Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(127,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.bj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.0794958511\) |
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 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1135.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.1135 |
Dual form | 1638.2.bj.d.127.2 |
$q$-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 \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 0.732051i | − | 0.327383i | −0.986512 | − | 0.163692i | \(-0.947660\pi\) | ||
0.986512 | − | 0.163692i | \(-0.0523402\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | − | 0.500000i | 0.327327 | − | 0.188982i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.366025 | − | 0.633975i | 0.115747 | − | 0.200480i | ||||
\(11\) | 3.23205 | + | 1.86603i | 0.974500 | + | 0.562628i | 0.900605 | − | 0.434638i | \(-0.143124\pi\) |
0.0738948 | + | 0.997266i | \(0.476457\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.866025 | − | 3.50000i | −0.240192 | − | 0.970725i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.133975 | − | 0.232051i | −0.0324936 | − | 0.0562806i | 0.849321 | − | 0.527876i | \(-0.177012\pi\) |
−0.881815 | + | 0.471596i | \(0.843678\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.86603 | − | 2.23205i | 0.886927 | − | 0.512068i | 0.0139909 | − | 0.999902i | \(-0.495546\pi\) |
0.872936 | + | 0.487835i | \(0.162213\pi\) | |||||||
\(20\) | 0.633975 | − | 0.366025i | 0.141761 | − | 0.0818458i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.86603 | + | 3.23205i | 0.397838 | + | 0.689076i | ||||
\(23\) | −1.73205 | + | 3.00000i | −0.361158 | + | 0.625543i | −0.988152 | − | 0.153481i | \(-0.950952\pi\) |
0.626994 | + | 0.779024i | \(0.284285\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.46410 | 0.892820 | ||||||||
\(26\) | 1.00000 | − | 3.46410i | 0.196116 | − | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.866025 | + | 0.500000i | 0.163663 | + | 0.0944911i | ||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.66025i | − | 1.37582i | −0.725795 | − | 0.687911i | \(-0.758528\pi\) | ||
0.725795 | − | 0.687911i | \(-0.241472\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 0.267949i | − | 0.0459529i | ||||||
\(35\) | −0.366025 | − | 0.633975i | −0.0618696 | − | 0.107161i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.09808 | + | 0.633975i | 0.180523 | + | 0.104225i | 0.587538 | − | 0.809196i | \(-0.300097\pi\) |
−0.407016 | + | 0.913421i | \(0.633431\pi\) | |||||||
\(38\) | 4.46410 | 0.724173 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.732051 | 0.115747 | ||||||||
\(41\) | 6.06218 | + | 3.50000i | 0.946753 | + | 0.546608i | 0.892071 | − | 0.451896i | \(-0.149252\pi\) |
0.0546823 | + | 0.998504i | \(0.482585\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.366025 | + | 0.633975i | 0.0558184 | + | 0.0966802i | 0.892584 | − | 0.450880i | \(-0.148890\pi\) |
−0.836766 | + | 0.547561i | \(0.815557\pi\) | |||||||
\(44\) | 3.73205i | 0.562628i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 1.73205i | −0.442326 | + | 0.255377i | ||||
\(47\) | − | 4.46410i | − | 0.651156i | −0.945515 | − | 0.325578i | \(-0.894441\pi\) | ||
0.945515 | − | 0.325578i | \(-0.105559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | 3.86603 | + | 2.23205i | 0.546739 | + | 0.315660i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.59808 | − | 2.50000i | 0.360288 | − | 0.346688i | ||||
\(53\) | 10.4641 | 1.43735 | 0.718677 | − | 0.695344i | \(-0.244748\pi\) | ||||
0.718677 | + | 0.695344i | \(0.244748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.36603 | − | 2.36603i | 0.184195 | − | 0.319035i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.59808 | + | 1.50000i | −0.341144 | + | 0.196960i | ||||
\(59\) | −0.803848 | + | 0.464102i | −0.104652 | + | 0.0604209i | −0.551413 | − | 0.834233i | \(-0.685911\pi\) |
0.446760 | + | 0.894654i | \(0.352578\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.86603 | + | 10.1603i | 0.751068 | + | 1.30089i | 0.947306 | + | 0.320331i | \(0.103794\pi\) |
−0.196238 | + | 0.980556i | \(0.562873\pi\) | |||||||
\(62\) | 3.83013 | − | 6.63397i | 0.486427 | − | 0.842516i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.56218 | + | 0.633975i | −0.317799 | + | 0.0786349i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1962 | − | 6.46410i | −1.36783 | − | 0.789716i | −0.377177 | − | 0.926141i | \(-0.623105\pi\) |
−0.990650 | + | 0.136425i | \(0.956439\pi\) | |||||||
\(68\) | 0.133975 | − | 0.232051i | 0.0162468 | − | 0.0281403i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 0.732051i | − | 0.0874968i | ||||||
\(71\) | −1.90192 | + | 1.09808i | −0.225717 | + | 0.130318i | −0.608595 | − | 0.793481i | \(-0.708266\pi\) |
0.382878 | + | 0.923799i | \(0.374933\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.53590i | 0.764969i | 0.923962 | + | 0.382485i | \(0.124931\pi\) | ||||
−0.923962 | + | 0.382485i | \(0.875069\pi\) | |||||||
\(74\) | 0.633975 | + | 1.09808i | 0.0736980 | + | 0.127649i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.86603 | + | 2.23205i | 0.443464 | + | 0.256034i | ||||
\(77\) | 3.73205 | 0.425307 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8564 | 1.22144 | 0.610721 | − | 0.791846i | \(-0.290880\pi\) | ||||
0.610721 | + | 0.791846i | \(0.290880\pi\) | |||||||
\(80\) | 0.633975 | + | 0.366025i | 0.0708805 | + | 0.0409229i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.50000 | + | 6.06218i | 0.386510 | + | 0.669456i | ||||
\(83\) | 5.66025i | 0.621294i | 0.950525 | + | 0.310647i | \(0.100546\pi\) | ||||
−0.950525 | + | 0.310647i | \(0.899454\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.169873 | + | 0.0980762i | −0.0184253 | + | 0.0106379i | ||||
\(86\) | 0.732051i | 0.0789391i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.86603 | + | 3.23205i | −0.198919 | + | 0.344538i | ||||
\(89\) | −5.59808 | − | 3.23205i | −0.593395 | − | 0.342597i | 0.173044 | − | 0.984914i | \(-0.444640\pi\) |
−0.766439 | + | 0.642317i | \(0.777973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | − | 2.59808i | −0.262071 | − | 0.272352i | ||||
\(92\) | −3.46410 | −0.361158 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.23205 | − | 3.86603i | 0.230218 | − | 0.398750i | ||||
\(95\) | −1.63397 | − | 2.83013i | −0.167642 | − | 0.290365i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.633975 | − | 0.366025i | 0.0643704 | − | 0.0371642i | −0.467469 | − | 0.884009i | \(-0.654834\pi\) |
0.531840 | + | 0.846845i | \(0.321501\pi\) | |||||||
\(98\) | 0.866025 | − | 0.500000i | 0.0874818 | − | 0.0505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.23205 | + | 3.86603i | 0.223205 | + | 0.386603i | ||||
\(101\) | 5.00000 | − | 8.66025i | 0.497519 | − | 0.861727i | −0.502477 | − | 0.864590i | \(-0.667578\pi\) |
0.999996 | + | 0.00286291i | \(0.000911295\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.1962 | 1.20172 | 0.600861 | − | 0.799353i | \(-0.294824\pi\) | ||||
0.600861 | + | 0.799353i | \(0.294824\pi\) | |||||||
\(104\) | 3.50000 | − | 0.866025i | 0.343203 | − | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.06218 | + | 5.23205i | 0.880197 | + | 0.508182i | ||||
\(107\) | −0.767949 | + | 1.33013i | −0.0742405 | + | 0.128588i | −0.900756 | − | 0.434326i | \(-0.856987\pi\) |
0.826515 | + | 0.562914i | \(0.190320\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.66025i | − | 0.350589i | −0.984516 | − | 0.175294i | \(-0.943912\pi\) | ||
0.984516 | − | 0.175294i | \(-0.0560877\pi\) | |||||||
\(110\) | 2.36603 | − | 1.36603i | 0.225592 | − | 0.130245i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | −5.09808 | − | 8.83013i | −0.479587 | − | 0.830668i | 0.520139 | − | 0.854081i | \(-0.325880\pi\) |
