Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(316,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.m (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: | \(6.74735897080\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.361 |
Dual form | 845.2.m.b.316.1 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | −0.773893 | − | 0.633316i | \(-0.781693\pi\) |
0.161521 | + | 0.986869i | \(0.448360\pi\) | |||||||
\(3\) | 1.00000 | + | 1.73205i | 0.577350 | + | 1.00000i | 0.995782 | + | 0.0917517i | \(0.0292466\pi\) |
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −1.73205 | − | 1.00000i | −0.707107 | − | 0.408248i | ||||
\(7\) | −3.46410 | − | 2.00000i | −1.30931 | − | 0.755929i | −0.327327 | − | 0.944911i | \(-0.606148\pi\) |
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | − | 3.00000i | − | 1.06066i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −1.73205 | + | 1.00000i | −0.522233 | + | 0.301511i | −0.737848 | − | 0.674967i | \(-0.764158\pi\) |
0.215615 | + | 0.976478i | \(0.430824\pi\) | |||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.00000 | 1.06904 | ||||||||
\(15\) | 1.73205 | − | 1.00000i | 0.447214 | − | 0.258199i | ||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 5.19615 | + | 3.00000i | 1.19208 | + | 0.688247i | 0.958778 | − | 0.284157i | \(-0.0917138\pi\) |
0.233301 | + | 0.972404i | \(0.425047\pi\) | |||||||
\(20\) | 0.866025 | + | 0.500000i | 0.193649 | + | 0.111803i | ||||
\(21\) | − | 8.00000i | − | 1.74574i | ||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 5.19615 | − | 3.00000i | 1.06066 | − | 0.612372i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 3.46410 | − | 2.00000i | 0.654654 | − | 0.377964i | ||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | −1.00000 | + | 1.73205i | −0.182574 | + | 0.316228i | ||||
\(31\) | − | 10.0000i | − | 1.79605i | −0.439941 | − | 0.898027i | \(-0.645001\pi\) | ||
0.439941 | − | 0.898027i | \(-0.354999\pi\) | |||||||
\(32\) | 4.33013 | + | 2.50000i | 0.765466 | + | 0.441942i | ||||
\(33\) | −3.46410 | − | 2.00000i | −0.603023 | − | 0.348155i | ||||
\(34\) | 2.00000i | 0.342997i | ||||||||
\(35\) | −2.00000 | + | 3.46410i | −0.338062 | + | 0.585540i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 1.73205 | − | 1.00000i | 0.284747 | − | 0.164399i | −0.350823 | − | 0.936442i | \(-0.614098\pi\) |
0.635571 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(38\) | −6.00000 | −0.973329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.00000 | −0.474342 | ||||||||
\(41\) | −5.19615 | + | 3.00000i | −0.811503 | + | 0.468521i | −0.847477 | − | 0.530831i | \(-0.821880\pi\) |
0.0359748 | + | 0.999353i | \(0.488546\pi\) | |||||||
\(42\) | 4.00000 | + | 6.92820i | 0.617213 | + | 1.06904i | ||||
\(43\) | 5.00000 | − | 8.66025i | 0.762493 | − | 1.32068i | −0.179069 | − | 0.983836i | \(-0.557309\pi\) |
0.941562 | − | 0.336840i | \(-0.109358\pi\) | |||||||
\(44\) | − | 2.00000i | − | 0.301511i | ||||||
\(45\) | 0.866025 | + | 0.500000i | 0.129099 | + | 0.0745356i | ||||
\(46\) | 5.19615 | + | 3.00000i | 0.766131 | + | 0.442326i | ||||
\(47\) | − | 4.00000i | − | 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | −1.00000 | + | 1.73205i | −0.144338 | + | 0.250000i | ||||
\(49\) | 4.50000 | + | 7.79423i | 0.642857 | + | 1.11346i | ||||
\(50\) | 0.866025 | − | 0.500000i | 0.122474 | − | 0.0707107i | ||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | −3.46410 | + | 2.00000i | −0.471405 | + | 0.272166i | ||||
\(55\) | 1.00000 | + | 1.73205i | 0.134840 | + | 0.233550i | ||||
\(56\) | −6.00000 | + | 10.3923i | −0.801784 | + | 1.38873i | ||||
\(57\) | 12.0000i | 1.58944i | ||||||||
\(58\) | 1.73205 | + | 1.00000i | 0.227429 | + | 0.131306i | ||||
\(59\) | 5.19615 | + | 3.00000i | 0.676481 | + | 0.390567i | 0.798528 | − | 0.601958i | \(-0.205612\pi\) |
−0.122047 | + | 0.992524i | \(0.538946\pi\) | |||||||
\(60\) | 2.00000i | 0.258199i | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | 5.00000 | + | 8.66025i | 0.635001 | + | 1.09985i | ||||
\(63\) | 3.46410 | − | 2.00000i | 0.436436 | − | 0.251976i | ||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | −3.46410 | + | 2.00000i | −0.423207 | + | 0.244339i | −0.696449 | − | 0.717607i | \(-0.745238\pi\) |
0.273241 | + | 0.961946i | \(0.411904\pi\) | |||||||
\(68\) | 1.00000 | + | 1.73205i | 0.121268 | + | 0.210042i | ||||
\(69\) | 6.00000 | − | 10.3923i | 0.722315 | − | 1.25109i | ||||
\(70\) | − | 4.00000i | − | 0.478091i | ||||||
\(71\) | −5.19615 | − | 3.00000i | −0.616670 | − | 0.356034i | 0.158901 | − | 0.987294i | \(-0.449205\pi\) |
−0.775571 | + | 0.631260i | \(0.782538\pi\) | |||||||
\(72\) | 2.59808 | + | 1.50000i | 0.306186 | + | 0.176777i | ||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | −1.00000 | − | 1.73205i | −0.115470 | − | 0.200000i | ||||
\(76\) | −5.19615 | + | 3.00000i | −0.596040 | + | 0.344124i | ||||
\(77\) | 8.00000 | 0.911685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | − | 16.0000i | − | 1.75623i | −0.478451 | − | 0.878114i | \(-0.658802\pi\) | ||
0.478451 | − | 0.878114i | \(-0.341198\pi\) | |||||||
\(84\) | 6.92820 | + | 4.00000i | 0.755929 | + | 0.436436i | ||||
\(85\) | −1.73205 | − | 1.00000i | −0.187867 | − | 0.108465i | ||||
\(86\) | 10.0000i | 1.07833i | ||||||||
\(87\) | 2.00000 | − | 3.46410i | 0.214423 | − | 0.371391i | ||||
\(88\) | 3.00000 | + | 5.19615i | 0.319801 | + | 0.553912i | ||||
\(89\) | −1.73205 | + | 1.00000i | −0.183597 | + | 0.106000i | −0.588982 | − | 0.808146i | \(-0.700471\pi\) |
0.405385 | + | 0.914146i | \(0.367138\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 17.3205 | − | 10.0000i | 1.79605 | − | 1.03695i | ||||
\(94\) | 2.00000 | + | 3.46410i | 0.206284 | + | 0.357295i | ||||
\(95\) | 3.00000 | − | 5.19615i | 0.307794 | − | 0.533114i | ||||
\(96\) | 10.0000i | 1.02062i | ||||||||
\(97\) | 1.73205 | + | 1.00000i | 0.175863 | + | 0.101535i | 0.585348 | − | 0.810782i | \(-0.300958\pi\) |
−0.409484 | + | 0.912317i | \(0.634291\pi\) | |||||||
\(98\) | −7.79423 | − | 4.50000i | −0.787336 | − | 0.454569i | ||||
\(99\) | − | 2.00000i | − | 0.201008i | ||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −9.00000 | − | 15.5885i | −0.895533 | − | 1.55111i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) |
−0.0623905 | − | 0.998052i | \(-0.519872\pi\) | |||||||
\(102\) | −3.46410 | + | 2.00000i | −0.342997 | + | 0.198030i | ||||
\(103\) | −2.00000 | −0.197066 | −0.0985329 | − | 0.995134i | \(-0.531415\pi\) | ||||
−0.0985329 | + | 0.995134i | \(0.531415\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | −1.73205 | + | 1.00000i | −0.168232 | + | 0.0971286i | ||||
\(107\) | −5.00000 | − | 8.66025i | −0.483368 | − | 0.837218i | 0.516449 | − | 0.856318i | \(-0.327253\pi\) |
−0.999818 | + | 0.0190994i | \(0.993920\pi\) | |||||||
\(108\) | −2.00000 | + | 3.46410i | −0.192450 | + | 0.333333i | ||||
\(109\) | 10.0000i | 0.957826i | 0.877862 | + | 0.478913i | \(0.158969\pi\) | ||||
−0.877862 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(110\) | −1.73205 | − | 1.00000i | −0.165145 | − | 0.0953463i | ||||
\(111\) | 3.46410 | + | 2.00000i | 0.328798 | + | 0.189832i | ||||
\(112\) | − | 4.00000i | − | 0.377964i | ||||||
\(113\) | 7.00000 | − | 12.1244i | 0.658505 | − | 1.14056i | −0.322498 | − | 0.946570i | \(-0.604523\pi\) |
0.981003 | − | 0.193993i | \(-0.0621440\pi\) | |||||||
\(114\) | −6.00000 | − | 10.3923i | −0.561951 | − | 0.973329i | ||||
\(115\) | −5.19615 | + | 3.00000i | −0.484544 | + | 0.279751i | ||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | −6.92820 | + | 4.00000i | −0.635107 | + | 0.366679i | ||||
\(120\) | −3.00000 | − | 5.19615i | −0.273861 | − | 0.474342i | ||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | − | 2.00000i | − | 0.181071i | ||||||
\(123\) | −10.3923 | − | 6.00000i | −0.937043 | − | 0.541002i | ||||
\(124\) | 8.66025 | + | 5.00000i | 0.777714 | + | 0.449013i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −2.00000 | + | 3.46410i | −0.178174 | + | 0.308607i | ||||
\(127\) | −1.00000 | − | 1.73205i | −0.0887357 | − | 0.153695i | 0.818241 | − | 0.574875i | \(-0.194949\pi\) |
−0.906977 | + | 0.421180i | \(0.861616\pi\) | |||||||
\(128\) | −2.59808 | + | 1.50000i | −0.229640 | + | 0.132583i | ||||
\(129\) | 20.0000 | 1.76090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.0000 | 1.74741 | 0.873704 | − | 0.486458i | \(-0.161711\pi\) | ||||
0.873704 | + | 0.486458i | \(0.161711\pi\) | |||||||
\(132\) | 3.46410 | − | 2.00000i | 0.301511 | − | 0.174078i | ||||
\(133\) | −12.0000 | − | 20.7846i | −1.04053 | − | 1.80225i | ||||
