Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,2,Mod(40,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.40");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.934249703649\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 40.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.40 |
Dual form | 117.2.e.a.79.1 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.707107 | − | 1.22474i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.258819 | − | 0.965926i | \(-0.416667\pi\) | |||||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | −2.00000 | + | 3.46410i | −0.894427 | + | 1.54919i | −0.0599153 | + | 0.998203i | \(0.519083\pi\) |
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | 3.46410i | 1.41421i | ||||||||
\(7\) | −1.00000 | − | 1.73205i | −0.377964 | − | 0.654654i | 0.612801 | − | 0.790237i | \(-0.290043\pi\) |
−0.990766 | + | 0.135583i | \(0.956709\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 8.00000 | 2.52982 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 3.00000 | − | 1.73205i | 0.866025 | − | 0.500000i | ||||
\(13\) | −0.500000 | + | 0.866025i | −0.138675 | + | 0.240192i | ||||
\(14\) | −2.00000 | + | 3.46410i | −0.534522 | + | 0.925820i | ||||
\(15\) | 6.00000 | − | 3.46410i | 1.54919 | − | 0.894427i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −5.00000 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(18\) | 3.00000 | − | 5.19615i | 0.707107 | − | 1.22474i | ||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | −4.00000 | − | 6.92820i | −0.894427 | − | 1.54919i | ||||
\(21\) | 3.46410i | 0.755929i | ||||||||
\(22\) | −2.00000 | + | 3.46410i | −0.426401 | + | 0.738549i | ||||
\(23\) | 1.50000 | − | 2.59808i | 0.312772 | − | 0.541736i | −0.666190 | − | 0.745782i | \(-0.732076\pi\) |
0.978961 | + | 0.204046i | \(0.0654092\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | − | 9.52628i | −1.10000 | − | 1.90526i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | 1.00000 | + | 1.73205i | 0.185695 | + | 0.321634i | 0.943811 | − | 0.330487i | \(-0.107213\pi\) |
−0.758115 | + | 0.652121i | \(0.773880\pi\) | |||||||
\(30\) | −12.0000 | − | 6.92820i | −2.19089 | − | 1.26491i | ||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 4.00000 | − | 6.92820i | 0.707107 | − | 1.22474i | ||||
\(33\) | 3.46410i | 0.603023i | ||||||||
\(34\) | 5.00000 | + | 8.66025i | 0.857493 | + | 1.48522i | ||||
\(35\) | 8.00000 | 1.35225 | ||||||||
\(36\) | −6.00000 | −1.00000 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 6.00000 | + | 10.3923i | 0.973329 | + | 1.68585i | ||||
\(39\) | 1.50000 | − | 0.866025i | 0.240192 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | − | 5.19615i | 0.468521 | − | 0.811503i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | 6.00000 | − | 3.46410i | 0.925820 | − | 0.534522i | ||||
\(43\) | 1.50000 | + | 2.59808i | 0.228748 | + | 0.396203i | 0.957437 | − | 0.288641i | \(-0.0932035\pi\) |
−0.728689 | + | 0.684844i | \(0.759870\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | −12.0000 | −1.78885 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | − | 6.92820i | − | 1.00000i | ||||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | −11.0000 | + | 19.0526i | −1.55563 | + | 2.69444i | ||||
\(51\) | 7.50000 | + | 4.33013i | 1.05021 | + | 0.606339i | ||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | −9.00000 | + | 5.19615i | −1.22474 | + | 0.707107i | ||||
\(55\) | 8.00000 | 1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.00000 | + | 5.19615i | 1.19208 | + | 0.688247i | ||||
\(58\) | 2.00000 | − | 3.46410i | 0.262613 | − | 0.454859i | ||||
\(59\) | −6.00000 | + | 10.3923i | −0.781133 | + | 1.35296i | 0.150148 | + | 0.988663i | \(0.452025\pi\) |
−0.931282 | + | 0.364299i | \(0.881308\pi\) | |||||||
\(60\) | 13.8564i | 1.78885i | ||||||||
\(61\) | 2.50000 | + | 4.33013i | 0.320092 | + | 0.554416i | 0.980507 | − | 0.196485i | \(-0.0629528\pi\) |
−0.660415 | + | 0.750901i | \(0.729619\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | 3.00000 | − | 5.19615i | 0.377964 | − | 0.654654i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | 6.00000 | − | 3.46410i | 0.738549 | − | 0.426401i | ||||
\(67\) | −2.00000 | + | 3.46410i | −0.244339 | + | 0.423207i | −0.961946 | − | 0.273241i | \(-0.911904\pi\) |
0.717607 | + | 0.696449i | \(0.245238\pi\) | |||||||
\(68\) | 5.00000 | − | 8.66025i | 0.606339 | − | 1.05021i | ||||
\(69\) | −4.50000 | + | 2.59808i | −0.541736 | + | 0.312772i | ||||
\(70\) | −8.00000 | − | 13.8564i | −0.956183 | − | 1.65616i | ||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | 19.0526i | 2.20000i | ||||||||
\(76\) | 6.00000 | − | 10.3923i | 0.688247 | − | 1.19208i | ||||
\(77\) | −2.00000 | + | 3.46410i | −0.227921 | + | 0.394771i | ||||
\(78\) | −3.00000 | − | 1.73205i | −0.339683 | − | 0.196116i | ||||
\(79\) | −2.50000 | − | 4.33013i | −0.281272 | − | 0.487177i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.971698 | + | 0.236225i | \(0.924090\pi\) | |||||||
\(80\) | −16.0000 | −1.78885 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −12.0000 | −1.32518 | ||||||||
\(83\) | −1.00000 | − | 1.73205i | −0.109764 | − | 0.190117i | 0.805910 | − | 0.592037i | \(-0.201676\pi\) |
−0.915675 | + | 0.401920i | \(0.868343\pi\) | |||||||
\(84\) | −6.00000 | − | 3.46410i | −0.654654 | − | 0.377964i | ||||
\(85\) | 10.0000 | − | 17.3205i | 1.08465 | − | 1.87867i | ||||
\(86\) | 3.00000 | − | 5.19615i | 0.323498 | − | 0.560316i | ||||
\(87\) | − | 3.46410i | − | 0.371391i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 12.0000 | + | 20.7846i | 1.26491 | + | 2.19089i | ||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 3.00000 | + | 5.19615i | 0.312772 | + | 0.541736i | ||||
\(93\) | 6.00000 | − | 3.46410i | 0.622171 | − | 0.359211i | ||||
\(94\) | −6.00000 | + | 10.3923i | −0.618853 | + | 1.07188i | ||||
\(95\) | 12.0000 | − | 20.7846i | 1.23117 | − | 2.13246i | ||||
\(96\) | −12.0000 | + | 6.92820i | −1.22474 | + | 0.707107i | ||||
\(97\) | 4.00000 | + | 6.92820i | 0.406138 | + | 0.703452i | 0.994453 | − | 0.105180i | \(-0.0335417\pi\) |
−0.588315 | + | 0.808632i | \(0.700208\pi\) | |||||||
\(98\) | −6.00000 | −0.606092 | ||||||||
\(99\) | 3.00000 | − | 5.19615i | 0.301511 | − | 0.522233i | ||||
\(100\) | 22.0000 | 2.20000 | ||||||||
\(101\) | −4.50000 | − | 7.79423i | −0.447767 | − | 0.775555i | 0.550474 | − | 0.834853i | \(-0.314447\pi\) |
−0.998240 | + | 0.0592978i | \(0.981114\pi\) | |||||||
\(102\) | − | 17.3205i | − | 1.71499i | ||||||
\(103\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.0000 | − | 6.92820i | −1.17108 | − | 0.676123i | ||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | 3.00000 | 0.290021 | 0.145010 | − | 0.989430i | \(-0.453678\pi\) | ||||
0.145010 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.866025 | + | 0.500000i | ||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | −8.00000 | − | 13.8564i | −0.762770 | − | 1.32116i | ||||
\(111\) | 3.00000 | + | 1.73205i | 0.284747 | + | 0.164399i | ||||
\(112\) | 4.00000 | − | 6.92820i | 0.377964 | − | 0.654654i | ||||
\(113\) | −10.5000 | + | 18.1865i | −0.987757 | + | 1.71085i | −0.358778 | + | 0.933423i | \(0.616806\pi\) |
−0.628979 | + | 0.777422i | \(0.716527\pi\) | |||||||
\(114\) | − | 20.7846i | − | 1.94666i | ||||||
\(115\) | 6.00000 | + | 10.3923i | 0.559503 | + | 0.969087i | ||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | −3.00000 | −0.277350 | ||||||||
\(118\) | 24.0000 | 2.20938 | ||||||||
\(119\) | 5.00000 | + | 8.66025i | 0.458349 | + | 0.793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 5.00000 | − | 8.66025i | 0.452679 | − | 0.784063i | ||||
\(123\) | −9.00000 | + | 5.19615i | −0.811503 | + | 0.468521i | ||||
\(124\) | −4.00000 | − | 6.92820i | −0.359211 | − | 0.622171i | ||||
\(125\) | 24.0000 | 2.14663 | ||||||||
\(126\) | −12.0000 | −1.06904 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 5.19615i | − | 0.457496i | ||||||
\(130\) | −4.00000 | + | 6.92820i | −0.350823 | + | 0.607644i | ||||
\(131\) | 0.500000 | − | 0.866025i | 0.0436852 | − | 0.0756650i | −0.843356 | − | 0.537355i | \(-0.819423\pi\) |
0.887041 | + | 0.461690i | \(0.152757\pi\) | |||||||
\(132\) | −6.00000 | − | 3.46410i | −0.522233 | − | 0.301511i | ||||
\(133\) | 6.00000 | + | 10.3923i | 0.520266 | + | 0.901127i | ||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 18.0000 | + | 10.3923i | 1.54919 | + | 0.894427i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 9.00000 | + | 5.19615i | 0.766131 | + | 0.442326i | ||||
