Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(79,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("735.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
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 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.79 |
Dual form | 735.2.q.a.214.2 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
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 | \(-0.218307\pi\) |
−0.161521 | + | 0.986869i | \(0.551640\pi\) | |||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.23205 | − | 0.133975i | −0.998203 | − | 0.0599153i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 3.00000i | − | 1.06066i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.86603 | − | 1.23205i | −0.590089 | − | 0.389609i | ||||
\(11\) | 3.00000 | + | 5.19615i | 0.904534 | + | 1.56670i | 0.821541 | + | 0.570149i | \(0.193114\pi\) |
0.0829925 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | − | 1.00000i | 0.516398 | − | 0.258199i | ||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 3.46410 | − | 2.00000i | 0.840168 | − | 0.485071i | −0.0171533 | − | 0.999853i | \(-0.505460\pi\) |
0.857321 | + | 0.514782i | \(0.172127\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | 1.00000 | + | 2.00000i | 0.223607 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.00000i | 1.27920i | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 1.50000 | + | 2.59808i | 0.306186 | + | 0.530330i | ||||
\(25\) | 4.96410 | + | 0.598076i | 0.992820 | + | 0.119615i | ||||
\(26\) | −1.00000 | + | 1.73205i | −0.196116 | + | 0.339683i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 2.23205 | + | 0.133975i | 0.407515 | + | 0.0244603i | ||||
\(31\) | 5.00000 | + | 8.66025i | 0.898027 | + | 1.55543i | 0.830014 | + | 0.557743i | \(0.188333\pi\) |
0.0680129 | + | 0.997684i | \(0.478334\pi\) | |||||||
\(32\) | −4.33013 | + | 2.50000i | −0.765466 | + | 0.441942i | ||||
\(33\) | −5.19615 | − | 3.00000i | −0.904534 | − | 0.522233i | ||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 3.46410 | + | 2.00000i | 0.569495 | + | 0.328798i | 0.756948 | − | 0.653476i | \(-0.226690\pi\) |
−0.187453 | + | 0.982274i | \(0.560023\pi\) | |||||||
\(38\) | −5.19615 | + | 3.00000i | −0.842927 | + | 0.486664i | ||||
\(39\) | −1.00000 | − | 1.73205i | −0.160128 | − | 0.277350i | ||||
\(40\) | −0.401924 | + | 6.69615i | −0.0635497 | + | 1.05875i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 3.00000 | − | 5.19615i | 0.452267 | − | 0.783349i | ||||
\(45\) | −1.23205 | + | 1.86603i | −0.183663 | + | 0.278171i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | 1.73205 | − | 1.00000i | 0.240192 | − | 0.138675i | ||||
\(53\) | −5.19615 | + | 3.00000i | −0.713746 | + | 0.412082i | −0.812447 | − | 0.583036i | \(-0.801865\pi\) |
0.0987002 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −6.00000 | − | 12.0000i | −0.809040 | − | 1.61808i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 1.73205 | + | 1.00000i | 0.227429 | + | 0.131306i | ||||
\(59\) | −4.00000 | − | 6.92820i | −0.520756 | − | 0.901975i | −0.999709 | − | 0.0241347i | \(-0.992317\pi\) |
0.478953 | − | 0.877841i | \(-0.341016\pi\) | |||||||
\(60\) | −1.86603 | − | 1.23205i | −0.240903 | − | 0.159057i | ||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 10.0000i | 1.27000i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0.267949 | − | 4.46410i | 0.0332350 | − | 0.553704i | ||||
\(66\) | −3.00000 | − | 5.19615i | −0.369274 | − | 0.639602i | ||||
\(67\) | −13.8564 | + | 8.00000i | −1.69283 | + | 0.977356i | −0.740613 | + | 0.671932i | \(0.765465\pi\) |
−0.952217 | + | 0.305424i | \(0.901202\pi\) | |||||||
\(68\) | −3.46410 | − | 2.00000i | −0.420084 | − | 0.242536i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | −2.59808 | − | 1.50000i | −0.306186 | − | 0.176777i | ||||
\(73\) | 5.19615 | − | 3.00000i | 0.608164 | − | 0.351123i | −0.164083 | − | 0.986447i | \(-0.552466\pi\) |
0.772246 | + | 0.635323i | \(0.219133\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | −4.59808 | + | 1.96410i | −0.530940 | + | 0.226795i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 2.00000i | − | 0.226455i | ||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | −1.23205 | + | 1.86603i | −0.137747 | + | 0.208628i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.73205 | + | 1.00000i | 0.191273 | + | 0.110432i | ||||
\(83\) | − | 8.00000i | − | 0.878114i | −0.898459 | − | 0.439057i | \(-0.855313\pi\) | ||
0.898459 | − | 0.439057i | \(-0.144687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | + | 4.00000i | −0.867722 | + | 0.433861i | ||||
\(86\) | −2.00000 | + | 3.46410i | −0.215666 | + | 0.373544i | ||||
\(87\) | −1.73205 | + | 1.00000i | −0.185695 | + | 0.107211i | ||||
\(88\) | 15.5885 | − | 9.00000i | 1.66174 | − | 0.959403i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | −2.00000 | + | 1.00000i | −0.210819 | + | 0.105409i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.66025 | − | 5.00000i | −0.898027 | − | 0.518476i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.39230 | − | 11.1962i | 0.758434 | − | 1.14870i | ||||
\(96\) | 2.50000 | − | 4.33013i | 0.255155 | − | 0.441942i | ||||
\(97\) | − | 2.00000i | − | 0.203069i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) | ||
0.994832 | − | 0.101535i | \(-0.0323753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | −1.96410 | − | 4.59808i | −0.196410 | − | 0.459808i | ||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | −3.46410 | + | 2.00000i | −0.342997 | + | 0.198030i | ||||
\(103\) | 6.92820 | + | 4.00000i | 0.682656 | + | 0.394132i | 0.800855 | − | 0.598858i | \(-0.204379\pi\) |
−0.118199 | + | 0.992990i | \(0.537712\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −3.46410 | − | 2.00000i | −0.334887 | − | 0.193347i | 0.323122 | − | 0.946357i | \(-0.395268\pi\) |
−0.658009 | + | 0.753010i | \(0.728601\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0.803848 | − | 13.3923i | 0.0766439 | − | 1.27691i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 3.00000 | − | 5.19615i | 0.280976 | − | 0.486664i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | − | 1.73205i | −0.0928477 | − | 0.160817i | ||||
\(117\) | 1.73205 | + | 1.00000i | 0.160128 | + | 0.0924500i | ||||
\(118\) | − | 8.00000i | − | 0.736460i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.00000 | − | 6.00000i | −0.273861 | − | 0.547723i | ||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | 1.73205 | − | 1.00000i | 0.156813 | − | 0.0905357i | ||||
\(123\) | −1.73205 | + | 1.00000i | −0.156174 | + | 0.0901670i | ||||
\(124\) | 5.00000 | − | 8.66025i | 0.449013 | − | 0.777714i | ||||
\(125\) | −11.0000 | − | 2.00000i | −0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000i | 1.77471i | 0.461084 | + | 0.887357i | \(0.347461\pi\) | ||||
−0.461084 | + | 0.887357i | \(0.652539\pi\) | |||||||
\(128\) | 2.59808 | + | 1.50000i | 0.229640 | + | 0.132583i | ||||
\(129\) | −2.00000 | − | 3.46410i | −0.176090 | − | 0.304997i | ||||
\(130\) | 2.46410 | − | 3.73205i | 0.216116 | − | 0.327323i | ||||
\(131\) | −2.00000 | + | 3.46410i | −0.174741 | + | 0.302660i | −0.940072 | − | 0.340977i | \(-0.889242\pi\) |
0.765331 | + | 0.643637i | \(0.222575\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −16.0000 | −1.38219 | ||||||||
\(135\) | 0.133975 | − | 2.23205i | 0.0115307 | − | 0.192104i | ||||
\(136\) | −6.00000 | − | 10.3923i | −0.514496 | − | 0.891133i | ||||
\(137\) | −5.19615 | + | 3.00000i | −0.443937 | + | 0.256307i | −0.705266 | − | 0.708942i | \(-0.749173\pi\) |
0.261329 | + | 0.965250i | \(0.415839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.66025 | + | 5.00000i | 0.726752 | + | 0.419591i | ||||
\(143\) | −10.3923 | + | 6.00000i | −0.869048 | + | 0.501745i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −4.46410 | − | 0.267949i | −0.370723 | − | 0.0222520i | ||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | −7.00000 | + | 12.1244i | −0.573462 | + | 0.993266i | 0.422744 | + | 0.906249i | \(0.361067\pi\) |