\(134\) | 2.00000 | − | 3.46410i | 0.172774 | − | 0.299253i | ||||
\(135\) | − | 4.00000i | − | 0.344265i | ||||||
\(136\) | −5.19615 | − | 3.00000i | −0.445566 | − | 0.257248i | ||||
\(137\) | −1.73205 | − | 1.00000i | −0.147979 | − | 0.0854358i | 0.424182 | − | 0.905577i | \(-0.360562\pi\) |
−0.572161 | + | 0.820141i | \(0.693895\pi\) | |||||||
\(138\) | 12.0000i | 1.02151i | ||||||||
\(139\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(140\) | −2.00000 | − | 3.46410i | −0.169031 | − | 0.292770i | ||||
\(141\) | 6.92820 | − | 4.00000i | 0.583460 | − | 0.336861i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −1.73205 | + | 1.00000i | −0.143839 | + | 0.0830455i | ||||
\(146\) | −3.00000 | − | 5.19615i | −0.248282 | − | 0.430037i | ||||
\(147\) | −9.00000 | + | 15.5885i | −0.742307 | + | 1.28571i | ||||
\(148\) | 2.00000i | 0.164399i | ||||||||
\(149\) | −15.5885 | − | 9.00000i | −1.27706 | − | 0.737309i | −0.300750 | − | 0.953703i | \(-0.597237\pi\) |
−0.976306 | + | 0.216394i | \(0.930570\pi\) | |||||||
\(150\) | 1.73205 | + | 1.00000i | 0.141421 | + | 0.0816497i | ||||
\(151\) | − | 10.0000i | − | 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | 9.00000 | − | 15.5885i | 0.729996 | − | 1.26439i | ||||
\(153\) | 1.00000 | + | 1.73205i | 0.0808452 | + | 0.140028i | ||||
\(154\) | −6.92820 | + | 4.00000i | −0.558291 | + | 0.322329i | ||||
\(155\) | −10.0000 | −0.803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 10.3923 | − | 6.00000i | 0.826767 | − | 0.477334i | ||||
\(159\) | 2.00000 | + | 3.46410i | 0.158610 | + | 0.274721i | ||||
\(160\) | 2.50000 | − | 4.33013i | 0.197642 | − | 0.342327i | ||||
\(161\) | 24.0000i | 1.89146i | ||||||||
\(162\) | −9.52628 | − | 5.50000i | −0.748455 | − | 0.432121i | ||||
\(163\) | −10.3923 | − | 6.00000i | −0.813988 | − | 0.469956i | 0.0343508 | − | 0.999410i | \(-0.489064\pi\) |
−0.848339 | + | 0.529454i | \(0.822397\pi\) | |||||||
\(164\) | − | 6.00000i | − | 0.468521i | ||||||
\(165\) | −2.00000 | + | 3.46410i | −0.155700 | + | 0.269680i | ||||
\(166\) | 8.00000 | + | 13.8564i | 0.620920 | + | 1.07547i | ||||
\(167\) | 10.3923 | − | 6.00000i | 0.804181 | − | 0.464294i | −0.0407502 | − | 0.999169i | \(-0.512975\pi\) |
0.844931 | + | 0.534875i | \(0.179641\pi\) | |||||||
\(168\) | −24.0000 | −1.85164 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | −5.19615 | + | 3.00000i | −0.397360 | + | 0.229416i | ||||
\(172\) | 5.00000 | + | 8.66025i | 0.381246 | + | 0.660338i | ||||
\(173\) | −3.00000 | + | 5.19615i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 4.00000i | 0.303239i | ||||||||
\(175\) | 3.46410 | + | 2.00000i | 0.261861 | + | 0.151186i | ||||
\(176\) | −1.73205 | − | 1.00000i | −0.130558 | − | 0.0753778i | ||||
\(177\) | 12.0000i | 0.901975i | ||||||||
\(178\) | 1.00000 | − | 1.73205i | 0.0749532 | − | 0.129823i | ||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | −0.866025 | + | 0.500000i | −0.0645497 | + | 0.0372678i | ||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | −15.5885 | + | 9.00000i | −1.14920 | + | 0.663489i | ||||
\(185\) | −1.00000 | − | 1.73205i | −0.0735215 | − | 0.127343i | ||||
\(186\) | −10.0000 | + | 17.3205i | −0.733236 | + | 1.27000i | ||||
\(187\) | 4.00000i | 0.292509i | ||||||||
\(188\) | 3.46410 | + | 2.00000i | 0.252646 | + | 0.145865i | ||||
\(189\) | −13.8564 | − | 8.00000i | −1.00791 | − | 0.581914i | ||||
\(190\) | 6.00000i | 0.435286i | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | −7.00000 | − | 12.1244i | −0.505181 | − | 0.875000i | ||||
\(193\) | 1.73205 | − | 1.00000i | 0.124676 | − | 0.0719816i | −0.436365 | − | 0.899770i | \(-0.643734\pi\) |
0.561041 | + | 0.827788i | \(0.310401\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.00000 | −0.642857 | ||||||||
\(197\) | −5.19615 | + | 3.00000i | −0.370211 | + | 0.213741i | −0.673550 | − | 0.739141i | \(-0.735232\pi\) |
0.303340 | + | 0.952882i | \(0.401898\pi\) | |||||||
\(198\) | 1.00000 | + | 1.73205i | 0.0710669 | + | 0.123091i | ||||
\(199\) | −8.00000 | + | 13.8564i | −0.567105 | + | 0.982255i | 0.429745 | + | 0.902950i | \(0.358603\pi\) |
−0.996850 | + | 0.0793045i | \(0.974730\pi\) | |||||||
\(200\) | 3.00000i | 0.212132i | ||||||||
\(201\) | −6.92820 | − | 4.00000i | −0.488678 | − | 0.282138i | ||||
\(202\) | 15.5885 | + | 9.00000i | 1.09680 | + | 0.633238i | ||||
\(203\) | 8.00000i | 0.561490i | ||||||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | 1.73205 | − | 1.00000i | 0.120678 | − | 0.0696733i | ||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 6.92820 | − | 4.00000i | 0.478091 | − | 0.276026i | ||||
\(211\) | −6.00000 | − | 10.3923i | −0.413057 | − | 0.715436i | 0.582165 | − | 0.813070i | \(-0.302206\pi\) |
−0.995222 | + | 0.0976347i | \(0.968872\pi\) | |||||||
\(212\) | −1.00000 | + | 1.73205i | −0.0686803 | + | 0.118958i | ||||
\(213\) | − | 12.0000i | − | 0.822226i | ||||||
\(214\) | 8.66025 | + | 5.00000i | 0.592003 | + | 0.341793i | ||||
\(215\) | −8.66025 | − | 5.00000i | −0.590624 | − | 0.340997i | ||||
\(216\) | − | 12.0000i | − | 0.816497i | ||||||
\(217\) | −20.0000 | + | 34.6410i | −1.35769 | + | 2.35159i | ||||
\(218\) | −5.00000 | − | 8.66025i | −0.338643 | − | 0.586546i | ||||
\(219\) | −10.3923 | + | 6.00000i | −0.702247 | + | 0.405442i | ||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.00000 | −0.268462 | ||||||||
\(223\) | 3.46410 | − | 2.00000i | 0.231973 | − | 0.133930i | −0.379509 | − | 0.925188i | \(-0.623907\pi\) |
0.611482 | + | 0.791258i | \(0.290574\pi\) | |||||||
\(224\) | −10.0000 | − | 17.3205i | −0.668153 | − | 1.15728i | ||||
\(225\) | 0.500000 | − | 0.866025i | 0.0333333 | − | 0.0577350i | ||||
\(226\) | 14.0000i | 0.931266i | ||||||||
\(227\) | −3.46410 | − | 2.00000i | −0.229920 | − | 0.132745i | 0.380615 | − | 0.924734i | \(-0.375712\pi\) |
−0.610535 | + | 0.791989i | \(0.709046\pi\) | |||||||
\(228\) | −10.3923 | − | 6.00000i | −0.688247 | − | 0.397360i | ||||
\(229\) | 22.0000i | 1.45380i | 0.686743 | + | 0.726900i | \(0.259040\pi\) | ||||
−0.686743 | + | 0.726900i | \(0.740960\pi\) | |||||||
\(230\) | 3.00000 | − | 5.19615i | 0.197814 | − | 0.342624i | ||||
\(231\) | 8.00000 | + | 13.8564i | 0.526361 | + | 0.911685i | ||||
\(232\) | −5.19615 | + | 3.00000i | −0.341144 | + | 0.196960i | ||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | −0.260931 | ||||||||
\(236\) | −5.19615 | + | 3.00000i | −0.338241 | + | 0.195283i | ||||
\(237\) | −12.0000 | − | 20.7846i | −0.779484 | − | 1.35011i | ||||
\(238\) | 4.00000 | − | 6.92820i | 0.259281 | − | 0.449089i | ||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 1.73205 | + | 1.00000i | 0.111803 | + | 0.0645497i | ||||
\(241\) | 8.66025 | + | 5.00000i | 0.557856 | + | 0.322078i | 0.752285 | − | 0.658838i | \(-0.228952\pi\) |
−0.194429 | + | 0.980917i | \(0.562285\pi\) | |||||||
\(242\) | − | 7.00000i | − | 0.449977i | ||||||
\(243\) | −5.00000 | + | 8.66025i | −0.320750 | + | 0.555556i | ||||
\(244\) | −1.00000 | − | 1.73205i | −0.0640184 | − | 0.110883i | ||||
\(245\) | 7.79423 | − | 4.50000i | 0.497955 | − | 0.287494i | ||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −30.0000 | −1.90500 | ||||||||
\(249\) | 27.7128 | − | 16.0000i | 1.75623 | − | 1.01396i | ||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | 12.0000 | − | 20.7846i | 0.757433 | − | 1.31191i | −0.186722 | − | 0.982413i | \(-0.559786\pi\) |
0.944156 | − | 0.329500i | \(-0.106880\pi\) | |||||||
\(252\) | 4.00000i | 0.251976i | ||||||||
\(253\) | 10.3923 | + | 6.00000i | 0.653359 | + | 0.377217i | ||||
\(254\) | 1.73205 | + | 1.00000i | 0.108679 | + | 0.0627456i | ||||
\(255\) | − | 4.00000i | − | 0.250490i | ||||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | 1.00000 | + | 1.73205i | 0.0623783 | + | 0.108042i | 0.895528 | − | 0.445005i | \(-0.146798\pi\) |
−0.833150 | + | 0.553047i | \(0.813465\pi\) | |||||||
\(258\) | −17.3205 | + | 10.0000i | −1.07833 | + | 0.622573i | ||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −17.3205 | + | 10.0000i | −1.07006 | + | 0.617802i | ||||
\(263\) | −7.00000 | − | 12.1244i | −0.431638 | − | 0.747620i | 0.565376 | − | 0.824833i | \(-0.308731\pi\) |
−0.997015 | + | 0.0772134i | \(0.975398\pi\) | |||||||
\(264\) | −6.00000 | + | 10.3923i | −0.369274 | + | 0.639602i | ||||
\(265\) | − | 2.00000i | − | 0.122859i | ||||||
\(266\) | 20.7846 | + | 12.0000i | 1.27439 | + | 0.735767i | ||||
\(267\) | −3.46410 | − | 2.00000i | −0.212000 | − | 0.122398i | ||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | −3.00000 | + | 5.19615i | −0.182913 | + | 0.316815i | −0.942871 | − | 0.333157i | \(-0.891886\pi\) |
0.759958 | + | 0.649972i | \(0.225219\pi\) | |||||||