\(139\) | 1.50000 | − | 2.59808i | 0.127228 | − | 0.220366i | −0.795373 | − | 0.606120i | \(-0.792725\pi\) |
0.922602 | + | 0.385754i | \(0.126059\pi\) | |||||||
\(140\) | −8.00000 | + | 13.8564i | −0.676123 | + | 1.17108i | ||||
\(141\) | 10.3923i | 0.875190i | ||||||||
\(142\) | −12.0000 | − | 20.7846i | −1.00702 | − | 1.74421i | ||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | −6.00000 | + | 10.3923i | −0.500000 | + | 0.866025i | ||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 4.00000 | + | 6.92820i | 0.331042 | + | 0.573382i | ||||
\(147\) | −4.50000 | + | 2.59808i | −0.371154 | + | 0.214286i | ||||
\(148\) | 2.00000 | − | 3.46410i | 0.164399 | − | 0.284747i | ||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 33.0000 | − | 19.0526i | 2.69444 | − | 1.55563i | ||||
\(151\) | 1.00000 | + | 1.73205i | 0.0813788 | + | 0.140952i | 0.903842 | − | 0.427865i | \(-0.140734\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.50000 | − | 12.9904i | −0.606339 | − | 1.05021i | ||||
\(154\) | 8.00000 | 0.644658 | ||||||||
\(155\) | −8.00000 | − | 13.8564i | −0.642575 | − | 1.11297i | ||||
\(156\) | 3.46410i | 0.277350i | ||||||||
\(157\) | −10.5000 | + | 18.1865i | −0.837991 | + | 1.45144i | 0.0535803 | + | 0.998564i | \(0.482937\pi\) |
−0.891572 | + | 0.452880i | \(0.850397\pi\) | |||||||
\(158\) | −5.00000 | + | 8.66025i | −0.397779 | + | 0.688973i | ||||
\(159\) | −4.50000 | − | 2.59808i | −0.356873 | − | 0.206041i | ||||
\(160\) | 16.0000 | + | 27.7128i | 1.26491 | + | 2.19089i | ||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 18.0000 | 1.41421 | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 6.00000 | + | 10.3923i | 0.468521 | + | 0.811503i | ||||
\(165\) | −12.0000 | − | 6.92820i | −0.934199 | − | 0.539360i | ||||
\(166\) | −2.00000 | + | 3.46410i | −0.155230 | + | 0.268866i | ||||
\(167\) | −1.00000 | + | 1.73205i | −0.0773823 | + | 0.134030i | −0.902120 | − | 0.431486i | \(-0.857990\pi\) |
0.824737 | + | 0.565516i | \(0.191323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | −40.0000 | −3.06786 | ||||||||
\(171\) | −9.00000 | − | 15.5885i | −0.688247 | − | 1.19208i | ||||
\(172\) | −6.00000 | −0.457496 | ||||||||
\(173\) | 1.50000 | + | 2.59808i | 0.114043 | + | 0.197528i | 0.917397 | − | 0.397974i | \(-0.130287\pi\) |
−0.803354 | + | 0.595502i | \(0.796953\pi\) | |||||||
\(174\) | −6.00000 | + | 3.46410i | −0.454859 | + | 0.262613i | ||||
\(175\) | −11.0000 | + | 19.0526i | −0.831522 | + | 1.44024i | ||||
\(176\) | 4.00000 | − | 6.92820i | 0.301511 | − | 0.522233i | ||||
\(177\) | 18.0000 | − | 10.3923i | 1.35296 | − | 0.781133i | ||||
\(178\) | 10.0000 | + | 17.3205i | 0.749532 | + | 1.29823i | ||||
\(179\) | −19.0000 | −1.42013 | −0.710063 | − | 0.704138i | \(-0.751334\pi\) | ||||
−0.710063 | + | 0.704138i | \(0.751334\pi\) | |||||||
\(180\) | 12.0000 | − | 20.7846i | 0.894427 | − | 1.54919i | ||||
\(181\) | 11.0000 | 0.817624 | 0.408812 | − | 0.912619i | \(-0.365943\pi\) | ||||
0.408812 | + | 0.912619i | \(0.365943\pi\) | |||||||
\(182\) | −2.00000 | − | 3.46410i | −0.148250 | − | 0.256776i | ||||
\(183\) | − | 8.66025i | − | 0.640184i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | − | 6.92820i | 0.294086 | − | 0.509372i | ||||
\(186\) | −12.0000 | − | 6.92820i | −0.879883 | − | 0.508001i | ||||
\(187\) | 5.00000 | + | 8.66025i | 0.365636 | + | 0.633300i | ||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | −9.00000 | + | 5.19615i | −0.654654 | + | 0.377964i | ||||
\(190\) | −48.0000 | −3.48229 | ||||||||
\(191\) | −9.50000 | − | 16.4545i | −0.687396 | − | 1.19060i | −0.972677 | − | 0.232161i | \(-0.925420\pi\) |
0.285282 | − | 0.958444i | \(-0.407913\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.866025 | + | 0.500000i | ||||
\(193\) | 12.0000 | − | 20.7846i | 0.863779 | − | 1.49611i | −0.00447566 | − | 0.999990i | \(-0.501425\pi\) |
0.868255 | − | 0.496119i | \(-0.165242\pi\) | |||||||
\(194\) | 8.00000 | − | 13.8564i | 0.574367 | − | 0.994832i | ||||
\(195\) | 6.92820i | 0.496139i | ||||||||
\(196\) | 3.00000 | + | 5.19615i | 0.214286 | + | 0.371154i | ||||
\(197\) | 24.0000 | 1.70993 | 0.854965 | − | 0.518686i | \(-0.173579\pi\) | ||||
0.854965 | + | 0.518686i | \(0.173579\pi\) | |||||||
\(198\) | −12.0000 | −0.852803 | ||||||||
\(199\) | 17.0000 | 1.20510 | 0.602549 | − | 0.798082i | \(-0.294152\pi\) | ||||
0.602549 | + | 0.798082i | \(0.294152\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | − | 3.46410i | 0.423207 | − | 0.244339i | ||||
\(202\) | −9.00000 | + | 15.5885i | −0.633238 | + | 1.09680i | ||||
\(203\) | 2.00000 | − | 3.46410i | 0.140372 | − | 0.243132i | ||||
\(204\) | −15.0000 | + | 8.66025i | −1.05021 | + | 0.606339i | ||||
\(205\) | 12.0000 | + | 20.7846i | 0.838116 | + | 1.45166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.00000 | 0.625543 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 6.00000 | + | 10.3923i | 0.415029 | + | 0.718851i | ||||
\(210\) | 27.7128i | 1.91237i | ||||||||
\(211\) | −0.500000 | + | 0.866025i | −0.0344214 | + | 0.0596196i | −0.882723 | − | 0.469894i | \(-0.844292\pi\) |
0.848301 | + | 0.529514i | \(0.177626\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | −18.0000 | − | 10.3923i | −1.23334 | − | 0.712069i | ||||
\(214\) | −3.00000 | − | 5.19615i | −0.205076 | − | 0.355202i | ||||
\(215\) | −12.0000 | −0.818393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 14.0000 | + | 24.2487i | 0.948200 | + | 1.64233i | ||||
\(219\) | 6.00000 | + | 3.46410i | 0.405442 | + | 0.234082i | ||||
\(220\) | −8.00000 | + | 13.8564i | −0.539360 | + | 0.934199i | ||||
\(221\) | 2.50000 | − | 4.33013i | 0.168168 | − | 0.291276i | ||||
\(222\) | − | 6.92820i | − | 0.464991i | ||||||
\(223\) | −8.00000 | − | 13.8564i | −0.535720 | − | 0.927894i | −0.999128 | − | 0.0417488i | \(-0.986707\pi\) |
0.463409 | − | 0.886145i | \(-0.346626\pi\) | |||||||
\(224\) | −16.0000 | −1.06904 | ||||||||
\(225\) | 16.5000 | − | 28.5788i | 1.10000 | − | 1.90526i | ||||
\(226\) | 42.0000 | 2.79380 | ||||||||
\(227\) | 2.00000 | + | 3.46410i | 0.132745 | + | 0.229920i | 0.924734 | − | 0.380615i | \(-0.124288\pi\) |
−0.791989 | + | 0.610535i | \(0.790954\pi\) | |||||||
\(228\) | −18.0000 | + | 10.3923i | −1.19208 | + | 0.688247i | ||||
\(229\) | 8.00000 | − | 13.8564i | 0.528655 | − | 0.915657i | −0.470787 | − | 0.882247i | \(-0.656030\pi\) |
0.999442 | − | 0.0334101i | \(-0.0106368\pi\) | |||||||
\(230\) | 12.0000 | − | 20.7846i | 0.791257 | − | 1.37050i | ||||
\(231\) | 6.00000 | − | 3.46410i | 0.394771 | − | 0.227921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.00000 | −0.458585 | −0.229293 | − | 0.973358i | \(-0.573641\pi\) | ||||
−0.229293 | + | 0.973358i | \(0.573641\pi\) | |||||||
\(234\) | 3.00000 | + | 5.19615i | 0.196116 | + | 0.339683i | ||||
\(235\) | 24.0000 | 1.56559 | ||||||||
\(236\) | −12.0000 | − | 20.7846i | −0.781133 | − | 1.35296i | ||||
\(237\) | 8.66025i | 0.562544i | ||||||||
\(238\) | 10.0000 | − | 17.3205i | 0.648204 | − | 1.12272i | ||||
\(239\) | 3.00000 | − | 5.19615i | 0.194054 | − | 0.336111i | −0.752536 | − | 0.658551i | \(-0.771170\pi\) |
0.946590 | + | 0.322440i | \(0.104503\pi\) | |||||||
\(240\) | 24.0000 | + | 13.8564i | 1.54919 | + | 0.894427i | ||||
\(241\) | −2.00000 | − | 3.46410i | −0.128831 | − | 0.223142i | 0.794393 | − | 0.607404i | \(-0.207789\pi\) |
−0.923224 | + | 0.384262i | \(0.874456\pi\) | |||||||
\(242\) | −14.0000 | −0.899954 | ||||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 6.00000 | + | 10.3923i | 0.383326 | + | 0.663940i | ||||
\(246\) | 18.0000 | + | 10.3923i | 1.14764 | + | 0.662589i | ||||
\(247\) | 3.00000 | − | 5.19615i | 0.190885 | − | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.46410i | 0.219529i | ||||||||
\(250\) | −24.0000 | − | 41.5692i | −1.51789 | − | 2.62907i | ||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | 6.00000 | + | 10.3923i | 0.377964 | + | 0.654654i | ||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 16.0000 | + | 27.7128i | 1.00393 | + | 1.73886i | ||||
\(255\) | −30.0000 | + | 17.3205i | −1.87867 | + | 1.08465i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −6.50000 | + | 11.2583i | −0.405459 | + | 0.702275i | −0.994375 | − | 0.105919i | \(-0.966222\pi\) |
0.588916 | + | 0.808194i | \(0.299555\pi\) | |||||||
\(258\) | −9.00000 | + | 5.19615i | −0.560316 | + | 0.323498i | ||||
\(259\) | 2.00000 | + | 3.46410i | 0.124274 | + | 0.215249i | ||||
