Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(52,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([8, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.52");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bs (of order \(12\), degree \(4\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 292.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.292 |
Dual form | 315.2.bs.b.178.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | − | 1.36603i | −0.965926 | − | 0.965926i | 0.0335125 | − | 0.999438i | \(-0.489331\pi\) |
−0.999438 | + | 0.0335125i | \(0.989331\pi\) | |||||||
\(3\) | 0.866025 | − | 1.50000i | 0.500000 | − | 0.866025i | ||||
\(4\) | 1.73205i | 0.866025i | ||||||||
\(5\) | 1.86603 | + | 1.23205i | 0.834512 | + | 0.550990i | ||||
\(6\) | −3.23205 | + | 0.866025i | −1.31948 | + | 0.353553i | ||||
\(7\) | 1.73205 | + | 2.00000i | 0.654654 | + | 0.755929i | ||||
\(8\) | −0.366025 | + | 0.366025i | −0.129410 | + | 0.129410i | ||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | −0.866025 | − | 4.23205i | −0.273861 | − | 1.33829i | ||||
\(11\) | 2.73205 | − | 4.73205i | 0.823744 | − | 1.42677i | −0.0791309 | − | 0.996864i | \(-0.525215\pi\) |
0.902875 | − | 0.429903i | \(-0.141452\pi\) | |||||||
\(12\) | 2.59808 | + | 1.50000i | 0.750000 | + | 0.433013i | ||||
\(13\) | 3.73205 | − | 1.00000i | 1.03508 | − | 0.277350i | 0.299010 | − | 0.954250i | \(-0.403344\pi\) |
0.736075 | + | 0.676900i | \(0.236677\pi\) | |||||||
\(14\) | 0.366025 | − | 5.09808i | 0.0978244 | − | 1.36252i | ||||
\(15\) | 3.46410 | − | 1.73205i | 0.894427 | − | 0.447214i | ||||
\(16\) | 4.46410 | 1.11603 | ||||||||
\(17\) | −2.73205 | − | 0.732051i | −0.662620 | − | 0.177548i | −0.0881917 | − | 0.996104i | \(-0.528109\pi\) |
−0.574428 | + | 0.818555i | \(0.694775\pi\) | |||||||
\(18\) | −1.50000 | + | 5.59808i | −0.353553 | + | 1.31948i | ||||
\(19\) | −1.63397 | + | 2.83013i | −0.374859 | + | 0.649276i | −0.990306 | − | 0.138903i | \(-0.955642\pi\) |
0.615447 | + | 0.788179i | \(0.288976\pi\) | |||||||
\(20\) | −2.13397 | + | 3.23205i | −0.477171 | + | 0.722709i | ||||
\(21\) | 4.50000 | − | 0.866025i | 0.981981 | − | 0.188982i | ||||
\(22\) | −10.1962 | + | 2.73205i | −2.17383 | + | 0.582475i | ||||
\(23\) | −4.59808 | − | 1.23205i | −0.958765 | − | 0.256900i | −0.254688 | − | 0.967023i | \(-0.581973\pi\) |
−0.704078 | + | 0.710123i | \(0.748639\pi\) | |||||||
\(24\) | 0.232051 | + | 0.866025i | 0.0473672 | + | 0.176777i | ||||
\(25\) | 1.96410 | + | 4.59808i | 0.392820 | + | 0.919615i | ||||
\(26\) | −6.46410 | − | 3.73205i | −1.26771 | − | 0.731915i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −3.46410 | + | 3.00000i | −0.654654 | + | 0.566947i | ||||
\(29\) | 6.00000 | − | 3.46410i | 1.11417 | − | 0.643268i | 0.174265 | − | 0.984699i | \(-0.444245\pi\) |
0.939907 | + | 0.341431i | \(0.110912\pi\) | |||||||
\(30\) | −7.09808 | − | 2.36603i | −1.29593 | − | 0.431975i | ||||
\(31\) | 0.196152i | 0.0352300i | 0.999845 | + | 0.0176150i | \(0.00560732\pi\) | ||||
−0.999845 | + | 0.0176150i | \(0.994393\pi\) | |||||||
\(32\) | −5.36603 | − | 5.36603i | −0.948588 | − | 0.948588i | ||||
\(33\) | −4.73205 | − | 8.19615i | −0.823744 | − | 1.42677i | ||||
\(34\) | 2.73205 | + | 4.73205i | 0.468543 | + | 0.811540i | ||||
\(35\) | 0.767949 | + | 5.86603i | 0.129807 | + | 0.991539i | ||||
\(36\) | 4.50000 | − | 2.59808i | 0.750000 | − | 0.433013i | ||||
\(37\) | −4.09808 | + | 1.09808i | −0.673720 | + | 0.180523i | −0.579430 | − | 0.815022i | \(-0.696725\pi\) |
−0.0942898 | + | 0.995545i | \(0.530058\pi\) | |||||||
\(38\) | 6.09808 | − | 1.63397i | 0.989239 | − | 0.265066i | ||||
\(39\) | 1.73205 | − | 6.46410i | 0.277350 | − | 1.03508i | ||||
\(40\) | −1.13397 | + | 0.232051i | −0.179297 | + | 0.0366905i | ||||
\(41\) | −2.19615 | − | 1.26795i | −0.342981 | − | 0.198020i | 0.318608 | − | 0.947886i | \(-0.396785\pi\) |
−0.661590 | + | 0.749866i | \(0.730118\pi\) | |||||||
\(42\) | −7.33013 | − | 4.96410i | −1.13106 | − | 0.765978i | ||||
\(43\) | 1.50000 | + | 0.401924i | 0.228748 | + | 0.0612928i | 0.371372 | − | 0.928484i | \(-0.378887\pi\) |
−0.142624 | + | 0.989777i | \(0.545554\pi\) | |||||||
\(44\) | 8.19615 | + | 4.73205i | 1.23562 | + | 0.713384i | ||||
\(45\) | 0.401924 | − | 6.69615i | 0.0599153 | − | 0.998203i | ||||
\(46\) | 4.59808 | + | 7.96410i | 0.677949 | + | 1.17424i | ||||
\(47\) | −9.29423 | + | 9.29423i | −1.35570 | + | 1.35570i | −0.476561 | + | 0.879141i | \(0.658117\pi\) |
−0.879141 | + | 0.476561i | \(0.841883\pi\) | |||||||
\(48\) | 3.86603 | − | 6.69615i | 0.558013 | − | 0.966506i | ||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 3.59808 | − | 8.96410i | 0.508845 | − | 1.26772i | ||||
\(51\) | −3.46410 | + | 3.46410i | −0.485071 | + | 0.485071i | ||||
\(52\) | 1.73205 | + | 6.46410i | 0.240192 | + | 0.896410i | ||||
\(53\) | 6.09808 | + | 1.63397i | 0.837635 | + | 0.224444i | 0.652042 | − | 0.758183i | \(-0.273913\pi\) |
0.185593 | + | 0.982627i | \(0.440579\pi\) | |||||||
\(54\) | 7.09808 | + | 7.09808i | 0.965926 | + | 0.965926i | ||||
\(55\) | 10.9282 | − | 5.46410i | 1.47356 | − | 0.736779i | ||||
\(56\) | −1.36603 | − | 0.0980762i | −0.182543 | − | 0.0131060i | ||||
\(57\) | 2.83013 | + | 4.90192i | 0.374859 | + | 0.649276i | ||||
\(58\) | −12.9282 | − | 3.46410i | −1.69756 | − | 0.454859i | ||||
\(59\) | 3.46410 | 0.450988 | 0.225494 | − | 0.974245i | \(-0.427600\pi\) | ||||
0.225494 | + | 0.974245i | \(0.427600\pi\) | |||||||
\(60\) | 3.00000 | + | 6.00000i | 0.387298 | + | 0.774597i | ||||
\(61\) | − | 11.3923i | − | 1.45864i | −0.684175 | − | 0.729318i | \(-0.739838\pi\) | ||
0.684175 | − | 0.729318i | \(-0.260162\pi\) | |||||||
\(62\) | 0.267949 | − | 0.267949i | 0.0340296 | − | 0.0340296i | ||||
\(63\) | 2.59808 | − | 7.50000i | 0.327327 | − | 0.944911i | ||||
\(64\) | 5.73205i | 0.716506i | ||||||||
\(65\) | 8.19615 | + | 2.73205i | 1.01661 | + | 0.338869i | ||||
\(66\) | −4.73205 | + | 17.6603i | −0.582475 | + | 2.17383i | ||||
\(67\) | 0.901924 | + | 0.901924i | 0.110188 | + | 0.110188i | 0.760051 | − | 0.649863i | \(-0.225174\pi\) |
−0.649863 | + | 0.760051i | \(0.725174\pi\) | |||||||
\(68\) | 1.26795 | − | 4.73205i | 0.153761 | − | 0.573845i | ||||
\(69\) | −5.83013 | + | 5.83013i | −0.701865 | + | 0.701865i | ||||
\(70\) | 6.96410 | − | 9.06218i | 0.832369 | − | 1.08314i | ||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 1.50000 | + | 0.401924i | 0.176777 | + | 0.0473672i | ||||
\(73\) | −2.36603 | + | 8.83013i | −0.276922 | + | 1.03349i | 0.677620 | + | 0.735412i | \(0.263012\pi\) |
−0.954542 | + | 0.298076i | \(0.903655\pi\) | |||||||
\(74\) | 7.09808 | + | 4.09808i | 0.825135 | + | 0.476392i | ||||
\(75\) | 8.59808 | + | 1.03590i | 0.992820 | + | 0.119615i | ||||
\(76\) | −4.90192 | − | 2.83013i | −0.562289 | − | 0.324638i | ||||
\(77\) | 14.1962 | − | 2.73205i | 1.61780 | − | 0.311346i | ||||
\(78\) | −11.1962 | + | 6.46410i | −1.26771 | + | 0.731915i | ||||
\(79\) | − | 4.53590i | − | 0.510328i | −0.966898 | − | 0.255164i | \(-0.917870\pi\) | ||
0.966898 | − | 0.255164i | \(-0.0821295\pi\) | |||||||
\(80\) | 8.33013 | + | 5.50000i | 0.931337 | + | 0.614919i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 1.26795 | + | 4.73205i | 0.140022 | + | 0.522568i | ||||
\(83\) | −0.366025 | + | 1.36603i | −0.0401765 | + | 0.149941i | −0.983100 | − | 0.183068i | \(-0.941397\pi\) |
0.942924 | + | 0.333009i | \(0.108064\pi\) | |||||||
\(84\) | 1.50000 | + | 7.79423i | 0.163663 | + | 0.850420i | ||||
\(85\) | −4.19615 | − | 4.73205i | −0.455137 | − | 0.513263i | ||||
\(86\) | −1.50000 | − | 2.59808i | −0.161749 | − | 0.280158i | ||||
\(87\) | − | 12.0000i | − | 1.28654i | ||||||
\(88\) | 0.732051 | + | 2.73205i | 0.0780369 | + | 0.291238i | ||||
\(89\) | −4.59808 | + | 7.96410i | −0.487395 | + | 0.844193i | −0.999895 | − | 0.0144942i | \(-0.995386\pi\) |
0.512500 | + | 0.858687i | \(0.328720\pi\) | |||||||
\(90\) | −9.69615 | + | 8.59808i | −1.02206 | + | 0.906317i | ||||
\(91\) | 8.46410 | + | 5.73205i | 0.887279 | + | 0.600882i | ||||
\(92\) | 2.13397 | − | 7.96410i | 0.222482 | − | 0.830315i | ||||
\(93\) | 0.294229 | + | 0.169873i | 0.0305101 | + | 0.0176150i | ||||
\(94\) | 25.3923 | 2.61902 | ||||||||
\(95\) | −6.53590 | + | 3.26795i | −0.670569 | + | 0.335285i | ||||
\(96\) | −12.6962 | + | 3.40192i | −1.29580 | + | 0.347207i | ||||
\(97\) | 7.83013 | + | 2.09808i | 0.795029 | + | 0.213027i | 0.633400 | − | 0.773824i | \(-0.281659\pi\) |
0.161629 | + | 0.986852i | \(0.448325\pi\) | |||||||
\(98\) | 10.8301 | − | 8.09808i | 1.09401 | − | 0.818029i | ||||
\(99\) | −16.3923 | −1.64749 | ||||||||
\(100\) | −7.96410 | + | 3.40192i | −0.796410 | + | 0.340192i | ||||
\(101\) | 15.2321 | + | 8.79423i | 1.51565 | + | 0.875058i | 0.999831 | + | 0.0183580i | \(0.00584386\pi\) |
0.515814 | + | 0.856700i | \(0.327489\pi\) | |||||||
\(102\) | 9.46410 | 0.937086 | ||||||||
\(103\) | 1.06218 | − | 3.96410i | 0.104659 | − | 0.390595i | −0.893647 | − | 0.448771i | \(-0.851862\pi\) |
0.998306 | + | 0.0581764i | \(0.0185286\pi\) | |||||||
\(104\) | −1.00000 | + | 1.73205i | −0.0980581 | + | 0.169842i | ||||
\(105\) | 9.46410 | + | 3.92820i | 0.923602 | + | 0.383353i | ||||
\(106\) | −6.09808 | − | 10.5622i | −0.592298 | − | 1.02589i | ||||
\(107\) | 2.36603 | − | 0.633975i | 0.228732 | − | 0.0612886i | −0.142632 | − | 0.989776i | \(-0.545557\pi\) |
0.371365 | + | 0.928487i | \(0.378890\pi\) | |||||||
\(108\) | − | 9.00000i | − | 0.866025i | ||||||
\(109\) | 1.73205 | − | 1.00000i | 0.165900 | − | 0.0957826i | −0.414751 | − | 0.909935i | \(-0.636131\pi\) |
0.580651 | + | 0.814152i | \(0.302798\pi\) | |||||||
\(110\) | −22.3923 | − | 7.46410i | −2.13502 | − | 0.711674i | ||||
\(111\) | −1.90192 | + | 7.09808i | −0.180523 | + | 0.673720i | ||||
\(112\) | 7.73205 | + | 8.92820i | 0.730610 | + | 0.843636i | ||||
\(113\) | 1.90192 | + | 7.09808i | 0.178918 | + | 0.667731i | 0.995851 | + | 0.0909984i | \(0.0290058\pi\) |
−0.816933 | + | 0.576732i | \(0.804328\pi\) | |||||||
\(114\) | 2.83013 | − | 10.5622i | 0.265066 | − | 0.989239i | ||||
\(115\) | −7.06218 | − | 7.96410i | −0.658551 | − | 0.742656i | ||||
\(116\) | 6.00000 | + | 10.3923i | 0.557086 | + | 0.964901i | ||||
\(117\) | −8.19615 | − | 8.19615i | −0.757735 | − | 0.757735i | ||||