\(270\) | 2.00000 | + | 3.46410i | 0.121716 | + | 0.210819i | ||||
\(271\) | −1.73205 | + | 1.00000i | −0.105215 | + | 0.0607457i | −0.551684 | − | 0.834053i | \(-0.686015\pi\) |
0.446469 | + | 0.894799i | \(0.352681\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 1.73205 | − | 1.00000i | 0.104447 | − | 0.0603023i | ||||
\(276\) | 6.00000 | + | 10.3923i | 0.361158 | + | 0.625543i | ||||
\(277\) | −7.00000 | + | 12.1244i | −0.420589 | + | 0.728482i | −0.995997 | − | 0.0893846i | \(-0.971510\pi\) |
0.575408 | + | 0.817867i | \(0.304843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.66025 | + | 5.00000i | 0.518476 | + | 0.299342i | ||||
\(280\) | 10.3923 | + | 6.00000i | 0.621059 | + | 0.358569i | ||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | −4.00000 | + | 6.92820i | −0.238197 | + | 0.412568i | ||||
\(283\) | 1.00000 | + | 1.73205i | 0.0594438 | + | 0.102960i | 0.894216 | − | 0.447636i | \(-0.147734\pi\) |
−0.834772 | + | 0.550596i | \(0.814401\pi\) | |||||||
\(284\) | 5.19615 | − | 3.00000i | 0.308335 | − | 0.178017i | ||||
\(285\) | 12.0000 | 0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | −4.33013 | + | 2.50000i | −0.255155 | + | 0.147314i | ||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 1.00000 | − | 1.73205i | 0.0587220 | − | 0.101710i | ||||
\(291\) | 4.00000i | 0.234484i | ||||||||
\(292\) | −5.19615 | − | 3.00000i | −0.304082 | − | 0.175562i | ||||
\(293\) | 19.0526 | + | 11.0000i | 1.11306 | + | 0.642627i | 0.939621 | − | 0.342217i | \(-0.111178\pi\) |
0.173442 | + | 0.984844i | \(0.444511\pi\) | |||||||
\(294\) | − | 18.0000i | − | 1.04978i | ||||||
\(295\) | 3.00000 | − | 5.19615i | 0.174667 | − | 0.302532i | ||||
\(296\) | −3.00000 | − | 5.19615i | −0.174371 | − | 0.302020i | ||||
\(297\) | −6.92820 | + | 4.00000i | −0.402015 | + | 0.232104i | ||||
\(298\) | 18.0000 | 1.04271 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.00000 | 0.115470 | ||||||||
\(301\) | −34.6410 | + | 20.0000i | −1.99667 | + | 1.15278i | ||||
\(302\) | 5.00000 | + | 8.66025i | 0.287718 | + | 0.498342i | ||||
\(303\) | 18.0000 | − | 31.1769i | 1.03407 | − | 1.79107i | ||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | 1.73205 | + | 1.00000i | 0.0991769 | + | 0.0572598i | ||||
\(306\) | −1.73205 | − | 1.00000i | −0.0990148 | − | 0.0571662i | ||||
\(307\) | − | 8.00000i | − | 0.456584i | −0.973593 | − | 0.228292i | \(-0.926686\pi\) | ||
0.973593 | − | 0.228292i | \(-0.0733141\pi\) | |||||||
\(308\) | −4.00000 | + | 6.92820i | −0.227921 | + | 0.394771i | ||||
\(309\) | −2.00000 | − | 3.46410i | −0.113776 | − | 0.197066i | ||||
\(310\) | 8.66025 | − | 5.00000i | 0.491869 | − | 0.283981i | ||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 5.19615 | − | 3.00000i | 0.293236 | − | 0.169300i | ||||
\(315\) | −2.00000 | − | 3.46410i | −0.112687 | − | 0.195180i | ||||
\(316\) | 6.00000 | − | 10.3923i | 0.337526 | − | 0.584613i | ||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | −3.46410 | − | 2.00000i | −0.194257 | − | 0.112154i | ||||
\(319\) | 3.46410 | + | 2.00000i | 0.193952 | + | 0.111979i | ||||
\(320\) | 7.00000i | 0.391312i | ||||||||
\(321\) | 10.0000 | − | 17.3205i | 0.558146 | − | 0.966736i | ||||
\(322\) | −12.0000 | − | 20.7846i | −0.668734 | − | 1.15828i | ||||
\(323\) | 10.3923 | − | 6.00000i | 0.578243 | − | 0.333849i | ||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | −17.3205 | + | 10.0000i | −0.957826 | + | 0.553001i | ||||
\(328\) | 9.00000 | + | 15.5885i | 0.496942 | + | 0.860729i | ||||
\(329\) | −8.00000 | + | 13.8564i | −0.441054 | + | 0.763928i | ||||
\(330\) | − | 4.00000i | − | 0.220193i | ||||||
\(331\) | 15.5885 | + | 9.00000i | 0.856819 | + | 0.494685i | 0.862946 | − | 0.505296i | \(-0.168617\pi\) |
−0.00612670 | + | 0.999981i | \(0.501950\pi\) | |||||||
\(332\) | 13.8564 | + | 8.00000i | 0.760469 | + | 0.439057i | ||||
\(333\) | 2.00000i | 0.109599i | ||||||||
\(334\) | −6.00000 | + | 10.3923i | −0.328305 | + | 0.568642i | ||||
\(335\) | 2.00000 | + | 3.46410i | 0.109272 | + | 0.189264i | ||||
\(336\) | 6.92820 | − | 4.00000i | 0.377964 | − | 0.218218i | ||||
\(337\) | −26.0000 | −1.41631 | −0.708155 | − | 0.706057i | \(-0.750472\pi\) | ||||
−0.708155 | + | 0.706057i | \(0.750472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.0000 | 1.52075 | ||||||||
\(340\) | 1.73205 | − | 1.00000i | 0.0939336 | − | 0.0542326i | ||||
\(341\) | 10.0000 | + | 17.3205i | 0.541530 | + | 0.937958i | ||||
\(342\) | 3.00000 | − | 5.19615i | 0.162221 | − | 0.280976i | ||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | −25.9808 | − | 15.0000i | −1.40079 | − | 0.808746i | ||||
\(345\) | −10.3923 | − | 6.00000i | −0.559503 | − | 0.323029i | ||||
\(346\) | − | 6.00000i | − | 0.322562i | ||||||
\(347\) | 11.0000 | − | 19.0526i | 0.590511 | − | 1.02279i | −0.403653 | − | 0.914912i | \(-0.632260\pi\) |
0.994164 | − | 0.107883i | \(-0.0344071\pi\) | |||||||
\(348\) | 2.00000 | + | 3.46410i | 0.107211 | + | 0.185695i | ||||
\(349\) | 25.9808 | − | 15.0000i | 1.39072 | − | 0.802932i | 0.397324 | − | 0.917679i | \(-0.369939\pi\) |
0.993395 | + | 0.114747i | \(0.0366057\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.0000 | −0.533002 | ||||||||
\(353\) | 15.5885 | − | 9.00000i | 0.829690 | − | 0.479022i | −0.0240566 | − | 0.999711i | \(-0.507658\pi\) |
0.853746 | + | 0.520689i | \(0.174325\pi\) | |||||||
\(354\) | −6.00000 | − | 10.3923i | −0.318896 | − | 0.552345i | ||||
\(355\) | −3.00000 | + | 5.19615i | −0.159223 | + | 0.275783i | ||||
\(356\) | − | 2.00000i | − | 0.106000i | ||||||
\(357\) | −13.8564 | − | 8.00000i | −0.733359 | − | 0.423405i | ||||
\(358\) | −10.3923 | − | 6.00000i | −0.549250 | − | 0.317110i | ||||
\(359\) | 10.0000i | 0.527780i | 0.964553 | + | 0.263890i | \(0.0850056\pi\) | ||||
−0.964553 | + | 0.263890i | \(0.914994\pi\) | |||||||
\(360\) | 1.50000 | − | 2.59808i | 0.0790569 | − | 0.136931i | ||||
\(361\) | 8.50000 | + | 14.7224i | 0.447368 | + | 0.774865i | ||||
\(362\) | −19.0526 | + | 11.0000i | −1.00138 | + | 0.578147i | ||||
\(363\) | −14.0000 | −0.734809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 3.46410 | − | 2.00000i | 0.181071 | − | 0.104542i | ||||
\(367\) | 7.00000 | + | 12.1244i | 0.365397 | + | 0.632886i | 0.988840 | − | 0.148983i | \(-0.0475999\pi\) |
−0.623443 | + | 0.781869i | \(0.714267\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | − | 6.00000i | − | 0.312348i | ||||||
\(370\) | 1.73205 | + | 1.00000i | 0.0900450 | + | 0.0519875i | ||||
\(371\) | −6.92820 | − | 4.00000i | −0.359694 | − | 0.207670i | ||||
\(372\) | 20.0000i | 1.03695i | ||||||||
\(373\) | −17.0000 | + | 29.4449i | −0.880227 | + | 1.52460i | −0.0291379 | + | 0.999575i | \(0.509276\pi\) |
−0.851089 | + | 0.525022i | \(0.824057\pi\) | |||||||
\(374\) | −2.00000 | − | 3.46410i | −0.103418 | − | 0.179124i | ||||
\(375\) | −1.73205 | + | 1.00000i | −0.0894427 | + | 0.0516398i | ||||
\(376\) | −12.0000 | −0.618853 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 16.0000 | 0.822951 | ||||||||
\(379\) | 8.66025 | − | 5.00000i | 0.444847 | − | 0.256833i | −0.260804 | − | 0.965392i | \(-0.583988\pi\) |
0.705652 | + | 0.708559i | \(0.250654\pi\) | |||||||
\(380\) | 3.00000 | + | 5.19615i | 0.153897 | + | 0.266557i | ||||
\(381\) | 2.00000 | − | 3.46410i | 0.102463 | − | 0.177471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.3923 | − | 6.00000i | −0.531022 | − | 0.306586i | 0.210411 | − | 0.977613i | \(-0.432520\pi\) |
−0.741433 | + | 0.671027i | \(0.765853\pi\) | |||||||
\(384\) | −5.19615 | − | 3.00000i | −0.265165 | − | 0.153093i | ||||
\(385\) | − | 8.00000i | − | 0.407718i | ||||||
\(386\) | −1.00000 | + | 1.73205i | −0.0508987 | + | 0.0881591i | ||||
\(387\) | 5.00000 | + | 8.66025i | 0.254164 | + | 0.440225i | ||||
\(388\) | −1.73205 | + | 1.00000i | −0.0879316 | + | 0.0507673i | ||||
\(389\) | 10.0000 | 0.507020 | 0.253510 | − | 0.967333i | \(-0.418415\pi\) | ||||
0.253510 | + | 0.967333i | \(0.418415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | 23.3827 | − | 13.5000i | 1.18100 | − | 0.681853i | ||||
\(393\) | 20.0000 | + | 34.6410i | 1.00887 | + | 1.74741i | ||||
\(394\) | 3.00000 | − | 5.19615i | 0.151138 | − | 0.261778i | ||||
\(395\) | 12.0000i | 0.603786i | ||||||||
\(396\) | 1.73205 | + | 1.00000i | 0.0870388 | + | 0.0502519i | ||||
\(397\) | 5.19615 | + | 3.00000i | 0.260787 | + | 0.150566i | 0.624694 | − | 0.780870i | \(-0.285224\pi\) |
−0.363906 | + | 0.931436i | \(0.618557\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | 24.0000 | − | 41.5692i | 1.20150 | − | 2.08106i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −8.66025 | + | 5.00000i | −0.432472 | + | 0.249688i | −0.700399 | − | 0.713751i | \(-0.746995\pi\) |