\(260\) | 8.00000 | 0.496139 | ||||||||
\(261\) | −3.00000 | + | 5.19615i | −0.185695 | + | 0.321634i | ||||
\(262\) | −2.00000 | −0.123560 | ||||||||
\(263\) | −7.50000 | − | 12.9904i | −0.462470 | − | 0.801021i | 0.536614 | − | 0.843828i | \(-0.319703\pi\) |
−0.999083 | + | 0.0428069i | \(0.986370\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | + | 10.3923i | −0.368577 | + | 0.638394i | ||||
\(266\) | 12.0000 | − | 20.7846i | 0.735767 | − | 1.27439i | ||||
\(267\) | 15.0000 | + | 8.66025i | 0.917985 | + | 0.529999i | ||||
\(268\) | −4.00000 | − | 6.92820i | −0.244339 | − | 0.423207i | ||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | − | 41.5692i | − | 2.52982i | ||||||
\(271\) | 24.0000 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(272\) | −10.0000 | − | 17.3205i | −0.606339 | − | 1.05021i | ||||
\(273\) | −3.00000 | − | 1.73205i | −0.181568 | − | 0.104828i | ||||
\(274\) | 12.0000 | − | 20.7846i | 0.724947 | − | 1.25564i | ||||
\(275\) | −11.0000 | + | 19.0526i | −0.663325 | + | 1.14891i | ||||
\(276\) | − | 10.3923i | − | 0.625543i | ||||||
\(277\) | −7.00000 | − | 12.1244i | −0.420589 | − | 0.728482i | 0.575408 | − | 0.817867i | \(-0.304843\pi\) |
−0.995997 | + | 0.0893846i | \(0.971510\pi\) | |||||||
\(278\) | −6.00000 | −0.359856 | ||||||||
\(279\) | −12.0000 | −0.718421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | − | 3.46410i | −0.119310 | − | 0.206651i | 0.800184 | − | 0.599754i | \(-0.204735\pi\) |
−0.919494 | + | 0.393103i | \(0.871402\pi\) | |||||||
\(282\) | 18.0000 | − | 10.3923i | 1.07188 | − | 0.618853i | ||||
\(283\) | 7.50000 | − | 12.9904i | 0.445829 | − | 0.772198i | −0.552281 | − | 0.833658i | \(-0.686242\pi\) |
0.998110 | + | 0.0614601i | \(0.0195757\pi\) | |||||||
\(284\) | −12.0000 | + | 20.7846i | −0.712069 | + | 1.23334i | ||||
\(285\) | −36.0000 | + | 20.7846i | −2.13246 | + | 1.23117i | ||||
\(286\) | −2.00000 | − | 3.46410i | −0.118262 | − | 0.204837i | ||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 24.0000 | 1.41421 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 8.00000 | + | 13.8564i | 0.469776 | + | 0.813676i | ||||
\(291\) | − | 13.8564i | − | 0.812277i | ||||||
\(292\) | 4.00000 | − | 6.92820i | 0.234082 | − | 0.405442i | ||||
\(293\) | 9.00000 | − | 15.5885i | 0.525786 | − | 0.910687i | −0.473763 | − | 0.880652i | \(-0.657105\pi\) |
0.999549 | − | 0.0300351i | \(-0.00956192\pi\) | |||||||
\(294\) | 9.00000 | + | 5.19615i | 0.524891 | + | 0.303046i | ||||
\(295\) | −24.0000 | − | 41.5692i | −1.39733 | − | 2.42025i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.00000 | + | 5.19615i | −0.522233 | + | 0.301511i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.50000 | + | 2.59808i | 0.0867472 | + | 0.150251i | ||||
\(300\) | −33.0000 | − | 19.0526i | −1.90526 | − | 1.10000i | ||||
\(301\) | 3.00000 | − | 5.19615i | 0.172917 | − | 0.299501i | ||||
\(302\) | 2.00000 | − | 3.46410i | 0.115087 | − | 0.199337i | ||||
\(303\) | 15.5885i | 0.895533i | ||||||||
\(304\) | −12.0000 | − | 20.7846i | −0.688247 | − | 1.19208i | ||||
\(305\) | −20.0000 | −1.14520 | ||||||||
\(306\) | −15.0000 | + | 25.9808i | −0.857493 | + | 1.48522i | ||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | −4.00000 | − | 6.92820i | −0.227921 | − | 0.394771i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.0000 | + | 27.7128i | −0.908739 | + | 1.57398i | ||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.00000 | − | 5.19615i | −0.169570 | − | 0.293704i | 0.768699 | − | 0.639611i | \(-0.220905\pi\) |
−0.938269 | + | 0.345907i | \(0.887571\pi\) | |||||||
\(314\) | 42.0000 | 2.37020 | ||||||||
\(315\) | 12.0000 | + | 20.7846i | 0.676123 | + | 1.17108i | ||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | 4.00000 | + | 6.92820i | 0.224662 | + | 0.389127i | 0.956218 | − | 0.292655i | \(-0.0945387\pi\) |
−0.731556 | + | 0.681782i | \(0.761205\pi\) | |||||||
\(318\) | 10.3923i | 0.582772i | ||||||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | 16.0000 | − | 27.7128i | 0.894427 | − | 1.54919i | ||||
\(321\) | −4.50000 | − | 2.59808i | −0.251166 | − | 0.145010i | ||||
\(322\) | 6.00000 | + | 10.3923i | 0.334367 | + | 0.579141i | ||||
\(323\) | 30.0000 | 1.66924 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.500000 | − | 0.866025i | ||||
\(325\) | 11.0000 | 0.610170 | ||||||||
\(326\) | 16.0000 | + | 27.7128i | 0.886158 | + | 1.53487i | ||||
\(327\) | 21.0000 | + | 12.1244i | 1.16130 | + | 0.670478i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.00000 | + | 10.3923i | −0.330791 | + | 0.572946i | ||||
\(330\) | 27.7128i | 1.52554i | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 4.00000 | 0.219529 | ||||||||
\(333\) | −3.00000 | − | 5.19615i | −0.164399 | − | 0.284747i | ||||
\(334\) | 4.00000 | 0.218870 | ||||||||
\(335\) | −8.00000 | − | 13.8564i | −0.437087 | − | 0.757056i | ||||
\(336\) | −12.0000 | + | 6.92820i | −0.654654 | + | 0.377964i | ||||
\(337\) | −13.5000 | + | 23.3827i | −0.735392 | + | 1.27374i | 0.219159 | + | 0.975689i | \(0.429669\pi\) |
−0.954551 | + | 0.298047i | \(0.903665\pi\) | |||||||
\(338\) | −1.00000 | + | 1.73205i | −0.0543928 | + | 0.0942111i | ||||
\(339\) | 31.5000 | − | 18.1865i | 1.71085 | − | 0.987757i | ||||
\(340\) | 20.0000 | + | 34.6410i | 1.08465 | + | 1.87867i | ||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | −18.0000 | + | 31.1769i | −0.973329 | + | 1.68585i | ||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 20.7846i | − | 1.11901i | ||||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | −16.5000 | + | 28.5788i | −0.885766 | + | 1.53419i | −0.0409337 | + | 0.999162i | \(0.513033\pi\) |
−0.844833 | + | 0.535031i | \(0.820300\pi\) | |||||||
\(348\) | 6.00000 | + | 3.46410i | 0.321634 | + | 0.185695i | ||||
\(349\) | 4.00000 | + | 6.92820i | 0.214115 | + | 0.370858i | 0.952998 | − | 0.302975i | \(-0.0979799\pi\) |
−0.738883 | + | 0.673833i | \(0.764647\pi\) | |||||||
\(350\) | 44.0000 | 2.35190 | ||||||||
\(351\) | 4.50000 | + | 2.59808i | 0.240192 | + | 0.138675i | ||||
\(352\) | −16.0000 | −0.852803 | ||||||||
\(353\) | 5.00000 | + | 8.66025i | 0.266123 | + | 0.460939i | 0.967857 | − | 0.251500i | \(-0.0809239\pi\) |
−0.701734 | + | 0.712439i | \(0.747591\pi\) | |||||||
\(354\) | −36.0000 | − | 20.7846i | −1.91338 | − | 1.10469i | ||||
\(355\) | −24.0000 | + | 41.5692i | −1.27379 | + | 2.20627i | ||||
\(356\) | 10.0000 | − | 17.3205i | 0.529999 | − | 0.917985i | ||||
\(357\) | − | 17.3205i | − | 0.916698i | ||||||
\(358\) | 19.0000 | + | 32.9090i | 1.00418 | + | 1.73929i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −11.0000 | − | 19.0526i | −0.578147 | − | 1.00138i | ||||
\(363\) | −10.5000 | + | 6.06218i | −0.551107 | + | 0.318182i | ||||
\(364\) | −2.00000 | + | 3.46410i | −0.104828 | + | 0.181568i | ||||
\(365\) | 8.00000 | − | 13.8564i | 0.418739 | − | 0.725277i | ||||
\(366\) | −15.0000 | + | 8.66025i | −0.784063 | + | 0.452679i | ||||
\(367\) | 2.50000 | + | 4.33013i | 0.130499 | + | 0.226031i | 0.923869 | − | 0.382709i | \(-0.125009\pi\) |
−0.793370 | + | 0.608740i | \(0.791675\pi\) | |||||||
\(368\) | 12.0000 | 0.625543 | ||||||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | −16.0000 | −0.831800 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 13.8564i | 0.718421i | ||||||||
\(373\) | −0.500000 | + | 0.866025i | −0.0258890 | + | 0.0448411i | −0.878680 | − | 0.477412i | \(-0.841575\pi\) |
0.852791 | + | 0.522253i | \(0.174908\pi\) | |||||||
\(374\) | 10.0000 | − | 17.3205i | 0.517088 | − | 0.895622i | ||||
\(375\) | −36.0000 | − | 20.7846i | −1.85903 | − | 1.07331i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.00000 | −0.103005 | ||||||||
\(378\) | 18.0000 | + | 10.3923i | 0.925820 | + | 0.534522i | ||||
\(379\) | 6.00000 | 0.308199 | 0.154100 | − | 0.988055i | \(-0.450752\pi\) | ||||
0.154100 | + | 0.988055i | \(0.450752\pi\) | |||||||
\(380\) | 24.0000 | + | 41.5692i | 1.23117 | + | 2.13246i | ||||
\(381\) | 24.0000 | + | 13.8564i | 1.22956 | + | 0.709885i | ||||
\(382\) | −19.0000 | + | 32.9090i | −0.972125 | + | 1.68377i | ||||
\(383\) | −17.0000 | + | 29.4449i | −0.868659 | + | 1.50456i | −0.00529229 | + | 0.999986i | \(0.501685\pi\) |
−0.863367 | + | 0.504576i | \(0.831649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | − | 13.8564i | −0.407718 | − | 0.706188i | ||||
\(386\) | −48.0000 | −2.44314 | ||||||||
\(387\) | −4.50000 | + | 7.79423i | −0.228748 | + | 0.396203i | ||||
\(388\) | −16.0000 | −0.812277 | ||||||||
