.2.r.a.324.2 | 4 | 7.5 | odd | 6 | |||
637.2.r.c.116.1 | 4 | 1.1 | even | 1 | trivial | ||
637.2.r.c.116.2 | 4 | 13.12 | even | 2 | inner | ||
637.2.r.c.324.1 | 4 | 91.51 | even | 6 | inner | ||
637.2.r.c.324.2 | 4 | 7.2 | even | 3 | inner | ||
8281.2.a.a.1.1 | 1 | 91.18 | odd | 12 | |||
8281.2.a.b.1.1 | 1 | 91.31 | even | 12 | |||
8281.2.a.k.1.1 | 1 | 91.60 | odd | 12 | |||
8281.2.a.m.1.1 | 1 | 91.73 | even | 12 |