0.267927 | + | 0.963439i | \(0.413661\pi\) | |||||||
\(402\) | 8.00000 | 0.399004 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | 9.52628 | − | 5.50000i | 0.473365 | − | 0.273297i | ||||
\(406\) | −4.00000 | − | 6.92820i | −0.198517 | − | 0.343841i | ||||
\(407\) | −2.00000 | + | 3.46410i | −0.0991363 | + | 0.171709i | ||||
\(408\) | − | 12.0000i | − | 0.594089i | ||||||
\(409\) | −15.5885 | − | 9.00000i | −0.770800 | − | 0.445021i | 0.0623602 | − | 0.998054i | \(-0.480137\pi\) |
−0.833160 | + | 0.553032i | \(0.813471\pi\) | |||||||
\(410\) | −5.19615 | − | 3.00000i | −0.256620 | − | 0.148159i | ||||
\(411\) | − | 4.00000i | − | 0.197305i | ||||||
\(412\) | 1.00000 | − | 1.73205i | 0.0492665 | − | 0.0853320i | ||||
\(413\) | −12.0000 | − | 20.7846i | −0.590481 | − | 1.02274i | ||||
\(414\) | −5.19615 | + | 3.00000i | −0.255377 | + | 0.147442i | ||||
\(415\) | −16.0000 | −0.785409 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.3923 | − | 6.00000i | 0.508304 | − | 0.293470i | ||||
\(419\) | 20.0000 | + | 34.6410i | 0.977064 | + | 1.69232i | 0.672949 | + | 0.739689i | \(0.265027\pi\) |
0.304115 | + | 0.952635i | \(0.401639\pi\) | |||||||
\(420\) | 4.00000 | − | 6.92820i | 0.195180 | − | 0.338062i | ||||
\(421\) | 10.0000i | 0.487370i | 0.969854 | + | 0.243685i | \(0.0783563\pi\) | ||||
−0.969854 | + | 0.243685i | \(0.921644\pi\) | |||||||
\(422\) | 10.3923 | + | 6.00000i | 0.505889 | + | 0.292075i | ||||
\(423\) | 3.46410 | + | 2.00000i | 0.168430 | + | 0.0972433i | ||||
\(424\) | − | 6.00000i | − | 0.291386i | ||||||
\(425\) | −1.00000 | + | 1.73205i | −0.0485071 | + | 0.0840168i | ||||
\(426\) | 6.00000 | + | 10.3923i | 0.290701 | + | 0.503509i | ||||
\(427\) | 6.92820 | − | 4.00000i | 0.335279 | − | 0.193574i | ||||
\(428\) | 10.0000 | 0.483368 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0000 | 0.482243 | ||||||||
\(431\) | 12.1244 | − | 7.00000i | 0.584010 | − | 0.337178i | −0.178716 | − | 0.983901i | \(-0.557194\pi\) |
0.762725 | + | 0.646723i | \(0.223861\pi\) | |||||||
\(432\) | 2.00000 | + | 3.46410i | 0.0962250 | + | 0.166667i | ||||
\(433\) | 5.00000 | − | 8.66025i | 0.240285 | − | 0.416185i | −0.720511 | − | 0.693444i | \(-0.756093\pi\) |
0.960795 | + | 0.277259i | \(0.0894259\pi\) | |||||||
\(434\) | − | 40.0000i | − | 1.92006i | ||||||
\(435\) | −3.46410 | − | 2.00000i | −0.166091 | − | 0.0958927i | ||||
\(436\) | −8.66025 | − | 5.00000i | −0.414751 | − | 0.239457i | ||||
\(437\) | − | 36.0000i | − | 1.72211i | ||||||
\(438\) | 6.00000 | − | 10.3923i | 0.286691 | − | 0.496564i | ||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 5.19615 | − | 3.00000i | 0.247717 | − | 0.143019i | ||||
\(441\) | −9.00000 | −0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.0000 | 0.665160 | 0.332580 | − | 0.943075i | \(-0.392081\pi\) | ||||
0.332580 | + | 0.943075i | \(0.392081\pi\) | |||||||
\(444\) | −3.46410 | + | 2.00000i | −0.164399 | + | 0.0949158i | ||||
\(445\) | 1.00000 | + | 1.73205i | 0.0474045 | + | 0.0821071i | ||||
\(446\) | −2.00000 | + | 3.46410i | −0.0947027 | + | 0.164030i | ||||
\(447\) | − | 36.0000i | − | 1.70274i | ||||||
\(448\) | 24.2487 | + | 14.0000i | 1.14564 | + | 0.661438i | ||||
\(449\) | −5.19615 | − | 3.00000i | −0.245222 | − | 0.141579i | 0.372353 | − | 0.928091i | \(-0.378551\pi\) |
−0.617574 | + | 0.786513i | \(0.711885\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | 6.00000 | − | 10.3923i | 0.282529 | − | 0.489355i | ||||
\(452\) | 7.00000 | + | 12.1244i | 0.329252 | + | 0.570282i | ||||
\(453\) | 17.3205 | − | 10.0000i | 0.813788 | − | 0.469841i | ||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 36.0000 | 1.68585 | ||||||||
\(457\) | 32.9090 | − | 19.0000i | 1.53942 | − | 0.888783i | 0.540544 | − | 0.841316i | \(-0.318219\pi\) |
0.998873 | − | 0.0474665i | \(-0.0151147\pi\) | |||||||
\(458\) | −11.0000 | − | 19.0526i | −0.513996 | − | 0.890268i | ||||
\(459\) | 4.00000 | − | 6.92820i | 0.186704 | − | 0.323381i | ||||
\(460\) | − | 6.00000i | − | 0.279751i | ||||||
\(461\) | −8.66025 | − | 5.00000i | −0.403348 | − | 0.232873i | 0.284579 | − | 0.958652i | \(-0.408146\pi\) |
−0.687928 | + | 0.725779i | \(0.741479\pi\) | |||||||
\(462\) | −13.8564 | − | 8.00000i | −0.644658 | − | 0.372194i | ||||
\(463\) | 24.0000i | 1.11537i | 0.830051 | + | 0.557687i | \(0.188311\pi\) | ||||
−0.830051 | + | 0.557687i | \(0.811689\pi\) | |||||||
\(464\) | 1.00000 | − | 1.73205i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | −10.0000 | − | 17.3205i | −0.463739 | − | 0.803219i | ||||
\(466\) | 8.66025 | − | 5.00000i | 0.401179 | − | 0.231621i | ||||
\(467\) | 10.0000 | 0.462745 | 0.231372 | − | 0.972865i | \(-0.425678\pi\) | ||||
0.231372 | + | 0.972865i | \(0.425678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 3.46410 | − | 2.00000i | 0.159787 | − | 0.0922531i | ||||
\(471\) | −6.00000 | − | 10.3923i | −0.276465 | − | 0.478852i | ||||
\(472\) | 9.00000 | − | 15.5885i | 0.414259 | − | 0.717517i | ||||
\(473\) | 20.0000i | 0.919601i | ||||||||
\(474\) | 20.7846 | + | 12.0000i | 0.954669 | + | 0.551178i | ||||
\(475\) | −5.19615 | − | 3.00000i | −0.238416 | − | 0.137649i | ||||
\(476\) | − | 8.00000i | − | 0.366679i | ||||||
\(477\) | −1.00000 | + | 1.73205i | −0.0457869 | + | 0.0793052i | ||||
\(478\) | 3.00000 | + | 5.19615i | 0.137217 | + | 0.237666i | ||||
\(479\) | −25.9808 | + | 15.0000i | −1.18709 | + | 0.685367i | −0.957644 | − | 0.287954i | \(-0.907025\pi\) |
−0.229447 | + | 0.973321i | \(0.573692\pi\) | |||||||
\(480\) | 10.0000 | 0.456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.0000 | −0.455488 | ||||||||
\(483\) | −41.5692 | + | 24.0000i | −1.89146 | + | 1.09204i | ||||
\(484\) | −3.50000 | − | 6.06218i | −0.159091 | − | 0.275554i | ||||
\(485\) | 1.00000 | − | 1.73205i | 0.0454077 | − | 0.0786484i | ||||
\(486\) | − | 10.0000i | − | 0.453609i | ||||||
\(487\) | 34.6410 | + | 20.0000i | 1.56973 | + | 0.906287i | 0.996199 | + | 0.0871056i | \(0.0277618\pi\) |
0.573535 | + | 0.819181i | \(0.305572\pi\) | |||||||
\(488\) | 5.19615 | + | 3.00000i | 0.235219 | + | 0.135804i | ||||
\(489\) | − | 24.0000i | − | 1.08532i | ||||||
\(490\) | −4.50000 | + | 7.79423i | −0.203289 | + | 0.352107i | ||||
\(491\) | −12.0000 | − | 20.7846i | −0.541552 | − | 0.937996i | −0.998815 | − | 0.0486647i | \(-0.984503\pi\) |
0.457263 | − | 0.889332i | \(-0.348830\pi\) | |||||||
\(492\) | 10.3923 | − | 6.00000i | 0.468521 | − | 0.270501i | ||||
\(493\) | −4.00000 | −0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | 8.66025 | − | 5.00000i | 0.388857 | − | 0.224507i | ||||
\(497\) | 12.0000 | + | 20.7846i | 0.538274 | + | 0.932317i | ||||
\(498\) | −16.0000 | + | 27.7128i | −0.716977 | + | 1.24184i | ||||
\(499\) | 10.0000i | 0.447661i | 0.974628 | + | 0.223831i | \(0.0718563\pi\) | ||||
−0.974628 | + | 0.223831i | \(0.928144\pi\) | |||||||
\(500\) | −0.866025 | − | 0.500000i | −0.0387298 | − | 0.0223607i | ||||
\(501\) | 20.7846 | + | 12.0000i | 0.928588 | + | 0.536120i | ||||
\(502\) | 24.0000i | 1.07117i | ||||||||
\(503\) | 9.00000 | − | 15.5885i | 0.401290 | − | 0.695055i | −0.592592 | − | 0.805503i | \(-0.701895\pi\) |
0.993882 | + | 0.110448i | \(0.0352286\pi\) | |||||||
\(504\) | −6.00000 | − | 10.3923i | −0.267261 | − | 0.462910i | ||||
\(505\) | −15.5885 | + | 9.00000i | −0.693677 | + | 0.400495i | ||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | −5.19615 | + | 3.00000i | −0.230315 | + | 0.132973i | −0.610718 | − | 0.791849i | \(-0.709119\pi\) |
0.380402 | + | 0.924821i | \(0.375786\pi\) | |||||||
\(510\) | 2.00000 | + | 3.46410i | 0.0885615 | + | 0.153393i | ||||
\(511\) | 12.0000 | − | 20.7846i | 0.530849 | − | 0.919457i | ||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | 20.7846 | + | 12.0000i | 0.917663 | + | 0.529813i | ||||
\(514\) | −1.73205 | − | 1.00000i | −0.0763975 | − | 0.0441081i | ||||
\(515\) | 2.00000i | 0.0881305i | ||||||||
\(516\) | −10.0000 | + | 17.3205i | −0.440225 | + | 0.762493i | ||||
\(517\) | 4.00000 | + | 6.92820i | 0.175920 | + | 0.304702i | ||||
\(518\) | 6.92820 | − | 4.00000i | 0.304408 | − | 0.175750i | ||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | −1.73205 | + | 1.00000i | −0.0758098 | + | 0.0437688i | ||||
\(523\) | −3.00000 | − | 5.19615i | −0.131181 | − | 0.227212i | 0.792951 | − | 0.609285i | \(-0.208544\pi\) |
−0.924132 | + | 0.382073i | \(0.875210\pi\) | |||||||
\(524\) | −10.0000 | + | 17.3205i | −0.436852 | + | 0.756650i | ||||
\(525\) | 8.00000i | 0.349149i | ||||||||