\(389\) | 0.500000 | + | 0.866025i | 0.0253510 | + | 0.0439092i | 0.878423 | − | 0.477885i | \(-0.158596\pi\) |
−0.853072 | + | 0.521794i | \(0.825263\pi\) | |||||||
\(390\) | 12.0000 | − | 6.92820i | 0.607644 | − | 0.350823i | ||||
\(391\) | −7.50000 | + | 12.9904i | −0.379291 | + | 0.656952i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.50000 | + | 0.866025i | −0.0756650 | + | 0.0436852i | ||||
\(394\) | −24.0000 | − | 41.5692i | −1.20910 | − | 2.09423i | ||||
\(395\) | 20.0000 | 1.00631 | ||||||||
\(396\) | 6.00000 | + | 10.3923i | 0.301511 | + | 0.522233i | ||||
\(397\) | 8.00000 | 0.401508 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(398\) | −17.0000 | − | 29.4449i | −0.852133 | − | 1.47594i | ||||
\(399\) | − | 20.7846i | − | 1.04053i | ||||||
\(400\) | 22.0000 | − | 38.1051i | 1.10000 | − | 1.90526i | ||||
\(401\) | −13.0000 | + | 22.5167i | −0.649189 | + | 1.12443i | 0.334128 | + | 0.942528i | \(0.391558\pi\) |
−0.983317 | + | 0.181901i | \(0.941775\pi\) | |||||||
\(402\) | −12.0000 | − | 6.92820i | −0.598506 | − | 0.345547i | ||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | −18.0000 | − | 31.1769i | −0.894427 | − | 1.54919i | ||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | 2.00000 | + | 3.46410i | 0.0991363 | + | 0.171709i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0000 | − | 27.7128i | 0.791149 | − | 1.37031i | −0.134107 | − | 0.990967i | \(-0.542817\pi\) |
0.925256 | − | 0.379344i | \(-0.123850\pi\) | |||||||
\(410\) | 24.0000 | − | 41.5692i | 1.18528 | − | 2.05296i | ||||
\(411\) | − | 20.7846i | − | 1.02523i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.0000 | 1.18096 | ||||||||
\(414\) | −9.00000 | − | 15.5885i | −0.442326 | − | 0.766131i | ||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 4.00000 | + | 6.92820i | 0.196116 | + | 0.339683i | ||||
\(417\) | −4.50000 | + | 2.59808i | −0.220366 | + | 0.127228i | ||||
\(418\) | 12.0000 | − | 20.7846i | 0.586939 | − | 1.01661i | ||||
\(419\) | 0.500000 | − | 0.866025i | 0.0244266 | − | 0.0423081i | −0.853554 | − | 0.521005i | \(-0.825557\pi\) |
0.877980 | + | 0.478697i | \(0.158891\pi\) | |||||||
\(420\) | 24.0000 | − | 13.8564i | 1.17108 | − | 0.676123i | ||||
\(421\) | −13.0000 | − | 22.5167i | −0.633581 | − | 1.09739i | −0.986814 | − | 0.161859i | \(-0.948251\pi\) |
0.353233 | − | 0.935536i | \(-0.385082\pi\) | |||||||
\(422\) | 2.00000 | 0.0973585 | ||||||||
\(423\) | 9.00000 | − | 15.5885i | 0.437595 | − | 0.757937i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.5000 | + | 47.6314i | 1.33395 | + | 2.31046i | ||||
\(426\) | 41.5692i | 2.01404i | ||||||||
\(427\) | 5.00000 | − | 8.66025i | 0.241967 | − | 0.419099i | ||||
\(428\) | −3.00000 | + | 5.19615i | −0.145010 | + | 0.251166i | ||||
\(429\) | −3.00000 | − | 1.73205i | −0.144841 | − | 0.0836242i | ||||
\(430\) | 12.0000 | + | 20.7846i | 0.578691 | + | 1.00232i | ||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 18.0000 | − | 10.3923i | 0.866025 | − | 0.500000i | ||||
\(433\) | −35.0000 | −1.68199 | −0.840996 | − | 0.541041i | \(-0.818030\pi\) | ||||
−0.840996 | + | 0.541041i | \(0.818030\pi\) | |||||||
\(434\) | −8.00000 | − | 13.8564i | −0.384012 | − | 0.665129i | ||||
\(435\) | 12.0000 | + | 6.92820i | 0.575356 | + | 0.332182i | ||||
\(436\) | 14.0000 | − | 24.2487i | 0.670478 | − | 1.16130i | ||||
\(437\) | −9.00000 | + | 15.5885i | −0.430528 | + | 0.745697i | ||||
\(438\) | − | 13.8564i | − | 0.662085i | ||||||
\(439\) | 0.500000 | + | 0.866025i | 0.0238637 | + | 0.0413331i | 0.877711 | − | 0.479191i | \(-0.159070\pi\) |
−0.853847 | + | 0.520524i | \(0.825737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | −10.0000 | −0.475651 | ||||||||
\(443\) | −15.5000 | − | 26.8468i | −0.736427 | − | 1.27553i | −0.954094 | − | 0.299506i | \(-0.903178\pi\) |
0.217667 | − | 0.976023i | \(-0.430155\pi\) | |||||||
\(444\) | −6.00000 | + | 3.46410i | −0.284747 | + | 0.164399i | ||||
\(445\) | 20.0000 | − | 34.6410i | 0.948091 | − | 1.64214i | ||||
\(446\) | −16.0000 | + | 27.7128i | −0.757622 | + | 1.31224i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | + | 13.8564i | 0.377964 | + | 0.654654i | ||||
\(449\) | −4.00000 | −0.188772 | −0.0943858 | − | 0.995536i | \(-0.530089\pi\) | ||||
−0.0943858 | + | 0.995536i | \(0.530089\pi\) | |||||||
\(450\) | −66.0000 | −3.11127 | ||||||||
\(451\) | −12.0000 | −0.565058 | ||||||||
\(452\) | −21.0000 | − | 36.3731i | −0.987757 | − | 1.71085i | ||||
\(453\) | − | 3.46410i | − | 0.162758i | ||||||
\(454\) | 4.00000 | − | 6.92820i | 0.187729 | − | 0.325157i | ||||
\(455\) | −4.00000 | + | 6.92820i | −0.187523 | + | 0.324799i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00000 | + | 13.8564i | 0.374224 | + | 0.648175i | 0.990211 | − | 0.139581i | \(-0.0445757\pi\) |
−0.615986 | + | 0.787757i | \(0.711242\pi\) | |||||||
\(458\) | −32.0000 | −1.49526 | ||||||||
\(459\) | 25.9808i | 1.21268i | ||||||||
\(460\) | −24.0000 | −1.11901 | ||||||||
\(461\) | 11.0000 | + | 19.0526i | 0.512321 | + | 0.887366i | 0.999898 | + | 0.0142861i | \(0.00454755\pi\) |
−0.487577 | + | 0.873080i | \(0.662119\pi\) | |||||||
\(462\) | −12.0000 | − | 6.92820i | −0.558291 | − | 0.322329i | ||||
\(463\) | −8.00000 | + | 13.8564i | −0.371792 | + | 0.643962i | −0.989841 | − | 0.142177i | \(-0.954590\pi\) |
0.618050 | + | 0.786139i | \(0.287923\pi\) | |||||||
\(464\) | −4.00000 | + | 6.92820i | −0.185695 | + | 0.321634i | ||||
\(465\) | 27.7128i | 1.28515i | ||||||||
\(466\) | 7.00000 | + | 12.1244i | 0.324269 | + | 0.561650i | ||||
\(467\) | 3.00000 | 0.138823 | 0.0694117 | − | 0.997588i | \(-0.477888\pi\) | ||||
0.0694117 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(468\) | 3.00000 | − | 5.19615i | 0.138675 | − | 0.240192i | ||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | −24.0000 | − | 41.5692i | −1.10704 | − | 1.91745i | ||||
\(471\) | 31.5000 | − | 18.1865i | 1.45144 | − | 0.837991i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 5.19615i | 0.137940 | − | 0.238919i | ||||
\(474\) | 15.0000 | − | 8.66025i | 0.688973 | − | 0.397779i | ||||
\(475\) | 33.0000 | + | 57.1577i | 1.51414 | + | 2.62257i | ||||
\(476\) | −20.0000 | −0.916698 | ||||||||
\(477\) | 4.50000 | + | 7.79423i | 0.206041 | + | 0.356873i | ||||
\(478\) | −12.0000 | −0.548867 | ||||||||
\(479\) | −18.0000 | − | 31.1769i | −0.822441 | − | 1.42451i | −0.903859 | − | 0.427830i | \(-0.859278\pi\) |
0.0814184 | − | 0.996680i | \(-0.474055\pi\) | |||||||
\(480\) | − | 55.4256i | − | 2.52982i | ||||||
\(481\) | 1.00000 | − | 1.73205i | 0.0455961 | − | 0.0789747i | ||||
\(482\) | −4.00000 | + | 6.92820i | −0.182195 | + | 0.315571i | ||||
\(483\) | 9.00000 | + | 5.19615i | 0.409514 | + | 0.236433i | ||||
\(484\) | 7.00000 | + | 12.1244i | 0.318182 | + | 0.551107i | ||||
\(485\) | −32.0000 | −1.45305 | ||||||||
\(486\) | −27.0000 | − | 15.5885i | −1.22474 | − | 0.707107i | ||||
\(487\) | 18.0000 | 0.815658 | 0.407829 | − | 0.913058i | \(-0.366286\pi\) | ||||
0.407829 | + | 0.913058i | \(0.366286\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0000 | + | 13.8564i | 1.08532 | + | 0.626608i | ||||
\(490\) | 12.0000 | − | 20.7846i | 0.542105 | − | 0.938953i | ||||
\(491\) | −6.00000 | + | 10.3923i | −0.270776 | + | 0.468998i | −0.969061 | − | 0.246822i | \(-0.920614\pi\) |
0.698285 | + | 0.715820i | \(0.253947\pi\) | |||||||
\(492\) | − | 20.7846i | − | 0.937043i | ||||||
\(493\) | −5.00000 | − | 8.66025i | −0.225189 | − | 0.390038i | ||||
\(494\) | −12.0000 | −0.539906 | ||||||||
\(495\) | 12.0000 | + | 20.7846i | 0.539360 | + | 0.934199i | ||||
\(496\) | −16.0000 | −0.718421 | ||||||||
\(497\) | −12.0000 | − | 20.7846i | −0.538274 | − | 0.932317i | ||||
\(498\) | 6.00000 | − | 3.46410i | 0.268866 | − | 0.155230i | ||||
\(499\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(500\) | −24.0000 | + | 41.5692i | −1.07331 | + | 1.85903i | ||||
\(501\) | 3.00000 | − | 1.73205i | 0.134030 | − | 0.0773823i | ||||
\(502\) | 15.0000 | + | 25.9808i | 0.669483 | + | 1.15958i | ||||
\(503\) | 29.0000 | 1.29305 | 0.646523 | − | 0.762894i | \(-0.276222\pi\) | ||||
0.646523 | + | 0.762894i | \(0.276222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 6.00000 | + | 10.3923i | 0.266733 | + | 0.461994i | ||||
\(507\) | 1.73205i | 0.0769231i | ||||||||
\(508\) | 16.0000 | − | 27.7128i | 0.709885 | − | 1.22956i | ||||
\(509\) | 8.00000 | − | 13.8564i | 0.354594 | − | 0.614174i | −0.632455 | − | 0.774597i | \(-0.717953\pi\) |