−0.999726 | + | 0.0234130i | \(0.992547\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.19615 | + | 1.26795i | 0.204792 | + | 0.118237i | ||||
\(116\) | −3.00000 | −0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.928203 | −0.0854480 | ||||||||
\(119\) | −0.232051 | − | 0.133975i | −0.0212721 | − | 0.0122814i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.46410 | + | 2.53590i | 0.133100 | + | 0.230536i | ||||
\(122\) | 11.7321i | 1.06217i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.63397 | − | 3.83013i | 0.595749 | − | 0.343956i | ||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.26795 | + | 10.8564i | −0.556191 | + | 0.963350i | 0.441619 | + | 0.897203i | \(0.354404\pi\) |
−0.997810 | + | 0.0661478i | \(0.978929\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.53590 | − | 0.732051i | −0.222413 | − | 0.0642051i | ||||
\(131\) | −18.9282 | −1.65376 | −0.826882 | − | 0.562375i | \(-0.809888\pi\) | ||||
−0.826882 | + | 0.562375i | \(0.809888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.23205 | − | 3.86603i | 0.193543 | − | 0.335227i | ||||
\(134\) | −6.46410 | − | 11.1962i | −0.558413 | − | 0.967200i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.232051 | − | 0.133975i | 0.0198982 | − | 0.0114882i | ||||
\(137\) | −13.3923 | + | 7.73205i | −1.14418 | + | 0.660594i | −0.947463 | − | 0.319866i | \(-0.896362\pi\) |
−0.196719 | + | 0.980460i | \(0.563029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.06218 | + | 15.6962i | 0.768644 | + | 1.33133i | 0.938298 | + | 0.345827i | \(0.112401\pi\) |
−0.169655 | + | 0.985504i | \(0.554265\pi\) | |||||||
\(140\) | 0.366025 | − | 0.633975i | 0.0309348 | − | 0.0535806i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.19615 | −0.184297 | ||||||||
\(143\) | 3.73205 | − | 12.9282i | 0.312090 | − | 1.08111i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.90192 | + | 1.09808i | 0.157946 | + | 0.0911903i | ||||
\(146\) | −3.26795 | + | 5.66025i | −0.270457 | + | 0.468446i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.26795i | 0.104225i | ||||||||
\(149\) | 16.3923 | − | 9.46410i | 1.34291 | − | 0.775329i | 0.355676 | − | 0.934609i | \(-0.384251\pi\) |
0.987233 | + | 0.159280i | \(0.0509172\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1962i | 1.07389i | 0.843618 | + | 0.536944i | \(0.180421\pi\) | ||||
−0.843618 | + | 0.536944i | \(0.819579\pi\) | |||||||
\(152\) | 2.23205 | + | 3.86603i | 0.181043 | + | 0.313576i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.23205 | + | 1.86603i | 0.260446 | + | 0.150369i | ||||
\(155\) | −5.60770 | −0.450421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4641 | −1.23417 | −0.617085 | − | 0.786897i | \(-0.711686\pi\) | ||||
−0.617085 | + | 0.786897i | \(0.711686\pi\) | |||||||
\(158\) | 9.40192 | + | 5.42820i | 0.747977 | + | 0.431845i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.366025 | + | 0.633975i | 0.0289368 | + | 0.0501201i | ||||
\(161\) | 3.46410i | 0.273009i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.75833 | + | 3.90192i | −0.529353 | + | 0.305622i | −0.740753 | − | 0.671777i | \(-0.765531\pi\) |
0.211400 | + | 0.977400i | \(0.432198\pi\) | |||||||
\(164\) | 7.00000i | 0.546608i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.83013 | + | 4.90192i | −0.219660 | + | 0.380463i | ||||
\(167\) | −5.07180 | − | 2.92820i | −0.392467 | − | 0.226591i | 0.290761 | − | 0.956796i | \(-0.406091\pi\) |
−0.683229 | + | 0.730204i | \(0.739425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | + | 6.06218i | −0.884615 | + | 0.466321i | ||||
\(170\) | −0.196152 | −0.0150442 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.366025 | + | 0.633975i | −0.0279092 | + | 0.0483401i | ||||
\(173\) | −10.3660 | − | 17.9545i | −0.788114 | − | 1.36505i | −0.927121 | − | 0.374763i | \(-0.877724\pi\) |
0.139007 | − | 0.990291i | \(-0.455609\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.86603 | − | 2.23205i | 0.292244 | − | 0.168727i | ||||
\(176\) | −3.23205 | + | 1.86603i | −0.243625 | + | 0.140657i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.23205 | − | 5.59808i | −0.242252 | − | 0.419594i | ||||
\(179\) | −11.1962 | + | 19.3923i | −0.836840 | + | 1.44945i | 0.0556840 | + | 0.998448i | \(0.482266\pi\) |
−0.892524 | + | 0.451000i | \(0.851067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.19615 | −0.0889093 | −0.0444547 | − | 0.999011i | \(-0.514155\pi\) | ||||
−0.0444547 | + | 0.999011i | \(0.514155\pi\) | |||||||
\(182\) | −0.866025 | − | 3.50000i | −0.0641941 | − | 0.259437i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | − | 1.73205i | −0.221163 | − | 0.127688i | ||||
\(185\) | 0.464102 | − | 0.803848i | 0.0341214 | − | 0.0591000i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.00000i | − | 0.0731272i | ||||||
\(188\) | 3.86603 | − | 2.23205i | 0.281959 | − | 0.162789i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 3.26795i | − | 0.237082i | ||||||
\(191\) | −2.09808 | − | 3.63397i | −0.151811 | − | 0.262945i | 0.780082 | − | 0.625677i | \(-0.215177\pi\) |
−0.931893 | + | 0.362732i | \(0.881844\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.8923 | − | 8.59808i | −1.07197 | − | 0.618903i | −0.143252 | − | 0.989686i | \(-0.545756\pi\) |
−0.928719 | + | 0.370783i | \(0.879089\pi\) | |||||||
\(194\) | 0.732051 | 0.0525582 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −1.96410 | − | 1.13397i | −0.139936 | − | 0.0807923i | 0.428397 | − | 0.903591i | \(-0.359078\pi\) |
−0.568334 | + | 0.822798i | \(0.692412\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.09808 | − | 3.63397i | −0.148729 | − | 0.257606i | 0.782029 | − | 0.623242i | \(-0.214185\pi\) |
−0.930758 | + | 0.365636i | \(0.880851\pi\) | |||||||
\(200\) | 4.46410i | 0.315660i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.66025 | − | 5.00000i | 0.609333 | − | 0.351799i | ||||
\(203\) | 3.00000i | 0.210559i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.56218 | − | 4.43782i | 0.178950 | − | 0.309951i | ||||
\(206\) | 10.5622 | + | 6.09808i | 0.735902 | + | 0.424873i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.46410 | + | 1.00000i | 0.240192 | + | 0.0693375i | ||||
\(209\) | 16.6603 | 1.15241 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.92820 | − | 13.7321i | 0.545800 | − | 0.945353i | −0.452756 | − | 0.891634i | \(-0.649559\pi\) |
0.998556 | − | 0.0537189i | \(-0.0171075\pi\) | |||||||
\(212\) | 5.23205 | + | 9.06218i | 0.359339 | + | 0.622393i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.33013 | + | 0.767949i | −0.0909256 | + | 0.0524959i | ||||
\(215\) | 0.464102 | − | 0.267949i | 0.0316515 | − | 0.0182740i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.83013 | − | 6.63397i | −0.260006 | − | 0.450344i | ||||
\(218\) | 1.83013 | − | 3.16987i | 0.123952 | − | 0.214691i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.73205 | 0.184195 | ||||||||
\(221\) | −0.696152 | + | 0.669873i | −0.0468283 | + | 0.0450605i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.26795 | + | 4.19615i | 0.486698 | + | 0.280995i | 0.723204 | − | 0.690635i | \(-0.242669\pi\) |
−0.236506 | + | 0.971630i | \(0.576002\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 10.1962i | − | 0.678238i | ||||||
\(227\) | −7.39230 | + | 4.26795i | −0.490645 | + | 0.283274i | −0.724842 | − | 0.688915i | \(-0.758087\pi\) |
0.234197 | + | 0.972189i | \(0.424754\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.3205i | − | 0.681998i | −0.940064 | − | 0.340999i | \(-0.889235\pi\) | ||
0.940064 | − | 0.340999i | \(-0.110765\pi\) | |||||||
\(230\) | 1.26795 | + | 2.19615i | 0.0836061 | + | 0.144810i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.59808 | − | 1.50000i | −0.170572 | − | 0.0984798i | ||||