\(526\) | 12.1244 | + | 7.00000i | 0.528647 | + | 0.305215i | ||||
\(527\) | −17.3205 | − | 10.0000i | −0.754493 | − | 0.435607i | ||||
\(528\) | − | 4.00000i | − | 0.174078i | ||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 1.00000 | + | 1.73205i | 0.0434372 | + | 0.0752355i | ||||
\(531\) | −5.19615 | + | 3.00000i | −0.225494 | + | 0.130189i | ||||
\(532\) | 24.0000 | 1.04053 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.00000 | 0.173097 | ||||||||
\(535\) | −8.66025 | + | 5.00000i | −0.374415 | + | 0.216169i | ||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | −12.0000 | + | 20.7846i | −0.517838 | + | 0.896922i | ||||
\(538\) | − | 6.00000i | − | 0.258678i | ||||||
\(539\) | −15.5885 | − | 9.00000i | −0.671442 | − | 0.387657i | ||||
\(540\) | 3.46410 | + | 2.00000i | 0.149071 | + | 0.0860663i | ||||
\(541\) | 22.0000i | 0.945854i | 0.881102 | + | 0.472927i | \(0.156803\pi\) | ||||
−0.881102 | + | 0.472927i | \(0.843197\pi\) | |||||||
\(542\) | 1.00000 | − | 1.73205i | 0.0429537 | − | 0.0743980i | ||||
\(543\) | 22.0000 | + | 38.1051i | 0.944110 | + | 1.63525i | ||||
\(544\) | 8.66025 | − | 5.00000i | 0.371305 | − | 0.214373i | ||||
\(545\) | 10.0000 | 0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.00000 | −0.256541 | −0.128271 | − | 0.991739i | \(-0.540943\pi\) | ||||
−0.128271 | + | 0.991739i | \(0.540943\pi\) | |||||||
\(548\) | 1.73205 | − | 1.00000i | 0.0739895 | − | 0.0427179i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | −1.00000 | + | 1.73205i | −0.0426401 | + | 0.0738549i | ||||
\(551\) | − | 12.0000i | − | 0.511217i | ||||||
\(552\) | −31.1769 | − | 18.0000i | −1.32698 | − | 0.766131i | ||||
\(553\) | 41.5692 | + | 24.0000i | 1.76770 | + | 1.02058i | ||||
\(554\) | − | 14.0000i | − | 0.594803i | ||||||
\(555\) | 2.00000 | − | 3.46410i | 0.0848953 | − | 0.147043i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.5167 | − | 13.0000i | 0.954062 | − | 0.550828i | 0.0597213 | − | 0.998215i | \(-0.480979\pi\) |
0.894340 | + | 0.447387i | \(0.147645\pi\) | |||||||
\(558\) | −10.0000 | −0.423334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.00000 | −0.169031 | ||||||||
\(561\) | −6.92820 | + | 4.00000i | −0.292509 | + | 0.168880i | ||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | −11.0000 | + | 19.0526i | −0.463595 | + | 0.802970i | −0.999137 | − | 0.0415389i | \(-0.986774\pi\) |
0.535542 | + | 0.844508i | \(0.320107\pi\) | |||||||
\(564\) | 8.00000i | 0.336861i | ||||||||
\(565\) | −12.1244 | − | 7.00000i | −0.510075 | − | 0.294492i | ||||
\(566\) | −1.73205 | − | 1.00000i | −0.0728035 | − | 0.0420331i | ||||
\(567\) | − | 44.0000i | − | 1.84783i | ||||||
\(568\) | −9.00000 | + | 15.5885i | −0.377632 | + | 0.654077i | ||||
\(569\) | −13.0000 | − | 22.5167i | −0.544988 | − | 0.943948i | −0.998608 | − | 0.0527519i | \(-0.983201\pi\) |
0.453619 | − | 0.891196i | \(-0.350133\pi\) | |||||||
\(570\) | −10.3923 | + | 6.00000i | −0.435286 | + | 0.251312i | ||||
\(571\) | −24.0000 | −1.00437 | −0.502184 | − | 0.864761i | \(-0.667470\pi\) | ||||
−0.502184 | + | 0.864761i | \(0.667470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −20.7846 | + | 12.0000i | −0.867533 | + | 0.500870i | ||||
\(575\) | 3.00000 | + | 5.19615i | 0.125109 | + | 0.216695i | ||||
\(576\) | 3.50000 | − | 6.06218i | 0.145833 | − | 0.252591i | ||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | −11.2583 | − | 6.50000i | −0.468285 | − | 0.270364i | ||||
\(579\) | 3.46410 | + | 2.00000i | 0.143963 | + | 0.0831172i | ||||
\(580\) | − | 2.00000i | − | 0.0830455i | ||||||
\(581\) | −32.0000 | + | 55.4256i | −1.32758 | + | 2.29944i | ||||
\(582\) | −2.00000 | − | 3.46410i | −0.0829027 | − | 0.143592i | ||||
\(583\) | −3.46410 | + | 2.00000i | −0.143468 | + | 0.0828315i | ||||
\(584\) | 18.0000 | 0.744845 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.0000 | −0.908812 | ||||||||
\(587\) | −38.1051 | + | 22.0000i | −1.57277 | + | 0.908037i | −0.576938 | + | 0.816788i | \(0.695753\pi\) |
−0.995828 | + | 0.0912496i | \(0.970914\pi\) | |||||||
\(588\) | −9.00000 | − | 15.5885i | −0.371154 | − | 0.642857i | ||||
\(589\) | 30.0000 | − | 51.9615i | 1.23613 | − | 2.14104i | ||||
\(590\) | 6.00000i | 0.247016i | ||||||||
\(591\) | −10.3923 | − | 6.00000i | −0.427482 | − | 0.246807i | ||||
\(592\) | 1.73205 | + | 1.00000i | 0.0711868 | + | 0.0410997i | ||||
\(593\) | − | 14.0000i | − | 0.574911i | −0.957794 | − | 0.287456i | \(-0.907191\pi\) | ||
0.957794 | − | 0.287456i | \(-0.0928094\pi\) | |||||||
\(594\) | 4.00000 | − | 6.92820i | 0.164122 | − | 0.284268i | ||||
\(595\) | 4.00000 | + | 6.92820i | 0.163984 | + | 0.284029i | ||||
\(596\) | 15.5885 | − | 9.00000i | 0.638528 | − | 0.368654i | ||||
\(597\) | −32.0000 | −1.30967 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.00000 | −0.163436 | −0.0817178 | − | 0.996656i | \(-0.526041\pi\) | ||||
−0.0817178 | + | 0.996656i | \(0.526041\pi\) | |||||||
\(600\) | −5.19615 | + | 3.00000i | −0.212132 | + | 0.122474i | ||||
\(601\) | −5.00000 | − | 8.66025i | −0.203954 | − | 0.353259i | 0.745845 | − | 0.666120i | \(-0.232046\pi\) |
−0.949799 | + | 0.312861i | \(0.898713\pi\) | |||||||
\(602\) | 20.0000 | − | 34.6410i | 0.815139 | − | 1.41186i | ||||
\(603\) | − | 4.00000i | − | 0.162893i | ||||||
\(604\) | 8.66025 | + | 5.00000i | 0.352381 | + | 0.203447i | ||||
\(605\) | 6.06218 | + | 3.50000i | 0.246463 | + | 0.142295i | ||||
\(606\) | 36.0000i | 1.46240i | ||||||||
\(607\) | −17.0000 | + | 29.4449i | −0.690009 | + | 1.19513i | 0.281826 | + | 0.959466i | \(0.409060\pi\) |
−0.971834 | + | 0.235665i | \(0.924273\pi\) | |||||||
\(608\) | 15.0000 | + | 25.9808i | 0.608330 | + | 1.05366i | ||||
\(609\) | −13.8564 | + | 8.00000i | −0.561490 | + | 0.324176i | ||||
\(610\) | −2.00000 | −0.0809776 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.00000 | −0.0808452 | ||||||||
\(613\) | −5.19615 | + | 3.00000i | −0.209871 | + | 0.121169i | −0.601251 | − | 0.799060i | \(-0.705331\pi\) |
0.391381 | + | 0.920229i | \(0.371998\pi\) | |||||||
\(614\) | 4.00000 | + | 6.92820i | 0.161427 | + | 0.279600i | ||||
\(615\) | −6.00000 | + | 10.3923i | −0.241943 | + | 0.419058i | ||||
\(616\) | − | 24.0000i | − | 0.966988i | ||||||
\(617\) | 36.3731 | + | 21.0000i | 1.46432 | + | 0.845428i | 0.999207 | − | 0.0398207i | \(-0.0126787\pi\) |
0.465118 | + | 0.885249i | \(0.346012\pi\) | |||||||
\(618\) | 3.46410 | + | 2.00000i | 0.139347 | + | 0.0804518i | ||||
\(619\) | 2.00000i | 0.0803868i | 0.999192 | + | 0.0401934i | \(0.0127974\pi\) | ||||
−0.999192 | + | 0.0401934i | \(0.987203\pi\) | |||||||
\(620\) | 5.00000 | − | 8.66025i | 0.200805 | − | 0.347804i | ||||
\(621\) | −12.0000 | − | 20.7846i | −0.481543 | − | 0.834058i | ||||
\(622\) | −3.46410 | + | 2.00000i | −0.138898 | + | 0.0801927i | ||||
\(623\) | 8.00000 | 0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.0526 | − | 11.0000i | 0.761493 | − | 0.439648i | ||||
\(627\) | −12.0000 | − | 20.7846i | −0.479234 | − | 0.830057i | ||||
\(628\) | 3.00000 | − | 5.19615i | 0.119713 | − | 0.207349i | ||||
\(629\) | − | 4.00000i | − | 0.159490i | ||||||
\(630\) | 3.46410 | + | 2.00000i | 0.138013 | + | 0.0796819i | ||||
\(631\) | −12.1244 | − | 7.00000i | −0.482663 | − | 0.278666i | 0.238863 | − | 0.971053i | \(-0.423225\pi\) |
−0.721526 | + | 0.692388i | \(0.756559\pi\) | |||||||
\(632\) | 36.0000i | 1.43200i | ||||||||
\(633\) | 12.0000 | − | 20.7846i | 0.476957 | − | 0.826114i | ||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | −1.73205 | + | 1.00000i | −0.0687343 | + | 0.0396838i | ||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 5.19615 | − | 3.00000i | 0.205557 | − | 0.118678i | ||||
\(640\) | 1.50000 | + | 2.59808i | 0.0592927 | + | 0.102698i | ||||
\(641\) | −23.0000 | + | 39.8372i | −0.908445 | + | 1.57347i | −0.0922210 | + | 0.995739i | \(0.529397\pi\) |
−0.816224 | + | 0.577735i | \(0.803937\pi\) | |||||||
\(642\) | 20.0000i | 0.789337i | ||||||||
\(643\) | 13.8564 | + | 8.00000i | 0.546443 | + | 0.315489i | 0.747686 | − | 0.664052i | \(-0.231165\pi\) |
−0.201243 | + | 0.979541i | \(0.564498\pi\) | |||||||
\(644\) | −20.7846 | − | 12.0000i | −0.819028 | − | 0.472866i | ||||
\(645\) | − | 20.0000i | − | 0.787499i | ||||||
\(646\) | −6.00000 | + | 10.3923i | −0.236067 | + | 0.408880i | ||||
\(647\) | 19.0000 | + | 32.9090i | 0.746967 | + | 1.29378i | 0.949270 | + | 0.314462i | \(0.101824\pi\) |
−0.202303 | + | 0.979323i | \(0.564843\pi\) | |||||||
\(648\) | 28.5788 | − | 16.5000i | 1.12268 | − | 0.648181i | ||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −80.0000 | −3.13545 | ||||||||