\(118\) | −4.73205 | − | 4.73205i | −0.435621 | − | 0.435621i | ||||
\(119\) | −3.26795 | − | 6.73205i | −0.299572 | − | 0.617126i | ||||
\(120\) | −0.633975 | + | 1.90192i | −0.0578737 | + | 0.173621i | ||||
\(121\) | −9.42820 | − | 16.3301i | −0.857109 | − | 1.48456i | ||||
\(122\) | −15.5622 | + | 15.5622i | −1.40893 | + | 1.40893i | ||||
\(123\) | −3.80385 | + | 2.19615i | −0.342981 | + | 0.198020i | ||||
\(124\) | −0.339746 | −0.0305101 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | −13.7942 | + | 6.69615i | −1.22889 | + | 0.596541i | ||||
\(127\) | −15.7583 | − | 15.7583i | −1.39833 | − | 1.39833i | −0.804857 | − | 0.593468i | \(-0.797758\pi\) |
−0.593468 | − | 0.804857i | \(-0.702242\pi\) | |||||||
\(128\) | −2.90192 | + | 2.90192i | −0.256496 | + | 0.256496i | ||||
\(129\) | 1.90192 | − | 1.90192i | 0.167455 | − | 0.167455i | ||||
\(130\) | −7.46410 | − | 14.9282i | −0.654645 | − | 1.30929i | ||||
\(131\) | −4.39230 | + | 2.53590i | −0.383757 | + | 0.221562i | −0.679452 | − | 0.733720i | \(-0.737782\pi\) |
0.295694 | + | 0.955283i | \(0.404449\pi\) | |||||||
\(132\) | 14.1962 | − | 8.19615i | 1.23562 | − | 0.713384i | ||||
\(133\) | −8.49038 | + | 1.63397i | −0.736209 | + | 0.141684i | ||||
\(134\) | − | 2.46410i | − | 0.212866i | ||||||
\(135\) | −9.69615 | − | 6.40192i | −0.834512 | − | 0.550990i | ||||
\(136\) | 1.26795 | − | 0.732051i | 0.108726 | − | 0.0627728i | ||||
\(137\) | −2.00000 | + | 0.535898i | −0.170872 | + | 0.0457849i | −0.343240 | − | 0.939248i | \(-0.611525\pi\) |
0.172369 | + | 0.985032i | \(0.444858\pi\) | |||||||
\(138\) | 15.9282 | 1.35590 | ||||||||
\(139\) | 3.46410 | − | 6.00000i | 0.293821 | − | 0.508913i | −0.680889 | − | 0.732387i | \(-0.738406\pi\) |
0.974710 | + | 0.223474i | \(0.0717396\pi\) | |||||||
\(140\) | −10.1603 | + | 1.33013i | −0.858698 | + | 0.112416i | ||||
\(141\) | 5.89230 | + | 21.9904i | 0.496222 | + | 1.85192i | ||||
\(142\) | 8.19615 | + | 8.19615i | 0.687806 | + | 0.687806i | ||||
\(143\) | 5.46410 | − | 20.3923i | 0.456931 | − | 1.70529i | ||||
\(144\) | −6.69615 | − | 11.5981i | −0.558013 | − | 0.966506i | ||||
\(145\) | 15.4641 | + | 0.928203i | 1.28422 | + | 0.0770831i | ||||
\(146\) | 15.2942 | − | 8.83013i | 1.26576 | − | 0.730787i | ||||
\(147\) | 9.52628 | + | 7.50000i | 0.785714 | + | 0.618590i | ||||
\(148\) | −1.90192 | − | 7.09808i | −0.156337 | − | 0.583458i | ||||
\(149\) | −2.89230 | + | 1.66987i | −0.236947 | + | 0.136801i | −0.613773 | − | 0.789483i | \(-0.710349\pi\) |
0.376826 | + | 0.926284i | \(0.377016\pi\) | |||||||
\(150\) | −10.3301 | − | 13.1603i | −0.843451 | − | 1.07453i | ||||
\(151\) | −2.36603 | + | 4.09808i | −0.192544 | + | 0.333497i | −0.946093 | − | 0.323896i | \(-0.895007\pi\) |
0.753548 | + | 0.657392i | \(0.228341\pi\) | |||||||
\(152\) | −0.437822 | − | 1.63397i | −0.0355121 | − | 0.132533i | ||||
\(153\) | 2.19615 | + | 8.19615i | 0.177548 | + | 0.662620i | ||||
\(154\) | −23.1244 | − | 15.6603i | −1.86341 | − | 1.26194i | ||||
\(155\) | −0.241670 | + | 0.366025i | −0.0194114 | + | 0.0293999i | ||||
\(156\) | 11.1962 | + | 3.00000i | 0.896410 | + | 0.240192i | ||||
\(157\) | 1.00000 | − | 1.00000i | 0.0798087 | − | 0.0798087i | −0.666076 | − | 0.745884i | \(-0.732027\pi\) |
0.745884 | + | 0.666076i | \(0.232027\pi\) | |||||||
\(158\) | −6.19615 | + | 6.19615i | −0.492939 | + | 0.492939i | ||||
\(159\) | 7.73205 | − | 7.73205i | 0.613192 | − | 0.613192i | ||||
\(160\) | −3.40192 | − | 16.6244i | −0.268946 | − | 1.31427i | ||||
\(161\) | −5.50000 | − | 11.3301i | −0.433461 | − | 0.892939i | ||||
\(162\) | 16.7942 | − | 4.50000i | 1.31948 | − | 0.353553i | ||||
\(163\) | 2.36603 | + | 8.83013i | 0.185321 | + | 0.691629i | 0.994562 | + | 0.104151i | \(0.0332125\pi\) |
−0.809240 | + | 0.587478i | \(0.800121\pi\) | |||||||
\(164\) | 2.19615 | − | 3.80385i | 0.171491 | − | 0.297031i | ||||
\(165\) | 1.26795 | − | 21.1244i | 0.0987097 | − | 1.64453i | ||||
\(166\) | 2.36603 | − | 1.36603i | 0.183639 | − | 0.106024i | ||||
\(167\) | 3.62436 | + | 13.5263i | 0.280461 | + | 1.04669i | 0.952093 | + | 0.305810i | \(0.0989271\pi\) |
−0.671632 | + | 0.740885i | \(0.734406\pi\) | |||||||
\(168\) | −1.33013 | + | 1.96410i | −0.102622 | + | 0.151534i | ||||
\(169\) | 1.66987 | − | 0.964102i | 0.128452 | − | 0.0741617i | ||||
\(170\) | −0.732051 | + | 12.1962i | −0.0561457 | + | 0.935402i | ||||
\(171\) | 9.80385 | 0.749719 | ||||||||
\(172\) | −0.696152 | + | 2.59808i | −0.0530811 | + | 0.198101i | ||||
\(173\) | 10.0000 | + | 10.0000i | 0.760286 | + | 0.760286i | 0.976374 | − | 0.216088i | \(-0.0693298\pi\) |
−0.216088 | + | 0.976374i | \(0.569330\pi\) | |||||||
\(174\) | −16.3923 | + | 16.3923i | −1.24270 | + | 1.24270i | ||||
\(175\) | −5.79423 | + | 11.8923i | −0.438003 | + | 0.898974i | ||||
\(176\) | 12.1962 | − | 21.1244i | 0.919320 | − | 1.59231i | ||||
\(177\) | 3.00000 | − | 5.19615i | 0.225494 | − | 0.390567i | ||||
\(178\) | 17.1603 | − | 4.59808i | 1.28622 | − | 0.344640i | ||||
\(179\) | −10.9019 | + | 6.29423i | −0.814848 | + | 0.470453i | −0.848637 | − | 0.528976i | \(-0.822576\pi\) |
0.0337886 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(180\) | 11.5981 | + | 0.696152i | 0.864470 | + | 0.0518881i | ||||
\(181\) | 11.4641i | 0.852120i | 0.904695 | + | 0.426060i | \(0.140099\pi\) | ||||
−0.904695 | + | 0.426060i | \(0.859901\pi\) | |||||||
\(182\) | −3.73205 | − | 19.3923i | −0.276638 | − | 1.43745i | ||||
\(183\) | −17.0885 | − | 9.86603i | −1.26322 | − | 0.729318i | ||||
\(184\) | 2.13397 | − | 1.23205i | 0.157319 | − | 0.0908280i | ||||
\(185\) | −9.00000 | − | 3.00000i | −0.661693 | − | 0.220564i | ||||
\(186\) | −0.169873 | − | 0.633975i | −0.0124557 | − | 0.0464853i | ||||
\(187\) | −10.9282 | + | 10.9282i | −0.799149 | + | 0.799149i | ||||
\(188\) | −16.0981 | − | 16.0981i | −1.17407 | − | 1.17407i | ||||
\(189\) | −9.00000 | − | 10.3923i | −0.654654 | − | 0.755929i | ||||
\(190\) | 13.3923 | + | 4.46410i | 0.971580 | + | 0.323860i | ||||
\(191\) | −17.6603 | −1.27785 | −0.638926 | − | 0.769269i | \(-0.720621\pi\) | ||||
−0.638926 | + | 0.769269i | \(0.720621\pi\) | |||||||
\(192\) | 8.59808 | + | 4.96410i | 0.620513 | + | 0.358253i | ||||
\(193\) | −14.4641 | + | 14.4641i | −1.04115 | + | 1.04115i | −0.0420326 | + | 0.999116i | \(0.513383\pi\) |
−0.999116 | + | 0.0420326i | \(0.986617\pi\) | |||||||
\(194\) | −7.83013 | − | 13.5622i | −0.562170 | − | 0.973708i | ||||
\(195\) | 11.1962 | − | 9.92820i | 0.801773 | − | 0.710973i | ||||
\(196\) | −12.0000 | − | 1.73205i | −0.857143 | − | 0.123718i | ||||
\(197\) | −17.4641 | − | 17.4641i | −1.24427 | − | 1.24427i | −0.958214 | − | 0.286051i | \(-0.907657\pi\) |
−0.286051 | − | 0.958214i | \(-0.592343\pi\) | |||||||
\(198\) | 22.3923 | + | 22.3923i | 1.59135 | + | 1.59135i | ||||
\(199\) | 3.92820 | + | 6.80385i | 0.278463 | + | 0.482312i | 0.971003 | − | 0.239068i | \(-0.0768417\pi\) |
−0.692540 | + | 0.721379i | \(0.743508\pi\) | |||||||
\(200\) | −2.40192 | − | 0.964102i | −0.169842 | − | 0.0681723i | ||||
\(201\) | 2.13397 | − | 0.571797i | 0.150519 | − | 0.0403314i | ||||
\(202\) | −8.79423 | − | 32.8205i | −0.618760 | − | 2.30924i | ||||
\(203\) | 17.3205 | + | 6.00000i | 1.21566 | + | 0.421117i | ||||
\(204\) | −6.00000 | − | 6.00000i | −0.420084 | − | 0.420084i | ||||
\(205\) | −2.53590 | − | 5.07180i | −0.177115 | − | 0.354230i | ||||
\(206\) | −6.86603 | + | 3.96410i | −0.478379 | + | 0.276192i | ||||
\(207\) | 3.69615 | + | 13.7942i | 0.256900 | + | 0.958765i | ||||
\(208\) | 16.6603 | − | 4.46410i | 1.15518 | − | 0.309530i | ||||
\(209\) | 8.92820 | + | 15.4641i | 0.617577 | + | 1.06967i | ||||
\(210\) | −7.56218 | − | 18.2942i | −0.521840 | − | 1.26242i | ||||
\(211\) | −4.46410 | + | 7.73205i | −0.307321 | + | 0.532296i | −0.977775 | − | 0.209655i | \(-0.932766\pi\) |
0.670454 | + | 0.741951i | \(0.266099\pi\) | |||||||
\(212\) | −2.83013 | + | 10.5622i | −0.194374 | + | 0.725413i | ||||
\(213\) | −5.19615 | + | 9.00000i | −0.356034 | + | 0.616670i | ||||
\(214\) | −4.09808 | − | 2.36603i | −0.280139 | − | 0.161738i | ||||
\(215\) | 2.30385 | + | 2.59808i | 0.157121 | + | 0.177187i | ||||
\(216\) | 1.90192 | − | 1.90192i | 0.129410 | − | 0.129410i | ||||
\(217\) | −0.392305 | + | 0.339746i | −0.0266314 | + | 0.0230635i | ||||
\(218\) | −3.73205 | − | 1.00000i | −0.252766 | − | 0.0677285i | ||||
\(219\) | 11.1962 | + | 11.1962i | 0.756566 | + | 0.756566i | ||||
\(220\) | 9.46410 | + | 18.9282i | 0.638070 | + | 1.27614i | ||||
\(221\) | −10.9282 | −0.735111 | ||||||||
\(222\) | 12.2942 | − | 7.09808i | 0.825135 | − | 0.476392i | ||||
\(223\) | 1.33013 | − | 4.96410i | 0.0890719 | − | 0.332421i | −0.906982 | − | 0.421169i | \(-0.861620\pi\) |
0.996054 | + | 0.0887481i | \(0.0282866\pi\) | |||||||
\(224\) | 1.43782 | − | 20.0263i | 0.0960685 | − | 1.33806i | ||||
\(225\) | 9.00000 | − | 12.0000i | 0.600000 | − | 0.800000i | ||||
\(226\) | 7.09808 | − | 12.2942i | 0.472157 | − | 0.817800i | ||||
\(227\) | −3.90192 | − | 14.5622i | −0.258980 | − | 0.966526i | −0.965833 | − | 0.259165i | \(-0.916553\pi\) |
0.706853 | − | 0.707360i | \(-0.250114\pi\) | |||||||
\(228\) | −8.49038 | + | 4.90192i | −0.562289 | + | 0.324638i | ||||
\(229\) | 2.33013 | + | 4.03590i | 0.153979 | + | 0.266700i | 0.932687 | − | 0.360687i | \(-0.117458\pi\) |
−0.778708 | + | 0.627387i | \(0.784124\pi\) | |||||||
\(230\) | −1.23205 | + | 20.5263i | −0.0812390 | + | 1.35346i | ||||
\(231\) | 8.19615 | − | 23.6603i | 0.539267 | − | 1.55673i | ||||
\(232\) | −0.928203 | + | 3.46410i | −0.0609395 | + | 0.227429i | ||||
\(233\) | 3.16987 | + | 11.8301i | 0.207665 | + | 0.775017i | 0.988621 | + | 0.150430i | \(0.0480660\pi\) |
−0.780955 | + | 0.624587i | \(0.785267\pi\) | |||||||
\(234\) | 22.3923i | 1.46383i | ||||||||
\(235\) | −28.7942 | + | 5.89230i | −1.87833 | + | 0.384372i | ||||
\(236\) | 6.00000i | 0.390567i | ||||||||
\(237\) | −6.80385 | − | 3.92820i | −0.441957 | − | 0.255164i | ||||
\(238\) | −4.73205 | + | 13.6603i | −0.306733 | + | 0.885463i | ||||
\(239\) | 19.0526 | + | 11.0000i | 1.23241 | + | 0.711531i | 0.967531 | − | 0.252752i | \(-0.0813355\pi\) |
0.264876 | + | 0.964282i | \(0.414669\pi\) | |||||||
\(240\) | 15.4641 | − | 7.73205i | 0.998203 | − | 0.499102i | ||||
\(241\) | 8.25833 | + | 4.76795i | 0.531966 | + | 0.307131i | 0.741817 | − | 0.670603i | \(-0.233964\pi\) |