\(233\) | 2.19615 | 0.143875 | 0.0719374 | − | 0.997409i | \(-0.477082\pi\) | ||||
0.0719374 | + | 0.997409i | \(0.477082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.26795 | −0.213177 | ||||||||
\(236\) | −0.803848 | − | 0.464102i | −0.0523260 | − | 0.0302104i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.133975 | − | 0.232051i | −0.00868428 | − | 0.0150416i | ||||
\(239\) | 13.8038i | 0.892897i | 0.894809 | + | 0.446448i | \(0.147311\pi\) | ||||
−0.894809 | + | 0.446448i | \(0.852689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0718 | + | 6.39230i | −0.713197 | + | 0.411765i | −0.812244 | − | 0.583318i | \(-0.801754\pi\) |
0.0990466 | + | 0.995083i | \(0.468421\pi\) | |||||||
\(242\) | 2.92820i | 0.188232i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.86603 | + | 10.1603i | −0.375534 | + | 0.650444i | ||||
\(245\) | −0.633975 | − | 0.366025i | −0.0405032 | − | 0.0233845i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1603 | − | 11.5981i | −0.710110 | − | 0.737968i | ||||
\(248\) | 7.66025 | 0.486427 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.46410 | − | 6.00000i | 0.219089 | − | 0.379473i | ||||
\(251\) | −9.09808 | − | 15.7583i | −0.574265 | − | 0.994657i | −0.996121 | − | 0.0879939i | \(-0.971954\pi\) |
0.421856 | − | 0.906663i | \(-0.361379\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.1962 | + | 6.46410i | −0.703896 | + | 0.406395i | ||||
\(254\) | −10.8564 | + | 6.26795i | −0.681192 | + | 0.393286i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −5.52628 | + | 9.57180i | −0.344720 | + | 0.597072i | −0.985303 | − | 0.170817i | \(-0.945359\pi\) |
0.640583 | + | 0.767889i | \(0.278693\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.26795 | 0.0787865 | ||||||||
\(260\) | −1.83013 | − | 1.90192i | −0.113500 | − | 0.117952i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.3923 | − | 9.46410i | −1.01272 | − | 0.584694i | ||||
\(263\) | −9.36603 | + | 16.2224i | −0.577534 | + | 1.00032i | 0.418227 | + | 0.908342i | \(0.362652\pi\) |
−0.995761 | + | 0.0919756i | \(0.970682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7.66025i | − | 0.470566i | ||||||
\(266\) | 3.86603 | − | 2.23205i | 0.237041 | − | 0.136856i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 12.9282i | − | 0.789716i | ||||||
\(269\) | −11.8564 | − | 20.5359i | −0.722898 | − | 1.25210i | −0.959833 | − | 0.280570i | \(-0.909476\pi\) |
0.236936 | − | 0.971525i | \(-0.423857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.6340 | + | 10.7583i | 1.13193 | + | 0.653522i | 0.944420 | − | 0.328740i | \(-0.106624\pi\) |
0.187513 | + | 0.982262i | \(0.439957\pi\) | |||||||
\(272\) | 0.267949 | 0.0162468 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.4641 | −0.934221 | ||||||||
\(275\) | 14.4282 | + | 8.33013i | 0.870053 | + | 0.502326i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1962 | − | 22.8564i | −0.792880 | − | 1.37331i | −0.924177 | − | 0.381965i | \(-0.875247\pi\) |
0.131297 | − | 0.991343i | \(-0.458086\pi\) | |||||||
\(278\) | 18.1244i | 1.08703i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.633975 | − | 0.366025i | 0.0378872 | − | 0.0218742i | ||||
\(281\) | − | 18.1962i | − | 1.08549i | −0.839897 | − | 0.542746i | \(-0.817385\pi\) | ||
0.839897 | − | 0.542746i | \(-0.182615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.4641 | + | 19.8564i | −0.681470 | + | 1.18034i | 0.293062 | + | 0.956093i | \(0.405326\pi\) |
−0.974532 | + | 0.224247i | \(0.928008\pi\) | |||||||
\(284\) | −1.90192 | − | 1.09808i | −0.112858 | − | 0.0651588i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.69615 | − | 9.33013i | 0.573346 | − | 0.551702i | ||||
\(287\) | 7.00000 | 0.413197 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.46410 | − | 14.6603i | 0.497888 | − | 0.862368i | ||||
\(290\) | 1.09808 | + | 1.90192i | 0.0644813 | + | 0.111685i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.66025 | + | 3.26795i | −0.331241 | + | 0.191242i | ||||
\(293\) | 11.0718 | − | 6.39230i | 0.646821 | − | 0.373442i | −0.140416 | − | 0.990093i | \(-0.544844\pi\) |
0.787237 | + | 0.616650i | \(0.211511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.339746 | + | 0.588457i | 0.0197808 | + | 0.0342613i | ||||
\(296\) | −0.633975 | + | 1.09808i | −0.0368490 | + | 0.0638244i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.9282 | 1.09648 | ||||||||
\(299\) | 12.0000 | + | 3.46410i | 0.693978 | + | 0.200334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.633975 | + | 0.366025i | 0.0365417 | + | 0.0210974i | ||||
\(302\) | −6.59808 | + | 11.4282i | −0.379677 | + | 0.657619i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.46410i | 0.256034i | ||||||||
\(305\) | 7.43782 | − | 4.29423i | 0.425888 | − | 0.245887i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 33.7846i | − | 1.92819i | −0.265558 | − | 0.964095i | \(-0.585556\pi\) | ||
0.265558 | − | 0.964095i | \(-0.414444\pi\) | |||||||
\(308\) | 1.86603 | + | 3.23205i | 0.106327 | + | 0.184163i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.85641 | − | 2.80385i | −0.275825 | − | 0.159248i | ||||
\(311\) | −19.1962 | −1.08851 | −0.544257 | − | 0.838919i | \(-0.683188\pi\) | ||||
−0.544257 | + | 0.838919i | \(0.683188\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.80385 | 0.101959 | 0.0509797 | − | 0.998700i | \(-0.483766\pi\) | ||||
0.0509797 | + | 0.998700i | \(0.483766\pi\) | |||||||
\(314\) | −13.3923 | − | 7.73205i | −0.755771 | − | 0.436345i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.42820 | + | 9.40192i | 0.305360 | + | 0.528900i | ||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.69615 | + | 5.59808i | −0.542880 | + | 0.313432i | ||||
\(320\) | 0.732051i | 0.0409229i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.73205 | + | 3.00000i | −0.0965234 | + | 0.167183i | ||||
\(323\) | −1.03590 | − | 0.598076i | −0.0576389 | − | 0.0332779i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.86603 | − | 15.6244i | −0.214449 | − | 0.866683i | ||||
\(326\) | −7.80385 | −0.432215 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.50000 | + | 6.06218i | −0.193255 | + | 0.334728i | ||||
\(329\) | −2.23205 | − | 3.86603i | −0.123057 | − | 0.213141i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.6603 | + | 8.46410i | −0.805800 | + | 0.465229i | −0.845495 | − | 0.533983i | \(-0.820695\pi\) |
0.0396949 | + | 0.999212i | \(0.487361\pi\) | |||||||
\(332\) | −4.90192 | + | 2.83013i | −0.269028 | + | 0.155323i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.92820 | − | 5.07180i | −0.160224 | − | 0.277516i | ||||
\(335\) | −4.73205 | + | 8.19615i | −0.258540 | + | 0.447804i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.7846 | −1.51352 | −0.756762 | − | 0.653690i | \(-0.773220\pi\) | ||||
−0.756762 | + | 0.653690i | \(0.773220\pi\) | |||||||
\(338\) | −12.9904 | − | 0.500000i | −0.706584 | − | 0.0271964i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.169873 | − | 0.0980762i | −0.00921266 | − | 0.00531893i | ||||
\(341\) | 14.2942 | − | 24.7583i | 0.774076 | − | 1.34074i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −0.633975 | + | 0.366025i | −0.0341816 | + | 0.0197348i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 20.7321i | − | 1.11456i | ||||||
\(347\) | 11.4282 | + | 19.7942i | 0.613498 | + | 1.06261i | 0.990646 | + | 0.136457i | \(0.0435715\pi\) |
−0.377148 | + | 0.926153i | \(0.623095\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.5359 | + | 11.8564i | 1.09926 | + | 0.634659i | 0.936027 | − | 0.351928i | \(-0.114474\pi\) |
0.163235 | + | 0.986587i | \(0.447807\pi\) | |||||||
\(350\) | 4.46410 | 0.238616 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.73205 | −0.198919 | ||||||||
\(353\) | 1.26795 | + | 0.732051i | 0.0674861 | + | 0.0389631i | 0.533363 | − | 0.845886i | \(-0.320928\pi\) |