\(652\) | 10.3923 | − | 6.00000i | 0.406994 | − | 0.234978i | ||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | 10.0000 | − | 17.3205i | 0.391031 | − | 0.677285i | ||||
\(655\) | − | 20.0000i | − | 0.781465i | ||||||
\(656\) | −5.19615 | − | 3.00000i | −0.202876 | − | 0.117130i | ||||
\(657\) | −5.19615 | − | 3.00000i | −0.202721 | − | 0.117041i | ||||
\(658\) | − | 16.0000i | − | 0.623745i | ||||||
\(659\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(660\) | −2.00000 | − | 3.46410i | −0.0778499 | − | 0.134840i | ||||
\(661\) | −1.73205 | + | 1.00000i | −0.0673690 | + | 0.0388955i | −0.533306 | − | 0.845922i | \(-0.679051\pi\) |
0.465937 | + | 0.884818i | \(0.345717\pi\) | |||||||
\(662\) | −18.0000 | −0.699590 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −48.0000 | −1.86276 | ||||||||
\(665\) | −20.7846 | + | 12.0000i | −0.805993 | + | 0.465340i | ||||
\(666\) | −1.00000 | − | 1.73205i | −0.0387492 | − | 0.0671156i | ||||
\(667\) | −6.00000 | + | 10.3923i | −0.232321 | + | 0.402392i | ||||
\(668\) | 12.0000i | 0.464294i | ||||||||
\(669\) | 6.92820 | + | 4.00000i | 0.267860 | + | 0.154649i | ||||
\(670\) | −3.46410 | − | 2.00000i | −0.133830 | − | 0.0772667i | ||||
\(671\) | − | 4.00000i | − | 0.154418i | ||||||
\(672\) | 20.0000 | − | 34.6410i | 0.771517 | − | 1.33631i | ||||
\(673\) | −15.0000 | − | 25.9808i | −0.578208 | − | 1.00148i | −0.995685 | − | 0.0927975i | \(-0.970419\pi\) |
0.417477 | − | 0.908687i | \(-0.362914\pi\) | |||||||
\(674\) | 22.5167 | − | 13.0000i | 0.867309 | − | 0.500741i | ||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | −24.2487 | + | 14.0000i | −0.931266 | + | 0.537667i | ||||
\(679\) | −4.00000 | − | 6.92820i | −0.153506 | − | 0.265880i | ||||
\(680\) | −3.00000 | + | 5.19615i | −0.115045 | + | 0.199263i | ||||
\(681\) | − | 8.00000i | − | 0.306561i | ||||||
\(682\) | −17.3205 | − | 10.0000i | −0.663237 | − | 0.382920i | ||||
\(683\) | −17.3205 | − | 10.0000i | −0.662751 | − | 0.382639i | 0.130573 | − | 0.991439i | \(-0.458318\pi\) |
−0.793324 | + | 0.608799i | \(0.791651\pi\) | |||||||
\(684\) | − | 6.00000i | − | 0.229416i | ||||||
\(685\) | −1.00000 | + | 1.73205i | −0.0382080 | + | 0.0661783i | ||||
\(686\) | 4.00000 | + | 6.92820i | 0.152721 | + | 0.264520i | ||||
\(687\) | −38.1051 | + | 22.0000i | −1.45380 | + | 0.839352i | ||||
\(688\) | 10.0000 | 0.381246 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 12.0000 | 0.456832 | ||||||||
\(691\) | 19.0526 | − | 11.0000i | 0.724793 | − | 0.418460i | −0.0917209 | − | 0.995785i | \(-0.529237\pi\) |
0.816514 | + | 0.577325i | \(0.195903\pi\) | |||||||
\(692\) | −3.00000 | − | 5.19615i | −0.114043 | − | 0.197528i | ||||
\(693\) | −4.00000 | + | 6.92820i | −0.151947 | + | 0.263181i | ||||
\(694\) | 22.0000i | 0.835109i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.3923 | − | 6.00000i | −0.393919 | − | 0.227429i | ||||
\(697\) | 12.0000i | 0.454532i | ||||||||
\(698\) | −15.0000 | + | 25.9808i | −0.567758 | + | 0.983386i | ||||
\(699\) | −10.0000 | − | 17.3205i | −0.378235 | − | 0.655122i | ||||
\(700\) | −3.46410 | + | 2.00000i | −0.130931 | + | 0.0755929i | ||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | 0.452589 | ||||||||
\(704\) | 12.1244 | − | 7.00000i | 0.456954 | − | 0.263822i | ||||
\(705\) | −4.00000 | − | 6.92820i | −0.150649 | − | 0.260931i | ||||
\(706\) | −9.00000 | + | 15.5885i | −0.338719 | + | 0.586679i | ||||
\(707\) | 72.0000i | 2.70784i | ||||||||
\(708\) | −10.3923 | − | 6.00000i | −0.390567 | − | 0.225494i | ||||
\(709\) | 8.66025 | + | 5.00000i | 0.325243 | + | 0.187779i | 0.653727 | − | 0.756730i | \(-0.273204\pi\) |
−0.328484 | + | 0.944509i | \(0.606538\pi\) | |||||||
\(710\) | − | 6.00000i | − | 0.225176i | ||||||
\(711\) | 6.00000 | − | 10.3923i | 0.225018 | − | 0.389742i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | −51.9615 | + | 30.0000i | −1.94597 | + | 1.12351i | ||||
\(714\) | 16.0000 | 0.598785 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 10.3923 | − | 6.00000i | 0.388108 | − | 0.224074i | ||||
\(718\) | −5.00000 | − | 8.66025i | −0.186598 | − | 0.323198i | ||||
\(719\) | −16.0000 | + | 27.7128i | −0.596699 | + | 1.03351i | 0.396605 | + | 0.917989i | \(0.370188\pi\) |
−0.993305 | + | 0.115524i | \(0.963145\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | 6.92820 | + | 4.00000i | 0.258020 | + | 0.148968i | ||||
\(722\) | −14.7224 | − | 8.50000i | −0.547912 | − | 0.316337i | ||||
\(723\) | 20.0000i | 0.743808i | ||||||||
\(724\) | −11.0000 | + | 19.0526i | −0.408812 | + | 0.708083i | ||||
\(725\) | 1.00000 | + | 1.73205i | 0.0371391 | + | 0.0643268i | ||||
\(726\) | 12.1244 | − | 7.00000i | 0.449977 | − | 0.259794i | ||||
\(727\) | 18.0000 | 0.667583 | 0.333792 | − | 0.942647i | \(-0.391672\pi\) | ||||
0.333792 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −5.19615 | + | 3.00000i | −0.192318 | + | 0.111035i | ||||
\(731\) | −10.0000 | − | 17.3205i | −0.369863 | − | 0.640622i | ||||
\(732\) | 2.00000 | − | 3.46410i | 0.0739221 | − | 0.128037i | ||||
\(733\) | 34.0000i | 1.25582i | 0.778287 | + | 0.627909i | \(0.216089\pi\) | ||||
−0.778287 | + | 0.627909i | \(0.783911\pi\) | |||||||
\(734\) | −12.1244 | − | 7.00000i | −0.447518 | − | 0.258375i | ||||
\(735\) | 15.5885 | + | 9.00000i | 0.574989 | + | 0.331970i | ||||
\(736\) | − | 30.0000i | − | 1.10581i | ||||||
\(737\) | 4.00000 | − | 6.92820i | 0.147342 | − | 0.255204i | ||||
\(738\) | 3.00000 | + | 5.19615i | 0.110432 | + | 0.191273i | ||||
\(739\) | −5.19615 | + | 3.00000i | −0.191144 | + | 0.110357i | −0.592518 | − | 0.805557i | \(-0.701866\pi\) |
0.401374 | + | 0.915914i | \(0.368533\pi\) | |||||||
\(740\) | 2.00000 | 0.0735215 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.00000 | 0.293689 | ||||||||
\(743\) | −10.3923 | + | 6.00000i | −0.381257 | + | 0.220119i | −0.678365 | − | 0.734725i | \(-0.737311\pi\) |
0.297108 | + | 0.954844i | \(0.403978\pi\) | |||||||
\(744\) | −30.0000 | − | 51.9615i | −1.09985 | − | 1.90500i | ||||
\(745\) | −9.00000 | + | 15.5885i | −0.329734 | + | 0.571117i | ||||
\(746\) | − | 34.0000i | − | 1.24483i | ||||||
\(747\) | 13.8564 | + | 8.00000i | 0.506979 | + | 0.292705i | ||||
\(748\) | −3.46410 | − | 2.00000i | −0.126660 | − | 0.0731272i | ||||
\(749\) | 40.0000i | 1.46157i | ||||||||
\(750\) | 1.00000 | − | 1.73205i | 0.0365148 | − | 0.0632456i | ||||
\(751\) | −14.0000 | − | 24.2487i | −0.510867 | − | 0.884848i | −0.999921 | − | 0.0125942i | \(-0.995991\pi\) |
0.489053 | − | 0.872254i | \(-0.337342\pi\) | |||||||
\(752\) | 3.46410 | − | 2.00000i | 0.126323 | − | 0.0729325i | ||||
\(753\) | 48.0000 | 1.74922 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0000 | −0.363937 | ||||||||
\(756\) | 13.8564 | − | 8.00000i | 0.503953 | − | 0.290957i | ||||
\(757\) | −1.00000 | − | 1.73205i | −0.0363456 | − | 0.0629525i | 0.847280 | − | 0.531146i | \(-0.178238\pi\) |
−0.883626 | + | 0.468193i | \(0.844905\pi\) | |||||||
\(758\) | −5.00000 | + | 8.66025i | −0.181608 | + | 0.314555i | ||||
\(759\) | 24.0000i | 0.871145i | ||||||||
\(760\) | −15.5885 | − | 9.00000i | −0.565453 | − | 0.326464i | ||||
\(761\) | 15.5885 | + | 9.00000i | 0.565081 | + | 0.326250i | 0.755182 | − | 0.655515i | \(-0.227548\pi\) |
−0.190101 | + | 0.981764i | \(0.560882\pi\) | |||||||
\(762\) | 4.00000i | 0.144905i | ||||||||
\(763\) | 20.0000 | − | 34.6410i | 0.724049 | − | 1.25409i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.73205 | − | 1.00000i | 0.0626224 | − | 0.0361551i | ||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 34.0000 | 1.22687 | ||||||||
\(769\) | 22.5167 | − | 13.0000i | 0.811972 | − | 0.468792i | −0.0356685 | − | 0.999364i | \(-0.511356\pi\) |
0.847640 | + | 0.530572i | \(0.178023\pi\) | |||||||
\(770\) | 4.00000 | + | 6.92820i | 0.144150 | + | 0.249675i | ||||
\(771\) | −2.00000 | + | 3.46410i | −0.0720282 | + | 0.124757i | ||||
\(772\) | 2.00000i | 0.0719816i | ||||||||
\(773\) | 1.73205 | + | 1.00000i | 0.0622975 | + | 0.0359675i | 0.530825 | − | 0.847481i | \(-0.321882\pi\) |
−0.468528 | + | 0.883449i | \(0.655215\pi\) | |||||||
\(774\) | −8.66025 | − | 5.00000i | −0.311286 | − | 0.179721i | ||||
\(775\) | 10.0000i | 0.359211i | ||||||||
\(776\) | 3.00000 | − | 5.19615i | 0.107694 | − | 0.186531i | ||||
\(777\) | −8.00000 | − | 13.8564i | −0.286998 | − | 0.497096i | ||||
\(778\) | −8.66025 | + | 5.00000i | −0.310485 | + | 0.179259i | ||||
\(779\) | −36.0000 | −1.28983 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | 0.429394 | ||||||||
\(782\) | 10.3923 | − | 6.00000i | 0.371628 | − | 0.214560i | ||||
\(783\) | −4.00000 | − | 6.92820i | −0.142948 | − | 0.247594i | ||||