−0.209851 | + | 0.977733i | \(0.567298\pi\) | |||||||
\(242\) | −9.42820 | + | 35.1865i | −0.606068 | + | 2.26188i | ||||
\(243\) | 7.79423 | + | 13.5000i | 0.500000 | + | 0.866025i | ||||
\(244\) | 19.7321 | 1.26322 | ||||||||
\(245\) | −10.4019 | + | 11.6962i | −0.664555 | + | 0.747240i | ||||
\(246\) | 8.19615 | + | 2.19615i | 0.522568 | + | 0.140022i | ||||
\(247\) | −3.26795 | + | 12.1962i | −0.207935 | + | 0.776023i | ||||
\(248\) | −0.0717968 | − | 0.0717968i | −0.00455910 | − | 0.00455910i | ||||
\(249\) | 1.73205 | + | 1.73205i | 0.109764 | + | 0.109764i | ||||
\(250\) | 17.7583 | − | 12.2942i | 1.12314 | − | 0.777555i | ||||
\(251\) | − | 5.85641i | − | 0.369653i | −0.982771 | − | 0.184827i | \(-0.940828\pi\) | ||
0.982771 | − | 0.184827i | \(-0.0591723\pi\) | |||||||
\(252\) | 12.9904 | + | 4.50000i | 0.818317 | + | 0.283473i | ||||
\(253\) | −18.3923 | + | 18.3923i | −1.15631 | + | 1.15631i | ||||
\(254\) | 43.0526i | 2.70136i | ||||||||
\(255\) | −10.7321 | + | 2.19615i | −0.672067 | + | 0.137528i | ||||
\(256\) | 19.3923 | 1.21202 | ||||||||
\(257\) | 12.0263 | + | 3.22243i | 0.750179 | + | 0.201010i | 0.613597 | − | 0.789619i | \(-0.289722\pi\) |
0.136581 | + | 0.990629i | \(0.456388\pi\) | |||||||
\(258\) | −5.19615 | −0.323498 | ||||||||
\(259\) | −9.29423 | − | 6.29423i | −0.577515 | − | 0.391104i | ||||
\(260\) | −4.73205 | + | 14.1962i | −0.293469 | + | 0.880408i | ||||
\(261\) | −18.0000 | − | 10.3923i | −1.11417 | − | 0.643268i | ||||
\(262\) | 9.46410 | + | 2.53590i | 0.584694 | + | 0.156668i | ||||
\(263\) | −7.35641 | − | 27.4545i | −0.453615 | − | 1.69292i | −0.692127 | − | 0.721776i | \(-0.743326\pi\) |
0.238511 | − | 0.971140i | \(-0.423341\pi\) | |||||||
\(264\) | 4.73205 | + | 1.26795i | 0.291238 | + | 0.0780369i | ||||
\(265\) | 9.36603 | + | 10.5622i | 0.575350 | + | 0.648829i | ||||
\(266\) | 13.8301 | + | 9.36603i | 0.847979 | + | 0.574268i | ||||
\(267\) | 7.96410 | + | 13.7942i | 0.487395 | + | 0.844193i | ||||
\(268\) | −1.56218 | + | 1.56218i | −0.0954252 | + | 0.0954252i | ||||
\(269\) | −4.96410 | − | 8.59808i | −0.302667 | − | 0.524234i | 0.674072 | − | 0.738665i | \(-0.264544\pi\) |
−0.976739 | + | 0.214431i | \(0.931210\pi\) | |||||||
\(270\) | 4.50000 | + | 21.9904i | 0.273861 | + | 1.33829i | ||||
\(271\) | −9.92820 | − | 5.73205i | −0.603095 | − | 0.348197i | 0.167163 | − | 0.985929i | \(-0.446539\pi\) |
−0.770258 | + | 0.637732i | \(0.779873\pi\) | |||||||
\(272\) | −12.1962 | − | 3.26795i | −0.739500 | − | 0.198149i | ||||
\(273\) | 15.9282 | − | 7.73205i | 0.964019 | − | 0.467965i | ||||
\(274\) | 3.46410 | + | 2.00000i | 0.209274 | + | 0.120824i | ||||
\(275\) | 27.1244 | + | 3.26795i | 1.63566 | + | 0.197065i | ||||
\(276\) | −10.0981 | − | 10.0981i | −0.607833 | − | 0.607833i | ||||
\(277\) | 19.3923 | − | 5.19615i | 1.16517 | − | 0.312207i | 0.376141 | − | 0.926562i | \(-0.377251\pi\) |
0.789029 | + | 0.614356i | \(0.210584\pi\) | |||||||
\(278\) | −12.9282 | + | 3.46410i | −0.775382 | + | 0.207763i | ||||
\(279\) | 0.509619 | − | 0.294229i | 0.0305101 | − | 0.0176150i | ||||
\(280\) | −2.42820 | − | 1.86603i | −0.145113 | − | 0.111516i | ||||
\(281\) | 6.86603 | + | 11.8923i | 0.409593 | + | 0.709435i | 0.994844 | − | 0.101417i | \(-0.0323375\pi\) |
−0.585251 | + | 0.810852i | \(0.699004\pi\) | |||||||
\(282\) | 21.9904 | − | 38.0885i | 1.30951 | − | 2.26813i | ||||
\(283\) | −15.7583 | − | 15.7583i | −0.936736 | − | 0.936736i | 0.0613790 | − | 0.998115i | \(-0.480450\pi\) |
−0.998115 | + | 0.0613790i | \(0.980450\pi\) | |||||||
\(284\) | − | 10.3923i | − | 0.616670i | ||||||
\(285\) | −0.758330 | + | 12.6340i | −0.0449196 | + | 0.748372i | ||||
\(286\) | −35.3205 | + | 20.3923i | −2.08855 | + | 1.20582i | ||||
\(287\) | −1.26795 | − | 6.58846i | −0.0748447 | − | 0.388904i | ||||
\(288\) | −5.89230 | + | 21.9904i | −0.347207 | + | 1.29580i | ||||
\(289\) | −7.79423 | − | 4.50000i | −0.458484 | − | 0.264706i | ||||
\(290\) | −19.8564 | − | 22.3923i | −1.16601 | − | 1.31492i | ||||
\(291\) | 9.92820 | − | 9.92820i | 0.582002 | − | 0.582002i | ||||
\(292\) | −15.2942 | − | 4.09808i | −0.895027 | − | 0.239822i | ||||
\(293\) | 20.2942 | − | 5.43782i | 1.18560 | − | 0.317681i | 0.388455 | − | 0.921468i | \(-0.373009\pi\) |
0.797146 | + | 0.603787i | \(0.206342\pi\) | |||||||
\(294\) | −2.76795 | − | 23.2583i | −0.161430 | − | 1.35645i | ||||
\(295\) | 6.46410 | + | 4.26795i | 0.376355 | + | 0.248490i | ||||
\(296\) | 1.09808 | − | 1.90192i | 0.0638244 | − | 0.110547i | ||||
\(297\) | −14.1962 | + | 24.5885i | −0.823744 | + | 1.42677i | ||||
\(298\) | 6.23205 | + | 1.66987i | 0.361013 | + | 0.0967331i | ||||
\(299\) | −18.3923 | −1.06365 | ||||||||
\(300\) | −1.79423 | + | 14.8923i | −0.103590 | + | 0.859808i | ||||
\(301\) | 1.79423 | + | 3.69615i | 0.103418 | + | 0.213043i | ||||
\(302\) | 8.83013 | − | 2.36603i | 0.508117 | − | 0.136149i | ||||
\(303\) | 26.3827 | − | 15.2321i | 1.51565 | − | 0.875058i | ||||
\(304\) | −7.29423 | + | 12.6340i | −0.418353 | + | 0.724608i | ||||
\(305\) | 14.0359 | − | 21.2583i | 0.803693 | − | 1.21725i | ||||
\(306\) | 8.19615 | − | 14.1962i | 0.468543 | − | 0.811540i | ||||
\(307\) | 17.5359 | − | 17.5359i | 1.00083 | − | 1.00083i | 0.000826926 | − | 1.00000i | \(-0.499737\pi\) |
1.00000 | 0.000826926i | \(-0.000263219\pi\) | ||||||||
\(308\) | 4.73205 | + | 24.5885i | 0.269634 | + | 1.40106i | ||||
\(309\) | −5.02628 | − | 5.02628i | −0.285935 | − | 0.285935i | ||||
\(310\) | 0.830127 | − | 0.169873i | 0.0471480 | − | 0.00964814i | ||||
\(311\) | 16.0000i | 0.907277i | 0.891186 | + | 0.453638i | \(0.149874\pi\) | ||||
−0.891186 | + | 0.453638i | \(0.850126\pi\) | |||||||
\(312\) | 1.73205 | + | 3.00000i | 0.0980581 | + | 0.169842i | ||||
\(313\) | −5.19615 | − | 5.19615i | −0.293704 | − | 0.293704i | 0.544838 | − | 0.838542i | \(-0.316591\pi\) |
−0.838542 | + | 0.544838i | \(0.816591\pi\) | |||||||
\(314\) | −2.73205 | −0.154179 | ||||||||
\(315\) | 14.0885 | − | 10.7942i | 0.793795 | − | 0.608186i | ||||
\(316\) | 7.85641 | 0.441957 | ||||||||
\(317\) | 8.46410 | + | 8.46410i | 0.475391 | + | 0.475391i | 0.903654 | − | 0.428263i | \(-0.140874\pi\) |
−0.428263 | + | 0.903654i | \(0.640874\pi\) | |||||||
\(318\) | −21.1244 | −1.18460 | ||||||||
\(319\) | − | 37.8564i | − | 2.11955i | ||||||
\(320\) | −7.06218 | + | 10.6962i | −0.394788 | + | 0.597933i | ||||
\(321\) | 1.09808 | − | 4.09808i | 0.0612886 | − | 0.228732i | ||||
\(322\) | −7.96410 | + | 22.9904i | −0.443822 | + | 1.28120i | ||||
\(323\) | 6.53590 | − | 6.53590i | 0.363667 | − | 0.363667i | ||||
\(324\) | −13.5000 | − | 7.79423i | −0.750000 | − | 0.433013i | ||||
\(325\) | 11.9282 | + | 15.1962i | 0.661658 | + | 0.842931i | ||||
\(326\) | 8.83013 | − | 15.2942i | 0.489056 | − | 0.847069i | ||||
\(327\) | − | 3.46410i | − | 0.191565i | ||||||
\(328\) | 1.26795 | − | 0.339746i | 0.0700108 | − | 0.0187593i | ||||
\(329\) | −34.6865 | − | 2.49038i | −1.91233 | − | 0.137299i | ||||
\(330\) | −30.5885 | + | 27.1244i | −1.68384 | + | 1.49315i | ||||
\(331\) | 18.3397 | 1.00804 | 0.504022 | − | 0.863691i | \(-0.331853\pi\) | ||||
0.504022 | + | 0.863691i | \(0.331853\pi\) | |||||||
\(332\) | −2.36603 | − | 0.633975i | −0.129853 | − | 0.0347939i | ||||
\(333\) | 9.00000 | + | 9.00000i | 0.493197 | + | 0.493197i | ||||
\(334\) | 13.5263 | − | 23.4282i | 0.740125 | − | 1.28193i | ||||
\(335\) | 0.571797 | + | 2.79423i | 0.0312406 | + | 0.152665i | ||||
\(336\) | 20.0885 | − | 3.86603i | 1.09592 | − | 0.210909i | ||||
\(337\) | 4.46410 | − | 1.19615i | 0.243175 | − | 0.0651586i | −0.135173 | − | 0.990822i | \(-0.543159\pi\) |
0.378348 | + | 0.925663i | \(0.376492\pi\) | |||||||
\(338\) | −3.59808 | − | 0.964102i | −0.195710 | − | 0.0524402i | ||||
\(339\) | 12.2942 | + | 3.29423i | 0.667731 | + | 0.178918i | ||||
\(340\) | 8.19615 | − | 7.26795i | 0.444499 | − | 0.394160i | ||||
\(341\) | 0.928203 | + | 0.535898i | 0.0502650 | + | 0.0290205i | ||||
\(342\) | −13.3923 | − | 13.3923i | −0.724173 | − | 0.724173i | ||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | −0.696152 | + | 0.401924i | −0.0375340 | + | 0.0216703i | ||||
\(345\) | −18.0622 | + | 3.69615i | −0.972435 | + | 0.198994i | ||||
\(346\) | − | 27.3205i | − | 1.46876i | ||||||
\(347\) | −14.8301 | − | 14.8301i | −0.796123 | − | 0.796123i | 0.186359 | − | 0.982482i | \(-0.440331\pi\) |
−0.982482 | + | 0.186359i | \(0.940331\pi\) | |||||||
\(348\) | 20.7846 | 1.11417 | ||||||||
\(349\) | −17.0622 | − | 29.5526i | −0.913317 | − | 1.58191i | −0.809346 | − | 0.587332i | \(-0.800178\pi\) |
−0.103971 | − | 0.994580i | \(-0.533155\pi\) | |||||||
\(350\) | 24.1603 | − | 8.33013i | 1.29142 | − | 0.445264i | ||||
\(351\) | −19.3923 | + | 5.19615i | −1.03508 | + | 0.277350i | ||||
\(352\) | −40.0526 | + | 10.7321i | −2.13481 | + | 0.572020i | ||||
\(353\) | −10.7321 | + | 2.87564i | −0.571209 | + | 0.153055i | −0.532851 | − | 0.846209i | \(-0.678879\pi\) |
−0.0383582 | + | 0.999264i | \(0.512213\pi\) | |||||||
\(354\) | −11.1962 | + | 3.00000i | −0.595069 | + | 0.159448i | ||||
\(355\) | −11.1962 | − | 7.39230i | −0.594230 | − | 0.392343i | ||||
\(356\) | −13.7942 | − | 7.96410i | −0.731093 | − | 0.422097i | ||||
\(357\) | −12.9282 | − | 0.928203i | −0.684233 | − | 0.0491257i | ||||
\(358\) | 23.4904 | + | 6.29423i | 1.24151 | + | 0.332660i | ||||
\(359\) | −17.9545 | − | 10.3660i | −0.947601 | − | 0.547098i | −0.0552664 | − | 0.998472i | \(-0.517601\pi\) |
−0.892335 | + | 0.451374i | \(0.850934\pi\) | |||||||
\(360\) | 2.30385 | + | 2.59808i | 0.121423 | + | 0.136931i | ||||
\(361\) | 4.16025 | + | 7.20577i | 0.218961 | + | 0.379251i | ||||
\(362\) | 15.6603 | − | 15.6603i | 0.823085 | − | 0.823085i | ||||
\(363\) | −32.6603 | −1.71422 | ||||||||
\(364\) | −9.92820 | + | 14.6603i | −0.520379 | + | 0.768406i | ||||
\(365\) | −15.2942 | + | 13.5622i | −0.800537 | + | 0.709877i | ||||
\(366\) | 9.86603 | + | 36.8205i | 0.515705 | + | 1.92464i | ||||
\(367\) | −1.76795 | − | 6.59808i | −0.0922862 | − | 0.344417i | 0.904308 | − | 0.426881i | \(-0.140388\pi\) |
−0.996594 | + | 0.0824642i | \(0.973721\pi\) | |||||||
\(368\) | −20.5263 | − | 5.50000i | −1.07001 | − | 0.286707i | ||||
\(369\) | 7.60770i | 0.396041i | ||||||||
\(370\) | 8.19615 | + | 16.3923i | 0.426098 | + | 0.852195i | ||||
\(371\) | 7.29423 | + | 15.0263i | 0.378697 | + | 0.780126i | ||||