−0.465877 | + | 0.884849i | \(0.654261\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.803848 | + | 1.39230i | 0.0426638 | + | 0.0738959i | ||||
\(356\) | − | 6.46410i | − | 0.342597i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.3923 | + | 11.1962i | −1.02492 | + | 0.591735i | ||||
\(359\) | − | 15.8038i | − | 0.834095i | −0.908885 | − | 0.417048i | \(-0.863065\pi\) | ||
0.908885 | − | 0.417048i | \(-0.136935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.464102 | − | 0.803848i | 0.0244264 | − | 0.0423078i | ||||
\(362\) | −1.03590 | − | 0.598076i | −0.0544456 | − | 0.0314342i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.00000 | − | 3.46410i | 0.0524142 | − | 0.181568i | ||||
\(365\) | 4.78461 | 0.250438 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.12436 | + | 14.0718i | −0.424088 | + | 0.734542i | −0.996335 | − | 0.0855396i | \(-0.972739\pi\) |
0.572247 | + | 0.820081i | \(0.306072\pi\) | |||||||
\(368\) | −1.73205 | − | 3.00000i | −0.0902894 | − | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.803848 | − | 0.464102i | 0.0417900 | − | 0.0241275i | ||||
\(371\) | 9.06218 | − | 5.23205i | 0.470485 | − | 0.271635i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2942 | + | 17.8301i | 0.533015 | + | 0.923209i | 0.999257 | + | 0.0385516i | \(0.0122744\pi\) |
−0.466242 | + | 0.884657i | \(0.654392\pi\) | |||||||
\(374\) | 0.500000 | − | 0.866025i | 0.0258544 | − | 0.0447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.46410 | 0.230218 | ||||||||
\(377\) | 10.3923 | + | 3.00000i | 0.535231 | + | 0.154508i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6340 | − | 7.29423i | −0.648964 | − | 0.374679i | 0.139095 | − | 0.990279i | \(-0.455581\pi\) |
−0.788059 | + | 0.615600i | \(0.788914\pi\) | |||||||
\(380\) | 1.63397 | − | 2.83013i | 0.0838211 | − | 0.145182i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 4.19615i | − | 0.214694i | ||||||
\(383\) | −12.6506 | + | 7.30385i | −0.646417 | + | 0.373209i | −0.787082 | − | 0.616848i | \(-0.788409\pi\) |
0.140665 | + | 0.990057i | \(0.455076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 2.73205i | − | 0.139238i | ||||||
\(386\) | −8.59808 | − | 14.8923i | −0.437631 | − | 0.757998i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.633975 | + | 0.366025i | 0.0321852 | + | 0.0185821i | ||||
\(389\) | −33.1769 | −1.68214 | −0.841068 | − | 0.540929i | \(-0.818073\pi\) | ||||
−0.841068 | + | 0.540929i | \(0.818073\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.928203 | 0.0469413 | ||||||||
\(392\) | 0.866025 | + | 0.500000i | 0.0437409 | + | 0.0252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.13397 | − | 1.96410i | −0.0571288 | − | 0.0989500i | ||||
\(395\) | − | 7.94744i | − | 0.399879i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.2583 | + | 8.23205i | −0.715605 | + | 0.413155i | −0.813133 | − | 0.582078i | \(-0.802240\pi\) |
0.0975279 | + | 0.995233i | \(0.468906\pi\) | |||||||
\(398\) | − | 4.19615i | − | 0.210334i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.23205 | + | 3.86603i | −0.111603 | + | 0.193301i | ||||
\(401\) | 8.66025 | + | 5.00000i | 0.432472 | + | 0.249688i | 0.700399 | − | 0.713751i | \(-0.253005\pi\) |
−0.267927 | + | 0.963439i | \(0.586339\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.8109 | + | 6.63397i | −1.33555 | + | 0.330462i | ||||
\(404\) | 10.0000 | 0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.50000 | + | 2.59808i | −0.0744438 | + | 0.128940i | ||||
\(407\) | 2.36603 | + | 4.09808i | 0.117280 | + | 0.203134i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.4904 | − | 6.63397i | 0.568163 | − | 0.328029i | −0.188252 | − | 0.982121i | \(-0.560282\pi\) |
0.756415 | + | 0.654092i | \(0.226949\pi\) | |||||||
\(410\) | 4.43782 | − | 2.56218i | 0.219168 | − | 0.126537i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.09808 | + | 10.5622i | 0.300431 | + | 0.520361i | ||||
\(413\) | −0.464102 | + | 0.803848i | −0.0228369 | + | 0.0395548i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.14359 | 0.203401 | ||||||||
\(416\) | 2.50000 | + | 2.59808i | 0.122573 | + | 0.127381i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.4282 | + | 8.33013i | 0.705706 | + | 0.407440i | ||||
\(419\) | −3.09808 | + | 5.36603i | −0.151351 | + | 0.262147i | −0.931724 | − | 0.363166i | \(-0.881696\pi\) |
0.780373 | + | 0.625314i | \(0.215029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 14.3923i | − | 0.701438i | −0.936481 | − | 0.350719i | \(-0.885937\pi\) | ||
0.936481 | − | 0.350719i | \(-0.114063\pi\) | |||||||
\(422\) | 13.7321 | − | 7.92820i | 0.668466 | − | 0.385939i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.4641i | 0.508182i | ||||||||
\(425\) | −0.598076 | − | 1.03590i | −0.0290110 | − | 0.0502485i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.1603 | + | 5.86603i | 0.491689 | + | 0.283877i | ||||
\(428\) | −1.53590 | −0.0742405 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.535898 | 0.0258433 | ||||||||
\(431\) | −18.2942 | − | 10.5622i | −0.881202 | − | 0.508762i | −0.0101474 | − | 0.999949i | \(-0.503230\pi\) |
−0.871055 | + | 0.491186i | \(0.836563\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.46410 | + | 7.73205i | 0.214531 | + | 0.371579i | 0.953127 | − | 0.302569i | \(-0.0978444\pi\) |
−0.738596 | + | 0.674148i | \(0.764511\pi\) | |||||||
\(434\) | − | 7.66025i | − | 0.367704i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.16987 | − | 1.83013i | 0.151809 | − | 0.0876472i | ||||
\(437\) | 15.4641i | 0.739748i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.19615 | + | 14.1962i | −0.391181 | + | 0.677545i | −0.992606 | − | 0.121384i | \(-0.961267\pi\) |
0.601425 | + | 0.798930i | \(0.294600\pi\) | |||||||
\(440\) | 2.36603 | + | 1.36603i | 0.112796 | + | 0.0651227i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.937822 | + | 0.232051i | −0.0446077 | + | 0.0110375i | ||||
\(443\) | 31.3923 | 1.49149 | 0.745747 | − | 0.666230i | \(-0.232093\pi\) | ||||
0.745747 | + | 0.666230i | \(0.232093\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.36603 | + | 4.09808i | −0.112160 | + | 0.194267i | ||||
\(446\) | 4.19615 | + | 7.26795i | 0.198694 | + | 0.344147i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.866025 | + | 0.500000i | −0.0409159 | + | 0.0236228i | ||||
\(449\) | 9.29423 | − | 5.36603i | 0.438622 | − | 0.253238i | −0.264391 | − | 0.964416i | \(-0.585171\pi\) |
0.703013 | + | 0.711177i | \(0.251838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.0622 | + | 22.6244i | 0.615074 | + | 1.06534i | ||||
\(452\) | 5.09808 | − | 8.83013i | 0.239793 | − | 0.415334i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.53590 | −0.400610 | ||||||||
\(455\) | −1.90192 | + | 1.83013i | −0.0891636 | + | 0.0857977i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.87564 | + | 3.39230i | 0.274851 | + | 0.158685i | 0.631090 | − | 0.775710i | \(-0.282608\pi\) |
−0.356239 | + | 0.934395i | \(0.615941\pi\) | |||||||
\(458\) | 5.16025 | − | 8.93782i | 0.241123 | − | 0.417637i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.53590i | 0.118237i | ||||||||
\(461\) | 24.0000 | − | 13.8564i | 1.11779 | − | 0.645357i | 0.176955 | − | 0.984219i | \(-0.443375\pi\) |
0.940836 | + | 0.338862i | \(0.110042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.19615i | − | 0.0555899i | −0.999614 | − | 0.0277950i | \(-0.991151\pi\) | ||
0.999614 | − | 0.0277950i | \(-0.00884855\pi\) | |||||||
\(464\) | −1.50000 | − | 2.59808i | −0.0696358 | − | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.90192 | + | 1.09808i | 0.0881049 | + | 0.0508674i | ||||
\(467\) | −9.85641 | −0.456100 | −0.228050 | − | 0.973649i | \(-0.573235\pi\) | ||||
−0.228050 | + | 0.973649i | \(0.573235\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.9282 | −0.596969 | ||||||||