−0.996207 | + | 0.0870170i | \(0.972267\pi\) | |||||||
\(150\) | −4.96410 | − | 0.598076i | −0.405317 | − | 0.0488327i | ||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | 15.5885 | + | 9.00000i | 1.26439 | + | 0.729996i | ||||
\(153\) | − | 4.00000i | − | 0.323381i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.0000 | − | 20.0000i | −0.803219 | − | 1.60644i | ||||
\(156\) | −1.00000 | + | 1.73205i | −0.0800641 | + | 0.138675i | ||||
\(157\) | 15.5885 | − | 9.00000i | 1.24409 | − | 0.718278i | 0.274169 | − | 0.961681i | \(-0.411597\pi\) |
0.969925 | + | 0.243403i | \(0.0782638\pi\) | |||||||
\(158\) | 3.46410 | − | 2.00000i | 0.275589 | − | 0.159111i | ||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | 10.0000 | − | 5.00000i | 0.790569 | − | 0.395285i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 3.46410 | + | 2.00000i | 0.271329 | + | 0.156652i | 0.629492 | − | 0.777007i | \(-0.283263\pi\) |
−0.358162 | + | 0.933659i | \(0.616597\pi\) | |||||||
\(164\) | −1.00000 | − | 1.73205i | −0.0780869 | − | 0.135250i | ||||
\(165\) | 11.1962 | + | 7.39230i | 0.871619 | + | 0.575490i | ||||
\(166\) | 4.00000 | − | 6.92820i | 0.310460 | − | 0.537733i | ||||
\(167\) | 12.0000i | 0.928588i | 0.885681 | + | 0.464294i | \(0.153692\pi\) | ||||
−0.885681 | + | 0.464294i | \(0.846308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | −8.92820 | − | 0.535898i | −0.684762 | − | 0.0411015i | ||||
\(171\) | 3.00000 | + | 5.19615i | 0.229416 | + | 0.397360i | ||||
\(172\) | 3.46410 | − | 2.00000i | 0.264135 | − | 0.152499i | ||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | 6.92820 | + | 4.00000i | 0.520756 | + | 0.300658i | ||||
\(178\) | 5.19615 | − | 3.00000i | 0.389468 | − | 0.224860i | ||||
\(179\) | −7.00000 | − | 12.1244i | −0.523205 | − | 0.906217i | −0.999635 | − | 0.0270049i | \(-0.991403\pi\) |
0.476431 | − | 0.879212i | \(-0.341930\pi\) | |||||||
\(180\) | 2.23205 | + | 0.133975i | 0.166367 | + | 0.00998588i | ||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.46410 | − | 4.92820i | −0.548772 | − | 0.362329i | ||||
\(186\) | −5.00000 | − | 8.66025i | −0.366618 | − | 0.635001i | ||||
\(187\) | 20.7846 | + | 12.0000i | 1.51992 | + | 0.877527i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0000 | − | 6.00000i | 0.870572 | − | 0.435286i | ||||
\(191\) | 9.00000 | − | 15.5885i | 0.651217 | − | 1.12794i | −0.331611 | − | 0.943416i | \(-0.607592\pi\) |
0.982828 | − | 0.184525i | \(-0.0590746\pi\) | |||||||
\(192\) | 6.06218 | − | 3.50000i | 0.437500 | − | 0.252591i | ||||
\(193\) | 6.92820 | − | 4.00000i | 0.498703 | − | 0.287926i | −0.229475 | − | 0.973315i | \(-0.573701\pi\) |
0.728178 | + | 0.685388i | \(0.240368\pi\) | |||||||
\(194\) | 1.00000 | − | 1.73205i | 0.0717958 | − | 0.124354i | ||||
\(195\) | 2.00000 | + | 4.00000i | 0.143223 | + | 0.286446i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 5.19615 | + | 3.00000i | 0.369274 | + | 0.213201i | ||||
\(199\) | 7.00000 | + | 12.1244i | 0.496217 | + | 0.859473i | 0.999990 | − | 0.00436292i | \(-0.00138876\pi\) |
−0.503774 | + | 0.863836i | \(0.668055\pi\) | |||||||
\(200\) | 1.79423 | − | 14.8923i | 0.126871 | − | 1.05304i | ||||
\(201\) | 8.00000 | − | 13.8564i | 0.564276 | − | 0.977356i | ||||
\(202\) | 6.00000i | 0.422159i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | −4.46410 | − | 0.267949i | −0.311786 | − | 0.0187144i | ||||
\(206\) | 4.00000 | + | 6.92820i | 0.278693 | + | 0.482711i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.73205 | + | 1.00000i | 0.120096 | + | 0.0693375i | ||||
\(209\) | −36.0000 | −2.49017 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 5.19615 | + | 3.00000i | 0.356873 | + | 0.206041i | ||||
\(213\) | −8.66025 | + | 5.00000i | −0.593391 | + | 0.342594i | ||||
\(214\) | −2.00000 | − | 3.46410i | −0.136717 | − | 0.236801i | ||||
\(215\) | 0.535898 | − | 8.92820i | 0.0365480 | − | 0.608898i | ||||
\(216\) | 3.00000 | 0.204124 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.00000i | 0.135457i | ||||||||
\(219\) | −3.00000 | + | 5.19615i | −0.202721 | + | 0.351123i | ||||
\(220\) | −7.39230 | + | 11.1962i | −0.498389 | + | 0.754844i | ||||
\(221\) | 4.00000 | + | 6.92820i | 0.269069 | + | 0.466041i | ||||
\(222\) | −3.46410 | − | 2.00000i | −0.232495 | − | 0.134231i | ||||
\(223\) | 24.0000i | 1.60716i | 0.595198 | + | 0.803579i | \(0.297074\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | − | 4.00000i | 0.200000 | − | 0.266667i | ||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | 6.92820 | − | 4.00000i | 0.459841 | − | 0.265489i | −0.252136 | − | 0.967692i | \(-0.581133\pi\) |
0.711977 | + | 0.702202i | \(0.247800\pi\) | |||||||
\(228\) | −5.19615 | + | 3.00000i | −0.344124 | + | 0.198680i | ||||
\(229\) | −5.00000 | + | 8.66025i | −0.330409 | + | 0.572286i | −0.982592 | − | 0.185776i | \(-0.940520\pi\) |
0.652183 | + | 0.758062i | \(0.273853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | −22.5167 | − | 13.0000i | −1.47512 | − | 0.851658i | −0.475509 | − | 0.879711i | \(-0.657736\pi\) |
−0.999606 | + | 0.0280525i | \(0.991069\pi\) | |||||||
\(234\) | 1.00000 | + | 1.73205i | 0.0653720 | + | 0.113228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.00000 | + | 6.92820i | −0.260378 | + | 0.450988i | ||||
\(237\) | 4.00000i | 0.259828i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0.133975 | − | 2.23205i | 0.00864802 | − | 0.144078i | ||||
\(241\) | −11.0000 | − | 19.0526i | −0.708572 | − | 1.22728i | −0.965387 | − | 0.260822i | \(-0.916006\pi\) |
0.256814 | − | 0.966461i | \(-0.417327\pi\) | |||||||
\(242\) | −21.6506 | + | 12.5000i | −1.39176 | + | 0.803530i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | −10.3923 | − | 6.00000i | −0.661247 | − | 0.381771i | ||||
\(248\) | 25.9808 | − | 15.0000i | 1.64978 | − | 0.952501i | ||||
\(249\) | 4.00000 | + | 6.92820i | 0.253490 | + | 0.439057i | ||||
\(250\) | −8.52628 | − | 7.23205i | −0.539249 | − | 0.457395i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.0000 | + | 17.3205i | −0.627456 | + | 1.08679i | ||||
\(255\) | 4.92820 | − | 7.46410i | 0.308616 | − | 0.467420i | ||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | −13.8564 | − | 8.00000i | −0.864339 | − | 0.499026i | 0.00112398 | − | 0.999999i | \(-0.499642\pi\) |
−0.865463 | + | 0.500973i | \(0.832976\pi\) | |||||||
\(258\) | − | 4.00000i | − | 0.249029i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.00000 | + | 2.00000i | −0.248069 | + | 0.124035i | ||||
\(261\) | 1.00000 | − | 1.73205i | 0.0618984 | − | 0.107211i | ||||
\(262\) | −3.46410 | + | 2.00000i | −0.214013 | + | 0.123560i | ||||
\(263\) | 20.7846 | − | 12.0000i | 1.28163 | − | 0.739952i | 0.304487 | − | 0.952517i | \(-0.401515\pi\) |
0.977147 | + | 0.212565i | \(0.0681817\pi\) | |||||||
\(264\) | −9.00000 | + | 15.5885i | −0.553912 | + | 0.959403i | ||||
\(265\) | 12.0000 | − | 6.00000i | 0.737154 | − | 0.368577i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000i | 0.367194i | ||||||||
\(268\) | 13.8564 | + | 8.00000i | 0.846415 | + | 0.488678i | ||||
\(269\) | −7.00000 | − | 12.1244i | −0.426798 | − | 0.739235i | 0.569789 | − | 0.821791i | \(-0.307025\pi\) |
−0.996586 | + | 0.0825561i | \(0.973692\pi\) | |||||||
\(270\) | 1.23205 | − | 1.86603i | 0.0749802 | − | 0.113563i | ||||
\(271\) | 7.00000 | − | 12.1244i | 0.425220 | − | 0.736502i | −0.571221 | − | 0.820796i | \(-0.693530\pi\) |
0.996441 | + | 0.0842940i | \(0.0268635\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 11.7846 | + | 27.5885i | 0.710639 | + | 1.66365i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.2487 | + | 14.0000i | −1.45696 | + | 0.841178i | −0.998861 | − | 0.0477206i | \(-0.984804\pi\) |
−0.458103 | + | 0.888899i | \(0.651471\pi\) | |||||||