\(372\) | −0.294229 | + | 0.509619i | −0.0152550 | + | 0.0264225i | ||||
\(373\) | −4.09808 | − | 1.09808i | −0.212190 | − | 0.0568562i | 0.151158 | − | 0.988510i | \(-0.451700\pi\) |
−0.363348 | + | 0.931653i | \(0.618366\pi\) | |||||||
\(374\) | 29.8564 | 1.54384 | ||||||||
\(375\) | 14.7679 | + | 12.5263i | 0.762614 | + | 0.646854i | ||||
\(376\) | − | 6.80385i | − | 0.350882i | ||||||
\(377\) | 18.9282 | − | 18.9282i | 0.974852 | − | 0.974852i | ||||
\(378\) | −1.90192 | + | 26.4904i | −0.0978244 | + | 1.36252i | ||||
\(379\) | − | 12.5359i | − | 0.643926i | −0.946752 | − | 0.321963i | \(-0.895657\pi\) | ||
0.946752 | − | 0.321963i | \(-0.104343\pi\) | |||||||
\(380\) | −5.66025 | − | 11.3205i | −0.290365 | − | 0.580730i | ||||
\(381\) | −37.2846 | + | 9.99038i | −1.91015 | + | 0.511823i | ||||
\(382\) | 24.1244 | + | 24.1244i | 1.23431 | + | 1.23431i | ||||
\(383\) | 4.23205 | − | 15.7942i | 0.216248 | − | 0.807047i | −0.769476 | − | 0.638676i | \(-0.779482\pi\) |
0.985724 | − | 0.168372i | \(-0.0538508\pi\) | |||||||
\(384\) | 1.83975 | + | 6.86603i | 0.0938841 | + | 0.350380i | ||||
\(385\) | 29.8564 | + | 12.3923i | 1.52162 | + | 0.631570i | ||||
\(386\) | 39.5167 | 2.01135 | ||||||||
\(387\) | −1.20577 | − | 4.50000i | −0.0612928 | − | 0.228748i | ||||
\(388\) | −3.63397 | + | 13.5622i | −0.184487 | + | 0.688515i | ||||
\(389\) | 1.03590 | + | 0.598076i | 0.0525221 | + | 0.0303237i | 0.526031 | − | 0.850465i | \(-0.323680\pi\) |
−0.473509 | + | 0.880789i | \(0.657013\pi\) | |||||||
\(390\) | −28.8564 | − | 1.73205i | −1.46120 | − | 0.0877058i | ||||
\(391\) | 11.6603 | + | 6.73205i | 0.589684 | + | 0.340454i | ||||
\(392\) | −2.16987 | − | 2.90192i | −0.109595 | − | 0.146569i | ||||
\(393\) | 8.78461i | 0.443125i | ||||||||
\(394\) | 47.7128i | 2.40374i | ||||||||
\(395\) | 5.58846 | − | 8.46410i | 0.281186 | − | 0.425875i | ||||
\(396\) | − | 28.3923i | − | 1.42677i | ||||||
\(397\) | 8.78461 | + | 32.7846i | 0.440887 | + | 1.64541i | 0.726573 | + | 0.687089i | \(0.241112\pi\) |
−0.285686 | + | 0.958323i | \(0.592221\pi\) | |||||||
\(398\) | 3.92820 | − | 14.6603i | 0.196903 | − | 0.734852i | ||||
\(399\) | −4.90192 | + | 14.1506i | −0.245403 | + | 0.708418i | ||||
\(400\) | 8.76795 | + | 20.5263i | 0.438397 | + | 1.02631i | ||||
\(401\) | −11.6962 | − | 20.2583i | −0.584078 | − | 1.01165i | −0.994990 | − | 0.0999776i | \(-0.968123\pi\) |
0.410912 | − | 0.911675i | \(-0.365210\pi\) | |||||||
\(402\) | −3.69615 | − | 2.13397i | −0.184347 | − | 0.106433i | ||||
\(403\) | 0.196152 | + | 0.732051i | 0.00977105 | + | 0.0364660i | ||||
\(404\) | −15.2321 | + | 26.3827i | −0.757823 | + | 1.31259i | ||||
\(405\) | −18.0000 | + | 9.00000i | −0.894427 | + | 0.447214i | ||||
\(406\) | −15.4641 | − | 31.8564i | −0.767470 | − | 1.58101i | ||||
\(407\) | −6.00000 | + | 22.3923i | −0.297409 | + | 1.10995i | ||||
\(408\) | − | 2.53590i | − | 0.125546i | ||||||
\(409\) | −5.39230 | −0.266632 | −0.133316 | − | 0.991074i | \(-0.542563\pi\) | ||||
−0.133316 | + | 0.991074i | \(0.542563\pi\) | |||||||
\(410\) | −3.46410 | + | 10.3923i | −0.171080 | + | 0.513239i | ||||
\(411\) | −0.928203 | + | 3.46410i | −0.0457849 | + | 0.170872i | ||||
\(412\) | 6.86603 | + | 1.83975i | 0.338265 | + | 0.0906378i | ||||
\(413\) | 6.00000 | + | 6.92820i | 0.295241 | + | 0.340915i | ||||
\(414\) | 13.7942 | − | 23.8923i | 0.677949 | − | 1.17424i | ||||
\(415\) | −2.36603 | + | 2.09808i | −0.116144 | + | 0.102991i | ||||
\(416\) | −25.3923 | − | 14.6603i | −1.24496 | − | 0.718778i | ||||
\(417\) | −6.00000 | − | 10.3923i | −0.293821 | − | 0.508913i | ||||
\(418\) | 8.92820 | − | 33.3205i | 0.436693 | − | 1.62976i | ||||
\(419\) | 4.00000 | − | 6.92820i | 0.195413 | − | 0.338465i | −0.751623 | − | 0.659593i | \(-0.770729\pi\) |
0.947036 | + | 0.321128i | \(0.104062\pi\) | |||||||
\(420\) | −6.80385 | + | 16.3923i | −0.331994 | + | 0.799863i | ||||
\(421\) | −11.5263 | − | 19.9641i | −0.561756 | − | 0.972991i | −0.997343 | − | 0.0728441i | \(-0.976792\pi\) |
0.435587 | − | 0.900147i | \(-0.356541\pi\) | |||||||
\(422\) | 16.6603 | − | 4.46410i | 0.811008 | − | 0.217309i | ||||
\(423\) | 38.0885 | + | 10.2058i | 1.85192 | + | 0.496222i | ||||
\(424\) | −2.83013 | + | 1.63397i | −0.137443 | + | 0.0793528i | ||||
\(425\) | −2.00000 | − | 14.0000i | −0.0970143 | − | 0.679100i | ||||
\(426\) | 19.3923 | − | 5.19615i | 0.939560 | − | 0.251754i | ||||
\(427\) | 22.7846 | − | 19.7321i | 1.10262 | − | 0.954901i | ||||
\(428\) | 1.09808 | + | 4.09808i | 0.0530775 | + | 0.198088i | ||||
\(429\) | −25.8564 | − | 25.8564i | −1.24836 | − | 1.24836i | ||||
\(430\) | 0.401924 | − | 6.69615i | 0.0193825 | − | 0.322917i | ||||
\(431\) | 12.0981 | + | 20.9545i | 0.582744 | + | 1.00934i | 0.995153 | + | 0.0983430i | \(0.0313542\pi\) |
−0.412409 | + | 0.910999i | \(0.635312\pi\) | |||||||
\(432\) | −23.1962 | −1.11603 | ||||||||
\(433\) | −9.80385 | − | 9.80385i | −0.471143 | − | 0.471143i | 0.431141 | − | 0.902284i | \(-0.358111\pi\) |
−0.902284 | + | 0.431141i | \(0.858111\pi\) | |||||||
\(434\) | 1.00000 | + | 0.0717968i | 0.0480015 | + | 0.00344636i | ||||
\(435\) | 14.7846 | − | 22.3923i | 0.708868 | − | 1.07363i | ||||
\(436\) | 1.73205 | + | 3.00000i | 0.0829502 | + | 0.143674i | ||||
\(437\) | 11.0000 | − | 11.0000i | 0.526201 | − | 0.526201i | ||||
\(438\) | − | 30.5885i | − | 1.46157i | ||||||
\(439\) | 5.85641 | 0.279511 | 0.139756 | − | 0.990186i | \(-0.455368\pi\) | ||||
0.139756 | + | 0.990186i | \(0.455368\pi\) | |||||||
\(440\) | −2.00000 | + | 6.00000i | −0.0953463 | + | 0.286039i | ||||
\(441\) | 19.5000 | − | 7.79423i | 0.928571 | − | 0.371154i | ||||
\(442\) | 14.9282 | + | 14.9282i | 0.710062 | + | 0.710062i | ||||
\(443\) | −0.660254 | + | 0.660254i | −0.0313696 | + | 0.0313696i | −0.722618 | − | 0.691248i | \(-0.757061\pi\) |
0.691248 | + | 0.722618i | \(0.257061\pi\) | |||||||
\(444\) | −12.2942 | − | 3.29423i | −0.583458 | − | 0.156337i | ||||
\(445\) | −18.3923 | + | 9.19615i | −0.871879 | + | 0.435939i | ||||
\(446\) | −8.59808 | + | 4.96410i | −0.407131 | + | 0.235057i | ||||
\(447\) | 5.78461i | 0.273603i | ||||||||
\(448\) | −11.4641 | + | 9.92820i | −0.541628 | + | 0.469064i | ||||
\(449\) | − | 1.58846i | − | 0.0749639i | −0.999297 | − | 0.0374820i | \(-0.988066\pi\) | ||
0.999297 | − | 0.0374820i | \(-0.0119337\pi\) | |||||||
\(450\) | −28.6865 | + | 4.09808i | −1.35230 | + | 0.193185i | ||||
\(451\) | −12.0000 | + | 6.92820i | −0.565058 | + | 0.326236i | ||||
\(452\) | −12.2942 | + | 3.29423i | −0.578272 | + | 0.154947i | ||||
\(453\) | 4.09808 | + | 7.09808i | 0.192544 | + | 0.333497i | ||||
\(454\) | −14.5622 | + | 25.2224i | −0.683437 | + | 1.18375i | ||||
\(455\) | 8.73205 | + | 21.1244i | 0.409365 | + | 0.990325i | ||||
\(456\) | −2.83013 | − | 0.758330i | −0.132533 | − | 0.0355121i | ||||
\(457\) | −7.33975 | − | 7.33975i | −0.343339 | − | 0.343339i | 0.514282 | − | 0.857621i | \(-0.328058\pi\) |
−0.857621 | + | 0.514282i | \(0.828058\pi\) | |||||||
\(458\) | 2.33013 | − | 8.69615i | 0.108880 | − | 0.406345i | ||||
\(459\) | 14.1962 | + | 3.80385i | 0.662620 | + | 0.177548i | ||||
\(460\) | 13.7942 | − | 12.2321i | 0.643159 | − | 0.570322i | ||||
\(461\) | 1.03590 | − | 0.598076i | 0.0482466 | − | 0.0278552i | −0.475683 | − | 0.879617i | \(-0.657799\pi\) |
0.523929 | + | 0.851762i | \(0.324466\pi\) | |||||||
\(462\) | −43.5167 | + | 21.1244i | −2.02458 | + | 0.982794i | ||||
\(463\) | −9.42820 | − | 35.1865i | −0.438166 | − | 1.63526i | −0.733375 | − | 0.679824i | \(-0.762056\pi\) |
0.295209 | − | 0.955433i | \(-0.404611\pi\) | |||||||
\(464\) | 26.7846 | − | 15.4641i | 1.24344 | − | 0.717903i | ||||
\(465\) | 0.339746 | + | 0.679492i | 0.0157553 | + | 0.0315107i | ||||
\(466\) | 11.8301 | − | 20.4904i | 0.548020 | − | 0.949199i | ||||
\(467\) | 3.47372 | + | 12.9641i | 0.160745 | + | 0.599907i | 0.998545 | + | 0.0539300i | \(0.0171748\pi\) |
−0.837800 | + | 0.545977i | \(0.816159\pi\) | |||||||
\(468\) | 14.1962 | − | 14.1962i | 0.656217 | − | 0.656217i | ||||
\(469\) | −0.241670 | + | 3.36603i | −0.0111593 | + | 0.155429i | ||||
\(470\) | 47.3827 | + | 31.2846i | 2.18560 | + | 1.44305i | ||||
\(471\) | −0.633975 | − | 2.36603i | −0.0292120 | − | 0.109021i | ||||
\(472\) | −1.26795 | + | 1.26795i | −0.0583621 | + | 0.0583621i | ||||
\(473\) | 6.00000 | − | 6.00000i | 0.275880 | − | 0.275880i | ||||
\(474\) | 3.92820 | + | 14.6603i | 0.180428 | + | 0.673368i | ||||
\(475\) | −16.2224 | − | 1.95448i | −0.744336 | − | 0.0896778i | ||||
\(476\) | 11.6603 | − | 5.66025i | 0.534447 | − | 0.259437i | ||||
\(477\) | −4.90192 | − | 18.2942i | −0.224444 | − | 0.837635i | ||||
\(478\) | −11.0000 | − | 41.0526i | −0.503128 | − | 1.87770i | ||||
\(479\) | −2.63397 | + | 4.56218i | −0.120349 | + | 0.208451i | −0.919905 | − | 0.392140i | \(-0.871735\pi\) |
0.799556 | + | 0.600591i | \(0.205068\pi\) | |||||||
\(480\) | −27.8827 | − | 9.29423i | −1.27266 | − | 0.424222i | ||||
\(481\) | −14.1962 | + | 8.19615i | −0.647289 | + | 0.373712i | ||||
\(482\) | −4.76795 | − | 17.7942i | −0.217174 | − | 0.810505i | ||||
\(483\) | −21.7583 | − | 1.56218i | −0.990038 | − | 0.0710816i | ||||
\(484\) | 28.2846 | − | 16.3301i | 1.28566 | − | 0.742279i | ||||
\(485\) | 12.0263 | + | 13.5622i | 0.546085 | + | 0.615827i | ||||
\(486\) | 7.79423 | − | 29.0885i | 0.353553 | − | 1.31948i | ||||
\(487\) | 8.68653 | − | 32.4186i | 0.393624 | − | 1.46903i | −0.430486 | − | 0.902597i | \(-0.641658\pi\) |
0.824110 | − | 0.566429i | \(-0.191675\pi\) | |||||||
\(488\) | 4.16987 | + | 4.16987i | 0.188761 | + | 0.188761i | ||||
\(489\) | 15.2942 | + | 4.09808i | 0.691629 | + | 0.185321i | ||||
\(490\) | 30.1865 | − | 1.76795i | 1.36369 | − | 0.0798678i | ||||
\(491\) | 8.46410 | − | 14.6603i | 0.381980 | − | 0.661608i | −0.609366 | − | 0.792889i | \(-0.708576\pi\) |
0.991345 | + | 0.131281i | \(0.0419091\pi\) | |||||||
\(492\) | −3.80385 | − | 6.58846i | −0.171491 | − | 0.297031i | ||||
\(493\) | −18.9282 | + | 5.07180i | −0.852483 | + | 0.228422i | ||||
\(494\) | 21.1244 | − | 12.1962i | 0.950430 | − | 0.548731i | ||||
\(495\) | −30.5885 | − | 20.1962i | −1.37485 | − | 0.907750i | ||||
\(496\) | 0.875644i | 0.0393176i | ||||||||
\(497\) | −10.3923 | − | 12.0000i | −0.466159 | − | 0.538274i | ||||
\(498\) | − | 4.73205i | − | 0.212048i | ||||||