0.987048 | + | 0.160423i | \(0.0512858\pi\) | |||||||
\(510\) | 60.0000 | + | 34.6410i | 2.65684 | + | 1.53393i | ||||
\(511\) | 4.00000 | + | 6.92820i | 0.176950 | + | 0.306486i | ||||
\(512\) | 32.0000 | 1.41421 | ||||||||
\(513\) | 31.1769i | 1.37649i | ||||||||
\(514\) | 26.0000 | 1.14681 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.00000 | + | 5.19615i | 0.396203 | + | 0.228748i | ||||
\(517\) | −6.00000 | + | 10.3923i | −0.263880 | + | 0.457053i | ||||
\(518\) | 4.00000 | − | 6.92820i | 0.175750 | − | 0.304408i | ||||
\(519\) | − | 5.19615i | − | 0.228086i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 12.0000 | 0.525226 | ||||||||
\(523\) | −28.0000 | −1.22435 | −0.612177 | − | 0.790721i | \(-0.709706\pi\) | ||||
−0.612177 | + | 0.790721i | \(0.709706\pi\) | |||||||
\(524\) | 1.00000 | + | 1.73205i | 0.0436852 | + | 0.0756650i | ||||
\(525\) | 33.0000 | − | 19.0526i | 1.44024 | − | 0.831522i | ||||
\(526\) | −15.0000 | + | 25.9808i | −0.654031 | + | 1.13282i | ||||
\(527\) | 10.0000 | − | 17.3205i | 0.435607 | − | 0.754493i | ||||
\(528\) | −12.0000 | + | 6.92820i | −0.522233 | + | 0.301511i | ||||
\(529\) | 7.00000 | + | 12.1244i | 0.304348 | + | 0.527146i | ||||
\(530\) | 24.0000 | 1.04249 | ||||||||
\(531\) | −36.0000 | −1.56227 | ||||||||
\(532\) | −24.0000 | −1.04053 | ||||||||
\(533\) | 3.00000 | + | 5.19615i | 0.129944 | + | 0.225070i | ||||
\(534\) | − | 34.6410i | − | 1.49906i | ||||||
\(535\) | −6.00000 | + | 10.3923i | −0.259403 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.5000 | + | 16.4545i | 1.22987 | + | 0.710063i | ||||
\(538\) | 10.0000 | + | 17.3205i | 0.431131 | + | 0.746740i | ||||
\(539\) | −6.00000 | −0.258438 | ||||||||
\(540\) | −36.0000 | + | 20.7846i | −1.54919 | + | 0.894427i | ||||
\(541\) | 36.0000 | 1.54776 | 0.773880 | − | 0.633332i | \(-0.218313\pi\) | ||||
0.773880 | + | 0.633332i | \(0.218313\pi\) | |||||||
\(542\) | −24.0000 | − | 41.5692i | −1.03089 | − | 1.78555i | ||||
\(543\) | −16.5000 | − | 9.52628i | −0.708083 | − | 0.408812i | ||||
\(544\) | −20.0000 | + | 34.6410i | −0.857493 | + | 1.48522i | ||||
\(545\) | 28.0000 | − | 48.4974i | 1.19939 | − | 2.07740i | ||||
\(546\) | 6.92820i | 0.296500i | ||||||||
\(547\) | −14.0000 | − | 24.2487i | −0.598597 | − | 1.03680i | −0.993028 | − | 0.117875i | \(-0.962392\pi\) |
0.394432 | − | 0.918925i | \(-0.370941\pi\) | |||||||
\(548\) | −24.0000 | −1.02523 | ||||||||
\(549\) | −7.50000 | + | 12.9904i | −0.320092 | + | 0.554416i | ||||
\(550\) | 44.0000 | 1.87617 | ||||||||
\(551\) | −6.00000 | − | 10.3923i | −0.255609 | − | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | + | 8.66025i | −0.212622 | + | 0.368271i | ||||
\(554\) | −14.0000 | + | 24.2487i | −0.594803 | + | 1.03023i | ||||
\(555\) | −12.0000 | + | 6.92820i | −0.509372 | + | 0.294086i | ||||
\(556\) | 3.00000 | + | 5.19615i | 0.127228 | + | 0.220366i | ||||
\(557\) | −18.0000 | −0.762684 | −0.381342 | − | 0.924434i | \(-0.624538\pi\) | ||||
−0.381342 | + | 0.924434i | \(0.624538\pi\) | |||||||
\(558\) | 12.0000 | + | 20.7846i | 0.508001 | + | 0.879883i | ||||
\(559\) | −3.00000 | −0.126886 | ||||||||
\(560\) | 16.0000 | + | 27.7128i | 0.676123 | + | 1.17108i | ||||
\(561\) | − | 17.3205i | − | 0.731272i | ||||||
\(562\) | −4.00000 | + | 6.92820i | −0.168730 | + | 0.292249i | ||||
\(563\) | 10.5000 | − | 18.1865i | 0.442522 | − | 0.766471i | −0.555354 | − | 0.831614i | \(-0.687417\pi\) |
0.997876 | + | 0.0651433i | \(0.0207504\pi\) | |||||||
\(564\) | −18.0000 | − | 10.3923i | −0.757937 | − | 0.437595i | ||||
\(565\) | −42.0000 | − | 72.7461i | −1.76695 | − | 3.06045i | ||||
\(566\) | −30.0000 | −1.26099 | ||||||||
\(567\) | 18.0000 | 0.755929 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.0000 | − | 32.9090i | −0.796521 | − | 1.37962i | −0.921869 | − | 0.387503i | \(-0.873338\pi\) |
0.125347 | − | 0.992113i | \(-0.459996\pi\) | |||||||
\(570\) | 72.0000 | + | 41.5692i | 3.01575 | + | 1.74114i | ||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | −2.00000 | + | 3.46410i | −0.0836242 | + | 0.144841i | ||||
\(573\) | 32.9090i | 1.37479i | ||||||||
\(574\) | 12.0000 | + | 20.7846i | 0.500870 | + | 0.867533i | ||||
\(575\) | −33.0000 | −1.37620 | ||||||||
\(576\) | −12.0000 | − | 20.7846i | −0.500000 | − | 0.866025i | ||||
\(577\) | 32.0000 | 1.33218 | 0.666089 | − | 0.745873i | \(-0.267967\pi\) | ||||
0.666089 | + | 0.745873i | \(0.267967\pi\) | |||||||
\(578\) | −8.00000 | − | 13.8564i | −0.332756 | − | 0.576351i | ||||
\(579\) | −36.0000 | + | 20.7846i | −1.49611 | + | 0.863779i | ||||
\(580\) | 8.00000 | − | 13.8564i | 0.332182 | − | 0.575356i | ||||
\(581\) | −2.00000 | + | 3.46410i | −0.0829740 | + | 0.143715i | ||||
\(582\) | −24.0000 | + | 13.8564i | −0.994832 | + | 0.574367i | ||||
\(583\) | −3.00000 | − | 5.19615i | −0.124247 | − | 0.215203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000 | − | 10.3923i | 0.248069 | − | 0.429669i | ||||
\(586\) | −36.0000 | −1.48715 | ||||||||
\(587\) | 11.0000 | + | 19.0526i | 0.454019 | + | 0.786383i | 0.998631 | − | 0.0523045i | \(-0.0166566\pi\) |
−0.544613 | + | 0.838688i | \(0.683323\pi\) | |||||||
\(588\) | − | 10.3923i | − | 0.428571i | ||||||
\(589\) | 12.0000 | − | 20.7846i | 0.494451 | − | 0.856415i | ||||
\(590\) | −48.0000 | + | 83.1384i | −1.97613 | + | 3.42276i | ||||
\(591\) | −36.0000 | − | 20.7846i | −1.48084 | − | 0.854965i | ||||
\(592\) | −4.00000 | − | 6.92820i | −0.164399 | − | 0.284747i | ||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 18.0000 | + | 10.3923i | 0.738549 | + | 0.426401i | ||||
\(595\) | −40.0000 | −1.63984 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.5000 | − | 14.7224i | −1.04365 | − | 0.602549i | ||||
\(598\) | 3.00000 | − | 5.19615i | 0.122679 | − | 0.212486i | ||||
\(599\) | −15.5000 | + | 26.8468i | −0.633313 | + | 1.09693i | 0.353557 | + | 0.935413i | \(0.384972\pi\) |
−0.986870 | + | 0.161517i | \(0.948361\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.5000 | + | 30.3109i | 0.713840 | + | 1.23641i | 0.963405 | + | 0.268049i | \(0.0863789\pi\) |
−0.249565 | + | 0.968358i | \(0.580288\pi\) | |||||||
\(602\) | −12.0000 | −0.489083 | ||||||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | −4.00000 | −0.162758 | ||||||||
\(605\) | 14.0000 | + | 24.2487i | 0.569181 | + | 0.985850i | ||||
\(606\) | 27.0000 | − | 15.5885i | 1.09680 | − | 0.633238i | ||||
\(607\) | 0.500000 | − | 0.866025i | 0.0202944 | − | 0.0351509i | −0.855700 | − | 0.517472i | \(-0.826873\pi\) |
0.875994 | + | 0.482322i | \(0.160206\pi\) | |||||||
\(608\) | −24.0000 | + | 41.5692i | −0.973329 | + | 1.68585i | ||||
\(609\) | −6.00000 | + | 3.46410i | −0.243132 | + | 0.140372i | ||||
\(610\) | 20.0000 | + | 34.6410i | 0.809776 | + | 1.40257i | ||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | 30.0000 | 1.21268 | ||||||||
\(613\) | 10.0000 | 0.403896 | 0.201948 | − | 0.979396i | \(-0.435273\pi\) | ||||
0.201948 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(614\) | 16.0000 | + | 27.7128i | 0.645707 | + | 1.11840i | ||||
\(615\) | − | 41.5692i | − | 1.67623i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.0000 | − | 34.6410i | 0.805170 | − | 1.39459i | −0.111007 | − | 0.993820i | \(-0.535408\pi\) |
0.916176 | − | 0.400775i | \(-0.131259\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000 | + | 20.7846i | 0.482321 | + | 0.835404i | 0.999794 | − | 0.0202954i | \(-0.00646066\pi\) |
−0.517473 | + | 0.855699i | \(0.673127\pi\) | |||||||
\(620\) | 32.0000 | 1.28515 | ||||||||
\(621\) | −13.5000 | − | 7.79423i | −0.541736 | − | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.0000 | + | 17.3205i | 0.400642 | + | 0.693932i | ||||
\(624\) | 6.00000 | + | 3.46410i | 0.240192 | + | 0.138675i | ||||
\(625\) | −20.5000 | + | 35.5070i | −0.820000 | + | 1.42028i | ||||
\(626\) | −6.00000 | + | 10.3923i | −0.239808 | + | 0.415360i | ||||
\(627\) | − | 20.7846i | − | 0.830057i | ||||||
\(628\) | −21.0000 | − | 36.3731i | −0.837991 | − | 1.45144i | ||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | 24.0000 | − | 41.5692i | 0.956183 | − | 1.65616i | ||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.50000 | − | 0.866025i | 0.0596196 | − | 0.0344214i | ||||
\(634\) | 8.00000 | − | 13.8564i | 0.317721 | − | 0.550308i | ||||
\(635\) | 32.0000 | − | 55.4256i | 1.26988 | − | 2.19950i | ||||
\(636\) | 9.00000 | − | 5.19615i | 0.356873 | − | 0.206041i | ||||
\(637\) | 1.50000 | + | 2.59808i | 0.0594322 | + | 0.102940i | ||||
\(638\) | −8.00000 | −0.316723 | ||||||||