\(278\) | −1.73205 | − | 1.00000i | −0.103882 | − | 0.0599760i | ||||
\(279\) | 10.0000 | 0.598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.3205 | + | 10.0000i | −1.02960 | + | 0.594438i | −0.916869 | − | 0.399188i | \(-0.869292\pi\) |
−0.112728 | + | 0.993626i | \(0.535959\pi\) | |||||||
\(284\) | −5.00000 | − | 8.66025i | −0.296695 | − | 0.513892i | ||||
\(285\) | −0.803848 | + | 13.3923i | −0.0476158 | + | 0.793292i | ||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.00000i | 0.294628i | ||||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | −3.73205 | − | 2.46410i | −0.219154 | − | 0.144697i | ||||
\(291\) | 1.00000 | + | 1.73205i | 0.0586210 | + | 0.101535i | ||||
\(292\) | −5.19615 | − | 3.00000i | −0.304082 | − | 0.175562i | ||||
\(293\) | − | 24.0000i | − | 1.40209i | −0.713115 | − | 0.701047i | \(-0.752716\pi\) | ||
0.713115 | − | 0.701047i | \(-0.247284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | + | 16.0000i | 0.465778 | + | 0.931556i | ||||
\(296\) | 6.00000 | − | 10.3923i | 0.348743 | − | 0.604040i | ||||
\(297\) | −5.19615 | + | 3.00000i | −0.301511 | + | 0.174078i | ||||
\(298\) | −12.1244 | + | 7.00000i | −0.702345 | + | 0.405499i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.00000 | + | 3.00000i | 0.230940 | + | 0.173205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 8.00000i | − | 0.460348i | ||||||
\(303\) | −5.19615 | − | 3.00000i | −0.298511 | − | 0.172345i | ||||
\(304\) | 3.00000 | + | 5.19615i | 0.172062 | + | 0.298020i | ||||
\(305\) | −2.46410 | + | 3.73205i | −0.141094 | + | 0.213697i | ||||
\(306\) | 2.00000 | − | 3.46410i | 0.114332 | − | 0.198030i | ||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 1.33975 | − | 22.3205i | 0.0760925 | − | 1.26772i | ||||
\(311\) | 12.0000 | + | 20.7846i | 0.680458 | + | 1.17859i | 0.974841 | + | 0.222900i | \(0.0715523\pi\) |
−0.294384 | + | 0.955687i | \(0.595114\pi\) | |||||||
\(312\) | −5.19615 | + | 3.00000i | −0.294174 | + | 0.169842i | ||||
\(313\) | 5.19615 | + | 3.00000i | 0.293704 | + | 0.169570i | 0.639611 | − | 0.768699i | \(-0.279095\pi\) |
−0.345907 | + | 0.938269i | \(0.612429\pi\) | |||||||
\(314\) | 18.0000 | 1.01580 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 15.5885 | + | 9.00000i | 0.875535 | + | 0.505490i | 0.869184 | − | 0.494489i | \(-0.164645\pi\) |
0.00635137 | + | 0.999980i | \(0.497978\pi\) | |||||||
\(318\) | 5.19615 | − | 3.00000i | 0.291386 | − | 0.168232i | ||||
\(319\) | 6.00000 | + | 10.3923i | 0.335936 | + | 0.581857i | ||||
\(320\) | 15.6244 | + | 0.937822i | 0.873428 | + | 0.0524259i | ||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −1.19615 | + | 9.92820i | −0.0663506 | + | 0.550718i | ||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | −1.73205 | − | 1.00000i | −0.0957826 | − | 0.0553001i | ||||
\(328\) | − | 6.00000i | − | 0.331295i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.00000 | + | 12.0000i | 0.330289 | + | 0.660578i | ||||
\(331\) | 12.0000 | − | 20.7846i | 0.659580 | − | 1.14243i | −0.321145 | − | 0.947030i | \(-0.604068\pi\) |
0.980725 | − | 0.195395i | \(-0.0625990\pi\) | |||||||
\(332\) | −6.92820 | + | 4.00000i | −0.380235 | + | 0.219529i | ||||
\(333\) | 3.46410 | − | 2.00000i | 0.189832 | − | 0.109599i | ||||
\(334\) | −6.00000 | + | 10.3923i | −0.328305 | + | 0.568642i | ||||
\(335\) | 32.0000 | − | 16.0000i | 1.74835 | − | 0.874173i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 24.0000i | − | 1.30736i | −0.756770 | − | 0.653682i | \(-0.773224\pi\) | ||
0.756770 | − | 0.653682i | \(-0.226776\pi\) | |||||||
\(338\) | 7.79423 | + | 4.50000i | 0.423950 | + | 0.244768i | ||||
\(339\) | 3.00000 | + | 5.19615i | 0.162938 | + | 0.282216i | ||||
\(340\) | 7.46410 | + | 4.92820i | 0.404798 | + | 0.267269i | ||||
\(341\) | −30.0000 | + | 51.9615i | −1.62459 | + | 2.81387i | ||||
\(342\) | 6.00000i | 0.324443i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.0000 | 0.646997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3923 | − | 6.00000i | 0.557888 | − | 0.322097i | −0.194409 | − | 0.980921i | \(-0.562279\pi\) |
0.752297 | + | 0.658824i | \(0.228946\pi\) | |||||||
\(348\) | 1.73205 | + | 1.00000i | 0.0928477 | + | 0.0536056i | ||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | −25.9808 | − | 15.0000i | −1.38478 | − | 0.799503i | ||||
\(353\) | −17.3205 | + | 10.0000i | −0.921878 | + | 0.532246i | −0.884234 | − | 0.467045i | \(-0.845319\pi\) |
−0.0376440 | + | 0.999291i | \(0.511985\pi\) | |||||||
\(354\) | 4.00000 | + | 6.92820i | 0.212598 | + | 0.368230i | ||||
\(355\) | −22.3205 | − | 1.33975i | −1.18465 | − | 0.0711063i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 14.0000i | − | 0.739923i | ||||||
\(359\) | 11.0000 | − | 19.0526i | 0.580558 | − | 1.00556i | −0.414855 | − | 0.909887i | \(-0.636168\pi\) |
0.995413 | − | 0.0956683i | \(-0.0304988\pi\) | |||||||
\(360\) | 5.59808 | + | 3.69615i | 0.295045 | + | 0.194804i | ||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | −5.19615 | − | 3.00000i | −0.273104 | − | 0.157676i | ||||
\(363\) | − | 25.0000i | − | 1.31216i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0000 | + | 6.00000i | −0.628109 | + | 0.314054i | ||||
\(366\) | −1.00000 | + | 1.73205i | −0.0522708 | + | 0.0905357i | ||||
\(367\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.00000 | − | 1.73205i | 0.0520579 | − | 0.0901670i | ||||
\(370\) | −4.00000 | − | 8.00000i | −0.207950 | − | 0.415900i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.0000i | 0.518476i | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 12.0000 | + | 20.7846i | 0.620505 | + | 1.07475i | ||||
\(375\) | 10.5263 | − | 3.76795i | 0.543575 | − | 0.194576i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00000i | 0.206010i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | −13.3923 | − | 0.803848i | −0.687011 | − | 0.0412365i | ||||
\(381\) | −10.0000 | − | 17.3205i | −0.512316 | − | 0.887357i | ||||
\(382\) | 15.5885 | − | 9.00000i | 0.797575 | − | 0.460480i | ||||
\(383\) | −17.3205 | − | 10.0000i | −0.885037 | − | 0.510976i | −0.0127209 | − | 0.999919i | \(-0.504049\pi\) |
−0.872316 | + | 0.488943i | \(0.837383\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | 3.46410 | + | 2.00000i | 0.176090 | + | 0.101666i | ||||
\(388\) | −1.73205 | + | 1.00000i | −0.0879316 | + | 0.0507673i | ||||
\(389\) | 13.0000 | + | 22.5167i | 0.659126 | + | 1.14164i | 0.980842 | + | 0.194804i | \(0.0624070\pi\) |
−0.321716 | + | 0.946836i | \(0.604260\pi\) | |||||||
\(390\) | −0.267949 | + | 4.46410i | −0.0135681 | + | 0.226049i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.00000i | − | 0.201773i | ||||||
\(394\) | −1.00000 | + | 1.73205i | −0.0503793 | + | 0.0872595i | ||||
\(395\) | −4.92820 | + | 7.46410i | −0.247965 | + | 0.375560i | ||||
\(396\) | −3.00000 | − | 5.19615i | −0.150756 | − | 0.261116i | ||||
\(397\) | −19.0526 | − | 11.0000i | −0.956221 | − | 0.552074i | −0.0612128 | − | 0.998125i | \(-0.519497\pi\) |
−0.895008 | + | 0.446051i | \(0.852830\pi\) | |||||||
\(398\) | 14.0000i | 0.701757i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | − | 4.00000i | 0.150000 | − | 0.200000i | ||||
\(401\) | 15.0000 | − | 25.9808i | 0.749064 | − | 1.29742i | −0.199207 | − | 0.979957i | \(-0.563837\pi\) |
0.948272 | − | 0.317460i | \(-0.102830\pi\) | |||||||
\(402\) | 13.8564 | − | 8.00000i | 0.691095 | − | 0.399004i | ||||
\(403\) | −17.3205 | + | 10.0000i | −0.862796 | + | 0.498135i | ||||
\(404\) | 3.00000 | − | 5.19615i | 0.149256 | − | 0.258518i | ||||
\(405\) | 1.00000 | + | 2.00000i | 0.0496904 | + | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000i | 1.18964i | ||||||||
\(408\) | 10.3923 | + | 6.00000i | 0.514496 | + | 0.297044i | ||||
\(409\) | −11.0000 | − | 19.0526i | −0.543915 | − | 0.942088i | −0.998674 | − | 0.0514740i | \(-0.983608\pi\) |