\(470\) | −2.83013 | − | 1.63397i | −0.130544 | − | 0.0753696i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.464102 | − | 0.803848i | −0.0213620 | − | 0.0370001i | ||||
\(473\) | 2.73205i | 0.125620i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.2583 | − | 9.96410i | 0.791866 | − | 0.457184i | ||||
\(476\) | − | 0.267949i | − | 0.0122814i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.90192 | + | 11.9545i | −0.315687 | + | 0.546785i | ||||
\(479\) | −27.1865 | − | 15.6962i | −1.24218 | − | 0.717176i | −0.272646 | − | 0.962114i | \(-0.587899\pi\) |
−0.969539 | + | 0.244939i | \(0.921232\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.26795 | − | 4.39230i | 0.0578135 | − | 0.200272i | ||||
\(482\) | −12.7846 | −0.582323 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.46410 | + | 2.53590i | −0.0665501 | + | 0.115268i | ||||
\(485\) | −0.267949 | − | 0.464102i | −0.0121669 | − | 0.0210738i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3564 | − | 10.5981i | 0.831808 | − | 0.480245i | −0.0226632 | − | 0.999743i | \(-0.507215\pi\) |
0.854471 | + | 0.519498i | \(0.173881\pi\) | |||||||
\(488\) | −10.1603 | + | 5.86603i | −0.459933 | + | 0.265542i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.366025 | − | 0.633975i | −0.0165353 | − | 0.0286401i | ||||
\(491\) | −18.1244 | + | 31.3923i | −0.817941 | + | 1.41671i | 0.0892562 | + | 0.996009i | \(0.471551\pi\) |
−0.907197 | + | 0.420706i | \(0.861782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.803848 | 0.0362035 | ||||||||
\(494\) | −3.86603 | − | 15.6244i | −0.173941 | − | 0.702973i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.63397 | + | 3.83013i | 0.297874 | + | 0.171978i | ||||
\(497\) | −1.09808 | + | 1.90192i | −0.0492554 | + | 0.0853129i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 12.9808i | − | 0.581099i | −0.956860 | − | 0.290549i | \(-0.906162\pi\) | ||
0.956860 | − | 0.290549i | \(-0.0938380\pi\) | |||||||
\(500\) | 6.00000 | − | 3.46410i | 0.268328 | − | 0.154919i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 18.1962i | − | 0.812134i | ||||||
\(503\) | −11.8564 | − | 20.5359i | −0.528651 | − | 0.915650i | −0.999442 | − | 0.0334056i | \(-0.989365\pi\) |
0.470791 | − | 0.882245i | \(-0.343969\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.33975 | − | 3.66025i | −0.282115 | − | 0.162879i | ||||
\(506\) | −12.9282 | −0.574729 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.5359 | −0.556191 | ||||||||
\(509\) | 22.5622 | + | 13.0263i | 1.00005 | + | 0.577380i | 0.908263 | − | 0.418399i | \(-0.137409\pi\) |
0.0917876 | + | 0.995779i | \(0.470742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.26795 | + | 5.66025i | 0.144566 | + | 0.250395i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.57180 | + | 5.52628i | −0.422194 | + | 0.243754i | ||||
\(515\) | − | 8.92820i | − | 0.393424i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.33013 | − | 14.4282i | 0.366359 | − | 0.634552i | ||||
\(518\) | 1.09808 | + | 0.633975i | 0.0482467 | + | 0.0278552i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.633975 | − | 2.56218i | −0.0278016 | − | 0.112359i | ||||
\(521\) | 2.26795 | 0.0993607 | 0.0496803 | − | 0.998765i | \(-0.484180\pi\) | ||||
0.0496803 | + | 0.998765i | \(0.484180\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.40192 | − | 16.2846i | 0.411117 | − | 0.712076i | −0.583895 | − | 0.811829i | \(-0.698472\pi\) |
0.995012 | + | 0.0997531i | \(0.0318053\pi\) | |||||||
\(524\) | −9.46410 | − | 16.3923i | −0.413441 | − | 0.716101i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.2224 | + | 9.36603i | −0.707332 | + | 0.408378i | ||||
\(527\) | −1.77757 | + | 1.02628i | −0.0774321 | + | 0.0447054i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.50000 | + | 9.52628i | 0.239130 | + | 0.414186i | ||||
\(530\) | 3.83013 | − | 6.63397i | 0.166370 | − | 0.288161i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.46410 | 0.193543 | ||||||||
\(533\) | 7.00000 | − | 24.2487i | 0.303204 | − | 1.05033i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.973721 | + | 0.562178i | 0.0420976 | + | 0.0243051i | ||||
\(536\) | 6.46410 | − | 11.1962i | 0.279207 | − | 0.483600i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 23.7128i | − | 1.02233i | ||||||
\(539\) | 3.23205 | − | 1.86603i | 0.139214 | − | 0.0803754i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.1962i | 1.29823i | 0.760689 | + | 0.649117i | \(0.224861\pi\) | ||||
−0.760689 | + | 0.649117i | \(0.775139\pi\) | |||||||
\(542\) | 10.7583 | + | 18.6340i | 0.462110 | + | 0.800398i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.232051 | + | 0.133975i | 0.00994910 | + | 0.00574411i | ||||
\(545\) | −2.67949 | −0.114777 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.8756 | −0.550523 | −0.275261 | − | 0.961369i | \(-0.588764\pi\) | ||||
−0.275261 | + | 0.961369i | \(0.588764\pi\) | |||||||
\(548\) | −13.3923 | − | 7.73205i | −0.572091 | − | 0.330297i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.33013 | + | 14.4282i | 0.355198 | + | 0.615221i | ||||
\(551\) | 13.3923i | 0.570531i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.40192 | − | 5.42820i | 0.399810 | − | 0.230831i | ||||
\(554\) | − | 26.3923i | − | 1.12130i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.06218 | + | 15.6962i | −0.384322 | + | 0.665665i | ||||
\(557\) | −31.7487 | − | 18.3301i | −1.34524 | − | 0.776672i | −0.357666 | − | 0.933850i | \(-0.616427\pi\) |
−0.987570 | + | 0.157177i | \(0.949761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.90192 | − | 1.83013i | 0.0804428 | − | 0.0774061i | ||||
\(560\) | 0.732051 | 0.0309348 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.09808 | − | 15.7583i | 0.383779 | − | 0.664725i | ||||
\(563\) | 16.6340 | + | 28.8109i | 0.701038 | + | 1.21423i | 0.968102 | + | 0.250555i | \(0.0806132\pi\) |
−0.267064 | + | 0.963679i | \(0.586053\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.46410 | + | 3.73205i | −0.271947 | + | 0.157009i | ||||
\(566\) | −19.8564 | + | 11.4641i | −0.834627 | + | 0.481872i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.09808 | − | 1.90192i | −0.0460743 | − | 0.0798029i | ||||
\(569\) | −11.3660 | + | 19.6865i | −0.476489 | + | 0.825302i | −0.999637 | − | 0.0269391i | \(-0.991424\pi\) |
0.523149 | + | 0.852242i | \(0.324757\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8038 | −0.828765 | −0.414383 | − | 0.910103i | \(-0.636002\pi\) | ||||
−0.414383 | + | 0.910103i | \(0.636002\pi\) | |||||||
\(572\) | 13.0622 | − | 3.23205i | 0.546157 | − | 0.135139i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.06218 | + | 3.50000i | 0.253030 | + | 0.146087i | ||||
\(575\) | −7.73205 | + | 13.3923i | −0.322449 | + | 0.558498i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 13.2679i | − | 0.552352i | −0.961107 | − | 0.276176i | \(-0.910933\pi\) | ||
0.961107 | − | 0.276176i | \(-0.0890673\pi\) | |||||||
\(578\) | 14.6603 | − | 8.46410i | 0.609786 | − | 0.352060i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.19615i | 0.0911903i | ||||||||
\(581\) | 2.83013 | + | 4.90192i | 0.117413 | + | 0.203366i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.8205 | + | 19.5263i | 1.40070 | + | 0.808696i | ||||
\(584\) | −6.53590 | −0.270457 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.7846 | 0.528127 | ||||||||
\(587\) | 27.1699 | + | 15.6865i | 1.12142 | + | 0.647453i | 0.941763 | − | 0.336277i | \(-0.109168\pi\) |
0.179657 | + | 0.983729i | \(0.442501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.0981 | − | 29.6147i | −0.704514 | − | 1.22025i | ||||
\(590\) | 0.679492i | 0.0279742i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.09808 | + | 0.633975i | −0.0451307 | + | 0.0260562i | ||||