\(639\) | 18.0000 | + | 31.1769i | 0.712069 | + | 1.23334i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.00000 | + | 12.1244i | 0.276483 | + | 0.478883i | 0.970508 | − | 0.241068i | \(-0.0774976\pi\) |
−0.694025 | + | 0.719951i | \(0.744164\pi\) | |||||||
\(642\) | 10.3923i | 0.410152i | ||||||||
\(643\) | 17.0000 | − | 29.4449i | 0.670415 | − | 1.16119i | −0.307372 | − | 0.951589i | \(-0.599450\pi\) |
0.977787 | − | 0.209603i | \(-0.0672170\pi\) | |||||||
\(644\) | 6.00000 | − | 10.3923i | 0.236433 | − | 0.409514i | ||||
\(645\) | 18.0000 | + | 10.3923i | 0.708749 | + | 0.409197i | ||||
\(646\) | −30.0000 | − | 51.9615i | −1.18033 | − | 2.04440i | ||||
\(647\) | −1.00000 | −0.0393141 | −0.0196570 | − | 0.999807i | \(-0.506257\pi\) | ||||
−0.0196570 | + | 0.999807i | \(0.506257\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | −11.0000 | − | 19.0526i | −0.431455 | − | 0.747303i | ||||
\(651\) | −12.0000 | − | 6.92820i | −0.470317 | − | 0.271538i | ||||
\(652\) | 16.0000 | − | 27.7128i | 0.626608 | − | 1.08532i | ||||
\(653\) | 9.00000 | − | 15.5885i | 0.352197 | − | 0.610023i | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | − | 48.4974i | − | 1.89640i | ||||||
\(655\) | 2.00000 | + | 3.46410i | 0.0781465 | + | 0.135354i | ||||
\(656\) | 24.0000 | 0.937043 | ||||||||
\(657\) | −6.00000 | − | 10.3923i | −0.234082 | − | 0.405442i | ||||
\(658\) | 24.0000 | 0.935617 | ||||||||
\(659\) | 20.0000 | + | 34.6410i | 0.779089 | + | 1.34942i | 0.932467 | + | 0.361255i | \(0.117652\pi\) |
−0.153378 | + | 0.988168i | \(0.549015\pi\) | |||||||
\(660\) | 24.0000 | − | 13.8564i | 0.934199 | − | 0.539360i | ||||
\(661\) | −24.0000 | + | 41.5692i | −0.933492 | + | 1.61686i | −0.156190 | + | 0.987727i | \(0.549921\pi\) |
−0.777302 | + | 0.629128i | \(0.783412\pi\) | |||||||
\(662\) | 4.00000 | − | 6.92820i | 0.155464 | − | 0.269272i | ||||
\(663\) | −7.50000 | + | 4.33013i | −0.291276 | + | 0.168168i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −48.0000 | −1.86136 | ||||||||
\(666\) | −6.00000 | + | 10.3923i | −0.232495 | + | 0.402694i | ||||
\(667\) | 6.00000 | 0.232321 | ||||||||
\(668\) | −2.00000 | − | 3.46410i | −0.0773823 | − | 0.134030i | ||||
\(669\) | 27.7128i | 1.07144i | ||||||||
\(670\) | −16.0000 | + | 27.7128i | −0.618134 | + | 1.07064i | ||||
\(671\) | 5.00000 | − | 8.66025i | 0.193023 | − | 0.334325i | ||||
\(672\) | 24.0000 | + | 13.8564i | 0.925820 | + | 0.534522i | ||||
\(673\) | 20.5000 | + | 35.5070i | 0.790217 | + | 1.36870i | 0.925832 | + | 0.377934i | \(0.123365\pi\) |
−0.135615 | + | 0.990762i | \(0.543301\pi\) | |||||||
\(674\) | 54.0000 | 2.08000 | ||||||||
\(675\) | −49.5000 | + | 28.5788i | −1.90526 | + | 1.10000i | ||||
\(676\) | 2.00000 | 0.0769231 | ||||||||
\(677\) | −19.0000 | − | 32.9090i | −0.730229 | − | 1.26479i | −0.956785 | − | 0.290796i | \(-0.906080\pi\) |
0.226556 | − | 0.973998i | \(-0.427253\pi\) | |||||||
\(678\) | −63.0000 | − | 36.3731i | −2.41950 | − | 1.39690i | ||||
\(679\) | 8.00000 | − | 13.8564i | 0.307012 | − | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6.92820i | − | 0.265489i | ||||||
\(682\) | −8.00000 | − | 13.8564i | −0.306336 | − | 0.530589i | ||||
\(683\) | 42.0000 | 1.60709 | 0.803543 | − | 0.595247i | \(-0.202946\pi\) | ||||
0.803543 | + | 0.595247i | \(0.202946\pi\) | |||||||
\(684\) | 36.0000 | 1.37649 | ||||||||
\(685\) | −48.0000 | −1.83399 | ||||||||
\(686\) | 20.0000 | + | 34.6410i | 0.763604 | + | 1.32260i | ||||
\(687\) | −24.0000 | + | 13.8564i | −0.915657 | + | 0.528655i | ||||
\(688\) | −6.00000 | + | 10.3923i | −0.228748 | + | 0.396203i | ||||
\(689\) | −1.50000 | + | 2.59808i | −0.0571454 | + | 0.0989788i | ||||
\(690\) | −36.0000 | + | 20.7846i | −1.37050 | + | 0.791257i | ||||
\(691\) | −21.0000 | − | 36.3731i | −0.798878 | − | 1.38370i | −0.920348 | − | 0.391102i | \(-0.872094\pi\) |
0.121470 | − | 0.992595i | \(-0.461239\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −12.0000 | −0.455842 | ||||||||
\(694\) | 66.0000 | 2.50533 | ||||||||
\(695\) | 6.00000 | + | 10.3923i | 0.227593 | + | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.0000 | + | 25.9808i | −0.568166 | + | 0.984092i | ||||
\(698\) | 8.00000 | − | 13.8564i | 0.302804 | − | 0.524473i | ||||
\(699\) | 10.5000 | + | 6.06218i | 0.397146 | + | 0.229293i | ||||
\(700\) | −22.0000 | − | 38.1051i | −0.831522 | − | 1.44024i | ||||
\(701\) | −5.00000 | −0.188847 | −0.0944237 | − | 0.995532i | \(-0.530101\pi\) | ||||
−0.0944237 | + | 0.995532i | \(0.530101\pi\) | |||||||
\(702\) | − | 10.3923i | − | 0.392232i | ||||||
\(703\) | 12.0000 | 0.452589 | ||||||||
\(704\) | 8.00000 | + | 13.8564i | 0.301511 | + | 0.522233i | ||||
\(705\) | −36.0000 | − | 20.7846i | −1.35584 | − | 0.782794i | ||||
\(706\) | 10.0000 | − | 17.3205i | 0.376355 | − | 0.651866i | ||||
\(707\) | −9.00000 | + | 15.5885i | −0.338480 | + | 0.586264i | ||||
\(708\) | 41.5692i | 1.56227i | ||||||||
\(709\) | −17.0000 | − | 29.4449i | −0.638448 | − | 1.10583i | −0.985773 | − | 0.168080i | \(-0.946243\pi\) |
0.347325 | − | 0.937745i | \(-0.387090\pi\) | |||||||
\(710\) | 96.0000 | 3.60282 | ||||||||
\(711\) | 7.50000 | − | 12.9904i | 0.281272 | − | 0.487177i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.00000 | + | 10.3923i | 0.224702 | + | 0.389195i | ||||
\(714\) | −30.0000 | + | 17.3205i | −1.12272 | + | 0.648204i | ||||
\(715\) | −4.00000 | + | 6.92820i | −0.149592 | + | 0.259100i | ||||
\(716\) | 19.0000 | − | 32.9090i | 0.710063 | − | 1.22987i | ||||
\(717\) | −9.00000 | + | 5.19615i | −0.336111 | + | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | −24.0000 | − | 41.5692i | −0.894427 | − | 1.54919i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.0000 | − | 29.4449i | −0.632674 | − | 1.09582i | ||||
\(723\) | 6.92820i | 0.257663i | ||||||||
\(724\) | −11.0000 | + | 19.0526i | −0.408812 | + | 0.708083i | ||||
\(725\) | 11.0000 | − | 19.0526i | 0.408530 | − | 0.707594i | ||||
\(726\) | 21.0000 | + | 12.1244i | 0.779383 | + | 0.449977i | ||||
\(727\) | 6.50000 | + | 11.2583i | 0.241072 | + | 0.417548i | 0.961020 | − | 0.276479i | \(-0.0891678\pi\) |
−0.719948 | + | 0.694028i | \(0.755834\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −32.0000 | −1.18437 | ||||||||
\(731\) | −7.50000 | − | 12.9904i | −0.277398 | − | 0.480467i | ||||
\(732\) | 15.0000 | + | 8.66025i | 0.554416 | + | 0.320092i | ||||
\(733\) | −3.00000 | + | 5.19615i | −0.110808 | + | 0.191924i | −0.916096 | − | 0.400959i | \(-0.868677\pi\) |
0.805289 | + | 0.592883i | \(0.202010\pi\) | |||||||
\(734\) | 5.00000 | − | 8.66025i | 0.184553 | − | 0.319656i | ||||
\(735\) | − | 20.7846i | − | 0.766652i | ||||||
\(736\) | −12.0000 | − | 20.7846i | −0.442326 | − | 0.766131i | ||||
\(737\) | 8.00000 | 0.294684 | ||||||||
\(738\) | −18.0000 | − | 31.1769i | −0.662589 | − | 1.14764i | ||||
\(739\) | −22.0000 | −0.809283 | −0.404642 | − | 0.914475i | \(-0.632604\pi\) | ||||
−0.404642 | + | 0.914475i | \(0.632604\pi\) | |||||||
\(740\) | 8.00000 | + | 13.8564i | 0.294086 | + | 0.509372i | ||||
\(741\) | −9.00000 | + | 5.19615i | −0.330623 | + | 0.190885i | ||||
\(742\) | −6.00000 | + | 10.3923i | −0.220267 | + | 0.381514i | ||||
\(743\) | −9.00000 | + | 15.5885i | −0.330178 | + | 0.571885i | −0.982547 | − | 0.186017i | \(-0.940442\pi\) |
0.652369 | + | 0.757902i | \(0.273775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.00000 | 0.0732252 | ||||||||
\(747\) | 3.00000 | − | 5.19615i | 0.109764 | − | 0.190117i | ||||
\(748\) | −20.0000 | −0.731272 | ||||||||
\(749\) | −3.00000 | − | 5.19615i | −0.109618 | − | 0.189863i | ||||
\(750\) | 83.1384i | 3.03579i | ||||||||
\(751\) | 14.0000 | − | 24.2487i | 0.510867 | − | 0.884848i | −0.489053 | − | 0.872254i | \(-0.662658\pi\) |
0.999921 | − | 0.0125942i | \(-0.00400897\pi\) | |||||||
\(752\) | 12.0000 | − | 20.7846i | 0.437595 | − | 0.757937i | ||||
\(753\) | 22.5000 | + | 12.9904i | 0.819946 | + | 0.473396i | ||||
\(754\) | 2.00000 | + | 3.46410i | 0.0728357 | + | 0.126155i | ||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | − | 20.7846i | − | 0.755929i | ||||||
\(757\) | −17.0000 | −0.617876 | −0.308938 | − | 0.951082i | \(-0.599973\pi\) | ||||
−0.308938 | + | 0.951082i | \(0.599973\pi\) | |||||||
\(758\) | −6.00000 | − | 10.3923i | −0.217930 | − | 0.377466i | ||||
\(759\) | 9.00000 | + | 5.19615i | 0.326679 | + | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.00000 | − | 1.73205i | 0.0362500 | − | 0.0627868i | −0.847331 | − | 0.531065i | \(-0.821792\pi\) |