\(499\) | −6.12436 | + | 3.53590i | −0.274164 | + | 0.158289i | −0.630778 | − | 0.775963i | \(-0.717264\pi\) |
0.356615 | + | 0.934252i | \(0.383931\pi\) | |||||||
\(500\) | −19.0526 | − | 3.46410i | −0.852056 | − | 0.154919i | ||||
\(501\) | 23.4282 | + | 6.27757i | 1.04669 | + | 0.280461i | ||||
\(502\) | −8.00000 | + | 8.00000i | −0.357057 | + | 0.357057i | ||||
\(503\) | −10.0718 | − | 10.0718i | −0.449079 | − | 0.449079i | 0.445969 | − | 0.895048i | \(-0.352859\pi\) |
−0.895048 | + | 0.445969i | \(0.852859\pi\) | |||||||
\(504\) | 1.79423 | + | 3.69615i | 0.0799213 | + | 0.164640i | ||||
\(505\) | 17.5885 | + | 35.1769i | 0.782676 | + | 1.56535i | ||||
\(506\) | 50.2487 | 2.23383 | ||||||||
\(507\) | − | 3.33975i | − | 0.148323i | ||||||
\(508\) | 27.2942 | − | 27.2942i | 1.21099 | − | 1.21099i | ||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | 17.6603 | + | 11.6603i | 0.782009 | + | 0.516325i | ||||
\(511\) | −21.7583 | + | 10.5622i | −0.962532 | + | 0.467243i | ||||
\(512\) | −20.6865 | − | 20.6865i | −0.914224 | − | 0.914224i | ||||
\(513\) | 8.49038 | − | 14.7058i | 0.374859 | − | 0.649276i | ||||
\(514\) | −12.0263 | − | 20.8301i | −0.530456 | − | 0.918778i | ||||
\(515\) | 6.86603 | − | 6.08846i | 0.302553 | − | 0.268289i | ||||
\(516\) | 3.29423 | + | 3.29423i | 0.145020 | + | 0.145020i | ||||
\(517\) | 18.5885 | + | 69.3731i | 0.817519 | + | 3.05102i | ||||
\(518\) | 4.09808 | + | 21.2942i | 0.180059 | + | 0.935615i | ||||
\(519\) | 23.6603 | − | 6.33975i | 1.03857 | − | 0.278284i | ||||
\(520\) | −4.00000 | + | 2.00000i | −0.175412 | + | 0.0877058i | ||||
\(521\) | 37.6244 | − | 21.7224i | 1.64835 | − | 0.951677i | 0.670626 | − | 0.741796i | \(-0.266026\pi\) |
0.977727 | − | 0.209881i | \(-0.0673078\pi\) | |||||||
\(522\) | 10.3923 | + | 38.7846i | 0.454859 | + | 1.69756i | ||||
\(523\) | −4.96410 | + | 1.33013i | −0.217065 | + | 0.0581624i | −0.365713 | − | 0.930728i | \(-0.619175\pi\) |
0.148648 | + | 0.988890i | \(0.452508\pi\) | |||||||
\(524\) | −4.39230 | − | 7.60770i | −0.191879 | − | 0.332344i | ||||
\(525\) | 12.8205 | + | 18.9904i | 0.559533 | + | 0.828808i | ||||
\(526\) | −27.4545 | + | 47.5526i | −1.19707 | + | 2.07339i | ||||
\(527\) | 0.143594 | − | 0.535898i | 0.00625503 | − | 0.0233441i | ||||
\(528\) | −21.1244 | − | 36.5885i | −0.919320 | − | 1.59231i | ||||
\(529\) | −0.294229 | − | 0.169873i | −0.0127925 | − | 0.00738578i | ||||
\(530\) | 1.63397 | − | 27.2224i | 0.0709753 | − | 1.18247i | ||||
\(531\) | −5.19615 | − | 9.00000i | −0.225494 | − | 0.390567i | ||||
\(532\) | −2.83013 | − | 14.7058i | −0.122702 | − | 0.637576i | ||||
\(533\) | −9.46410 | − | 2.53590i | −0.409936 | − | 0.109842i | ||||
\(534\) | 7.96410 | − | 29.7224i | 0.344640 | − | 1.28622i | ||||
\(535\) | 5.19615 | + | 1.73205i | 0.224649 | + | 0.0748831i | ||||
\(536\) | −0.660254 | −0.0285186 | ||||||||
\(537\) | 21.8038i | 0.940905i | ||||||||
\(538\) | −4.96410 | + | 18.5263i | −0.214018 | + | 0.798725i | ||||
\(539\) | 30.0526 | + | 23.6603i | 1.29446 | + | 1.01912i | ||||
\(540\) | 11.0885 | − | 16.7942i | 0.477171 | − | 0.722709i | ||||
\(541\) | 4.96410 | − | 8.59808i | 0.213423 | − | 0.369660i | −0.739360 | − | 0.673310i | \(-0.764872\pi\) |
0.952784 | + | 0.303650i | \(0.0982053\pi\) | |||||||
\(542\) | 5.73205 | + | 21.3923i | 0.246213 | + | 0.918878i | ||||
\(543\) | 17.1962 | + | 9.92820i | 0.737958 | + | 0.426060i | ||||
\(544\) | 10.7321 | + | 18.5885i | 0.460133 | + | 0.796974i | ||||
\(545\) | 4.46410 | + | 0.267949i | 0.191221 | + | 0.0114777i | ||||
\(546\) | −32.3205 | − | 11.1962i | −1.38319 | − | 0.479151i | ||||
\(547\) | 3.31347 | − | 12.3660i | 0.141674 | − | 0.528733i | −0.858207 | − | 0.513303i | \(-0.828422\pi\) |
0.999881 | − | 0.0154299i | \(-0.00491169\pi\) | |||||||
\(548\) | −0.928203 | − | 3.46410i | −0.0396509 | − | 0.147979i | ||||
\(549\) | −29.5981 | + | 17.0885i | −1.26322 | + | 0.729318i | ||||
\(550\) | −32.5885 | − | 41.5167i | −1.38958 | − | 1.77028i | ||||
\(551\) | 22.6410i | 0.964540i | ||||||||
\(552\) | − | 4.26795i | − | 0.181656i | ||||||
\(553\) | 9.07180 | − | 7.85641i | 0.385772 | − | 0.334088i | ||||
\(554\) | −33.5885 | − | 19.3923i | −1.42704 | − | 0.823900i | ||||
\(555\) | −12.2942 | + | 10.9019i | −0.521861 | + | 0.462761i | ||||
\(556\) | 10.3923 | + | 6.00000i | 0.440732 | + | 0.254457i | ||||
\(557\) | 4.09808 | − | 15.2942i | 0.173641 | − | 0.648037i | −0.823138 | − | 0.567841i | \(-0.807779\pi\) |
0.996779 | − | 0.0801960i | \(-0.0255546\pi\) | |||||||
\(558\) | −1.09808 | − | 0.294229i | −0.0464853 | − | 0.0124557i | ||||
\(559\) | 6.00000 | 0.253773 | ||||||||
\(560\) | 3.42820 | + | 26.1865i | 0.144868 | + | 1.10658i | ||||
\(561\) | 6.92820 | + | 25.8564i | 0.292509 | + | 1.09166i | ||||
\(562\) | 6.86603 | − | 25.6244i | 0.289626 | − | 1.08090i | ||||
\(563\) | −15.1699 | − | 15.1699i | −0.639334 | − | 0.639334i | 0.311057 | − | 0.950391i | \(-0.399317\pi\) |
−0.950391 | + | 0.311057i | \(0.899317\pi\) | |||||||
\(564\) | −38.0885 | + | 10.2058i | −1.60381 | + | 0.429740i | ||||
\(565\) | −5.19615 | + | 15.5885i | −0.218604 | + | 0.655811i | ||||
\(566\) | 43.0526i | 1.80963i | ||||||||
\(567\) | −23.3827 | + | 4.50000i | −0.981981 | + | 0.188982i | ||||
\(568\) | 2.19615 | − | 2.19615i | 0.0921485 | − | 0.0921485i | ||||
\(569\) | − | 18.7846i | − | 0.787492i | −0.919219 | − | 0.393746i | \(-0.871179\pi\) | ||
0.919219 | − | 0.393746i | \(-0.128821\pi\) | |||||||
\(570\) | 18.2942 | − | 16.2224i | 0.766261 | − | 0.679483i | ||||
\(571\) | −20.2487 | −0.847382 | −0.423691 | − | 0.905807i | \(-0.639266\pi\) | ||||
−0.423691 | + | 0.905807i | \(0.639266\pi\) | |||||||
\(572\) | 35.3205 | + | 9.46410i | 1.47682 | + | 0.395714i | ||||
\(573\) | −15.2942 | + | 26.4904i | −0.638926 | + | 1.10665i | ||||
\(574\) | −7.26795 | + | 10.7321i | −0.303358 | + | 0.447947i | ||||
\(575\) | −3.36603 | − | 23.5622i | −0.140373 | − | 0.982611i | ||||
\(576\) | 14.8923 | − | 8.59808i | 0.620513 | − | 0.358253i | ||||
\(577\) | 4.92820 | + | 1.32051i | 0.205164 | + | 0.0549735i | 0.359937 | − | 0.932977i | \(-0.382798\pi\) |
−0.154773 | + | 0.987950i | \(0.549465\pi\) | |||||||
\(578\) | 4.50000 | + | 16.7942i | 0.187175 | + | 0.698548i | ||||
\(579\) | 9.16987 | + | 34.2224i | 0.381087 | + | 1.42224i | ||||
\(580\) | −1.60770 | + | 26.7846i | −0.0667559 | + | 1.11217i | ||||
\(581\) | −3.36603 | + | 1.63397i | −0.139646 | + | 0.0677887i | ||||
\(582\) | −27.1244 | −1.12434 | ||||||||
\(583\) | 24.3923 | − | 24.3923i | 1.01023 | − | 1.01023i | ||||
\(584\) | −2.36603 | − | 4.09808i | −0.0979068 | − | 0.169580i | ||||
\(585\) | −5.19615 | − | 25.3923i | −0.214834 | − | 1.04984i | ||||
\(586\) | −35.1506 | − | 20.2942i | −1.45206 | − | 0.838347i | ||||
\(587\) | −32.1865 | − | 8.62436i | −1.32848 | − | 0.355965i | −0.476332 | − | 0.879265i | \(-0.658034\pi\) |
−0.852148 | + | 0.523300i | \(0.824701\pi\) | |||||||
\(588\) | −12.9904 | + | 16.5000i | −0.535714 | + | 0.680449i | ||||
\(589\) | −0.555136 | − | 0.320508i | −0.0228740 | − | 0.0132063i | ||||
\(590\) | −3.00000 | − | 14.6603i | −0.123508 | − | 0.603553i | ||||
\(591\) | −41.3205 | + | 11.0718i | −1.69970 | + | 0.455433i | ||||
\(592\) | −18.2942 | + | 4.90192i | −0.751888 | + | 0.201468i | ||||
\(593\) | −2.73205 | + | 0.732051i | −0.112192 | + | 0.0300617i | −0.314478 | − | 0.949265i | \(-0.601830\pi\) |
0.202286 | + | 0.979326i | \(0.435163\pi\) | |||||||
\(594\) | 52.9808 | − | 14.1962i | 2.17383 | − | 0.582475i | ||||
\(595\) | 2.19615 | − | 16.5885i | 0.0900335 | − | 0.680060i | ||||
\(596\) | −2.89230 | − | 5.00962i | −0.118473 | − | 0.205202i | ||||
\(597\) | 13.6077 | 0.556926 | ||||||||
\(598\) | 25.1244 | + | 25.1244i | 1.02741 | + | 1.02741i | ||||
\(599\) | 30.9808i | 1.26584i | 0.774217 | + | 0.632920i | \(0.218144\pi\) | ||||
−0.774217 | + | 0.632920i | \(0.781856\pi\) | |||||||
\(600\) | −3.52628 | + | 2.76795i | −0.143960 | + | 0.113001i | ||||
\(601\) | 20.6603 | − | 11.9282i | 0.842749 | − | 0.486562i | −0.0154485 | − | 0.999881i | \(-0.504918\pi\) |
0.858198 | + | 0.513319i | \(0.171584\pi\) | |||||||
\(602\) | 2.59808 | − | 7.50000i | 0.105890 | − | 0.305677i | ||||
\(603\) | 0.990381 | − | 3.69615i | 0.0403314 | − | 0.150519i | ||||
\(604\) | −7.09808 | − | 4.09808i | −0.288817 | − | 0.166748i | ||||
\(605\) | 2.52628 | − | 42.0885i | 0.102708 | − | 1.71114i | ||||
\(606\) | −56.8468 | − | 15.2321i | −2.30924 | − | 0.618760i | ||||
\(607\) | −4.09808 | − | 1.09808i | −0.166336 | − | 0.0445695i | 0.174690 | − | 0.984623i | \(-0.444108\pi\) |
−0.341026 | + | 0.940054i | \(0.610774\pi\) | |||||||
\(608\) | 23.9545 | − | 6.41858i | 0.971483 | − | 0.260308i | ||||
\(609\) | 24.0000 | − | 20.7846i | 0.972529 | − | 0.842235i | ||||
\(610\) | −48.2128 | + | 9.86603i | −1.95208 | + | 0.399464i | ||||
\(611\) | −25.3923 | + | 43.9808i | −1.02726 | + | 1.77927i | ||||
\(612\) | −14.1962 | + | 3.80385i | −0.573845 | + | 0.153761i | ||||
\(613\) | 41.4186 | + | 11.0981i | 1.67288 | + | 0.448247i | 0.965885 | − | 0.258971i | \(-0.0833833\pi\) |
0.706996 | + | 0.707218i | \(0.250050\pi\) | |||||||
\(614\) | −47.9090 | −1.93345 | ||||||||
\(615\) | −9.80385 | − | 0.588457i | −0.395329 | − | 0.0237289i | ||||
\(616\) | −4.19615 | + | 6.19615i | −0.169068 | + | 0.249650i | ||||
\(617\) | −2.09808 | + | 0.562178i | −0.0844654 | + | 0.0226324i | −0.300804 | − | 0.953686i | \(-0.597255\pi\) |
0.216339 | + | 0.976318i | \(0.430588\pi\) | |||||||
\(618\) | 13.7321i | 0.552384i | ||||||||
\(619\) | −12.4904 | + | 21.6340i | −0.502031 | + | 0.869543i | 0.497966 | + | 0.867196i | \(0.334080\pi\) |
−0.999997 | + | 0.00234656i | \(0.999253\pi\) | |||||||
\(620\) | −0.633975 | − | 0.418584i | −0.0254610 | − | 0.0168107i | ||||
\(621\) | 23.8923 | + | 6.40192i | 0.958765 | + | 0.256900i | ||||
\(622\) | 21.8564 | − | 21.8564i | 0.876362 | − | 0.876362i | ||||
\(623\) | −23.8923 | + | 4.59808i | −0.957225 | + | 0.184218i | ||||
\(624\) | 7.73205 | − | 28.8564i | 0.309530 | − | 1.15518i | ||||
\(625\) | −17.2846 | + | 18.0622i | −0.691384 | + | 0.722487i | ||||
\(626\) | 14.1962i | 0.567392i | ||||||||
\(627\) | 30.9282 | 1.23515 | ||||||||
\(628\) | 1.73205 | + | 1.73205i | 0.0691164 | + | 0.0691164i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | −33.9904 | − | 4.50000i | −1.35421 | − | 0.179284i | ||||