\(593\) | − | 13.6795i | − | 0.561749i | −0.959744 | − | 0.280875i | \(-0.909375\pi\) | ||
0.959744 | − | 0.280875i | \(-0.0906245\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0980762 | + | 0.169873i | −0.00402073 | + | 0.00696411i | ||||
\(596\) | 16.3923 | + | 9.46410i | 0.671455 | + | 0.387665i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.66025 | + | 9.00000i | 0.354144 | + | 0.368037i | ||||
\(599\) | 21.7128 | 0.887161 | 0.443581 | − | 0.896234i | \(-0.353708\pi\) | ||||
0.443581 | + | 0.896234i | \(0.353708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.43782 | − | 11.1506i | 0.262604 | − | 0.454844i | −0.704329 | − | 0.709874i | \(-0.748752\pi\) |
0.966933 | + | 0.255030i | \(0.0820853\pi\) | |||||||
\(602\) | 0.366025 | + | 0.633975i | 0.0149181 | + | 0.0258389i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.4282 | + | 6.59808i | −0.465007 | + | 0.268472i | ||||
\(605\) | 1.85641 | − | 1.07180i | 0.0754737 | − | 0.0435747i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9545 | − | 34.5622i | −0.809927 | − | 1.40284i | −0.912914 | − | 0.408153i | \(-0.866173\pi\) |
0.102986 | − | 0.994683i | \(-0.467160\pi\) | |||||||
\(608\) | −2.23205 | + | 3.86603i | −0.0905216 | + | 0.156788i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.58846 | 0.347736 | ||||||||
\(611\) | −15.6244 | + | 3.86603i | −0.632094 | + | 0.156403i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.2487 | + | 20.9282i | 1.46407 | + | 0.845282i | 0.999196 | − | 0.0400938i | \(-0.0127657\pi\) |
0.464876 | + | 0.885376i | \(0.346099\pi\) | |||||||
\(614\) | 16.8923 | − | 29.2583i | 0.681718 | − | 1.18077i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.73205i | 0.150369i | ||||||||
\(617\) | −35.9545 | + | 20.7583i | −1.44747 | + | 0.835699i | −0.998330 | − | 0.0577612i | \(-0.981604\pi\) |
−0.449143 | + | 0.893460i | \(0.648270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.32051i | 0.0932691i | 0.998912 | + | 0.0466345i | \(0.0148496\pi\) | ||||
−0.998912 | + | 0.0466345i | \(0.985150\pi\) | |||||||
\(620\) | −2.80385 | − | 4.85641i | −0.112605 | − | 0.195038i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16.6244 | − | 9.59808i | −0.666576 | − | 0.384848i | ||||
\(623\) | −6.46410 | −0.258979 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 1.56218 | + | 0.901924i | 0.0624372 | + | 0.0360481i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.73205 | − | 13.3923i | −0.308542 | − | 0.534411i | ||||
\(629\) | − | 0.339746i | − | 0.0135466i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.8397 | + | 7.99038i | −0.550952 | + | 0.318092i | −0.749506 | − | 0.661998i | \(-0.769709\pi\) |
0.198554 | + | 0.980090i | \(0.436375\pi\) | |||||||
\(632\) | 10.8564i | 0.431845i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.00000 | + | 15.5885i | −0.357436 | + | 0.619097i | ||||
\(635\) | 7.94744 | + | 4.58846i | 0.315385 | + | 0.182087i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.46410 | − | 1.00000i | −0.137253 | − | 0.0396214i | ||||
\(638\) | −11.1962 | −0.443260 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.366025 | + | 0.633975i | −0.0144684 | + | 0.0250600i | ||||
\(641\) | 8.12436 | + | 14.0718i | 0.320893 | + | 0.555803i | 0.980672 | − | 0.195656i | \(-0.0626838\pi\) |
−0.659780 | + | 0.751459i | \(0.729350\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.45448 | − | 0.839746i | 0.0573592 | − | 0.0331163i | −0.471046 | − | 0.882109i | \(-0.656123\pi\) |
0.528405 | + | 0.848992i | \(0.322790\pi\) | |||||||
\(644\) | −3.00000 | + | 1.73205i | −0.118217 | + | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.598076 | − | 1.03590i | −0.0235310 | − | 0.0407569i | ||||
\(647\) | −0.866025 | + | 1.50000i | −0.0340470 | + | 0.0589711i | −0.882547 | − | 0.470225i | \(-0.844173\pi\) |
0.848500 | + | 0.529196i | \(0.177506\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.46410 | −0.135978 | ||||||||
\(650\) | 4.46410 | − | 15.4641i | 0.175096 | − | 0.606552i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.75833 | − | 3.90192i | −0.264677 | − | 0.152811i | ||||
\(653\) | 5.83975 | − | 10.1147i | 0.228527 | − | 0.395820i | −0.728845 | − | 0.684679i | \(-0.759942\pi\) |
0.957372 | + | 0.288859i | \(0.0932758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8564i | 0.541415i | ||||||||
\(656\) | −6.06218 | + | 3.50000i | −0.236688 | + | 0.136652i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 4.46410i | − | 0.174029i | ||||||
\(659\) | 16.9641 | + | 29.3827i | 0.660828 | + | 1.14459i | 0.980399 | + | 0.197025i | \(0.0631279\pi\) |
−0.319571 | + | 0.947562i | \(0.603539\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.9090 | + | 13.8038i | 0.929951 | + | 0.536907i | 0.886796 | − | 0.462161i | \(-0.152926\pi\) |
0.0431549 | + | 0.999068i | \(0.486259\pi\) | |||||||
\(662\) | −16.9282 | −0.657933 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.66025 | −0.219660 | ||||||||
\(665\) | −2.83013 | − | 1.63397i | −0.109748 | − | 0.0633628i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.19615 | − | 9.00000i | −0.201196 | − | 0.348481i | ||||
\(668\) | − | 5.85641i | − | 0.226591i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.19615 | + | 4.73205i | −0.316645 | + | 0.182815i | ||||
\(671\) | 43.7846i | 1.69029i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.9641 | + | 41.5070i | −0.923748 | + | 1.59998i | −0.130186 | + | 0.991490i | \(0.541557\pi\) |
−0.793562 | + | 0.608489i | \(0.791776\pi\) | |||||||
\(674\) | −24.0622 | − | 13.8923i | −0.926840 | − | 0.535112i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | 47.7654 | 1.83577 | 0.917886 | − | 0.396844i | \(-0.129895\pi\) | ||||
0.917886 | + | 0.396844i | \(0.129895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.366025 | − | 0.633975i | 0.0140468 | − | 0.0243297i | ||||
\(680\) | −0.0980762 | − | 0.169873i | −0.00376105 | − | 0.00651433i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 24.7583 | − | 14.2942i | 0.948045 | − | 0.547354i | ||||
\(683\) | 22.8564 | − | 13.1962i | 0.874576 | − | 0.504937i | 0.00570987 | − | 0.999984i | \(-0.498182\pi\) |
0.868866 | + | 0.495047i | \(0.164849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.66025 | + | 9.80385i | 0.216267 | + | 0.374586i | ||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.732051 | −0.0279092 | ||||||||
\(689\) | −9.06218 | − | 36.6244i | −0.345241 | − | 1.39528i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.3205 | + | 20.3923i | 1.34366 | + | 0.775760i | 0.987342 | − | 0.158607i | \(-0.0507002\pi\) |
0.356314 | + | 0.934366i | \(0.384033\pi\) | |||||||
\(692\) | 10.3660 | − | 17.9545i | 0.394057 | − | 0.682527i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.8564i | 0.867617i | ||||||||
\(695\) | 11.4904 | − | 6.63397i | 0.435855 | − | 0.251641i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.87564i | − | 0.0710451i | ||||||
\(698\) | 11.8564 | + | 20.5359i | 0.448772 | + | 0.777295i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.86603 | + | 2.23205i | 0.146122 | + | 0.0843636i | ||||
\(701\) | 14.3205 | 0.540878 | 0.270439 | − | 0.962737i | \(-0.412831\pi\) | ||||
0.270439 | + | 0.962737i | \(0.412831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.66025 | 0.213481 | ||||||||
\(704\) | −3.23205 | − | 1.86603i | −0.121812 | − | 0.0703285i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.732051 | + | 1.26795i | 0.0275511 | + | 0.0477199i | ||||
\(707\) | − | 10.0000i | − | 0.376089i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.8301 | − | 12.0263i | 0.782292 | − | 0.451656i | −0.0549501 | − | 0.998489i | \(-0.517500\pi\) |
0.837242 | + | 0.546833i | \(0.184167\pi\) | |||||||
\(710\) | 1.60770i | 0.0603357i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.23205 | − | 5.59808i | 0.121126 | − | 0.209797i | ||||