0.454759 | − | 0.890614i | \(-0.349725\pi\) | |||||||
\(410\) | −3.73205 | − | 2.46410i | −0.184313 | − | 0.121693i | ||||
\(411\) | 3.00000 | − | 5.19615i | 0.147979 | − | 0.256307i | ||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.07180 | + | 17.8564i | −0.0526124 | + | 0.876537i | ||||
\(416\) | −5.00000 | − | 8.66025i | −0.245145 | − | 0.424604i | ||||
\(417\) | 1.73205 | − | 1.00000i | 0.0848189 | − | 0.0489702i | ||||
\(418\) | −31.1769 | − | 18.0000i | −1.52491 | − | 0.880409i | ||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | −13.8564 | − | 8.00000i | −0.674519 | − | 0.389434i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.00000 | + | 15.5885i | 0.437079 | + | 0.757042i | ||||
\(425\) | 18.3923 | − | 7.85641i | 0.892158 | − | 0.381092i | ||||
\(426\) | −10.0000 | −0.484502 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.00000i | 0.193347i | ||||||||
\(429\) | 6.00000 | − | 10.3923i | 0.289683 | − | 0.501745i | ||||
\(430\) | 4.92820 | − | 7.46410i | 0.237659 | − | 0.359951i | ||||
\(431\) | 7.00000 | + | 12.1244i | 0.337178 | + | 0.584010i | 0.983901 | − | 0.178716i | \(-0.0571942\pi\) |
−0.646723 | + | 0.762725i | \(0.723861\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 34.0000i | 1.63394i | 0.576683 | + | 0.816968i | \(0.304347\pi\) | ||||
−0.576683 | + | 0.816968i | \(0.695653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.00000 | − | 2.00000i | 0.191785 | − | 0.0958927i | ||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −5.19615 | + | 3.00000i | −0.248282 | + | 0.143346i | ||||
\(439\) | 3.00000 | − | 5.19615i | 0.143182 | − | 0.247999i | −0.785511 | − | 0.618848i | \(-0.787600\pi\) |
0.928693 | + | 0.370849i | \(0.120933\pi\) | |||||||
\(440\) | −36.0000 | + | 18.0000i | −1.71623 | + | 0.858116i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.00000i | 0.380521i | ||||||||
\(443\) | −3.46410 | − | 2.00000i | −0.164584 | − | 0.0950229i | 0.415445 | − | 0.909618i | \(-0.363626\pi\) |
−0.580030 | + | 0.814595i | \(0.696959\pi\) | |||||||
\(444\) | 2.00000 | + | 3.46410i | 0.0949158 | + | 0.164399i | ||||
\(445\) | −7.39230 | + | 11.1962i | −0.350429 | + | 0.530749i | ||||
\(446\) | −12.0000 | + | 20.7846i | −0.568216 | + | 0.984180i | ||||
\(447\) | − | 14.0000i | − | 0.662177i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 4.59808 | − | 1.96410i | 0.216755 | − | 0.0925886i | ||||
\(451\) | 6.00000 | + | 10.3923i | 0.282529 | + | 0.489355i | ||||
\(452\) | −5.19615 | + | 3.00000i | −0.244406 | + | 0.141108i | ||||
\(453\) | 6.92820 | + | 4.00000i | 0.325515 | + | 0.187936i | ||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.0000 | −0.842927 | ||||||||
\(457\) | 17.3205 | + | 10.0000i | 0.810219 | + | 0.467780i | 0.847032 | − | 0.531542i | \(-0.178387\pi\) |
−0.0368128 | + | 0.999322i | \(0.511721\pi\) | |||||||
\(458\) | −8.66025 | + | 5.00000i | −0.404667 | + | 0.233635i | ||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0000 | 1.39724 | 0.698620 | − | 0.715493i | \(-0.253798\pi\) | ||||
0.698620 | + | 0.715493i | \(0.253798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 36.0000i | − | 1.67306i | −0.547920 | − | 0.836531i | \(-0.684580\pi\) | ||
0.547920 | − | 0.836531i | \(-0.315420\pi\) | |||||||
\(464\) | 1.00000 | − | 1.73205i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | 18.6603 | + | 12.3205i | 0.865349 | + | 0.571350i | ||||
\(466\) | −13.0000 | − | 22.5167i | −0.602213 | − | 1.04306i | ||||
\(467\) | 20.7846 | + | 12.0000i | 0.961797 | + | 0.555294i | 0.896726 | − | 0.442587i | \(-0.145939\pi\) |
0.0650714 | + | 0.997881i | \(0.479272\pi\) | |||||||
\(468\) | − | 2.00000i | − | 0.0924500i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.00000 | + | 15.5885i | −0.414698 | + | 0.718278i | ||||
\(472\) | −20.7846 | + | 12.0000i | −0.956689 | + | 0.552345i | ||||
\(473\) | −20.7846 | + | 12.0000i | −0.955677 | + | 0.551761i | ||||
\(474\) | −2.00000 | + | 3.46410i | −0.0918630 | + | 0.159111i | ||||
\(475\) | −18.0000 | + | 24.0000i | −0.825897 | + | 1.10120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | 5.19615 | + | 3.00000i | 0.237666 | + | 0.137217i | ||||
\(479\) | 12.0000 | + | 20.7846i | 0.548294 | + | 0.949673i | 0.998392 | + | 0.0566937i | \(0.0180558\pi\) |
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(480\) | −6.16025 | + | 9.33013i | −0.281176 | + | 0.425860i | ||||
\(481\) | −4.00000 | + | 6.92820i | −0.182384 | + | 0.315899i | ||||
\(482\) | − | 22.0000i | − | 1.00207i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.0000 | 1.13636 | ||||||||
\(485\) | −0.267949 | + | 4.46410i | −0.0121669 | + | 0.202704i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 10.3923 | − | 6.00000i | 0.470920 | − | 0.271886i | −0.245705 | − | 0.969345i | \(-0.579019\pi\) |
0.716625 | + | 0.697459i | \(0.245686\pi\) | |||||||
\(488\) | −5.19615 | − | 3.00000i | −0.235219 | − | 0.135804i | ||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0000 | 0.451294 | 0.225647 | − | 0.974209i | \(-0.427550\pi\) | ||||
0.225647 | + | 0.974209i | \(0.427550\pi\) | |||||||
\(492\) | 1.73205 | + | 1.00000i | 0.0780869 | + | 0.0450835i | ||||
\(493\) | 6.92820 | − | 4.00000i | 0.312031 | − | 0.180151i | ||||
\(494\) | −6.00000 | − | 10.3923i | −0.269953 | − | 0.467572i | ||||
\(495\) | −13.3923 | − | 0.803848i | −0.601939 | − | 0.0361303i | ||||
\(496\) | 10.0000 | 0.449013 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.00000i | 0.358489i | ||||||||
\(499\) | 2.00000 | − | 3.46410i | 0.0895323 | − | 0.155074i | −0.817781 | − | 0.575529i | \(-0.804796\pi\) |
0.907314 | + | 0.420455i | \(0.138129\pi\) | |||||||
\(500\) | 3.76795 | + | 10.5263i | 0.168508 | + | 0.470750i | ||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.0000i | 1.60516i | 0.596544 | + | 0.802580i | \(0.296540\pi\) | ||||
−0.596544 | + | 0.802580i | \(0.703460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | − | 12.0000i | −0.266996 | − | 0.533993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.79423 | + | 4.50000i | −0.346154 | + | 0.199852i | ||||
\(508\) | 17.3205 | − | 10.0000i | 0.768473 | − | 0.443678i | ||||
\(509\) | 15.0000 | − | 25.9808i | 0.664863 | − | 1.15158i | −0.314459 | − | 0.949271i | \(-0.601823\pi\) |
0.979322 | − | 0.202306i | \(-0.0648436\pi\) | |||||||
\(510\) | 8.00000 | − | 4.00000i | 0.354246 | − | 0.177123i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | −5.19615 | − | 3.00000i | −0.229416 | − | 0.132453i | ||||
\(514\) | −8.00000 | − | 13.8564i | −0.352865 | − | 0.611180i | ||||
\(515\) | −14.9282 | − | 9.85641i | −0.657815 | − | 0.434325i | ||||
\(516\) | −2.00000 | + | 3.46410i | −0.0880451 | + | 0.152499i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.3923 | − | 0.803848i | −0.587291 | − | 0.0352510i | ||||
\(521\) | −19.0000 | − | 32.9090i | −0.832405 | − | 1.44177i | −0.896126 | − | 0.443800i | \(-0.853630\pi\) |
0.0637207 | − | 0.997968i | \(-0.479703\pi\) | |||||||
\(522\) | 1.73205 | − | 1.00000i | 0.0758098 | − | 0.0437688i | ||||
\(523\) | 17.3205 | + | 10.0000i | 0.757373 | + | 0.437269i | 0.828352 | − | 0.560208i | \(-0.189279\pi\) |
−0.0709788 | + | 0.997478i | \(0.522612\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 34.6410 | + | 20.0000i | 1.50899 | + | 0.871214i | ||||
\(528\) | −5.19615 | + | 3.00000i | −0.226134 | + | 0.130558i | ||||
\(529\) | −11.5000 | − | 19.9186i | −0.500000 | − | 0.866025i | ||||
\(530\) | 13.3923 | + | 0.803848i | 0.581725 | + | 0.0349169i | ||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000i | 0.173259i | ||||||||
\(534\) | −3.00000 | + | 5.19615i | −0.129823 | + | 0.224860i | ||||
\(535\) | 7.46410 | + | 4.92820i | 0.322701 | + | 0.213065i | ||||
\(536\) | 24.0000 | + | 41.5692i | 1.03664 | + | 1.79552i | ||||
\(537\) | 12.1244 | + | 7.00000i | 0.523205 | + | 0.302072i | ||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.00000 | + | 1.00000i | −0.0860663 | + | 0.0430331i | ||||