\(631\) | 37.3205 | 1.48571 | 0.742853 | − | 0.669455i | \(-0.233472\pi\) | ||||
0.742853 | + | 0.669455i | \(0.233472\pi\) | |||||||
\(632\) | 1.66025 | + | 1.66025i | 0.0660414 | + | 0.0660414i | ||||
\(633\) | 7.73205 | + | 13.3923i | 0.307321 | + | 0.532296i | ||||
\(634\) | − | 23.1244i | − | 0.918385i | ||||||
\(635\) | −9.99038 | − | 48.8205i | −0.396456 | − | 1.93738i | ||||
\(636\) | 13.3923 | + | 13.3923i | 0.531039 | + | 0.531039i | ||||
\(637\) | 3.19615 | + | 26.8564i | 0.126636 | + | 1.06409i | ||||
\(638\) | −51.7128 | + | 51.7128i | −2.04733 | + | 2.04733i | ||||
\(639\) | 9.00000 | + | 15.5885i | 0.356034 | + | 0.616670i | ||||
\(640\) | −8.99038 | + | 1.83975i | −0.355376 | + | 0.0727223i | ||||
\(641\) | 15.7224 | − | 27.2321i | 0.620999 | − | 1.07560i | −0.368301 | − | 0.929706i | \(-0.620061\pi\) |
0.989300 | − | 0.145895i | \(-0.0466061\pi\) | |||||||
\(642\) | −7.09808 | + | 4.09808i | −0.280139 | + | 0.161738i | ||||
\(643\) | 0.696152 | − | 0.186533i | 0.0274536 | − | 0.00735616i | −0.245066 | − | 0.969506i | \(-0.578810\pi\) |
0.272520 | + | 0.962150i | \(0.412143\pi\) | |||||||
\(644\) | 19.6244 | − | 9.52628i | 0.773308 | − | 0.375388i | ||||
\(645\) | 5.89230 | − | 1.20577i | 0.232009 | − | 0.0474772i | ||||
\(646\) | −17.8564 | −0.702551 | ||||||||
\(647\) | 18.8301 | + | 5.04552i | 0.740289 | + | 0.198360i | 0.609206 | − | 0.793012i | \(-0.291488\pi\) |
0.131082 | + | 0.991371i | \(0.458155\pi\) | |||||||
\(648\) | −1.20577 | − | 4.50000i | −0.0473672 | − | 0.176777i | ||||
\(649\) | 9.46410 | − | 16.3923i | 0.371498 | − | 0.643454i | ||||
\(650\) | 4.46410 | − | 37.0526i | 0.175096 | − | 1.45332i | ||||
\(651\) | 0.169873 | + | 0.882686i | 0.00665785 | + | 0.0345952i | ||||
\(652\) | −15.2942 | + | 4.09808i | −0.598968 | + | 0.160493i | ||||
\(653\) | −24.2224 | − | 6.49038i | −0.947897 | − | 0.253988i | −0.248427 | − | 0.968651i | \(-0.579914\pi\) |
−0.699470 | + | 0.714662i | \(0.746580\pi\) | |||||||
\(654\) | −4.73205 | + | 4.73205i | −0.185038 | + | 0.185038i | ||||
\(655\) | −11.3205 | − | 0.679492i | −0.442329 | − | 0.0265499i | ||||
\(656\) | −9.80385 | − | 5.66025i | −0.382776 | − | 0.220996i | ||||
\(657\) | 26.4904 | − | 7.09808i | 1.03349 | − | 0.276922i | ||||
\(658\) | 43.9808 | + | 50.7846i | 1.71455 | + | 1.97979i | ||||
\(659\) | −22.5167 | + | 13.0000i | −0.877125 | + | 0.506408i | −0.869709 | − | 0.493564i | \(-0.835694\pi\) |
−0.00741531 | + | 0.999973i | \(0.502360\pi\) | |||||||
\(660\) | 36.5885 | + | 2.19615i | 1.42420 | + | 0.0854851i | ||||
\(661\) | 11.0000i | 0.427850i | 0.976850 | + | 0.213925i | \(0.0686249\pi\) | ||||
−0.976850 | + | 0.213925i | \(0.931375\pi\) | |||||||
\(662\) | −25.0526 | − | 25.0526i | −0.973695 | − | 0.973695i | ||||
\(663\) | −9.46410 | + | 16.3923i | −0.367555 | + | 0.636624i | ||||
\(664\) | −0.366025 | − | 0.633975i | −0.0142045 | − | 0.0246030i | ||||
\(665\) | −17.8564 | − | 7.41154i | −0.692442 | − | 0.287407i | ||||
\(666\) | − | 24.5885i | − | 0.952783i | ||||||
\(667\) | −31.8564 | + | 8.53590i | −1.23348 | + | 0.330511i | ||||
\(668\) | −23.4282 | + | 6.27757i | −0.906464 | + | 0.242886i | ||||
\(669\) | −6.29423 | − | 6.29423i | −0.243349 | − | 0.243349i | ||||
\(670\) | 3.03590 | − | 4.59808i | 0.117287 | − | 0.177639i | ||||
\(671\) | −53.9090 | − | 31.1244i | −2.08113 | − | 1.20154i | ||||
\(672\) | −28.7942 | − | 19.5000i | −1.11076 | − | 0.752229i | ||||
\(673\) | 25.8564 | + | 6.92820i | 0.996691 | + | 0.267063i | 0.720059 | − | 0.693913i | \(-0.244115\pi\) |
0.276633 | + | 0.960976i | \(0.410782\pi\) | |||||||
\(674\) | −7.73205 | − | 4.46410i | −0.297827 | − | 0.171951i | ||||
\(675\) | −10.2058 | − | 23.8923i | −0.392820 | − | 0.919615i | ||||
\(676\) | 1.66987 | + | 2.89230i | 0.0642259 | + | 0.111242i | ||||
\(677\) | 35.9090 | − | 35.9090i | 1.38009 | − | 1.38009i | 0.535660 | − | 0.844434i | \(-0.320063\pi\) |
0.844434 | − | 0.535660i | \(-0.179937\pi\) | |||||||
\(678\) | −12.2942 | − | 21.2942i | −0.472157 | − | 0.817800i | ||||
\(679\) | 9.36603 | + | 19.2942i | 0.359435 | + | 0.740445i | ||||
\(680\) | 3.26795 | + | 0.196152i | 0.125320 | + | 0.00752210i | ||||
\(681\) | −25.2224 | − | 6.75833i | −0.966526 | − | 0.258980i | ||||
\(682\) | −0.535898 | − | 2.00000i | −0.0205206 | − | 0.0765840i | ||||
\(683\) | 14.9641 | + | 4.00962i | 0.572585 | + | 0.153424i | 0.533482 | − | 0.845811i | \(-0.320883\pi\) |
0.0391034 | + | 0.999235i | \(0.487550\pi\) | |||||||
\(684\) | 16.9808i | 0.649276i | ||||||||
\(685\) | −4.39230 | − | 1.46410i | −0.167821 | − | 0.0559404i | ||||
\(686\) | 34.9545 | + | 7.63397i | 1.33457 | + | 0.291467i | ||||
\(687\) | 8.07180 | 0.307958 | ||||||||
\(688\) | 6.69615 | + | 1.79423i | 0.255288 | + | 0.0684043i | ||||
\(689\) | 24.3923 | 0.929273 | ||||||||
\(690\) | 29.7224 | + | 19.6244i | 1.13151 | + | 0.747086i | ||||
\(691\) | 10.5885i | 0.402804i | 0.979509 | + | 0.201402i | \(0.0645497\pi\) | ||||
−0.979509 | + | 0.201402i | \(0.935450\pi\) | |||||||
\(692\) | −17.3205 | + | 17.3205i | −0.658427 | + | 0.658427i | ||||
\(693\) | −28.3923 | − | 32.7846i | −1.07853 | − | 1.24538i | ||||
\(694\) | 40.5167i | 1.53799i | ||||||||
\(695\) | 13.8564 | − | 6.92820i | 0.525603 | − | 0.262802i | ||||
\(696\) | 4.39230 | + | 4.39230i | 0.166490 | + | 0.166490i | ||||
\(697\) | 5.07180 | + | 5.07180i | 0.192108 | + | 0.192108i | ||||
\(698\) | −17.0622 | + | 63.6769i | −0.645813 | + | 2.41021i | ||||
\(699\) | 20.4904 | + | 5.49038i | 0.775017 | + | 0.207665i | ||||
\(700\) | −20.5981 | − | 10.0359i | −0.778534 | − | 0.379321i | ||||
\(701\) | −47.4641 | −1.79269 | −0.896347 | − | 0.443353i | \(-0.853789\pi\) | ||||
−0.896347 | + | 0.443353i | \(0.853789\pi\) | |||||||
\(702\) | 33.5885 | + | 19.3923i | 1.26771 | + | 0.731915i | ||||
\(703\) | 3.58846 | − | 13.3923i | 0.135341 | − | 0.505100i | ||||
\(704\) | 27.1244 | + | 15.6603i | 1.02229 | + | 0.590218i | ||||
\(705\) | −16.0981 | + | 48.2942i | −0.606289 | + | 1.81887i | ||||
\(706\) | 18.5885 | + | 10.7321i | 0.699586 | + | 0.403906i | ||||
\(707\) | 8.79423 | + | 45.6962i | 0.330741 | + | 1.71858i | ||||
\(708\) | 9.00000 | + | 5.19615i | 0.338241 | + | 0.195283i | ||||
\(709\) | 6.71281i | 0.252105i | 0.992024 | + | 0.126052i | \(0.0402308\pi\) | ||||
−0.992024 | + | 0.126052i | \(0.959769\pi\) | |||||||
\(710\) | 5.19615 | + | 25.3923i | 0.195008 | + | 0.952956i | ||||
\(711\) | −11.7846 | + | 6.80385i | −0.441957 | + | 0.255164i | ||||
\(712\) | −1.23205 | − | 4.59808i | −0.0461731 | − | 0.172320i | ||||
\(713\) | 0.241670 | − | 0.901924i | 0.00905060 | − | 0.0337773i | ||||
\(714\) | 16.3923 | + | 18.9282i | 0.613467 | + | 0.708370i | ||||
\(715\) | 35.3205 | − | 31.3205i | 1.32091 | − | 1.17132i | ||||
\(716\) | −10.9019 | − | 18.8827i | −0.407424 | − | 0.705679i | ||||
\(717\) | 33.0000 | − | 19.0526i | 1.23241 | − | 0.711531i | ||||
\(718\) | 10.3660 | + | 38.6865i | 0.386857 | + | 1.44377i | ||||
\(719\) | −15.5622 | + | 26.9545i | −0.580371 | + | 1.00523i | 0.415064 | + | 0.909792i | \(0.363759\pi\) |
−0.995435 | + | 0.0954403i | \(0.969574\pi\) | |||||||
\(720\) | 1.79423 | − | 29.8923i | 0.0668670 | − | 1.11402i | ||||
\(721\) | 9.76795 | − | 4.74167i | 0.363777 | − | 0.176589i | ||||
\(722\) | 4.16025 | − | 15.5263i | 0.154829 | − | 0.577828i | ||||
\(723\) | 14.3038 | − | 8.25833i | 0.531966 | − | 0.307131i | ||||
\(724\) | −19.8564 | −0.737958 | ||||||||
\(725\) | 27.7128 | + | 20.7846i | 1.02923 | + | 0.771921i | ||||
\(726\) | 44.6147 | + | 44.6147i | 1.65581 | + | 1.65581i | ||||
\(727\) | 5.13397 | + | 1.37564i | 0.190409 | + | 0.0510198i | 0.352763 | − | 0.935713i | \(-0.385242\pi\) |
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(728\) | −5.19615 | + | 1.00000i | −0.192582 | + | 0.0370625i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 39.4186 | + | 2.36603i | 1.45895 | + | 0.0875705i | ||||
\(731\) | −3.80385 | − | 2.19615i | −0.140690 | − | 0.0812276i | ||||
\(732\) | 17.0885 | − | 29.5981i | 0.631608 | − | 1.09398i | ||||
\(733\) | −5.73205 | + | 21.3923i | −0.211718 | + | 0.790143i | 0.775578 | + | 0.631252i | \(0.217459\pi\) |
−0.987296 | + | 0.158891i | \(0.949208\pi\) | |||||||
\(734\) | −6.59808 | + | 11.4282i | −0.243539 | + | 0.421823i | ||||
\(735\) | 8.53590 | + | 25.7321i | 0.314851 | + | 0.949141i | ||||
\(736\) | 18.0622 | + | 31.2846i | 0.665781 | + | 1.15317i | ||||
\(737\) | 6.73205 | − | 1.80385i | 0.247978 | − | 0.0664456i | ||||
\(738\) | 10.3923 | − | 10.3923i | 0.382546 | − | 0.382546i | ||||
\(739\) | 21.1244 | − | 12.1962i | 0.777072 | − | 0.448643i | −0.0583196 | − | 0.998298i | \(-0.518574\pi\) |
0.835392 | + | 0.549655i | \(0.185241\pi\) | |||||||
\(740\) | 5.19615 | − | 15.5885i | 0.191014 | − | 0.573043i | ||||
\(741\) | 15.4641 | + | 15.4641i | 0.568088 | + | 0.568088i | ||||
\(742\) | 10.5622 | − | 30.4904i | 0.387750 | − | 1.11934i | ||||
\(743\) | −2.36603 | − | 8.83013i | −0.0868011 | − | 0.323946i | 0.908848 | − | 0.417127i | \(-0.136963\pi\) |
−0.995649 | + | 0.0931813i | \(0.970296\pi\) | |||||||
\(744\) | −0.169873 | + | 0.0455173i | −0.00622785 | + | 0.00166875i | ||||
\(745\) | −7.45448 | − | 0.447441i | −0.273111 | − | 0.0163930i | ||||
\(746\) | 4.09808 | + | 7.09808i | 0.150041 | + | 0.259879i | ||||
\(747\) | 4.09808 | − | 1.09808i | 0.149941 | − | 0.0401765i | ||||
\(748\) | −18.9282 | − | 18.9282i | −0.692084 | − | 0.692084i | ||||
\(749\) | 5.36603 | + | 3.63397i | 0.196070 | + | 0.132783i | ||||
\(750\) | −3.06218 | − | 37.2846i | −0.111815 | − | 1.36144i | ||||
\(751\) | 23.5622 | + | 40.8109i | 0.859796 | + | 1.48921i | 0.872123 | + | 0.489286i | \(0.162743\pi\) |
−0.0123270 | + | 0.999924i | \(0.503924\pi\) | |||||||
\(752\) | −41.4904 | + | 41.4904i | −1.51300 | + | 1.51300i | ||||
\(753\) | −8.78461 | − | 5.07180i | −0.320129 | − | 0.184827i | ||||
\(754\) | −51.7128 | −1.88327 | ||||||||
\(755\) | −9.46410 | + | 4.73205i | −0.344434 | + | 0.172217i | ||||
\(756\) | 18.0000 | − | 15.5885i | 0.654654 | − | 0.566947i | ||||
\(757\) | −8.26795 | − | 8.26795i | −0.300504 | − | 0.300504i | 0.540707 | − | 0.841211i | \(-0.318157\pi\) |
−0.841211 | + | 0.540707i | \(0.818157\pi\) | |||||||
\(758\) | −17.1244 | + | 17.1244i | −0.621985 | + | 0.621985i | ||||
\(759\) | 11.6603 | + | 43.5167i | 0.423240 | + | 1.57955i | ||||