\(713\) | 22.9808 | + | 13.2679i | 0.860636 | + | 0.496889i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.46410 | − | 2.73205i | −0.353937 | − | 0.102173i | ||||
\(716\) | −22.3923 | −0.836840 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.90192 | − | 13.6865i | 0.294897 | − | 0.510777i | ||||
\(719\) | −1.52628 | − | 2.64359i | −0.0569206 | − | 0.0985894i | 0.836161 | − | 0.548484i | \(-0.184795\pi\) |
−0.893082 | + | 0.449895i | \(0.851462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.5622 | − | 6.09808i | 0.393356 | − | 0.227104i | ||||
\(722\) | 0.803848 | − | 0.464102i | 0.0299161 | − | 0.0172721i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.598076 | − | 1.03590i | −0.0222273 | − | 0.0384989i | ||||
\(725\) | −6.69615 | + | 11.5981i | −0.248689 | + | 0.430742i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.46410 | −0.0543005 | −0.0271503 | − | 0.999631i | \(-0.508643\pi\) | ||||
−0.0271503 | + | 0.999631i | \(0.508643\pi\) | |||||||
\(728\) | 2.59808 | − | 2.50000i | 0.0962911 | − | 0.0926562i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.14359 | + | 2.39230i | 0.153361 | + | 0.0885432i | ||||
\(731\) | 0.0980762 | − | 0.169873i | 0.00362748 | − | 0.00628298i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 6.85641i | − | 0.253247i | −0.991951 | − | 0.126624i | \(-0.959586\pi\) | ||
0.991951 | − | 0.126624i | \(-0.0404140\pi\) | |||||||
\(734\) | −14.0718 | + | 8.12436i | −0.519399 | + | 0.299875i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.46410i | − | 0.127688i | ||||||
\(737\) | −24.1244 | − | 41.7846i | −0.888632 | − | 1.53916i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.53590 | + | 3.19615i | 0.203641 | + | 0.117572i | 0.598353 | − | 0.801233i | \(-0.295822\pi\) |
−0.394712 | + | 0.918805i | \(0.629155\pi\) | |||||||
\(740\) | 0.928203 | 0.0341214 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.4641 | 0.384149 | ||||||||
\(743\) | 16.9019 | + | 9.75833i | 0.620071 | + | 0.357998i | 0.776897 | − | 0.629628i | \(-0.216793\pi\) |
−0.156825 | + | 0.987626i | \(0.550126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.92820 | − | 12.0000i | −0.253830 | − | 0.439646i | ||||
\(746\) | 20.5885i | 0.753797i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.866025 | − | 0.500000i | 0.0316650 | − | 0.0182818i | ||||
\(749\) | 1.53590i | 0.0561205i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.42820 | + | 5.93782i | −0.125097 | + | 0.216674i | −0.921771 | − | 0.387735i | \(-0.873258\pi\) |
0.796674 | + | 0.604409i | \(0.206591\pi\) | |||||||
\(752\) | 3.86603 | + | 2.23205i | 0.140979 | + | 0.0813945i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.50000 | + | 7.79423i | 0.273134 | + | 0.283849i | ||||
\(755\) | 9.66025 | 0.351573 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0263 | − | 32.9545i | 0.691522 | − | 1.19775i | −0.279817 | − | 0.960053i | \(-0.590274\pi\) |
0.971339 | − | 0.237698i | \(-0.0763928\pi\) | |||||||
\(758\) | −7.29423 | − | 12.6340i | −0.264938 | − | 0.458887i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.83013 | − | 1.63397i | 0.102659 | − | 0.0592705i | ||||
\(761\) | 0.588457 | − | 0.339746i | 0.0213316 | − | 0.0123158i | −0.489296 | − | 0.872118i | \(-0.662746\pi\) |
0.510628 | + | 0.859802i | \(0.329413\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.83013 | − | 3.16987i | −0.0662550 | − | 0.114757i | ||||
\(764\) | 2.09808 | − | 3.63397i | 0.0759057 | − | 0.131473i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.6077 | −0.527797 | ||||||||
\(767\) | 2.32051 | + | 2.41154i | 0.0837887 | + | 0.0870758i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.1699 | + | 12.2224i | 0.763405 | + | 0.440752i | 0.830517 | − | 0.556993i | \(-0.188045\pi\) |
−0.0671118 | + | 0.997745i | \(0.521378\pi\) | |||||||
\(770\) | 1.36603 | − | 2.36603i | 0.0492281 | − | 0.0852656i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 17.1962i | − | 0.618903i | ||||||
\(773\) | −36.7128 | + | 21.1962i | −1.32047 | + | 0.762373i | −0.983803 | − | 0.179252i | \(-0.942632\pi\) |
−0.336665 | + | 0.941625i | \(0.609299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 34.1962i | − | 1.22836i | ||||||
\(776\) | 0.366025 | + | 0.633975i | 0.0131395 | + | 0.0227584i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.7321 | − | 16.5885i | −1.03009 | − | 0.594725i | ||||
\(779\) | 31.2487 | 1.11960 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.19615 | −0.293281 | ||||||||
\(782\) | 0.803848 | + | 0.464102i | 0.0287455 | + | 0.0165962i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.500000 | + | 0.866025i | 0.0178571 | + | 0.0309295i | ||||
\(785\) | 11.3205i | 0.404046i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.3109 | + | 27.8923i | −1.72210 | + | 0.994253i | −0.807522 | + | 0.589837i | \(0.799192\pi\) |
−0.914575 | + | 0.404416i | \(0.867475\pi\) | |||||||
\(788\) | − | 2.26795i | − | 0.0807923i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.97372 | − | 6.88269i | 0.141379 | − | 0.244875i | ||||
\(791\) | −8.83013 | − | 5.09808i | −0.313963 | − | 0.181267i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.4808 | − | 29.3301i | 1.08240 | − | 1.04154i | ||||
\(794\) | −16.4641 | −0.584289 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.09808 | − | 3.63397i | 0.0743643 | − | 0.128803i | ||||
\(797\) | 0.366025 | + | 0.633975i | 0.0129653 | + | 0.0224565i | 0.872435 | − | 0.488730i | \(-0.162540\pi\) |
−0.859470 | + | 0.511186i | \(0.829206\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.03590 | + | 0.598076i | −0.0366475 | + | 0.0211584i | ||||
\(800\) | −3.86603 | + | 2.23205i | −0.136685 | + | 0.0789149i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.00000 | + | 8.66025i | 0.176556 | + | 0.305804i | ||||
\(803\) | −12.1962 | + | 21.1244i | −0.430393 | + | 0.745462i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.53590 | 0.0893787 | ||||||||
\(806\) | −26.5359 | − | 7.66025i | −0.934687 | − | 0.269821i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.66025 | + | 5.00000i | 0.304667 | + | 0.175899i | ||||
\(809\) | −0.0980762 | + | 0.169873i | −0.00344818 | + | 0.00597242i | −0.867744 | − | 0.497011i | \(-0.834431\pi\) |
0.864296 | + | 0.502983i | \(0.167764\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.4641i | − | 0.543018i | −0.962436 | − | 0.271509i | \(-0.912477\pi\) | ||
0.962436 | − | 0.271509i | \(-0.0875227\pi\) | |||||||
\(812\) | −2.59808 | + | 1.50000i | −0.0911746 | + | 0.0526397i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.73205i | 0.165858i | ||||||||
\(815\) | 2.85641 | + | 4.94744i | 0.100056 | + | 0.173301i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.83013 | + | 1.63397i | 0.0990136 | + | 0.0571655i | ||||
\(818\) | 13.2679 | 0.463903 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.12436 | 0.178950 | ||||||||
\(821\) | 39.4808 | + | 22.7942i | 1.37789 | + | 0.795524i | 0.991905 | − | 0.126982i | \(-0.0405290\pi\) |
0.385983 | + | 0.922506i | \(0.373862\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.53590 | + | 6.12436i | 0.123254 | + | 0.213482i | 0.921049 | − | 0.389447i | \(-0.127334\pi\) |
−0.797795 | + | 0.602928i | \(0.794000\pi\) | |||||||
\(824\) | 12.1962i | 0.424873i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.803848 | + | 0.464102i | −0.0279694 | + | 0.0161482i | ||||
\(827\) | 19.6077i | 0.681826i | 0.940095 | + | 0.340913i | \(0.110736\pi\) | ||||
−0.940095 | + | 0.340913i | \(0.889264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.33013 | − | 14.4282i | 0.289317 | − | 0.501112i | −0.684330 | − | 0.729173i | \(-0.739905\pi\) |
0.973647 | + | 0.228061i | \(0.0732384\pi\) | |||||||