\(541\) | −3.00000 | + | 5.19615i | −0.128980 | + | 0.223400i | −0.923282 | − | 0.384124i | \(-0.874504\pi\) |
0.794302 | + | 0.607524i | \(0.207837\pi\) | |||||||
\(542\) | 12.1244 | − | 7.00000i | 0.520786 | − | 0.300676i | ||||
\(543\) | 5.19615 | − | 3.00000i | 0.222988 | − | 0.128742i | ||||
\(544\) | −10.0000 | + | 17.3205i | −0.428746 | + | 0.742611i | ||||
\(545\) | −2.00000 | − | 4.00000i | −0.0856706 | − | 0.171341i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.0000i | − | 0.684111i | −0.939680 | − | 0.342055i | \(-0.888877\pi\) | ||
0.939680 | − | 0.342055i | \(-0.111123\pi\) | |||||||
\(548\) | 5.19615 | + | 3.00000i | 0.221969 | + | 0.128154i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | −3.58846 | + | 29.7846i | −0.153012 | + | 1.27002i | ||||
\(551\) | −6.00000 | + | 10.3923i | −0.255609 | + | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −28.0000 | −1.18961 | ||||||||
\(555\) | 8.92820 | + | 0.535898i | 0.378981 | + | 0.0227476i | ||||
\(556\) | 1.00000 | + | 1.73205i | 0.0424094 | + | 0.0734553i | ||||
\(557\) | 32.9090 | − | 19.0000i | 1.39440 | − | 0.805056i | 0.400599 | − | 0.916253i | \(-0.368802\pi\) |
0.993798 | + | 0.111198i | \(0.0354686\pi\) | |||||||
\(558\) | 8.66025 | + | 5.00000i | 0.366618 | + | 0.211667i | ||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | −1.73205 | − | 1.00000i | −0.0730622 | − | 0.0421825i | ||||
\(563\) | 31.1769 | − | 18.0000i | 1.31395 | − | 0.758610i | 0.331202 | − | 0.943560i | \(-0.392546\pi\) |
0.982748 | + | 0.184950i | \(0.0592124\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.803848 | + | 13.3923i | −0.0338181 | + | 0.563418i | ||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 30.0000i | − | 1.25877i | ||||||
\(569\) | −15.0000 | + | 25.9808i | −0.628833 | + | 1.08917i | 0.358954 | + | 0.933355i | \(0.383134\pi\) |
−0.987786 | + | 0.155815i | \(0.950200\pi\) | |||||||
\(570\) | −7.39230 | + | 11.1962i | −0.309630 | + | 0.468955i | ||||
\(571\) | −18.0000 | − | 31.1769i | −0.753277 | − | 1.30471i | −0.946227 | − | 0.323505i | \(-0.895139\pi\) |
0.192950 | − | 0.981209i | \(-0.438194\pi\) | |||||||
\(572\) | 10.3923 | + | 6.00000i | 0.434524 | + | 0.250873i | ||||
\(573\) | 18.0000i | 0.751961i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.50000 | + | 6.06218i | −0.145833 | + | 0.252591i | ||||
\(577\) | 12.1244 | − | 7.00000i | 0.504744 | − | 0.291414i | −0.225927 | − | 0.974144i | \(-0.572541\pi\) |
0.730670 | + | 0.682730i | \(0.239208\pi\) | |||||||
\(578\) | −0.866025 | + | 0.500000i | −0.0360219 | + | 0.0207973i | ||||
\(579\) | −4.00000 | + | 6.92820i | −0.166234 | + | 0.287926i | ||||
\(580\) | 2.00000 | + | 4.00000i | 0.0830455 | + | 0.166091i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.00000i | 0.0829027i | ||||||||
\(583\) | −31.1769 | − | 18.0000i | −1.29122 | − | 0.745484i | ||||
\(584\) | −9.00000 | − | 15.5885i | −0.372423 | − | 0.645055i | ||||
\(585\) | −3.73205 | − | 2.46410i | −0.154301 | − | 0.101878i | ||||
\(586\) | 12.0000 | − | 20.7846i | 0.495715 | − | 0.858604i | ||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.0000 | −2.47226 | ||||||||
\(590\) | −1.07180 | + | 17.8564i | −0.0441252 | + | 0.735137i | ||||
\(591\) | −1.00000 | − | 1.73205i | −0.0411345 | − | 0.0712470i | ||||
\(592\) | 3.46410 | − | 2.00000i | 0.142374 | − | 0.0821995i | ||||
\(593\) | 38.1051 | + | 22.0000i | 1.56479 | + | 0.903432i | 0.996761 | + | 0.0804231i | \(0.0256271\pi\) |
0.568029 | + | 0.823009i | \(0.307706\pi\) | |||||||
\(594\) | −6.00000 | −0.246183 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.0000 | 0.573462 | ||||||||
\(597\) | −12.1244 | − | 7.00000i | −0.496217 | − | 0.286491i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.00000 | − | 1.73205i | −0.0408589 | − | 0.0707697i | 0.844873 | − | 0.534967i | \(-0.179676\pi\) |
−0.885732 | + | 0.464198i | \(0.846343\pi\) | |||||||
\(600\) | 5.89230 | + | 13.7942i | 0.240552 | + | 0.563147i | ||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.0000i | 0.651570i | ||||||||
\(604\) | −4.00000 | + | 6.92820i | −0.162758 | + | 0.281905i | ||||
\(605\) | 30.8013 | − | 46.6506i | 1.25225 | − | 1.89662i | ||||
\(606\) | −3.00000 | − | 5.19615i | −0.121867 | − | 0.211079i | ||||
\(607\) | −20.7846 | − | 12.0000i | −0.843621 | − | 0.487065i | 0.0148722 | − | 0.999889i | \(-0.495266\pi\) |
−0.858494 | + | 0.512824i | \(0.828599\pi\) | |||||||
\(608\) | − | 30.0000i | − | 1.21666i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.00000 | + | 2.00000i | −0.161955 | + | 0.0809776i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.46410 | + | 2.00000i | −0.140028 | + | 0.0808452i | ||||
\(613\) | −3.46410 | + | 2.00000i | −0.139914 | + | 0.0807792i | −0.568323 | − | 0.822806i | \(-0.692408\pi\) |
0.428409 | + | 0.903585i | \(0.359074\pi\) | |||||||
\(614\) | −2.00000 | + | 3.46410i | −0.0807134 | + | 0.139800i | ||||
\(615\) | 4.00000 | − | 2.00000i | 0.161296 | − | 0.0806478i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 26.0000i | − | 1.04672i | −0.852111 | − | 0.523360i | \(-0.824678\pi\) | ||
0.852111 | − | 0.523360i | \(-0.175322\pi\) | |||||||
\(618\) | −6.92820 | − | 4.00000i | −0.278693 | − | 0.160904i | ||||
\(619\) | 5.00000 | + | 8.66025i | 0.200967 | + | 0.348085i | 0.948840 | − | 0.315757i | \(-0.102258\pi\) |
−0.747873 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(620\) | −12.3205 | + | 18.6603i | −0.494804 | + | 0.749414i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000i | 0.962312i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 3.00000 | + | 5.19615i | 0.119904 | + | 0.207680i | ||||
\(627\) | 31.1769 | − | 18.0000i | 1.24509 | − | 0.718851i | ||||
\(628\) | −15.5885 | − | 9.00000i | −0.622047 | − | 0.359139i | ||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | −10.3923 | − | 6.00000i | −0.413384 | − | 0.238667i | ||||
\(633\) | 13.8564 | − | 8.00000i | 0.550743 | − | 0.317971i | ||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | 2.67949 | − | 44.6410i | 0.106332 | − | 1.77152i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | 5.00000 | − | 8.66025i | 0.197797 | − | 0.342594i | ||||
\(640\) | −5.59808 | − | 3.69615i | −0.221283 | − | 0.146103i | ||||
\(641\) | 1.00000 | + | 1.73205i | 0.0394976 | + | 0.0684119i | 0.885098 | − | 0.465404i | \(-0.154091\pi\) |
−0.845601 | + | 0.533816i | \(0.820758\pi\) | |||||||
\(642\) | 3.46410 | + | 2.00000i | 0.136717 | + | 0.0789337i | ||||
\(643\) | 20.0000i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | + | 8.00000i | 0.157500 | + | 0.315000i | ||||
\(646\) | −12.0000 | + | 20.7846i | −0.472134 | + | 0.817760i | ||||
\(647\) | −17.3205 | + | 10.0000i | −0.680939 | + | 0.393141i | −0.800209 | − | 0.599721i | \(-0.795278\pi\) |
0.119269 | + | 0.992862i | \(0.461945\pi\) | |||||||
\(648\) | −2.59808 | + | 1.50000i | −0.102062 | + | 0.0589256i | ||||
\(649\) | 24.0000 | − | 41.5692i | 0.942082 | − | 1.63173i | ||||
\(650\) | −6.00000 | + | 8.00000i | −0.235339 | + | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 4.00000i | − | 0.156652i | ||||||
\(653\) | 1.73205 | + | 1.00000i | 0.0677804 | + | 0.0391330i | 0.533507 | − | 0.845796i | \(-0.320874\pi\) |
−0.465727 | + | 0.884929i | \(0.654207\pi\) | |||||||
\(654\) | −1.00000 | − | 1.73205i | −0.0391031 | − | 0.0677285i | ||||
\(655\) | 4.92820 | − | 7.46410i | 0.192561 | − | 0.291647i | ||||
\(656\) | 1.00000 | − | 1.73205i | 0.0390434 | − | 0.0676252i | ||||
\(657\) | − | 6.00000i | − | 0.234082i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0000 | 0.701180 | 0.350590 | − | 0.936529i | \(-0.385981\pi\) | ||||
0.350590 | + | 0.936529i | \(0.385981\pi\) | |||||||
\(660\) | 0.803848 | − | 13.3923i | 0.0312897 | − | 0.521295i | ||||
\(661\) | 9.00000 | + | 15.5885i | 0.350059 | + | 0.606321i | 0.986260 | − | 0.165203i | \(-0.0528281\pi\) |