\(760\) | 1.19615 | − | 3.58846i | 0.0433890 | − | 0.130167i | ||||
\(761\) | 16.9641 | − | 9.79423i | 0.614948 | − | 0.355041i | −0.159951 | − | 0.987125i | \(-0.551134\pi\) |
0.774900 | + | 0.632084i | \(0.217800\pi\) | |||||||
\(762\) | 64.5788 | + | 37.2846i | 2.33944 | + | 1.35068i | ||||
\(763\) | 5.00000 | + | 1.73205i | 0.181012 | + | 0.0627044i | ||||
\(764\) | − | 30.5885i | − | 1.10665i | ||||||
\(765\) | −6.00000 | + | 18.0000i | −0.216930 | + | 0.650791i | ||||
\(766\) | −27.3564 | + | 15.7942i | −0.988427 | + | 0.570669i | ||||
\(767\) | 12.9282 | − | 3.46410i | 0.466810 | − | 0.125081i | ||||
\(768\) | 16.7942 | − | 29.0885i | 0.606010 | − | 1.04964i | ||||
\(769\) | 7.99038 | − | 13.8397i | 0.288141 | − | 0.499074i | −0.685225 | − | 0.728331i | \(-0.740296\pi\) |
0.973366 | + | 0.229257i | \(0.0736296\pi\) | |||||||
\(770\) | −23.8564 | − | 57.7128i | −0.859725 | − | 2.07983i | ||||
\(771\) | 15.2487 | − | 15.2487i | 0.549169 | − | 0.549169i | ||||
\(772\) | −25.0526 | − | 25.0526i | −0.901661 | − | 0.901661i | ||||
\(773\) | −1.88269 | + | 7.02628i | −0.0677155 | + | 0.252718i | −0.991483 | − | 0.130236i | \(-0.958426\pi\) |
0.923768 | + | 0.382954i | \(0.125093\pi\) | |||||||
\(774\) | −4.50000 | + | 7.79423i | −0.161749 | + | 0.280158i | ||||
\(775\) | −0.901924 | + | 0.385263i | −0.0323981 | + | 0.0138391i | ||||
\(776\) | −3.63397 | + | 2.09808i | −0.130452 | + | 0.0753165i | ||||
\(777\) | −17.4904 | + | 8.49038i | −0.627464 | + | 0.304591i | ||||
\(778\) | −0.598076 | − | 2.23205i | −0.0214421 | − | 0.0800229i | ||||
\(779\) | 7.17691 | − | 4.14359i | 0.257140 | − | 0.148460i | ||||
\(780\) | 17.1962 | + | 19.3923i | 0.615721 | + | 0.694356i | ||||
\(781\) | −16.3923 | + | 28.3923i | −0.586563 | + | 1.01596i | ||||
\(782\) | −6.73205 | − | 25.1244i | −0.240738 | − | 0.898445i | ||||
\(783\) | −31.1769 | + | 18.0000i | −1.11417 | + | 0.643268i | ||||
\(784\) | −4.46410 | + | 30.9282i | −0.159432 | + | 1.10458i | ||||
\(785\) | 3.09808 | − | 0.633975i | 0.110575 | − | 0.0226275i | ||||
\(786\) | 12.0000 | − | 12.0000i | 0.428026 | − | 0.428026i | ||||
\(787\) | 11.2942 | − | 11.2942i | 0.402596 | − | 0.402596i | −0.476551 | − | 0.879147i | \(-0.658113\pi\) |
0.879147 | + | 0.476551i | \(0.158113\pi\) | |||||||
\(788\) | 30.2487 | − | 30.2487i | 1.07757 | − | 1.07757i | ||||
\(789\) | −47.5526 | − | 12.7417i | −1.69292 | − | 0.453615i | ||||
\(790\) | −19.1962 | + | 3.92820i | −0.682968 | + | 0.139759i | ||||
\(791\) | −10.9019 | + | 16.0981i | −0.387628 | + | 0.572382i | ||||
\(792\) | 6.00000 | − | 6.00000i | 0.213201 | − | 0.213201i | ||||
\(793\) | −11.3923 | − | 42.5167i | −0.404553 | − | 1.50981i | ||||
\(794\) | 32.7846 | − | 56.7846i | 1.16348 | − | 2.01521i | ||||
\(795\) | 23.9545 | − | 4.90192i | 0.849578 | − | 0.173853i | ||||
\(796\) | −11.7846 | + | 6.80385i | −0.417694 | + | 0.241156i | ||||
\(797\) | −10.0788 | − | 37.6147i | −0.357011 | − | 1.33238i | −0.877935 | − | 0.478780i | \(-0.841079\pi\) |
0.520924 | − | 0.853603i | \(-0.325587\pi\) | |||||||
\(798\) | 26.0263 | − | 12.6340i | 0.921320 | − | 0.447238i | ||||
\(799\) | 32.1962 | − | 18.5885i | 1.13902 | − | 0.657612i | ||||
\(800\) | 14.1340 | − | 35.2128i | 0.499711 | − | 1.24496i | ||||
\(801\) | 27.5885 | 0.974790 | ||||||||
\(802\) | −11.6962 | + | 43.6506i | −0.413005 | + | 1.54136i | ||||
\(803\) | 35.3205 | + | 35.3205i | 1.24643 | + | 1.24643i | ||||
\(804\) | 0.990381 | + | 3.69615i | 0.0349280 | + | 0.130353i | ||||
\(805\) | 3.69615 | − | 27.9186i | 0.130272 | − | 0.984001i | ||||
\(806\) | 0.732051 | − | 1.26795i | 0.0257854 | − | 0.0446616i | ||||
\(807\) | −17.1962 | −0.605333 | ||||||||
\(808\) | −8.79423 | + | 2.35641i | −0.309380 | + | 0.0828981i | ||||
\(809\) | −36.4019 | + | 21.0167i | −1.27982 | + | 0.738906i | −0.976816 | − | 0.214082i | \(-0.931324\pi\) |
−0.303008 | + | 0.952988i | \(0.597991\pi\) | |||||||
\(810\) | 36.8827 | + | 12.2942i | 1.29593 | + | 0.431975i | ||||
\(811\) | 1.85641i | 0.0651872i | 0.999469 | + | 0.0325936i | \(0.0103767\pi\) | ||||
−0.999469 | + | 0.0325936i | \(0.989623\pi\) | |||||||
\(812\) | −10.3923 | + | 30.0000i | −0.364698 | + | 1.05279i | ||||
\(813\) | −17.1962 | + | 9.92820i | −0.603095 | + | 0.348197i | ||||
\(814\) | 38.7846 | − | 22.3923i | 1.35940 | − | 0.784850i | ||||
\(815\) | −6.46410 | + | 19.3923i | −0.226428 | + | 0.679283i | ||||
\(816\) | −15.4641 | + | 15.4641i | −0.541352 | + | 0.541352i | ||||
\(817\) | −3.58846 | + | 3.58846i | −0.125544 | + | 0.125544i | ||||
\(818\) | 7.36603 | + | 7.36603i | 0.257547 | + | 0.257547i | ||||
\(819\) | 2.19615 | − | 30.5885i | 0.0767398 | − | 1.06885i | ||||
\(820\) | 8.78461 | − | 4.39230i | 0.306772 | − | 0.153386i | ||||
\(821\) | −24.6603 | −0.860649 | −0.430324 | − | 0.902674i | \(-0.641601\pi\) | ||||
−0.430324 | + | 0.902674i | \(0.641601\pi\) | |||||||
\(822\) | 6.00000 | − | 3.46410i | 0.209274 | − | 0.120824i | ||||
\(823\) | −14.0718 | + | 14.0718i | −0.490512 | + | 0.490512i | −0.908468 | − | 0.417956i | \(-0.862747\pi\) |
0.417956 | + | 0.908468i | \(0.362747\pi\) | |||||||
\(824\) | 1.06218 | + | 1.83975i | 0.0370027 | + | 0.0640906i | ||||
\(825\) | 28.3923 | − | 37.8564i | 0.988493 | − | 1.31799i | ||||
\(826\) | 1.26795 | − | 17.6603i | 0.0441176 | − | 0.614479i | ||||
\(827\) | 21.3923 | + | 21.3923i | 0.743883 | + | 0.743883i | 0.973323 | − | 0.229440i | \(-0.0736893\pi\) |
−0.229440 | + | 0.973323i | \(0.573689\pi\) | |||||||
\(828\) | −23.8923 | + | 6.40192i | −0.830315 | + | 0.222482i | ||||
\(829\) | −22.1603 | − | 38.3827i | −0.769657 | − | 1.33309i | −0.937749 | − | 0.347314i | \(-0.887094\pi\) |
0.168091 | − | 0.985771i | \(-0.446240\pi\) | |||||||
\(830\) | 6.09808 | + | 0.366025i | 0.211667 | + | 0.0127049i | ||||
\(831\) | 9.00000 | − | 33.5885i | 0.312207 | − | 1.16517i | ||||
\(832\) | 5.73205 | + | 21.3923i | 0.198723 | + | 0.741645i | ||||
\(833\) | 7.80385 | − | 18.1962i | 0.270387 | − | 0.630459i | ||||
\(834\) | −6.00000 | + | 22.3923i | −0.207763 | + | 0.775382i | ||||
\(835\) | −9.90192 | + | 29.7058i | −0.342670 | + | 1.02801i | ||||
\(836\) | −26.7846 | + | 15.4641i | −0.926365 | + | 0.534837i | ||||
\(837\) | − | 1.01924i | − | 0.0352300i | ||||||
\(838\) | −14.9282 | + | 4.00000i | −0.515686 | + | 0.138178i | ||||
\(839\) | 0.0262794 | + | 0.0455173i | 0.000907267 | + | 0.00157143i | 0.866479 | − | 0.499214i | \(-0.166378\pi\) |
−0.865571 | + | 0.500786i | \(0.833045\pi\) | |||||||
\(840\) | −4.90192 | + | 2.02628i | −0.169132 | + | 0.0699133i | ||||
\(841\) | 9.50000 | − | 16.4545i | 0.327586 | − | 0.567396i | ||||
\(842\) | −11.5263 | + | 43.0167i | −0.397222 | + | 1.48245i | ||||
\(843\) | 23.7846 | 0.819185 | ||||||||
\(844\) | −13.3923 | − | 7.73205i | −0.460982 | − | 0.266148i | ||||
\(845\) | 4.30385 | + | 0.258330i | 0.148057 | + | 0.00888683i | ||||
\(846\) | −38.0885 | − | 65.9711i | −1.30951 | − | 2.26813i | ||||
\(847\) | 16.3301 | − | 47.1410i | 0.561110 | − | 1.61978i | ||||
\(848\) | 27.2224 | + | 7.29423i | 0.934822 | + | 0.250485i | ||||
\(849\) | −37.2846 | + | 9.99038i | −1.27960 | + | 0.342869i | ||||
\(850\) | −16.3923 | + | 21.8564i | −0.562251 | + | 0.749669i | ||||
\(851\) | 20.1962 | 0.692315 | ||||||||
\(852\) | −15.5885 | − | 9.00000i | −0.534052 | − | 0.308335i | ||||
\(853\) | 10.8564 | − | 40.5167i | 0.371716 | − | 1.38726i | −0.486368 | − | 0.873754i | \(-0.661678\pi\) |
0.858084 | − | 0.513510i | \(-0.171655\pi\) | |||||||
\(854\) | −58.0788 | − | 4.16987i | −1.98742 | − | 0.142690i | ||||
\(855\) | 18.2942 | + | 12.0788i | 0.625649 | + | 0.413088i | ||||
\(856\) | −0.633975 | + | 1.09808i | −0.0216688 | + | 0.0375315i | ||||
\(857\) | 7.70577 | + | 28.7583i | 0.263224 | + | 0.982366i | 0.963328 | + | 0.268325i | \(0.0864702\pi\) |
−0.700104 | + | 0.714041i | \(0.746863\pi\) | |||||||
\(858\) | 70.6410i | 2.41164i | ||||||||
\(859\) | −21.4904 | − | 37.2224i | −0.733242 | − | 1.27001i | −0.955490 | − | 0.295023i | \(-0.904673\pi\) |
0.222248 | − | 0.974990i | \(-0.428661\pi\) | |||||||
\(860\) | −4.50000 | + | 3.99038i | −0.153449 | + | 0.136071i | ||||
\(861\) | −10.9808 | − | 3.80385i | −0.374223 | − | 0.129635i | ||||
\(862\) | 12.0981 | − | 45.1506i | 0.412062 | − | 1.53784i | ||||
\(863\) | −6.54552 | − | 24.4282i | −0.222812 | − | 0.831546i | −0.983269 | − | 0.182158i | \(-0.941692\pi\) |
0.760457 | − | 0.649388i | \(-0.224975\pi\) | |||||||
\(864\) | 27.8827 | + | 27.8827i | 0.948588 | + | 0.948588i | ||||
\(865\) | 6.33975 | + | 30.9808i | 0.215558 | + | 1.05338i | ||||
\(866\) | 26.7846i | 0.910178i | ||||||||
\(867\) | −13.5000 | + | 7.79423i | −0.458484 | + | 0.264706i | ||||
\(868\) | −0.588457 | − | 0.679492i | −0.0199735 | − | 0.0230635i | ||||
\(869\) | −21.4641 | − | 12.3923i | −0.728120 | − | 0.420380i | ||||
\(870\) | −50.7846 | + | 10.3923i | −1.72176 | + | 0.352332i | ||||
\(871\) | 4.26795 | + | 2.46410i | 0.144614 | + | 0.0834929i | ||||
\(872\) | −0.267949 | + | 1.00000i | −0.00907390 | + | 0.0338643i | ||||
\(873\) | −6.29423 | − | 23.4904i | −0.213027 | − | 0.795029i | ||||
\(874\) | −30.0526 | −1.01654 | ||||||||
\(875\) | −25.4641 | + | 15.0526i | −0.860844 | + | 0.508869i | ||||
\(876\) | −19.3923 | + | 19.3923i | −0.655205 | + | 0.655205i | ||||
\(877\) | 3.09808 | − | 11.5622i | 0.104615 | − | 0.390427i | −0.893687 | − | 0.448692i | \(-0.851890\pi\) |
0.998301 | + | 0.0582648i | \(0.0185568\pi\) | |||||||
\(878\) | −8.00000 | − | 8.00000i | −0.269987 | − | 0.269987i | ||||
\(879\) | 9.41858 | − | 35.1506i | 0.317681 | − | 1.18560i | ||||
\(880\) | 48.7846 | − | 24.3923i | 1.64453 | − | 0.822264i | ||||
\(881\) | 17.7846i | 0.599179i | 0.954068 | + | 0.299589i | \(0.0968497\pi\) | ||||
−0.954068 | + | 0.299589i | \(0.903150\pi\) | |||||||
\(882\) | −37.2846 | − | 15.9904i | −1.25544 | − | 0.538424i | ||||
\(883\) | −24.5429 | + | 24.5429i | −0.825936 | + | 0.825936i | −0.986952 | − | 0.161016i | \(-0.948523\pi\) |
0.161016 | + | 0.986952i | \(0.448523\pi\) | |||||||
\(884\) | − | 18.9282i | − | 0.636624i | ||||||
\(885\) | 12.0000 | − | 6.00000i | 0.403376 | − | 0.201688i | ||||
\(886\) | 1.80385 | 0.0606014 | ||||||||
\(887\) | 17.7942 | + | 4.76795i | 0.597472 | + | 0.160092i | 0.544866 | − | 0.838523i | \(-0.316581\pi\) |
0.0526060 | + | 0.998615i | \(0.483247\pi\) | |||||||