\(784\) | −4.50000 | + | 7.79423i | −0.160714 | + | 0.278365i | ||||
\(785\) | 6.00000i | 0.214149i | ||||||||
\(786\) | −34.6410 | − | 20.0000i | −1.23560 | − | 0.713376i | ||||
\(787\) | 6.92820 | + | 4.00000i | 0.246964 | + | 0.142585i | 0.618373 | − | 0.785885i | \(-0.287792\pi\) |
−0.371409 | + | 0.928469i | \(0.621125\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | 14.0000 | − | 24.2487i | 0.498413 | − | 0.863277i | ||||
\(790\) | −6.00000 | − | 10.3923i | −0.213470 | − | 0.369742i | ||||
\(791\) | −48.4974 | + | 28.0000i | −1.72437 | + | 0.995565i | ||||
\(792\) | −6.00000 | −0.213201 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −6.00000 | −0.212932 | ||||||||
\(795\) | 3.46410 | − | 2.00000i | 0.122859 | − | 0.0709327i | ||||
\(796\) | −8.00000 | − | 13.8564i | −0.283552 | − | 0.491127i | ||||
\(797\) | 21.0000 | − | 36.3731i | 0.743858 | − | 1.28840i | −0.206868 | − | 0.978369i | \(-0.566327\pi\) |
0.950726 | − | 0.310031i | \(-0.100340\pi\) | |||||||
\(798\) | 48.0000i | 1.69918i | ||||||||
\(799\) | −6.92820 | − | 4.00000i | −0.245102 | − | 0.141510i | ||||
\(800\) | −4.33013 | − | 2.50000i | −0.153093 | − | 0.0883883i | ||||
\(801\) | − | 2.00000i | − | 0.0706665i | ||||||
\(802\) | 5.00000 | − | 8.66025i | 0.176556 | − | 0.305804i | ||||
\(803\) | −6.00000 | − | 10.3923i | −0.211735 | − | 0.366736i | ||||
\(804\) | 6.92820 | − | 4.00000i | 0.244339 | − | 0.141069i | ||||
\(805\) | 24.0000 | 0.845889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.0000 | −0.422420 | ||||||||
\(808\) | −46.7654 | + | 27.0000i | −1.64520 | + | 0.949857i | ||||
\(809\) | 1.00000 | + | 1.73205i | 0.0351581 | + | 0.0608957i | 0.883069 | − | 0.469243i | \(-0.155473\pi\) |
−0.847911 | + | 0.530139i | \(0.822140\pi\) | |||||||
\(810\) | −5.50000 | + | 9.52628i | −0.193250 | + | 0.334719i | ||||
\(811\) | − | 42.0000i | − | 1.47482i | −0.675446 | − | 0.737410i | \(-0.736049\pi\) | ||
0.675446 | − | 0.737410i | \(-0.263951\pi\) | |||||||
\(812\) | −6.92820 | − | 4.00000i | −0.243132 | − | 0.140372i | ||||
\(813\) | −3.46410 | − | 2.00000i | −0.121491 | − | 0.0701431i | ||||
\(814\) | − | 4.00000i | − | 0.140200i | ||||||
\(815\) | −6.00000 | + | 10.3923i | −0.210171 | + | 0.364027i | ||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | 51.9615 | − | 30.0000i | 1.81790 | − | 1.04957i | ||||
\(818\) | 18.0000 | 0.629355 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.00000 | −0.209529 | ||||||||
\(821\) | 43.3013 | − | 25.0000i | 1.51122 | − | 0.872506i | 0.511311 | − | 0.859396i | \(-0.329160\pi\) |
0.999914 | − | 0.0131101i | \(-0.00417319\pi\) | |||||||
\(822\) | 2.00000 | + | 3.46410i | 0.0697580 | + | 0.120824i | ||||
\(823\) | −23.0000 | + | 39.8372i | −0.801730 | + | 1.38864i | 0.116747 | + | 0.993162i | \(0.462753\pi\) |
−0.918477 | + | 0.395475i | \(0.870580\pi\) | |||||||
\(824\) | 6.00000i | 0.209020i | ||||||||
\(825\) | 3.46410 | + | 2.00000i | 0.120605 | + | 0.0696311i | ||||
\(826\) | 20.7846 | + | 12.0000i | 0.723189 | + | 0.417533i | ||||
\(827\) | 32.0000i | 1.11275i | 0.830932 | + | 0.556375i | \(0.187808\pi\) | ||||
−0.830932 | + | 0.556375i | \(0.812192\pi\) | |||||||
\(828\) | −3.00000 | + | 5.19615i | −0.104257 | + | 0.180579i | ||||
\(829\) | 17.0000 | + | 29.4449i | 0.590434 | + | 1.02266i | 0.994174 | + | 0.107788i | \(0.0343769\pi\) |
−0.403739 | + | 0.914874i | \(0.632290\pi\) | |||||||
\(830\) | 13.8564 | − | 8.00000i | 0.480963 | − | 0.277684i | ||||
\(831\) | −28.0000 | −0.971309 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | − | 10.3923i | −0.207639 | − | 0.359641i | ||||
\(836\) | 6.00000 | − | 10.3923i | 0.207514 | − | 0.359425i | ||||
\(837\) | − | 40.0000i | − | 1.38260i | ||||||
\(838\) | −34.6410 | − | 20.0000i | −1.19665 | − | 0.690889i | ||||
\(839\) | 32.9090 | + | 19.0000i | 1.13614 | + | 0.655953i | 0.945473 | − | 0.325701i | \(-0.105600\pi\) |
0.190671 | + | 0.981654i | \(0.438934\pi\) | |||||||
\(840\) | 24.0000i | 0.828079i | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | −5.00000 | − | 8.66025i | −0.172311 | − | 0.298452i | ||||
\(843\) | −10.3923 | + | 6.00000i | −0.357930 | + | 0.206651i | ||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.00000 | −0.137523 | ||||||||
\(847\) | 24.2487 | − | 14.0000i | 0.833196 | − | 0.481046i | ||||
\(848\) | 1.00000 | + | 1.73205i | 0.0343401 | + | 0.0594789i | ||||
\(849\) | −2.00000 | + | 3.46410i | −0.0686398 | + | 0.118888i | ||||
\(850\) | − | 2.00000i | − | 0.0685994i | ||||||
\(851\) | −10.3923 | − | 6.00000i | −0.356244 | − | 0.205677i | ||||
\(852\) | 10.3923 | + | 6.00000i | 0.356034 | + | 0.205557i | ||||
\(853\) | − | 6.00000i | − | 0.205436i | −0.994711 | − | 0.102718i | \(-0.967246\pi\) | ||
0.994711 | − | 0.102718i | \(-0.0327539\pi\) | |||||||
\(854\) | −4.00000 | + | 6.92820i | −0.136877 | + | 0.237078i | ||||
\(855\) | 3.00000 | + | 5.19615i | 0.102598 | + | 0.177705i | ||||
\(856\) | −25.9808 | + | 15.0000i | −0.888004 | + | 0.512689i | ||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0000 | 1.36478 | 0.682391 | − | 0.730987i | \(-0.260940\pi\) | ||||
0.682391 | + | 0.730987i | \(0.260940\pi\) | |||||||
\(860\) | 8.66025 | − | 5.00000i | 0.295312 | − | 0.170499i | ||||
\(861\) | 24.0000 | + | 41.5692i | 0.817918 | + | 1.41668i | ||||
\(862\) | −7.00000 | + | 12.1244i | −0.238421 | + | 0.412957i | ||||
\(863\) | 12.0000i | 0.408485i | 0.978920 | + | 0.204242i | \(0.0654731\pi\) | ||||
−0.978920 | + | 0.204242i | \(0.934527\pi\) | |||||||
\(864\) | 17.3205 | + | 10.0000i | 0.589256 | + | 0.340207i | ||||
\(865\) | 5.19615 | + | 3.00000i | 0.176674 | + | 0.102003i | ||||
\(866\) | 10.0000i | 0.339814i | ||||||||
\(867\) | −13.0000 | + | 22.5167i | −0.441503 | + | 0.764706i | ||||
\(868\) | −20.0000 | − | 34.6410i | −0.678844 | − | 1.17579i | ||||
\(869\) | 20.7846 | − | 12.0000i | 0.705070 | − | 0.407072i | ||||
\(870\) | 4.00000 | 0.135613 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 30.0000 | 1.01593 | ||||||||
\(873\) | −1.73205 | + | 1.00000i | −0.0586210 | + | 0.0338449i | ||||
\(874\) | 18.0000 | + | 31.1769i | 0.608859 | + | 1.05457i | ||||
\(875\) | 2.00000 | − | 3.46410i | 0.0676123 | − | 0.117108i | ||||
\(876\) | − | 12.0000i | − | 0.405442i | ||||||
\(877\) | −15.5885 | − | 9.00000i | −0.526385 | − | 0.303908i | 0.213158 | − | 0.977018i | \(-0.431625\pi\) |
−0.739543 | + | 0.673109i | \(0.764958\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44.0000i | 1.48408i | ||||||||
\(880\) | −1.00000 | + | 1.73205i | −0.0337100 | + | 0.0583874i | ||||
\(881\) | 19.0000 | + | 32.9090i | 0.640126 | + | 1.10873i | 0.985404 | + | 0.170231i | \(0.0544513\pi\) |
−0.345278 | + | 0.938500i | \(0.612215\pi\) | |||||||
\(882\) | 7.79423 | − | 4.50000i | 0.262445 | − | 0.151523i | ||||
\(883\) | 22.0000 | 0.740359 | 0.370179 | − | 0.928960i | \(-0.379296\pi\) | ||||
0.370179 | + | 0.928960i | \(0.379296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0000 | 0.403376 | ||||||||
\(886\) | −12.1244 | + | 7.00000i | −0.407326 | + | 0.235170i | ||||
\(887\) | −29.0000 | − | 50.2295i | −0.973725 | − | 1.68654i | −0.684081 | − | 0.729406i | \(-0.739796\pi\) |
−0.289644 | − | 0.957135i | \(-0.593537\pi\) | |||||||
\(888\) | 6.00000 | − | 10.3923i | 0.201347 | − | 0.348743i | ||||
\(889\) | 8.00000i | 0.268311i | ||||||||
\(890\) | −1.73205 | − | 1.00000i | −0.0580585 | − | 0.0335201i | ||||
\(891\) | −19.0526 | − | 11.0000i | −0.638285 | − | 0.368514i | ||||
\(892\) | 4.00000i | 0.133930i | ||||||||
\(893\) | 12.0000 | − | 20.7846i | 0.401565 | − | 0.695530i | ||||
\(894\) | 18.0000 | + | 31.1769i | 0.602010 | + | 1.04271i | ||||
\(895\) | 10.3923 | − | 6.00000i | 0.347376 | − | 0.200558i | ||||
\(896\) | 12.0000 | 0.400892 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00000 | 0.200223 | ||||||||
\(899\) | −17.3205 | + | 10.0000i | −0.577671 | + | 0.333519i | ||||
\(900\) | 0.500000 | + | 0.866025i | 0.0166667 | + | 0.0288675i | ||||
\(901\) | 2.00000 | − | 3.46410i | 0.0666297 | − | 0.115406i | ||||
\(902\) | 12.0000i | 0.399556i | ||||||||
\(903\) | −69.2820 | − | 40.0000i | −2.30556 | − | 1.33112i | ||||
\(904\) | −36.3731 | − | 21.0000i | −1.20975 | − | 0.698450i | ||||
\(905\) | − | 22.0000i | − | 0.731305i | ||||||
\(906\) | −10.0000 | + | 17.3205i | −0.332228 | + | 0.575435i | ||||
\(907\) | −17.0000 | − | 29.4449i | −0.564476 | − | 0.977701i | −0.997098 | − | 0.0761255i | \(-0.975745\pi\) |
0.432623 | − | 0.901575i | \(-0.357588\pi\) | |||||||
\(908\) | 3.46410 | − | 2.00000i | 0.114960 | − | 0.0663723i | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | −10.3923 | + | 6.00000i | −0.344124 | + | 0.198680i | ||||