−0.636200 | + | 0.771524i | \(0.719495\pi\) | |||||||
\(662\) | 20.7846 | − | 12.0000i | 0.807817 | − | 0.466393i | ||||
\(663\) | −6.92820 | − | 4.00000i | −0.269069 | − | 0.155347i | ||||
\(664\) | −24.0000 | −0.931381 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 10.3923 | − | 6.00000i | 0.402090 | − | 0.232147i | ||||
\(669\) | −12.0000 | − | 20.7846i | −0.463947 | − | 0.803579i | ||||
\(670\) | 35.7128 | + | 2.14359i | 1.37971 | + | 0.0828142i | ||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.0000i | 1.38770i | 0.720121 | + | 0.693849i | \(0.244086\pi\) | ||||
−0.720121 | + | 0.693849i | \(0.755914\pi\) | |||||||
\(674\) | 12.0000 | − | 20.7846i | 0.462223 | − | 0.800593i | ||||
\(675\) | −0.598076 | + | 4.96410i | −0.0230200 | + | 0.191068i | ||||
\(676\) | −4.50000 | − | 7.79423i | −0.173077 | − | 0.299778i | ||||
\(677\) | −27.7128 | − | 16.0000i | −1.06509 | − | 0.614930i | −0.138254 | − | 0.990397i | \(-0.544149\pi\) |
−0.926836 | + | 0.375467i | \(0.877482\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.0000 | + | 24.0000i | 0.460179 | + | 0.920358i | ||||
\(681\) | −4.00000 | + | 6.92820i | −0.153280 | + | 0.265489i | ||||
\(682\) | −51.9615 | + | 30.0000i | −1.98971 | + | 1.14876i | ||||
\(683\) | −24.2487 | + | 14.0000i | −0.927851 | + | 0.535695i | −0.886131 | − | 0.463434i | \(-0.846617\pi\) |
−0.0417198 | + | 0.999129i | \(0.513284\pi\) | |||||||
\(684\) | 3.00000 | − | 5.19615i | 0.114708 | − | 0.198680i | ||||
\(685\) | 12.0000 | − | 6.00000i | 0.458496 | − | 0.229248i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 10.0000i | − | 0.381524i | ||||||
\(688\) | 3.46410 | + | 2.00000i | 0.132068 | + | 0.0762493i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.0000 | − | 43.3013i | 0.951045 | − | 1.64726i | 0.207875 | − | 0.978155i | \(-0.433345\pi\) |
0.743170 | − | 0.669102i | \(-0.233321\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 4.46410 | + | 0.267949i | 0.169333 | + | 0.0101639i | ||||
\(696\) | 3.00000 | + | 5.19615i | 0.113715 | + | 0.196960i | ||||
\(697\) | 6.92820 | − | 4.00000i | 0.262424 | − | 0.151511i | ||||
\(698\) | 1.73205 | + | 1.00000i | 0.0655591 | + | 0.0378506i | ||||
\(699\) | 26.0000 | 0.983410 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.0000 | −0.377695 | −0.188847 | − | 0.982006i | \(-0.560475\pi\) | ||||
−0.188847 | + | 0.982006i | \(0.560475\pi\) | |||||||
\(702\) | −1.73205 | − | 1.00000i | −0.0653720 | − | 0.0377426i | ||||
\(703\) | −20.7846 | + | 12.0000i | −0.783906 | + | 0.452589i | ||||
\(704\) | −21.0000 | − | 36.3731i | −0.791467 | − | 1.37086i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.0000 | −0.752710 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 8.00000i | − | 0.300658i | ||||||
\(709\) | 13.0000 | − | 22.5167i | 0.488225 | − | 0.845631i | −0.511683 | − | 0.859174i | \(-0.670978\pi\) |
0.999908 | + | 0.0135434i | \(0.00431112\pi\) | |||||||
\(710\) | −18.6603 | − | 12.3205i | −0.700307 | − | 0.462380i | ||||
\(711\) | −2.00000 | − | 3.46410i | −0.0750059 | − | 0.129914i | ||||
\(712\) | −15.5885 | − | 9.00000i | −0.584202 | − | 0.337289i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | − | 12.0000i | 0.897549 | − | 0.448775i | ||||
\(716\) | −7.00000 | + | 12.1244i | −0.261602 | + | 0.453108i | ||||
\(717\) | −5.19615 | + | 3.00000i | −0.194054 | + | 0.112037i | ||||
\(718\) | 19.0526 | − | 11.0000i | 0.711035 | − | 0.410516i | ||||
\(719\) | 6.00000 | − | 10.3923i | 0.223762 | − | 0.387568i | −0.732185 | − | 0.681106i | \(-0.761499\pi\) |
0.955947 | + | 0.293538i | \(0.0948328\pi\) | |||||||
\(720\) | 1.00000 | + | 2.00000i | 0.0372678 | + | 0.0745356i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | 19.0526 | + | 11.0000i | 0.708572 | + | 0.409094i | ||||
\(724\) | 3.00000 | + | 5.19615i | 0.111494 | + | 0.193113i | ||||
\(725\) | 9.92820 | + | 1.19615i | 0.368724 | + | 0.0444240i | ||||
\(726\) | 12.5000 | − | 21.6506i | 0.463919 | − | 0.803530i | ||||
\(727\) | − | 40.0000i | − | 1.48352i | −0.670667 | − | 0.741759i | \(-0.733992\pi\) | ||
0.670667 | − | 0.741759i | \(-0.266008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −13.3923 | − | 0.803848i | −0.495671 | − | 0.0297517i | ||||
\(731\) | 8.00000 | + | 13.8564i | 0.295891 | + | 0.512498i | ||||
\(732\) | 1.73205 | − | 1.00000i | 0.0640184 | − | 0.0369611i | ||||
\(733\) | 19.0526 | + | 11.0000i | 0.703722 | + | 0.406294i | 0.808732 | − | 0.588177i | \(-0.200154\pi\) |
−0.105010 | + | 0.994471i | \(0.533487\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −83.1384 | − | 48.0000i | −3.06244 | − | 1.76810i | ||||
\(738\) | 1.73205 | − | 1.00000i | 0.0637577 | − | 0.0368105i | ||||
\(739\) | −22.0000 | − | 38.1051i | −0.809283 | − | 1.40172i | −0.913361 | − | 0.407150i | \(-0.866523\pi\) |
0.104078 | − | 0.994569i | \(-0.466811\pi\) | |||||||
\(740\) | −0.535898 | + | 8.92820i | −0.0197000 | + | 0.328207i | ||||
\(741\) | 12.0000 | 0.440831 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 40.0000i | − | 1.46746i | −0.679442 | − | 0.733729i | \(-0.737778\pi\) | ||
0.679442 | − | 0.733729i | \(-0.262222\pi\) | |||||||
\(744\) | −15.0000 | + | 25.9808i | −0.549927 | + | 0.952501i | ||||
\(745\) | 17.2487 | − | 26.1244i | 0.631944 | − | 0.957122i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.92820 | − | 4.00000i | −0.253490 | − | 0.146352i | ||||
\(748\) | − | 24.0000i | − | 0.877527i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.0000 | + | 2.00000i | 0.401663 | + | 0.0730297i | ||||
\(751\) | 6.00000 | − | 10.3923i | 0.218943 | − | 0.379221i | −0.735542 | − | 0.677479i | \(-0.763072\pi\) |
0.954485 | + | 0.298259i | \(0.0964058\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.00000 | + | 3.46410i | −0.0728357 | + | 0.126155i | ||||
\(755\) | 8.00000 | + | 16.0000i | 0.291150 | + | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 40.0000i | − | 1.45382i | −0.686730 | − | 0.726912i | \(-0.740955\pi\) | ||
0.686730 | − | 0.726912i | \(-0.259045\pi\) | |||||||
\(758\) | 24.2487 | + | 14.0000i | 0.880753 | + | 0.508503i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −33.5885 | − | 22.1769i | −1.21838 | − | 0.804441i | ||||
\(761\) | 11.0000 | − | 19.0526i | 0.398750 | − | 0.690655i | −0.594822 | − | 0.803857i | \(-0.702778\pi\) |
0.993572 | + | 0.113203i | \(0.0361109\pi\) | |||||||
\(762\) | − | 20.0000i | − | 0.724524i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | −0.535898 | + | 8.92820i | −0.0193754 | + | 0.322800i | ||||
\(766\) | −10.0000 | − | 17.3205i | −0.361315 | − | 0.625815i | ||||
\(767\) | 13.8564 | − | 8.00000i | 0.500326 | − | 0.288863i | ||||
\(768\) | −14.7224 | − | 8.50000i | −0.531250 | − | 0.306717i | ||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0000 | 0.576226 | ||||||||
\(772\) | −6.92820 | − | 4.00000i | −0.249351 | − | 0.143963i | ||||
\(773\) | −20.7846 | + | 12.0000i | −0.747570 | + | 0.431610i | −0.824815 | − | 0.565402i | \(-0.808721\pi\) |
0.0772449 | + | 0.997012i | \(0.475388\pi\) | |||||||
\(774\) | 2.00000 | + | 3.46410i | 0.0718885 | + | 0.124515i | ||||
\(775\) | 19.6410 | + | 45.9808i | 0.705526 | + | 1.65168i | ||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.0000i | 0.932145i | ||||||||
\(779\) | −6.00000 | + | 10.3923i | −0.214972 | + | 0.372343i | ||||
\(780\) | 2.46410 | − | 3.73205i | 0.0882290 | − | 0.133629i | ||||
\(781\) | 30.0000 | + | 51.9615i | 1.07348 | + | 1.85933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | + | 18.0000i | −1.28490 | + | 0.642448i | ||||
\(786\) | 2.00000 | − | 3.46410i | 0.0713376 | − | 0.123560i | ||||
\(787\) | −3.46410 | + | 2.00000i | −0.123482 | + | 0.0712923i | −0.560469 | − | 0.828176i | \(-0.689379\pi\) |
0.436987 | + | 0.899468i | \(0.356046\pi\) | |||||||
\(788\) | 1.73205 | − | 1.00000i | 0.0617018 | − | 0.0356235i | ||||
\(789\) | −12.0000 | + | 20.7846i | −0.427211 | + | 0.739952i | ||||