\(888\) | −1.90192 | − | 3.29423i | −0.0638244 | − | 0.110547i | ||||
\(889\) | 4.22243 | − | 58.8109i | 0.141616 | − | 1.97245i | ||||
\(890\) | 37.6865 | + | 12.5622i | 1.26326 | + | 0.421085i | ||||
\(891\) | 24.5885 | + | 42.5885i | 0.823744 | + | 1.42677i | ||||
\(892\) | 8.59808 | + | 2.30385i | 0.287885 | + | 0.0771385i | ||||
\(893\) | −11.1173 | − | 41.4904i | −0.372027 | − | 1.38842i | ||||
\(894\) | 7.90192 | − | 7.90192i | 0.264280 | − | 0.264280i | ||||
\(895\) | −28.0981 | − | 1.68653i | −0.939215 | − | 0.0563746i | ||||
\(896\) | −10.8301 | − | 0.777568i | −0.361809 | − | 0.0259767i | ||||
\(897\) | −15.9282 | + | 27.5885i | −0.531827 | + | 0.921152i | ||||
\(898\) | −2.16987 | + | 2.16987i | −0.0724096 | + | 0.0724096i | ||||
\(899\) | 0.679492 | + | 1.17691i | 0.0226623 | + | 0.0392523i | ||||
\(900\) | 20.7846 | + | 15.5885i | 0.692820 | + | 0.519615i | ||||
\(901\) | −15.4641 | − | 8.92820i | −0.515184 | − | 0.297442i | ||||
\(902\) | 25.8564 | + | 6.92820i | 0.860924 | + | 0.230684i | ||||
\(903\) | 7.09808 | + | 0.509619i | 0.236209 | + | 0.0169591i | ||||
\(904\) | −3.29423 | − | 1.90192i | −0.109564 | − | 0.0632570i | ||||
\(905\) | −14.1244 | + | 21.3923i | −0.469509 | + | 0.711104i | ||||
\(906\) | 4.09808 | − | 15.2942i | 0.136149 | − | 0.508117i | ||||
\(907\) | −20.2942 | + | 5.43782i | −0.673859 | + | 0.180560i | −0.579492 | − | 0.814978i | \(-0.696749\pi\) |
−0.0943664 | + | 0.995538i | \(0.530083\pi\) | |||||||
\(908\) | 25.2224 | − | 6.75833i | 0.837036 | − | 0.224283i | ||||
\(909\) | − | 52.7654i | − | 1.75012i | ||||||
\(910\) | 16.9282 | − | 40.7846i | 0.561164 | − | 1.35200i | ||||
\(911\) | −7.43782 | − | 12.8827i | −0.246426 | − | 0.426822i | 0.716106 | − | 0.697992i | \(-0.245923\pi\) |
−0.962532 | + | 0.271170i | \(0.912590\pi\) | |||||||
\(912\) | 12.6340 | + | 21.8827i | 0.418353 | + | 0.724608i | ||||
\(913\) | 5.46410 | + | 5.46410i | 0.180835 | + | 0.180835i | ||||
\(914\) | 20.0526i | 0.663280i | ||||||||
\(915\) | −19.7321 | − | 39.4641i | −0.652321 | − | 1.30464i | ||||
\(916\) | −6.99038 | + | 4.03590i | −0.230969 | + | 0.133350i | ||||
\(917\) | −12.6795 | − | 4.39230i | −0.418714 | − | 0.145047i | ||||
\(918\) | −14.1962 | − | 24.5885i | −0.468543 | − | 0.811540i | ||||
\(919\) | 45.3731 | + | 26.1962i | 1.49672 | + | 0.864131i | 0.999993 | − | 0.00377579i | \(-0.00120188\pi\) |
0.496727 | + | 0.867907i | \(0.334535\pi\) | |||||||
\(920\) | 5.50000 | + | 0.330127i | 0.181330 | + | 0.0108840i | ||||
\(921\) | −11.1173 | − | 41.4904i | −0.366328 | − | 1.36715i | ||||
\(922\) | −2.23205 | − | 0.598076i | −0.0735087 | − | 0.0196966i | ||||
\(923\) | −22.3923 | + | 6.00000i | −0.737052 | + | 0.197492i | ||||
\(924\) | 40.9808 | + | 14.1962i | 1.34817 | + | 0.467019i | ||||
\(925\) | −13.0981 | − | 16.6865i | −0.430662 | − | 0.548650i | ||||
\(926\) | −35.1865 | + | 60.9449i | −1.15630 | + | 2.00277i | ||||
\(927\) | −11.8923 | + | 3.18653i | −0.390595 | + | 0.104659i | ||||
\(928\) | −50.7846 | − | 13.6077i | −1.66709 | − | 0.446694i | ||||
\(929\) | 36.3205 | 1.19164 | 0.595819 | − | 0.803119i | \(-0.296828\pi\) | ||||
0.595819 | + | 0.803119i | \(0.296828\pi\) | |||||||
\(930\) | 0.464102 | − | 1.39230i | 0.0152185 | − | 0.0456555i | ||||
\(931\) | −17.9737 | − | 14.1506i | −0.589065 | − | 0.463768i | ||||
\(932\) | −20.4904 | + | 5.49038i | −0.671185 | + | 0.179843i | ||||
\(933\) | 24.0000 | + | 13.8564i | 0.785725 | + | 0.453638i | ||||
\(934\) | 12.9641 | − | 22.4545i | 0.424198 | − | 0.734733i | ||||
\(935\) | −33.8564 | + | 6.92820i | −1.10722 | + | 0.226576i | ||||
\(936\) | 6.00000 | 0.196116 | ||||||||
\(937\) | 9.46410 | − | 9.46410i | 0.309179 | − | 0.309179i | −0.535412 | − | 0.844591i | \(-0.679844\pi\) |
0.844591 | + | 0.535412i | \(0.179844\pi\) | |||||||
\(938\) | 4.92820 | − | 4.26795i | 0.160912 | − | 0.139353i | ||||
\(939\) | −12.2942 | + | 3.29423i | −0.401207 | + | 0.107503i | ||||
\(940\) | −10.2058 | − | 49.8731i | −0.332876 | − | 1.62668i | ||||
\(941\) | 37.9808i | 1.23814i | 0.785337 | + | 0.619069i | \(0.212490\pi\) | ||||
−0.785337 | + | 0.619069i | \(0.787510\pi\) | |||||||
\(942\) | −2.36603 | + | 4.09808i | −0.0770893 | + | 0.133523i | ||||
\(943\) | 8.53590 | + | 8.53590i | 0.277967 | + | 0.277967i | ||||
\(944\) | 15.4641 | 0.503314 | ||||||||
\(945\) | −3.99038 | − | 30.4808i | −0.129807 | − | 0.991539i | ||||
\(946\) | −16.3923 | −0.532960 | ||||||||
\(947\) | 18.2224 | + | 18.2224i | 0.592149 | + | 0.592149i | 0.938212 | − | 0.346062i | \(-0.112481\pi\) |
−0.346062 | + | 0.938212i | \(0.612481\pi\) | |||||||
\(948\) | 6.80385 | − | 11.7846i | 0.220979 | − | 0.382746i | ||||
\(949\) | 35.3205i | 1.14655i | ||||||||
\(950\) | 19.4904 | + | 24.8301i | 0.632351 | + | 0.805596i | ||||
\(951\) | 20.0263 | − | 5.36603i | 0.649397 | − | 0.174005i | ||||
\(952\) | 3.66025 | + | 1.26795i | 0.118630 | + | 0.0410945i | ||||
\(953\) | 21.0000 | − | 21.0000i | 0.680257 | − | 0.680257i | −0.279801 | − | 0.960058i | \(-0.590269\pi\) |
0.960058 | + | 0.279801i | \(0.0902686\pi\) | |||||||
\(954\) | −18.2942 | + | 31.6865i | −0.592298 | + | 1.02589i | ||||
\(955\) | −32.9545 | − | 21.7583i | −1.06638 | − | 0.704083i | ||||
\(956\) | −19.0526 | + | 33.0000i | −0.616204 | + | 1.06730i | ||||
\(957\) | −56.7846 | − | 32.7846i | −1.83559 | − | 1.05978i | ||||
\(958\) | 9.83013 | − | 2.63397i | 0.317597 | − | 0.0850999i | ||||
\(959\) | −4.53590 | − | 3.07180i | −0.146472 | − | 0.0991935i | ||||
\(960\) | 9.92820 | + | 19.8564i | 0.320431 | + | 0.640863i | ||||
\(961\) | 30.9615 | 0.998759 | ||||||||
\(962\) | 30.5885 | + | 8.19615i | 0.986211 | + | 0.264255i | ||||
\(963\) | −5.19615 | − | 5.19615i | −0.167444 | − | 0.167444i | ||||
\(964\) | −8.25833 | + | 14.3038i | −0.265983 | + | 0.460696i | ||||
\(965\) | −44.8109 | + | 9.16987i | −1.44251 | + | 0.295189i | ||||
\(966\) | 27.5885 | + | 31.8564i | 0.887644 | + | 1.02496i | ||||
\(967\) | −1.66987 | + | 0.447441i | −0.0536995 | + | 0.0143887i | −0.285569 | − | 0.958358i | \(-0.592183\pi\) |
0.231869 | + | 0.972747i | \(0.425516\pi\) | |||||||
\(968\) | 9.42820 | + | 2.52628i | 0.303034 | + | 0.0811977i | ||||
\(969\) | −4.14359 | − | 15.4641i | −0.133111 | − | 0.496779i | ||||
\(970\) | 2.09808 | − | 34.9545i | 0.0673652 | − | 1.12232i | ||||
\(971\) | −2.53590 | − | 1.46410i | −0.0813809 | − | 0.0469853i | 0.458757 | − | 0.888562i | \(-0.348295\pi\) |
−0.540138 | + | 0.841576i | \(0.681628\pi\) | |||||||
\(972\) | −23.3827 | + | 13.5000i | −0.750000 | + | 0.433013i | ||||
\(973\) | 18.0000 | − | 3.46410i | 0.577054 | − | 0.111054i | ||||
\(974\) | −56.1506 | + | 32.4186i | −1.79918 | + | 1.03876i | ||||
\(975\) | 33.1244 | − | 4.73205i | 1.06083 | − | 0.151547i | ||||
\(976\) | − | 50.8564i | − | 1.62787i | ||||||
\(977\) | −33.1769 | − | 33.1769i | −1.06142 | − | 1.06142i | −0.997986 | − | 0.0634377i | \(-0.979794\pi\) |
−0.0634377 | − | 0.997986i | \(-0.520206\pi\) | |||||||
\(978\) | −15.2942 | − | 26.4904i | −0.489056 | − | 0.847069i | ||||
\(979\) | 25.1244 | + | 43.5167i | 0.802978 | + | 1.39080i | ||||
\(980\) | −20.2583 | − | 18.0167i | −0.647129 | − | 0.575521i | ||||
\(981\) | −5.19615 | − | 3.00000i | −0.165900 | − | 0.0957826i | ||||
\(982\) | −31.5885 | + | 8.46410i | −1.00803 | + | 0.270100i | ||||
\(983\) | −3.56218 | + | 0.954483i | −0.113616 | + | 0.0304433i | −0.315179 | − | 0.949032i | \(-0.602065\pi\) |
0.201563 | + | 0.979476i | \(0.435398\pi\) | |||||||
\(984\) | 0.588457 | − | 2.19615i | 0.0187593 | − | 0.0700108i | ||||
\(985\) | −11.0718 | − | 54.1051i | −0.352777 | − | 1.72393i | ||||
\(986\) | 32.7846 | + | 18.9282i | 1.04407 | + | 0.602797i | ||||
\(987\) | −33.7750 | + | 49.8731i | −1.07507 | + | 1.58748i | ||||
\(988\) | −21.1244 | − | 5.66025i | −0.672055 | − | 0.180077i | ||||
\(989\) | −6.40192 | − | 3.69615i | −0.203569 | − | 0.117531i | ||||
\(990\) | 14.1962 | + | 69.3731i | 0.451183 | + | 2.20482i | ||||
\(991\) | 8.73205 | + | 15.1244i | 0.277383 | + | 0.480441i | 0.970734 | − | 0.240159i | \(-0.0771997\pi\) |
−0.693351 | + | 0.720600i | \(0.743866\pi\) | |||||||
\(992\) | 1.05256 | − | 1.05256i | 0.0334188 | − | 0.0334188i | ||||
\(993\) | 15.8827 | − | 27.5096i | 0.504022 | − | 0.872991i | ||||
\(994\) | −2.19615 | + | 30.5885i | −0.0696577 | + | 0.970207i | ||||
\(995\) | −1.05256 | + | 17.5359i | −0.0333684 | + | 0.555925i | ||||
\(996\) | −3.00000 | + | 3.00000i | −0.0950586 | + | 0.0950586i | ||||
\(997\) | −11.7058 | − | 43.6865i | −0.370725 | − | 1.38357i | −0.859491 | − | 0.511151i | \(-0.829219\pi\) |
0.488765 | − | 0.872415i | \(-0.337447\pi\) | |||||||
\(998\) | 13.1962 | + | 3.53590i | 0.417717 | + | 0.111927i | ||||
\(999\) | 21.2942 | − | 5.70577i | 0.673720 | − | 0.180523i |
(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 | 315.2.bs.b.292.1 | yes | 4 | |
3.2 | odd | 2 | 945.2.bv.a.712.1 | 4 | |||
5.3 | odd | 4 | 315.2.bs.c.103.1 | yes | 4 | ||
7.3 | odd | 6 | 315.2.cg.c.157.1 | yes | 4 | ||
9.2 | odd | 6 | 945.2.cj.d.397.1 | 4 | |||
9.7 | even | 3 | 315.2.cg.a.187.1 | yes | 4 | ||
15.8 | even | 4 | 945.2.bv.d.523.1 | 4 | |||
21.17 | even | 6 | 945.2.cj.a.577.1 | 4 | |||
35.3 | even | 12 | 315.2.cg.a.283.1 | yes | 4 | ||
45.38 | even | 12 | 945.2.cj.a.208.1 | 4 | |||
45.43 | odd | 12 | 315.2.cg.c.313.1 | yes | 4 | ||
63.38 | even | 6 | 945.2.bv.d.262.1 | 4 | |||
63.52 | odd | 6 | 315.2.bs.c.52.1 | yes | 4 | ||
105.38 | odd | 12 | 945.2.cj.d.388.1 | 4 | |||
315.38 | odd | 12 | 945.2.bv.a.73.1 | 4 | |||
315.178 | even | 12 | inner | 315.2.bs.b.178.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bs.b.178.1 | ✓ | 4 | 315.178 | even | 12 | inner | |
315.2.bs.b.292.1 | yes | 4 | 1.1 | even | 1 | trivial | |
315.2.bs.c.52.1 | yes | 4 | 63.52 | odd | 6 | ||
315.2.bs.c.103.1 | yes | 4 | 5.3 | odd | 4 | ||
315.2.cg.a.187.1 | yes | 4 | 9.7 | even | 3 | ||
315.2.cg.a.283.1 | yes | 4 | 35.3 | even | 12 | ||
315.2.cg.c.157.1 | yes | 4 | 7.3 | odd | 6 | ||
315.2.cg.c.313.1 | yes | 4 | 45.43 | odd | 12 | ||
945.2.bv.a.73.1 | 4 | 315.38 | odd | 12 | |||
945.2.bv.a.712.1 | 4 | 3.2 | odd | 2 | |||
945.2.bv.d.262.1 | 4 | 63.38 | even | 6 | |||
945.2.bv.d.523.1 | 4 | 15.8 | even | 4 | |||
945.2.cj.a.208.1 | 4 | 45.38 | even | 12 | |||
945.2.cj.a.577.1 | 4 | 21.17 | even | 6 | |||
945.2.cj.d.388.1 | 4 | 105.38 | odd | 12 | |||
945.2.cj.d.397.1 | 4 | 9.2 | odd | 6 |