0.883581 | + | 0.468278i | \(0.155125\pi\) | |||||||
\(762\) | − | 55.4256i | − | 2.00786i | ||||||
\(763\) | 14.0000 | + | 24.2487i | 0.506834 | + | 0.877862i | ||||
\(764\) | 38.0000 | 1.37479 | ||||||||
\(765\) | 60.0000 | 2.16930 | ||||||||
\(766\) | 68.0000 | 2.45694 | ||||||||
\(767\) | −6.00000 | − | 10.3923i | −0.216647 | − | 0.375244i | ||||
\(768\) | 24.0000 | − | 13.8564i | 0.866025 | − | 0.500000i | ||||
\(769\) | −12.0000 | + | 20.7846i | −0.432731 | + | 0.749512i | −0.997107 | − | 0.0760054i | \(-0.975783\pi\) |
0.564376 | + | 0.825518i | \(0.309117\pi\) | |||||||
\(770\) | −16.0000 | + | 27.7128i | −0.576600 | + | 0.998700i | ||||
\(771\) | 19.5000 | − | 11.2583i | 0.702275 | − | 0.405459i | ||||
\(772\) | 24.0000 | + | 41.5692i | 0.863779 | + | 1.49611i | ||||
\(773\) | −4.00000 | −0.143870 | −0.0719350 | − | 0.997409i | \(-0.522917\pi\) | ||||
−0.0719350 | + | 0.997409i | \(0.522917\pi\) | |||||||
\(774\) | 18.0000 | 0.646997 | ||||||||
\(775\) | 44.0000 | 1.58053 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.92820i | − | 0.248548i | ||||||
\(778\) | 1.00000 | − | 1.73205i | 0.0358517 | − | 0.0620970i | ||||
\(779\) | −18.0000 | + | 31.1769i | −0.644917 | + | 1.11703i | ||||
\(780\) | −12.0000 | − | 6.92820i | −0.429669 | − | 0.248069i | ||||
\(781\) | −12.0000 | − | 20.7846i | −0.429394 | − | 0.743732i | ||||
\(782\) | 30.0000 | 1.07280 | ||||||||
\(783\) | 9.00000 | − | 5.19615i | 0.321634 | − | 0.185695i | ||||
\(784\) | 12.0000 | 0.428571 | ||||||||
\(785\) | −42.0000 | − | 72.7461i | −1.49904 | − | 2.59642i | ||||
\(786\) | 3.00000 | + | 1.73205i | 0.107006 | + | 0.0617802i | ||||
\(787\) | 10.0000 | − | 17.3205i | 0.356462 | − | 0.617409i | −0.630905 | − | 0.775860i | \(-0.717316\pi\) |
0.987367 | + | 0.158450i | \(0.0506498\pi\) | |||||||
\(788\) | −24.0000 | + | 41.5692i | −0.854965 | + | 1.48084i | ||||
\(789\) | 25.9808i | 0.924940i | ||||||||
\(790\) | −20.0000 | − | 34.6410i | −0.711568 | − | 1.23247i | ||||
\(791\) | 42.0000 | 1.49335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.00000 | −0.177555 | ||||||||
\(794\) | −8.00000 | − | 13.8564i | −0.283909 | − | 0.491745i | ||||
\(795\) | 18.0000 | − | 10.3923i | 0.638394 | − | 0.368577i | ||||
\(796\) | −17.0000 | + | 29.4449i | −0.602549 | + | 1.04365i | ||||
\(797\) | −1.00000 | + | 1.73205i | −0.0354218 | + | 0.0613524i | −0.883193 | − | 0.469010i | \(-0.844611\pi\) |
0.847771 | + | 0.530362i | \(0.177944\pi\) | |||||||
\(798\) | −36.0000 | + | 20.7846i | −1.27439 | + | 0.735767i | ||||
\(799\) | 15.0000 | + | 25.9808i | 0.530662 | + | 0.919133i | ||||
\(800\) | −88.0000 | −3.11127 | ||||||||
\(801\) | −15.0000 | − | 25.9808i | −0.529999 | − | 0.917985i | ||||
\(802\) | 52.0000 | 1.83618 | ||||||||
\(803\) | 4.00000 | + | 6.92820i | 0.141157 | + | 0.244491i | ||||
\(804\) | 13.8564i | 0.488678i | ||||||||
\(805\) | 12.0000 | − | 20.7846i | 0.422944 | − | 0.732561i | ||||
\(806\) | −4.00000 | + | 6.92820i | −0.140894 | + | 0.244036i | ||||
\(807\) | 15.0000 | + | 8.66025i | 0.528025 | + | 0.304855i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.00000 | −0.105474 | −0.0527372 | − | 0.998608i | \(-0.516795\pi\) | ||||
−0.0527372 | + | 0.998608i | \(0.516795\pi\) | |||||||
\(810\) | −36.0000 | + | 62.3538i | −1.26491 | + | 2.19089i | ||||
\(811\) | −52.0000 | −1.82597 | −0.912983 | − | 0.407997i | \(-0.866228\pi\) | ||||
−0.912983 | + | 0.407997i | \(0.866228\pi\) | |||||||
\(812\) | 4.00000 | + | 6.92820i | 0.140372 | + | 0.243132i | ||||
\(813\) | −36.0000 | − | 20.7846i | −1.26258 | − | 0.728948i | ||||
\(814\) | 4.00000 | − | 6.92820i | 0.140200 | − | 0.242833i | ||||
\(815\) | 32.0000 | − | 55.4256i | 1.12091 | − | 1.94147i | ||||
\(816\) | 34.6410i | 1.21268i | ||||||||
\(817\) | −9.00000 | − | 15.5885i | −0.314870 | − | 0.545371i | ||||
\(818\) | −64.0000 | −2.23771 | ||||||||
\(819\) | 3.00000 | + | 5.19615i | 0.104828 | + | 0.181568i | ||||
\(820\) | −48.0000 | −1.67623 | ||||||||
\(821\) | 4.00000 | + | 6.92820i | 0.139601 | + | 0.241796i | 0.927346 | − | 0.374206i | \(-0.122085\pi\) |
−0.787745 | + | 0.616002i | \(0.788751\pi\) | |||||||
\(822\) | −36.0000 | + | 20.7846i | −1.25564 | + | 0.724947i | ||||
\(823\) | −13.5000 | + | 23.3827i | −0.470580 | + | 0.815069i | −0.999434 | − | 0.0336440i | \(-0.989289\pi\) |
0.528853 | + | 0.848713i | \(0.322622\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 33.0000 | − | 19.0526i | 1.14891 | − | 0.663325i | ||||
\(826\) | −24.0000 | − | 41.5692i | −0.835067 | − | 1.44638i | ||||
\(827\) | 2.00000 | 0.0695468 | 0.0347734 | − | 0.999395i | \(-0.488929\pi\) | ||||
0.0347734 | + | 0.999395i | \(0.488929\pi\) | |||||||
\(828\) | −9.00000 | + | 15.5885i | −0.312772 | + | 0.541736i | ||||
\(829\) | −46.0000 | −1.59765 | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||||
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | −8.00000 | − | 13.8564i | −0.277684 | − | 0.480963i | ||||
\(831\) | 24.2487i | 0.841178i | ||||||||
\(832\) | 4.00000 | − | 6.92820i | 0.138675 | − | 0.240192i | ||||
\(833\) | −7.50000 | + | 12.9904i | −0.259860 | + | 0.450090i | ||||
\(834\) | 9.00000 | + | 5.19615i | 0.311645 | + | 0.179928i | ||||
\(835\) | −4.00000 | − | 6.92820i | −0.138426 | − | 0.239760i | ||||
\(836\) | −24.0000 | −0.830057 | ||||||||
\(837\) | 18.0000 | + | 10.3923i | 0.622171 | + | 0.359211i | ||||
\(838\) | −2.00000 | −0.0690889 | ||||||||
\(839\) | 18.0000 | + | 31.1769i | 0.621429 | + | 1.07635i | 0.989220 | + | 0.146438i | \(0.0467809\pi\) |
−0.367791 | + | 0.929909i | \(0.619886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | −26.0000 | + | 45.0333i | −0.896019 | + | 1.55195i | ||||
\(843\) | 6.92820i | 0.238620i | ||||||||
\(844\) | −1.00000 | − | 1.73205i | −0.0344214 | − | 0.0596196i | ||||
\(845\) | 4.00000 | 0.137604 | ||||||||
\(846\) | −36.0000 | −1.23771 | ||||||||
\(847\) | −14.0000 | −0.481046 | ||||||||
\(848\) | 6.00000 | + | 10.3923i | 0.206041 | + | 0.356873i | ||||
\(849\) | −22.5000 | + | 12.9904i | −0.772198 | + | 0.445829i | ||||
\(850\) | 55.0000 | − | 95.2628i | 1.88648 | − | 3.26749i | ||||
\(851\) | −3.00000 | + | 5.19615i | −0.102839 | + | 0.178122i | ||||
\(852\) | 36.0000 | − | 20.7846i | 1.23334 | − | 0.712069i | ||||
\(853\) | −18.0000 | − | 31.1769i | −0.616308 | − | 1.06748i | −0.990153 | − | 0.139986i | \(-0.955294\pi\) |
0.373845 | − | 0.927491i | \(-0.378039\pi\) | |||||||
\(854\) | −20.0000 | −0.684386 | ||||||||
\(855\) | 72.0000 | 2.46235 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.00000 | + | 12.1244i | 0.239115 | + | 0.414160i | 0.960461 | − | 0.278416i | \(-0.0898092\pi\) |
−0.721345 | + | 0.692576i | \(0.756476\pi\) | |||||||
\(858\) | 6.92820i | 0.236525i | ||||||||
\(859\) | 20.5000 | − | 35.5070i | 0.699451 | − | 1.21148i | −0.269206 | − | 0.963083i | \(-0.586761\pi\) |
0.968657 | − | 0.248402i | \(-0.0799054\pi\) | |||||||
\(860\) | 12.0000 | − | 20.7846i | 0.409197 | − | 0.708749i | ||||
\(861\) | 18.0000 | + | 10.3923i | 0.613438 | + | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.0000 | 1.49778 | 0.748889 | − | 0.662696i | \(-0.230588\pi\) | ||||
0.748889 | + | 0.662696i | \(0.230588\pi\) | |||||||
\(864\) | −36.0000 | − | 20.7846i | −1.22474 | − | 0.707107i | ||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | 35.0000 | + | 60.6218i | 1.18935 | + | 2.06001i | ||||
\(867\) | −12.0000 | − | 6.92820i | −0.407541 | − | 0.235294i | ||||
\(868\) | −8.00000 | + | 13.8564i | −0.271538 | + | 0.470317i | ||||
\(869\) | −5.00000 | + | 8.66025i | −0.169613 | + | 0.293779i | ||||
\(870\) | − | 27.7128i | − | 0.939552i | ||||||
\(871\) | −2.00000 | − | 3.46410i | −0.0677674 | − | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.0000 | + | 20.7846i | −0.406138 | + | 0.703452i | ||||
\(874\) | 36.0000 | 1.21772 | ||||||||
\(875\) | −24.0000 | − | 41.5692i | −0.811348 | − | 1.40530i | ||||
\(876\) | −12.0000 | + | 6.92820i | −0.405442 | + | 0.234082i | ||||
\(877\) | −1.00000 | + | 1.73205i | −0.0337676 | + | 0.0584872i | −0.882415 | − | 0.470471i | \(-0.844084\pi\) |
0.848648 | + | 0.528958i | \(0.177417\pi\) | |||||||
\(878\) | 1.00000 | − | 1.73205i | 0.0337484 | − | 0.0584539i | ||||
\(879\) | −27.0000 | + | 15.5885i | −0.910687 | + | 0.525786i | ||||
\(880\) | 16.0000 | + | 27.7128i | 0.539360 | + | 0.934199i | ||||
\(881\) | −7.00000 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(882\) | −9.00000 | − | 15.5885i | −0.303046 | − | 0.524891i | ||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 5.00000 | + | 8.66025i | 0.168168 | + | 0.291276i | ||||