\(790\) | −8.00000 | + | 4.00000i | −0.284627 | + | 0.142314i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 18.0000i | − | 0.639602i | ||||||
\(793\) | 3.46410 | + | 2.00000i | 0.123014 | + | 0.0710221i | ||||
\(794\) | −11.0000 | − | 19.0526i | −0.390375 | − | 0.676150i | ||||
\(795\) | −7.39230 | + | 11.1962i | −0.262178 | + | 0.397087i | ||||
\(796\) | 7.00000 | − | 12.1244i | 0.248108 | − | 0.429736i | ||||
\(797\) | − | 16.0000i | − | 0.566749i | −0.959009 | − | 0.283375i | \(-0.908546\pi\) | ||
0.959009 | − | 0.283375i | \(-0.0914540\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −22.9904 | + | 9.82051i | −0.812833 | + | 0.347207i | ||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 25.9808 | − | 15.0000i | 0.917413 | − | 0.529668i | ||||
\(803\) | 31.1769 | + | 18.0000i | 1.10021 | + | 0.635206i | ||||
\(804\) | −16.0000 | −0.564276 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | 12.1244 | + | 7.00000i | 0.426798 | + | 0.246412i | ||||
\(808\) | 15.5885 | − | 9.00000i | 0.548400 | − | 0.316619i | ||||
\(809\) | −9.00000 | − | 15.5885i | −0.316423 | − | 0.548061i | 0.663316 | − | 0.748340i | \(-0.269149\pi\) |
−0.979739 | + | 0.200279i | \(0.935815\pi\) | |||||||
\(810\) | −0.133975 | + | 2.23205i | −0.00470739 | + | 0.0784263i | ||||
\(811\) | 34.0000 | 1.19390 | 0.596951 | − | 0.802278i | \(-0.296379\pi\) | ||||
0.596951 | + | 0.802278i | \(0.296379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0000i | 0.491001i | ||||||||
\(814\) | −12.0000 | + | 20.7846i | −0.420600 | + | 0.728500i | ||||
\(815\) | −7.46410 | − | 4.92820i | −0.261456 | − | 0.172627i | ||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | −20.7846 | − | 12.0000i | −0.727161 | − | 0.419827i | ||||
\(818\) | − | 22.0000i | − | 0.769212i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.00000 | + | 4.00000i | 0.0698430 | + | 0.139686i | ||||
\(821\) | 1.00000 | − | 1.73205i | 0.0349002 | − | 0.0604490i | −0.848048 | − | 0.529920i | \(-0.822222\pi\) |
0.882948 | + | 0.469471i | \(0.155555\pi\) | |||||||
\(822\) | 5.19615 | − | 3.00000i | 0.181237 | − | 0.104637i | ||||
\(823\) | −38.1051 | + | 22.0000i | −1.32826 | + | 0.766872i | −0.985031 | − | 0.172379i | \(-0.944854\pi\) |
−0.343230 | + | 0.939251i | \(0.611521\pi\) | |||||||
\(824\) | 12.0000 | − | 20.7846i | 0.418040 | − | 0.724066i | ||||
\(825\) | −24.0000 | − | 18.0000i | −0.835573 | − | 0.626680i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.00000 | − | 5.19615i | −0.104194 | − | 0.180470i | 0.809214 | − | 0.587513i | \(-0.199893\pi\) |
−0.913409 | + | 0.407044i | \(0.866560\pi\) | |||||||
\(830\) | −9.85641 | + | 14.9282i | −0.342121 | + | 0.518165i | ||||
\(831\) | 14.0000 | − | 24.2487i | 0.485655 | − | 0.841178i | ||||
\(832\) | − | 14.0000i | − | 0.485363i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.00000 | 0.0692543 | ||||||||
\(835\) | 1.60770 | − | 26.7846i | 0.0556366 | − | 0.926920i | ||||
\(836\) | 18.0000 | + | 31.1769i | 0.622543 | + | 1.07828i | ||||
\(837\) | −8.66025 | + | 5.00000i | −0.299342 | + | 0.172825i | ||||
\(838\) | 10.3923 | + | 6.00000i | 0.358996 | + | 0.207267i | ||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 15.5885 | + | 9.00000i | 0.537214 | + | 0.310160i | ||||
\(843\) | 1.73205 | − | 1.00000i | 0.0596550 | − | 0.0344418i | ||||
\(844\) | 8.00000 | + | 13.8564i | 0.275371 | + | 0.476957i | ||||
\(845\) | −20.0885 | − | 1.20577i | −0.691064 | − | 0.0414798i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | 10.0000 | − | 17.3205i | 0.343199 | − | 0.594438i | ||||
\(850\) | 19.8564 | + | 2.39230i | 0.681069 | + | 0.0820554i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 8.66025 | + | 5.00000i | 0.296695 | + | 0.171297i | ||||
\(853\) | − | 30.0000i | − | 1.02718i | −0.858036 | − | 0.513590i | \(-0.828315\pi\) | ||
0.858036 | − | 0.513590i | \(-0.171685\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | − | 12.0000i | −0.205196 | − | 0.410391i | ||||
\(856\) | −6.00000 | + | 10.3923i | −0.205076 | + | 0.355202i | ||||
\(857\) | −20.7846 | + | 12.0000i | −0.709989 | + | 0.409912i | −0.811057 | − | 0.584967i | \(-0.801107\pi\) |
0.101068 | + | 0.994880i | \(0.467774\pi\) | |||||||
\(858\) | 10.3923 | − | 6.00000i | 0.354787 | − | 0.204837i | ||||
\(859\) | −13.0000 | + | 22.5167i | −0.443554 | + | 0.768259i | −0.997950 | − | 0.0639945i | \(-0.979616\pi\) |
0.554396 | + | 0.832253i | \(0.312949\pi\) | |||||||
\(860\) | −8.00000 | + | 4.00000i | −0.272798 | + | 0.136399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.0000i | 0.476842i | ||||||||
\(863\) | −20.7846 | − | 12.0000i | −0.707516 | − | 0.408485i | 0.102624 | − | 0.994720i | \(-0.467276\pi\) |
−0.810141 | + | 0.586235i | \(0.800609\pi\) | |||||||
\(864\) | −2.50000 | − | 4.33013i | −0.0850517 | − | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.0000 | + | 29.4449i | −0.577684 | + | 1.00058i | ||||
\(867\) | − | 1.00000i | − | 0.0339618i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 4.46410 | + | 0.267949i | 0.151347 | + | 0.00908433i | ||||
\(871\) | −16.0000 | − | 27.7128i | −0.542139 | − | 0.939013i | ||||
\(872\) | 5.19615 | − | 3.00000i | 0.175964 | − | 0.101593i | ||||
\(873\) | −1.73205 | − | 1.00000i | −0.0586210 | − | 0.0338449i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | 3.46410 | + | 2.00000i | 0.116974 | + | 0.0675352i | 0.557346 | − | 0.830281i | \(-0.311820\pi\) |
−0.440371 | + | 0.897816i | \(0.645153\pi\) | |||||||
\(878\) | 5.19615 | − | 3.00000i | 0.175362 | − | 0.101245i | ||||
\(879\) | 12.0000 | + | 20.7846i | 0.404750 | + | 0.701047i | ||||
\(880\) | −13.3923 | − | 0.803848i | −0.451455 | − | 0.0270977i | ||||
\(881\) | 14.0000 | 0.471672 | 0.235836 | − | 0.971793i | \(-0.424217\pi\) | ||||
0.235836 | + | 0.971793i | \(0.424217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.0000i | 1.61533i | 0.589643 | + | 0.807664i | \(0.299269\pi\) | ||||
−0.589643 | + | 0.807664i | \(0.700731\pi\) | |||||||
\(884\) | 4.00000 | − | 6.92820i | 0.134535 | − | 0.233021i | ||||
\(885\) | −14.9282 | − | 9.85641i | −0.501806 | − | 0.331319i | ||||
\(886\) | −2.00000 | − | 3.46410i | −0.0671913 | − | 0.116379i | ||||
\(887\) | −6.92820 | − | 4.00000i | −0.232626 | − | 0.134307i | 0.379157 | − | 0.925332i | \(-0.376214\pi\) |
−0.611783 | + | 0.791026i | \(0.709547\pi\) | |||||||
\(888\) | 12.0000i | 0.402694i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.0000 | + | 6.00000i | −0.402241 | + | 0.201120i | ||||
\(891\) | 3.00000 | − | 5.19615i | 0.100504 | − | 0.174078i | ||||
\(892\) | 20.7846 | − | 12.0000i | 0.695920 | − | 0.401790i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 7.00000 | − | 12.1244i | 0.234115 | − | 0.405499i | ||||
\(895\) | 14.0000 | + | 28.0000i | 0.467968 | + | 0.935937i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.66025 | − | 5.00000i | −0.288996 | − | 0.166852i | ||||
\(899\) | 10.0000 | + | 17.3205i | 0.333519 | + | 0.577671i | ||||
\(900\) | −4.96410 | − | 0.598076i | −0.165470 | − | 0.0199359i | ||||
\(901\) | −12.0000 | + | 20.7846i | −0.399778 | + | 0.692436i | ||||
\(902\) | 12.0000i | 0.399556i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 13.3923 | + | 0.803848i | 0.445175 | + | 0.0267208i | ||||
\(906\) | 4.00000 | + | 6.92820i | 0.132891 | + | 0.230174i | ||||
\(907\) | 13.8564 | − | 8.00000i | 0.460094 | − | 0.265636i | −0.251990 | − | 0.967730i | \(-0.581085\pi\) |
0.712084 | + | 0.702094i | \(0.247752\pi\) | |||||||
\(908\) | −6.92820 | − | 4.00000i | −0.229920 | − | 0.132745i | ||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | −5.19615 | − | 3.00000i | −0.172062 | − | 0.0993399i | ||||
\(913\) | 41.5692 | − | 24.0000i | 1.37574 | − | 0.794284i | ||||
\(914\) | 10.0000 | + | 17.3205i | 0.330771 | + | 0.572911i | ||||
\(915\) | 0.267949 | − | 4.46410i | 0.00885813 | − | 0.147579i | ||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.00000i | 0.132020i | ||||||||