\(913\) | 16.0000 | + | 27.7128i | 0.529523 | + | 0.917160i | ||||
\(914\) | −19.0000 | + | 32.9090i | −0.628464 | + | 1.08853i | ||||
\(915\) | 4.00000i | 0.132236i | ||||||||
\(916\) | −19.0526 | − | 11.0000i | −0.629514 | − | 0.363450i | ||||
\(917\) | −69.2820 | − | 40.0000i | −2.28789 | − | 1.32092i | ||||
\(918\) | 8.00000i | 0.264039i | ||||||||
\(919\) | 26.0000 | − | 45.0333i | 0.857661 | − | 1.48551i | −0.0164935 | − | 0.999864i | \(-0.505250\pi\) |
0.874154 | − | 0.485648i | \(-0.161416\pi\) | |||||||
\(920\) | 9.00000 | + | 15.5885i | 0.296721 | + | 0.513936i | ||||
\(921\) | 13.8564 | − | 8.00000i | 0.456584 | − | 0.263609i | ||||
\(922\) | 10.0000 | 0.329332 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −16.0000 | −0.526361 | ||||||||
\(925\) | −1.73205 | + | 1.00000i | −0.0569495 | + | 0.0328798i | ||||
\(926\) | −12.0000 | − | 20.7846i | −0.394344 | − | 0.683025i | ||||
\(927\) | 1.00000 | − | 1.73205i | 0.0328443 | − | 0.0568880i | ||||
\(928\) | − | 10.0000i | − | 0.328266i | ||||||
\(929\) | 32.9090 | + | 19.0000i | 1.07971 | + | 0.623370i | 0.930818 | − | 0.365484i | \(-0.119096\pi\) |
0.148890 | + | 0.988854i | \(0.452430\pi\) | |||||||
\(930\) | 17.3205 | + | 10.0000i | 0.567962 | + | 0.327913i | ||||
\(931\) | 54.0000i | 1.76978i | ||||||||
\(932\) | 5.00000 | − | 8.66025i | 0.163780 | − | 0.283676i | ||||
\(933\) | 4.00000 | + | 6.92820i | 0.130954 | + | 0.226819i | ||||
\(934\) | −8.66025 | + | 5.00000i | −0.283372 | + | 0.163605i | ||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0000 | −0.980057 | −0.490029 | − | 0.871706i | \(-0.663014\pi\) | ||||
−0.490029 | + | 0.871706i | \(0.663014\pi\) | |||||||
\(938\) | −13.8564 | + | 8.00000i | −0.452428 | + | 0.261209i | ||||
\(939\) | −22.0000 | − | 38.1051i | −0.717943 | − | 1.24351i | ||||
\(940\) | 2.00000 | − | 3.46410i | 0.0652328 | − | 0.112987i | ||||
\(941\) | 18.0000i | 0.586783i | 0.955992 | + | 0.293392i | \(0.0947840\pi\) | ||||
−0.955992 | + | 0.293392i | \(0.905216\pi\) | |||||||
\(942\) | 10.3923 | + | 6.00000i | 0.338600 | + | 0.195491i | ||||
\(943\) | 31.1769 | + | 18.0000i | 1.01526 | + | 0.586161i | ||||
\(944\) | 6.00000i | 0.195283i | ||||||||
\(945\) | −8.00000 | + | 13.8564i | −0.260240 | + | 0.450749i | ||||
\(946\) | −10.0000 | − | 17.3205i | −0.325128 | − | 0.563138i | ||||
\(947\) | −20.7846 | + | 12.0000i | −0.675409 | + | 0.389948i | −0.798123 | − | 0.602494i | \(-0.794174\pi\) |
0.122714 | + | 0.992442i | \(0.460840\pi\) | |||||||
\(948\) | 24.0000 | 0.779484 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.00000 | 0.194666 | ||||||||
\(951\) | 31.1769 | − | 18.0000i | 1.01098 | − | 0.583690i | ||||
\(952\) | 12.0000 | + | 20.7846i | 0.388922 | + | 0.673633i | ||||
\(953\) | 9.00000 | − | 15.5885i | 0.291539 | − | 0.504960i | −0.682635 | − | 0.730759i | \(-0.739166\pi\) |
0.974174 | + | 0.225800i | \(0.0724995\pi\) | |||||||
\(954\) | − | 2.00000i | − | 0.0647524i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.19615 | + | 3.00000i | 0.168056 | + | 0.0970269i | ||||
\(957\) | 8.00000i | 0.258603i | ||||||||
\(958\) | 15.0000 | − | 25.9808i | 0.484628 | − | 0.839400i | ||||
\(959\) | 4.00000 | + | 6.92820i | 0.129167 | + | 0.223723i | ||||
\(960\) | −12.1244 | + | 7.00000i | −0.391312 | + | 0.225924i | ||||
\(961\) | −69.0000 | −2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.0000 | 0.322245 | ||||||||
\(964\) | −8.66025 | + | 5.00000i | −0.278928 | + | 0.161039i | ||||
\(965\) | −1.00000 | − | 1.73205i | −0.0321911 | − | 0.0557567i | ||||
\(966\) | 24.0000 | − | 41.5692i | 0.772187 | − | 1.33747i | ||||
\(967\) | − | 8.00000i | − | 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | 18.1865 | + | 10.5000i | 0.584537 | + | 0.337483i | ||||
\(969\) | 20.7846 | + | 12.0000i | 0.667698 | + | 0.385496i | ||||
\(970\) | 2.00000i | 0.0642161i | ||||||||
\(971\) | 14.0000 | − | 24.2487i | 0.449281 | − | 0.778178i | −0.549058 | − | 0.835784i | \(-0.685013\pi\) |
0.998339 | + | 0.0576061i | \(0.0183467\pi\) | |||||||
\(972\) | −5.00000 | − | 8.66025i | −0.160375 | − | 0.277778i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −40.0000 | −1.28168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | 15.5885 | − | 9.00000i | 0.498719 | − | 0.287936i | −0.229465 | − | 0.973317i | \(-0.573698\pi\) |
0.728184 | + | 0.685381i | \(0.240364\pi\) | |||||||
\(978\) | 12.0000 | + | 20.7846i | 0.383718 | + | 0.664619i | ||||
\(979\) | 2.00000 | − | 3.46410i | 0.0639203 | − | 0.110713i | ||||
\(980\) | 9.00000i | 0.287494i | ||||||||
\(981\) | −8.66025 | − | 5.00000i | −0.276501 | − | 0.159638i | ||||
\(982\) | 20.7846 | + | 12.0000i | 0.663264 | + | 0.382935i | ||||
\(983\) | − | 56.0000i | − | 1.78612i | −0.449935 | − | 0.893061i | \(-0.648553\pi\) | ||
0.449935 | − | 0.893061i | \(-0.351447\pi\) | |||||||
\(984\) | −18.0000 | + | 31.1769i | −0.573819 | + | 0.993884i | ||||
\(985\) | 3.00000 | + | 5.19615i | 0.0955879 | + | 0.165563i | ||||
\(986\) | 3.46410 | − | 2.00000i | 0.110319 | − | 0.0636930i | ||||
\(987\) | −32.0000 | −1.01857 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −60.0000 | −1.90789 | ||||||||
\(990\) | 1.73205 | − | 1.00000i | 0.0550482 | − | 0.0317821i | ||||
\(991\) | −24.0000 | − | 41.5692i | −0.762385 | − | 1.32049i | −0.941618 | − | 0.336683i | \(-0.890695\pi\) |
0.179233 | − | 0.983807i | \(-0.442638\pi\) | |||||||
\(992\) | 25.0000 | − | 43.3013i | 0.793751 | − | 1.37482i | ||||
\(993\) | 36.0000i | 1.14243i | ||||||||
\(994\) | −20.7846 | − | 12.0000i | −0.659248 | − | 0.380617i | ||||
\(995\) | 13.8564 | + | 8.00000i | 0.439278 | + | 0.253617i | ||||
\(996\) | 32.0000i | 1.01396i | ||||||||
\(997\) | 11.0000 | − | 19.0526i | 0.348373 | − | 0.603401i | −0.637587 | − | 0.770378i | \(-0.720067\pi\) |
0.985961 | + | 0.166978i | \(0.0534008\pi\) | |||||||
\(998\) | −5.00000 | − | 8.66025i | −0.158272 | − | 0.274136i | ||||
\(999\) | 6.92820 | − | 4.00000i | 0.219199 | − | 0.126554i |
(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 | 845.2.m.b.361.1 | 4 | ||
13.2 | odd | 12 | 65.2.a.a.1.1 | ✓ | 1 | ||
13.3 | even | 3 | 845.2.c.a.506.1 | 2 | |||
13.4 | even | 6 | inner | 845.2.m.b.316.1 | 4 | ||
13.5 | odd | 4 | 845.2.e.b.146.1 | 2 | |||
13.6 | odd | 12 | 845.2.e.b.191.1 | 2 | |||
13.7 | odd | 12 | 845.2.e.a.191.1 | 2 | |||
13.8 | odd | 4 | 845.2.e.a.146.1 | 2 | |||
13.9 | even | 3 | inner | 845.2.m.b.316.2 | 4 | ||
13.10 | even | 6 | 845.2.c.a.506.2 | 2 | |||
13.11 | odd | 12 | 845.2.a.a.1.1 | 1 | |||
13.12 | even | 2 | inner | 845.2.m.b.361.2 | 4 | ||
39.2 | even | 12 | 585.2.a.h.1.1 | 1 | |||
39.11 | even | 12 | 7605.2.a.f.1.1 | 1 | |||
52.15 | even | 12 | 1040.2.a.f.1.1 | 1 | |||
65.2 | even | 12 | 325.2.b.b.274.1 | 2 | |||
65.24 | odd | 12 | 4225.2.a.g.1.1 | 1 | |||
65.28 | even | 12 | 325.2.b.b.274.2 | 2 | |||
65.54 | odd | 12 | 325.2.a.d.1.1 | 1 | |||
91.41 | even | 12 | 3185.2.a.e.1.1 | 1 | |||
104.67 | even | 12 | 4160.2.a.f.1.1 | 1 | |||
104.93 | odd | 12 | 4160.2.a.q.1.1 | 1 | |||
143.54 | even | 12 | 7865.2.a.c.1.1 | 1 | |||
156.119 | odd | 12 | 9360.2.a.ca.1.1 | 1 | |||
195.2 | odd | 12 | 2925.2.c.h.2224.2 | 2 | |||
195.119 | even | 12 | 2925.2.a.f.1.1 | 1 | |||
195.158 | odd | 12 | 2925.2.c.h.2224.1 | 2 | |||
260.119 | even | 12 | 5200.2.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.a.1.1 | ✓ | 1 | 13.2 | odd | 12 | ||
325.2.a.d.1.1 | 1 | 65.54 | odd | 12 | |||
325.2.b.b.274.1 | 2 | 65.2 | even | 12 | |||
325.2.b.b.274.2 | 2 | 65.28 | even | 12 | |||
585.2.a.h.1.1 | 1 | 39.2 | even | 12 | |||
845.2.a.a.1.1 | 1 | 13.11 | odd | 12 | |||
845.2.c.a.506.1 | 2 | 13.3 | even | 3 | |||
845.2.c.a.506.2 | 2 | 13.10 | even | 6 | |||
845.2.e.a.146.1 | 2 | 13.8 | odd | 4 | |||
845.2.e.a.191.1 | 2 | 13.7 | odd | 12 | |||
845.2.e.b.146.1 | 2 | 13.5 | odd | 4 | |||
845.2.e.b.191.1 | 2 | 13.6 | odd | 12 | |||
845.2.m.b.316.1 | 4 | 13.4 | even | 6 | inner | ||
845.2.m.b.316.2 | 4 | 13.9 | even | 3 | inner | ||
845.2.m.b.361.1 | 4 | 1.1 | even | 1 | trivial | ||
845.2.m.b.361.2 | 4 | 13.12 | even | 2 | inner | ||
1040.2.a.f.1.1 | 1 | 52.15 | even | 12 | |||
2925.2.a.f.1.1 | 1 | 195.119 | even | 12 | |||
2925.2.c.h.2224.1 | 2 | 195.158 | odd | 12 | |||
2925.2.c.h.2224.2 | 2 | 195.2 | odd | 12 | |||
3185.2.a.e.1.1 | 1 | 91.41 | even | 12 | |||
4160.2.a.f.1.1 | 1 | 104.67 | even | 12 | |||
4160.2.a.q.1.1 | 1 | 104.93 | odd | 12 | |||
4225.2.a.g.1.1 | 1 | 65.24 | odd | 12 | |||
5200.2.a.d.1.1 | 1 | 260.119 | even | 12 | |||
7605.2.a.f.1.1 | 1 | 39.11 | even | 12 | |||
7865.2.a.c.1.1 | 1 | 143.54 | even | 12 | |||
9360.2.a.ca.1.1 | 1 | 156.119 | odd | 12 |