\(885\) | 83.1384i | 2.79467i | ||||||||
\(886\) | −31.0000 | + | 53.6936i | −1.04147 | + | 1.80387i | ||||
\(887\) | 7.50000 | − | 12.9904i | 0.251825 | − | 0.436174i | −0.712203 | − | 0.701974i | \(-0.752302\pi\) |
0.964028 | + | 0.265799i | \(0.0856358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | + | 27.7128i | 0.536623 | + | 0.929458i | ||||
\(890\) | −80.0000 | −2.68161 | ||||||||
\(891\) | 18.0000 | 0.603023 | ||||||||
\(892\) | 32.0000 | 1.07144 | ||||||||
\(893\) | 18.0000 | + | 31.1769i | 0.602347 | + | 1.04330i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.0000 | − | 65.8179i | 1.27020 | − | 2.20005i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.19615i | − | 0.173494i | ||||||
\(898\) | 4.00000 | + | 6.92820i | 0.133482 | + | 0.231197i | ||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | 33.0000 | + | 57.1577i | 1.10000 | + | 1.90526i | ||||
\(901\) | −15.0000 | −0.499722 | ||||||||
\(902\) | 12.0000 | + | 20.7846i | 0.399556 | + | 0.692052i | ||||
\(903\) | −9.00000 | + | 5.19615i | −0.299501 | + | 0.172917i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.0000 | + | 38.1051i | −0.731305 | + | 1.26666i | ||||
\(906\) | −6.00000 | + | 3.46410i | −0.199337 | + | 0.115087i | ||||
\(907\) | −16.5000 | − | 28.5788i | −0.547874 | − | 0.948945i | −0.998420 | − | 0.0561918i | \(-0.982104\pi\) |
0.450546 | − | 0.892753i | \(-0.351229\pi\) | |||||||
\(908\) | −8.00000 | −0.265489 | ||||||||
\(909\) | 13.5000 | − | 23.3827i | 0.447767 | − | 0.775555i | ||||
\(910\) | 16.0000 | 0.530395 | ||||||||
\(911\) | 8.50000 | + | 14.7224i | 0.281618 | + | 0.487776i | 0.971783 | − | 0.235875i | \(-0.0757957\pi\) |
−0.690166 | + | 0.723651i | \(0.742462\pi\) | |||||||
\(912\) | 41.5692i | 1.37649i | ||||||||
\(913\) | −2.00000 | + | 3.46410i | −0.0661903 | + | 0.114645i | ||||
\(914\) | 16.0000 | − | 27.7128i | 0.529233 | − | 0.916658i | ||||
\(915\) | 30.0000 | + | 17.3205i | 0.991769 | + | 0.572598i | ||||
\(916\) | 16.0000 | + | 27.7128i | 0.528655 | + | 0.915657i | ||||
\(917\) | −2.00000 | −0.0660458 | ||||||||
\(918\) | 45.0000 | − | 25.9808i | 1.48522 | − | 0.857493i | ||||
\(919\) | 15.0000 | 0.494804 | 0.247402 | − | 0.968913i | \(-0.420423\pi\) | ||||
0.247402 | + | 0.968913i | \(0.420423\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.0000 | + | 13.8564i | 0.790827 | + | 0.456584i | ||||
\(922\) | 22.0000 | − | 38.1051i | 0.724531 | − | 1.25493i | ||||
\(923\) | −6.00000 | + | 10.3923i | −0.197492 | + | 0.342067i | ||||
\(924\) | 13.8564i | 0.455842i | ||||||||
\(925\) | 11.0000 | + | 19.0526i | 0.361678 | + | 0.626444i | ||||
\(926\) | 32.0000 | 1.05159 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.0000 | 0.525226 | ||||||||
\(929\) | −3.00000 | − | 5.19615i | −0.0984268 | − | 0.170480i | 0.812607 | − | 0.582812i | \(-0.198048\pi\) |
−0.911034 | + | 0.412332i | \(0.864714\pi\) | |||||||
\(930\) | 48.0000 | − | 27.7128i | 1.57398 | − | 0.908739i | ||||
\(931\) | −9.00000 | + | 15.5885i | −0.294963 | + | 0.510891i | ||||
\(932\) | 7.00000 | − | 12.1244i | 0.229293 | − | 0.397146i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.00000 | − | 5.19615i | −0.0981630 | − | 0.170023i | ||||
\(935\) | −40.0000 | −1.30814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.0000 | 0.751377 | 0.375689 | − | 0.926746i | \(-0.377406\pi\) | ||||
0.375689 | + | 0.926746i | \(0.377406\pi\) | |||||||
\(938\) | −8.00000 | − | 13.8564i | −0.261209 | − | 0.452428i | ||||
\(939\) | 10.3923i | 0.339140i | ||||||||
\(940\) | −24.0000 | + | 41.5692i | −0.782794 | + | 1.35584i | ||||
\(941\) | 5.00000 | − | 8.66025i | 0.162995 | − | 0.282316i | −0.772946 | − | 0.634472i | \(-0.781218\pi\) |
0.935942 | + | 0.352155i | \(0.114551\pi\) | |||||||
\(942\) | −63.0000 | − | 36.3731i | −2.05265 | − | 1.18510i | ||||
\(943\) | −9.00000 | − | 15.5885i | −0.293080 | − | 0.507630i | ||||
\(944\) | −48.0000 | −1.56227 | ||||||||
\(945\) | − | 41.5692i | − | 1.35225i | ||||||
\(946\) | −12.0000 | −0.390154 | ||||||||
\(947\) | −9.00000 | − | 15.5885i | −0.292461 | − | 0.506557i | 0.681930 | − | 0.731417i | \(-0.261141\pi\) |
−0.974391 | + | 0.224860i | \(0.927807\pi\) | |||||||
\(948\) | −15.0000 | − | 8.66025i | −0.487177 | − | 0.281272i | ||||
\(949\) | 2.00000 | − | 3.46410i | 0.0649227 | − | 0.112449i | ||||
\(950\) | 66.0000 | − | 114.315i | 2.14132 | − | 3.70888i | ||||
\(951\) | − | 13.8564i | − | 0.449325i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000 | 0.583077 | 0.291539 | − | 0.956559i | \(-0.405833\pi\) | ||||
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(954\) | 9.00000 | − | 15.5885i | 0.291386 | − | 0.504695i | ||||
\(955\) | 76.0000 | 2.45930 | ||||||||
\(956\) | 6.00000 | + | 10.3923i | 0.194054 | + | 0.336111i | ||||
\(957\) | −6.00000 | + | 3.46410i | −0.193952 | + | 0.111979i | ||||
\(958\) | −36.0000 | + | 62.3538i | −1.16311 | + | 2.01456i | ||||
\(959\) | 12.0000 | − | 20.7846i | 0.387500 | − | 0.671170i | ||||
\(960\) | −48.0000 | + | 27.7128i | −1.54919 | + | 0.894427i | ||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | −4.00000 | −0.128965 | ||||||||
\(963\) | 4.50000 | + | 7.79423i | 0.145010 | + | 0.251166i | ||||
\(964\) | 8.00000 | 0.257663 | ||||||||
\(965\) | 48.0000 | + | 83.1384i | 1.54517 | + | 2.67632i | ||||
\(966\) | − | 20.7846i | − | 0.668734i | ||||||
\(967\) | −16.0000 | + | 27.7128i | −0.514525 | + | 0.891184i | 0.485333 | + | 0.874330i | \(0.338699\pi\) |
−0.999858 | + | 0.0168544i | \(0.994635\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −45.0000 | − | 25.9808i | −1.44561 | − | 0.834622i | ||||
\(970\) | 32.0000 | + | 55.4256i | 1.02746 | + | 1.77961i | ||||
\(971\) | −36.0000 | −1.15529 | −0.577647 | − | 0.816286i | \(-0.696029\pi\) | ||||
−0.577647 | + | 0.816286i | \(0.696029\pi\) | |||||||
\(972\) | 31.1769i | 1.00000i | ||||||||
\(973\) | −6.00000 | −0.192351 | ||||||||
\(974\) | −18.0000 | − | 31.1769i | −0.576757 | − | 0.998973i | ||||
\(975\) | −16.5000 | − | 9.52628i | −0.528423 | − | 0.305085i | ||||
\(976\) | −10.0000 | + | 17.3205i | −0.320092 | + | 0.554416i | ||||
\(977\) | 18.0000 | − | 31.1769i | 0.575871 | − | 0.997438i | −0.420075 | − | 0.907489i | \(-0.637996\pi\) |
0.995946 | − | 0.0899487i | \(-0.0286703\pi\) | |||||||
\(978\) | − | 55.4256i | − | 1.77232i | ||||||
\(979\) | 10.0000 | + | 17.3205i | 0.319601 | + | 0.553566i | ||||
\(980\) | −24.0000 | −0.766652 | ||||||||
\(981\) | −21.0000 | − | 36.3731i | −0.670478 | − | 1.16130i | ||||
\(982\) | 24.0000 | 0.765871 | ||||||||
\(983\) | 26.0000 | + | 45.0333i | 0.829271 | + | 1.43634i | 0.898611 | + | 0.438747i | \(0.144577\pi\) |
−0.0693395 | + | 0.997593i | \(0.522089\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.0000 | + | 83.1384i | −1.52941 | + | 2.64901i | ||||
\(986\) | −10.0000 | + | 17.3205i | −0.318465 | + | 0.551597i | ||||
\(987\) | 18.0000 | − | 10.3923i | 0.572946 | − | 0.330791i | ||||
\(988\) | 6.00000 | + | 10.3923i | 0.190885 | + | 0.330623i | ||||
\(989\) | 9.00000 | 0.286183 | ||||||||
\(990\) | 24.0000 | − | 41.5692i | 0.762770 | − | 1.32116i | ||||
\(991\) | 37.0000 | 1.17534 | 0.587672 | − | 0.809099i | \(-0.300045\pi\) | ||||
0.587672 | + | 0.809099i | \(0.300045\pi\) | |||||||
\(992\) | 16.0000 | + | 27.7128i | 0.508001 | + | 0.879883i | ||||
\(993\) | − | 6.92820i | − | 0.219860i | ||||||
\(994\) | −24.0000 | + | 41.5692i | −0.761234 | + | 1.31850i | ||||
\(995\) | −34.0000 | + | 58.8897i | −1.07787 | + | 1.86693i | ||||
\(996\) | −6.00000 | − | 3.46410i | −0.190117 | − | 0.109764i | ||||
\(997\) | 8.50000 | + | 14.7224i | 0.269198 | + | 0.466264i | 0.968655 | − | 0.248410i | \(-0.0799082\pi\) |
−0.699457 | + | 0.714675i | \(0.746575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.3923i | 0.328798i |
(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 | 117.2.e.a.40.1 | ✓ | 2 | |
3.2 | odd | 2 | 351.2.e.a.118.1 | 2 | |||
9.2 | odd | 6 | 351.2.e.a.235.1 | 2 | |||
9.4 | even | 3 | 1053.2.a.d.1.1 | 1 | |||
9.5 | odd | 6 | 1053.2.a.a.1.1 | 1 | |||
9.7 | even | 3 | inner | 117.2.e.a.79.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.e.a.40.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
117.2.e.a.79.1 | yes | 2 | 9.7 | even | 3 | inner | |
351.2.e.a.118.1 | 2 | 3.2 | odd | 2 | |||
351.2.e.a.235.1 | 2 | 9.2 | odd | 6 | |||
1053.2.a.a.1.1 | 1 | 9.5 | odd | 6 | |||
1053.2.a.d.1.1 | 1 | 9.4 | even | 3 |