\(919\) | 14.0000 | − | 24.2487i | 0.461817 | − | 0.799891i | −0.537234 | − | 0.843433i | \(-0.680531\pi\) |
0.999052 | + | 0.0435419i | \(0.0138642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.00000 | − | 3.46410i | −0.0659022 | − | 0.114146i | ||||
\(922\) | 25.9808 | + | 15.0000i | 0.855631 | + | 0.493999i | ||||
\(923\) | 20.0000i | 0.658308i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0000 | + | 12.0000i | 0.526077 | + | 0.394558i | ||||
\(926\) | 18.0000 | − | 31.1769i | 0.591517 | − | 1.02454i | ||||
\(927\) | 6.92820 | − | 4.00000i | 0.227552 | − | 0.131377i | ||||
\(928\) | −8.66025 | + | 5.00000i | −0.284287 | + | 0.164133i | ||||
\(929\) | −7.00000 | + | 12.1244i | −0.229663 | + | 0.397787i | −0.957708 | − | 0.287742i | \(-0.907096\pi\) |
0.728046 | + | 0.685529i | \(0.240429\pi\) | |||||||
\(930\) | 10.0000 | + | 20.0000i | 0.327913 | + | 0.655826i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.0000i | 0.851658i | ||||||||
\(933\) | −20.7846 | − | 12.0000i | −0.680458 | − | 0.392862i | ||||
\(934\) | 12.0000 | + | 20.7846i | 0.392652 | + | 0.680093i | ||||
\(935\) | −44.7846 | − | 29.5692i | −1.46461 | − | 0.967017i | ||||
\(936\) | 3.00000 | − | 5.19615i | 0.0980581 | − | 0.169842i | ||||
\(937\) | 2.00000i | 0.0653372i | 0.999466 | + | 0.0326686i | \(0.0104006\pi\) | ||||
−0.999466 | + | 0.0326686i | \(0.989599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0000 | + | 36.3731i | 0.684580 | + | 1.18573i | 0.973568 | + | 0.228395i | \(0.0733479\pi\) |
−0.288988 | + | 0.957333i | \(0.593319\pi\) | |||||||
\(942\) | −15.5885 | + | 9.00000i | −0.507899 | + | 0.293236i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | 31.1769 | + | 18.0000i | 1.01311 | + | 0.584921i | 0.912102 | − | 0.409964i | \(-0.134459\pi\) |
0.101012 | + | 0.994885i | \(0.467792\pi\) | |||||||
\(948\) | 3.46410 | − | 2.00000i | 0.112509 | − | 0.0649570i | ||||
\(949\) | 6.00000 | + | 10.3923i | 0.194768 | + | 0.337348i | ||||
\(950\) | −27.5885 | + | 11.7846i | −0.895088 | + | 0.382343i | ||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | −3.00000 | + | 5.19615i | −0.0971286 | + | 0.168232i | ||||
\(955\) | −22.1769 | + | 33.5885i | −0.717628 | + | 1.08690i | ||||
\(956\) | −3.00000 | − | 5.19615i | −0.0970269 | − | 0.168056i | ||||
\(957\) | −10.3923 | − | 6.00000i | −0.335936 | − | 0.193952i | ||||
\(958\) | 24.0000i | 0.775405i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −14.0000 | + | 7.00000i | −0.451848 | + | 0.225924i | ||||
\(961\) | −34.5000 | + | 59.7558i | −1.11290 | + | 1.92760i | ||||
\(962\) | −6.92820 | + | 4.00000i | −0.223374 | + | 0.128965i | ||||
\(963\) | −3.46410 | + | 2.00000i | −0.111629 | + | 0.0644491i | ||||
\(964\) | −11.0000 | + | 19.0526i | −0.354286 | + | 0.613642i | ||||
\(965\) | −16.0000 | + | 8.00000i | −0.515058 | + | 0.257529i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.0000i | 1.28631i | 0.765735 | + | 0.643157i | \(0.222376\pi\) | ||||
−0.765735 | + | 0.643157i | \(0.777624\pi\) | |||||||
\(968\) | 64.9519 | + | 37.5000i | 2.08763 | + | 1.20530i | ||||
\(969\) | −12.0000 | − | 20.7846i | −0.385496 | − | 0.667698i | ||||
\(970\) | −2.46410 | + | 3.73205i | −0.0791175 | + | 0.119829i | ||||
\(971\) | 4.00000 | − | 6.92820i | 0.128366 | − | 0.222337i | −0.794678 | − | 0.607032i | \(-0.792360\pi\) |
0.923044 | + | 0.384695i | \(0.125693\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.0000 | 0.384505 | ||||||||
\(975\) | −3.92820 | − | 9.19615i | −0.125803 | − | 0.294513i | ||||
\(976\) | −1.00000 | − | 1.73205i | −0.0320092 | − | 0.0554416i | ||||
\(977\) | 25.9808 | − | 15.0000i | 0.831198 | − | 0.479893i | −0.0230645 | − | 0.999734i | \(-0.507342\pi\) |
0.854263 | + | 0.519841i | \(0.174009\pi\) | |||||||
\(978\) | −3.46410 | − | 2.00000i | −0.110770 | − | 0.0639529i | ||||
\(979\) | 36.0000 | 1.15056 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 8.66025 | + | 5.00000i | 0.276360 | + | 0.159556i | ||||
\(983\) | −20.7846 | + | 12.0000i | −0.662926 | + | 0.382741i | −0.793391 | − | 0.608712i | \(-0.791686\pi\) |
0.130465 | + | 0.991453i | \(0.458353\pi\) | |||||||
\(984\) | 3.00000 | + | 5.19615i | 0.0956365 | + | 0.165647i | ||||
\(985\) | 0.267949 | − | 4.46410i | 0.00853757 | − | 0.142238i | ||||
\(986\) | 8.00000 | 0.254772 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.0000i | 0.381771i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −11.1962 | − | 7.39230i | −0.355837 | − | 0.234943i | ||||
\(991\) | −2.00000 | − | 3.46410i | −0.0635321 | − | 0.110041i | 0.832510 | − | 0.554010i | \(-0.186903\pi\) |
−0.896042 | + | 0.443969i | \(0.853570\pi\) | |||||||
\(992\) | −43.3013 | − | 25.0000i | −1.37482 | − | 0.793751i | ||||
\(993\) | 24.0000i | 0.761617i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0000 | − | 28.0000i | −0.443830 | − | 0.887660i | ||||
\(996\) | 4.00000 | − | 6.92820i | 0.126745 | − | 0.219529i | ||||
\(997\) | 12.1244 | − | 7.00000i | 0.383982 | − | 0.221692i | −0.295567 | − | 0.955322i | \(-0.595509\pi\) |
0.679549 | + | 0.733630i | \(0.262175\pi\) | |||||||
\(998\) | 3.46410 | − | 2.00000i | 0.109654 | − | 0.0633089i | ||||
\(999\) | −2.00000 | + | 3.46410i | −0.0632772 | + | 0.109599i |
(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 | 735.2.q.a.79.2 | 4 | ||
5.4 | even | 2 | inner | 735.2.q.a.79.1 | 4 | ||
7.2 | even | 3 | 105.2.d.a.64.1 | ✓ | 2 | ||
7.3 | odd | 6 | 735.2.q.b.214.1 | 4 | |||
7.4 | even | 3 | inner | 735.2.q.a.214.1 | 4 | ||
7.5 | odd | 6 | 735.2.d.a.589.1 | 2 | |||
7.6 | odd | 2 | 735.2.q.b.79.2 | 4 | |||
21.2 | odd | 6 | 315.2.d.c.64.2 | 2 | |||
21.5 | even | 6 | 2205.2.d.f.1324.2 | 2 | |||
28.23 | odd | 6 | 1680.2.t.f.1009.2 | 2 | |||
35.2 | odd | 12 | 525.2.a.c.1.1 | 1 | |||
35.4 | even | 6 | inner | 735.2.q.a.214.2 | 4 | ||
35.9 | even | 6 | 105.2.d.a.64.2 | yes | 2 | ||
35.12 | even | 12 | 3675.2.a.l.1.1 | 1 | |||
35.19 | odd | 6 | 735.2.d.a.589.2 | 2 | |||
35.23 | odd | 12 | 525.2.a.b.1.1 | 1 | |||
35.24 | odd | 6 | 735.2.q.b.214.2 | 4 | |||
35.33 | even | 12 | 3675.2.a.d.1.1 | 1 | |||
35.34 | odd | 2 | 735.2.q.b.79.1 | 4 | |||
84.23 | even | 6 | 5040.2.t.e.1009.1 | 2 | |||
105.2 | even | 12 | 1575.2.a.e.1.1 | 1 | |||
105.23 | even | 12 | 1575.2.a.i.1.1 | 1 | |||
105.44 | odd | 6 | 315.2.d.c.64.1 | 2 | |||
105.89 | even | 6 | 2205.2.d.f.1324.1 | 2 | |||
140.23 | even | 12 | 8400.2.a.bj.1.1 | 1 | |||
140.79 | odd | 6 | 1680.2.t.f.1009.1 | 2 | |||
140.107 | even | 12 | 8400.2.a.ch.1.1 | 1 | |||
420.359 | even | 6 | 5040.2.t.e.1009.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.a.64.1 | ✓ | 2 | 7.2 | even | 3 | ||
105.2.d.a.64.2 | yes | 2 | 35.9 | even | 6 | ||
315.2.d.c.64.1 | 2 | 105.44 | odd | 6 | |||
315.2.d.c.64.2 | 2 | 21.2 | odd | 6 | |||
525.2.a.b.1.1 | 1 | 35.23 | odd | 12 | |||
525.2.a.c.1.1 | 1 | 35.2 | odd | 12 | |||
735.2.d.a.589.1 | 2 | 7.5 | odd | 6 | |||
735.2.d.a.589.2 | 2 | 35.19 | odd | 6 | |||
735.2.q.a.79.1 | 4 | 5.4 | even | 2 | inner | ||
735.2.q.a.79.2 | 4 | 1.1 | even | 1 | trivial | ||
735.2.q.a.214.1 | 4 | 7.4 | even | 3 | inner | ||
735.2.q.a.214.2 | 4 | 35.4 | even | 6 | inner | ||
735.2.q.b.79.1 | 4 | 35.34 | odd | 2 | |||
735.2.q.b.79.2 | 4 | 7.6 | odd | 2 | |||
735.2.q.b.214.1 | 4 | 7.3 | odd | 6 | |||
735.2.q.b.214.2 | 4 | 35.24 | odd | 6 | |||
1575.2.a.e.1.1 | 1 | 105.2 | even | 12 | |||
1575.2.a.i.1.1 | 1 | 105.23 | even | 12 | |||
1680.2.t.f.1009.1 | 2 | 140.79 | odd | 6 | |||
1680.2.t.f.1009.2 | 2 | 28.23 | odd | 6 | |||
2205.2.d.f.1324.1 | 2 | 105.89 | even | 6 | |||
2205.2.d.f.1324.2 | 2 | 21.5 | even | 6 | |||
3675.2.a.d.1.1 | 1 | 35.33 | even | 12 | |||
3675.2.a.l.1.1 | 1 | 35.12 | even | 12 | |||
5040.2.t.e.1009.1 | 2 | 84.23 | even | 6 | |||
5040.2.t.e.1009.2 | 2 | 420.359 | even | 6 | |||
8400.2.a.bj.1.1 | 1 | 140.23 | even | 12 | |||
8400.2.a.ch.1.1 | 1 | 140.107 | even | 12 |