\(830\) | 3.58846 | + | 2.07180i | 0.124557 | + | 0.0719131i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.866025 | + | 3.50000i | 0.0300240 | + | 0.121341i | ||||
\(833\) | −0.267949 | −0.00928389 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.14359 | + | 3.71281i | −0.0741821 | + | 0.128487i | ||||
\(836\) | 8.33013 | + | 14.4282i | 0.288103 | + | 0.499010i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.36603 | + | 3.09808i | −0.185366 | + | 0.107021i | ||||
\(839\) | −5.53590 | + | 3.19615i | −0.191120 | + | 0.110343i | −0.592507 | − | 0.805565i | \(-0.701862\pi\) |
0.401387 | + | 0.915909i | \(0.368528\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 7.19615 | − | 12.4641i | 0.247996 | − | 0.429541i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.8564 | 0.545800 | ||||||||
\(845\) | 4.43782 | + | 8.41858i | 0.152666 | + | 0.289608i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.53590 | + | 1.46410i | 0.0871345 | + | 0.0503071i | ||||
\(848\) | −5.23205 | + | 9.06218i | −0.179669 | + | 0.311196i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 1.19615i | − | 0.0410277i | ||||||
\(851\) | −3.80385 | + | 2.19615i | −0.130394 | + | 0.0752831i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.6077i | 0.431679i | 0.976429 | + | 0.215840i | \(0.0692488\pi\) | ||||
−0.976429 | + | 0.215840i | \(0.930751\pi\) | |||||||
\(854\) | 5.86603 | + | 10.1603i | 0.200731 | + | 0.347677i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.33013 | − | 0.767949i | −0.0454628 | − | 0.0262480i | ||||
\(857\) | −42.3923 | −1.44809 | −0.724047 | − | 0.689751i | \(-0.757720\pi\) | ||||
−0.724047 | + | 0.689751i | \(0.757720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.94744 | −0.237044 | −0.118522 | − | 0.992951i | \(-0.537816\pi\) | ||||
−0.118522 | + | 0.992951i | \(0.537816\pi\) | |||||||
\(860\) | 0.464102 | + | 0.267949i | 0.0158257 | + | 0.00913699i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.5622 | − | 18.2942i | −0.359749 | − | 0.623104i | ||||
\(863\) | − | 40.6410i | − | 1.38344i | −0.722168 | − | 0.691718i | \(-0.756854\pi\) | ||
0.722168 | − | 0.691718i | \(-0.243146\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.1436 | + | 7.58846i | −0.446896 | + | 0.258015i | ||||
\(866\) | 8.92820i | 0.303393i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.83013 | − | 6.63397i | 0.130003 | − | 0.225172i | ||||
\(869\) | 35.0885 | + | 20.2583i | 1.19029 | + | 0.687217i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.9282 | + | 44.7846i | −0.438055 | + | 1.51747i | ||||
\(872\) | 3.66025 | 0.123952 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.73205 | + | 13.3923i | −0.261541 | + | 0.453001i | ||||
\(875\) | −3.46410 | − | 6.00000i | −0.117108 | − | 0.202837i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.5622 | − | 25.1506i | 1.47099 | − | 0.849277i | 0.471521 | − | 0.881855i | \(-0.343705\pi\) |
0.999469 | + | 0.0325782i | \(0.0103718\pi\) | |||||||
\(878\) | −14.1962 | + | 8.19615i | −0.479097 | + | 0.276607i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.36603 | + | 2.36603i | 0.0460487 | + | 0.0797587i | ||||
\(881\) | −7.46410 | + | 12.9282i | −0.251472 | + | 0.435562i | −0.963931 | − | 0.266151i | \(-0.914248\pi\) |
0.712459 | + | 0.701713i | \(0.247581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.4449 | 0.822635 | 0.411318 | − | 0.911492i | \(-0.365069\pi\) | ||||
0.411318 | + | 0.911492i | \(0.365069\pi\) | |||||||
\(884\) | −0.928203 | − | 0.267949i | −0.0312189 | − | 0.00901211i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.1865 | + | 15.6962i | 0.913349 | + | 0.527323i | ||||
\(887\) | 3.47372 | − | 6.01666i | 0.116636 | − | 0.202020i | −0.801796 | − | 0.597597i | \(-0.796122\pi\) |
0.918433 | + | 0.395578i | \(0.129456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.5359i | 0.420441i | ||||||||
\(890\) | −4.09808 | + | 2.36603i | −0.137368 | + | 0.0793094i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.39230i | 0.280995i | ||||||||
\(893\) | −9.96410 | − | 17.2583i | −0.333436 | − | 0.577528i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.1962 | + | 8.19615i | 0.474525 | + | 0.273967i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.7321 | 0.358133 | ||||||||
\(899\) | 19.9019 | + | 11.4904i | 0.663766 | + | 0.383226i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.40192 | − | 2.42820i | −0.0467049 | − | 0.0808952i | ||||
\(902\) | 26.1244i | 0.869846i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.83013 | − | 5.09808i | 0.293686 | − | 0.169559i | ||||
\(905\) | 0.875644i | 0.0291074i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2679 | + | 17.7846i | −0.340942 | + | 0.590528i | −0.984608 | − | 0.174778i | \(-0.944079\pi\) |
0.643666 | + | 0.765306i | \(0.277413\pi\) | |||||||
\(908\) | −7.39230 | − | 4.26795i | −0.245322 | − | 0.141637i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.56218 | + | 0.633975i | −0.0849354 | + | 0.0210161i | ||||
\(911\) | −38.0526 | −1.26074 | −0.630369 | − | 0.776296i | \(-0.717096\pi\) | ||||
−0.630369 | + | 0.776296i | \(0.717096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5622 | + | 18.2942i | −0.349557 | + | 0.605451i | ||||
\(914\) | 3.39230 | + | 5.87564i | 0.112207 | + | 0.194349i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.93782 | − | 5.16025i | 0.295314 | − | 0.170500i | ||||
\(917\) | −16.3923 | + | 9.46410i | −0.541322 | + | 0.312532i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.8205 | + | 23.9378i | 0.455896 | + | 0.789636i | 0.998739 | − | 0.0501985i | \(-0.0159854\pi\) |
−0.542843 | + | 0.839834i | \(0.682652\pi\) | |||||||
\(920\) | −1.26795 | + | 2.19615i | −0.0418030 | + | 0.0724050i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.7128 | 0.912673 | ||||||||
\(923\) | 5.49038 | + | 5.70577i | 0.180718 | + | 0.187808i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.90192 | + | 2.83013i | 0.161174 | + | 0.0930540i | ||||
\(926\) | 0.598076 | − | 1.03590i | 0.0196540 | − | 0.0340417i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 3.00000i | − | 0.0984798i | ||||||
\(929\) | −43.7032 | + | 25.2321i | −1.43386 | + | 0.827837i | −0.997412 | − | 0.0718951i | \(-0.977095\pi\) |
−0.436443 | + | 0.899732i | \(0.643762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.46410i | − | 0.146305i | ||||||
\(932\) | 1.09808 | + | 1.90192i | 0.0359687 | + | 0.0622996i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.53590 | − | 4.92820i | −0.279303 | − | 0.161256i | ||||
\(935\) | −0.732051 | −0.0239406 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.5692 | −1.22733 | −0.613666 | − | 0.789565i | \(-0.710306\pi\) | ||||
−0.613666 | + | 0.789565i | \(0.710306\pi\) | |||||||
\(938\) | −11.1962 | − | 6.46410i | −0.365567 | − | 0.211060i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.63397 | − | 2.83013i | −0.0532944 | − | 0.0923086i | ||||
\(941\) | − | 13.1769i | − | 0.429555i | −0.976663 | − | 0.214778i | \(-0.931097\pi\) | ||
0.976663 | − | 0.214778i | \(-0.0689027\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.0000 | + | 12.1244i | −0.683854 | + | 0.394823i | ||||
\(944\) | − | 0.928203i | − | 0.0302104i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.36603 | + | 2.36603i | −0.0444133 | + | 0.0769261i | ||||
\(947\) | 44.2128 | + | 25.5263i | 1.43672 | + | 0.829493i | 0.997621 | − | 0.0689442i | \(-0.0219630\pi\) |
0.439103 | + | 0.898437i | \(0.355296\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.8756 | − | 5.66025i | 0.742575 | − | 0.183740i | ||||
\(950\) | 19.9282 | 0.646556 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.133975 | − | 0.232051i | 0.00434214 | − | 0.00752081i | ||||
\(953\) | −25.6865 | − | 44.4904i | −0.832068 | − | 1.44118i | −0.896395 | − | 0.443256i | \(-0.853823\pi\) |
0.0643267 | − | 0.997929i | \(-0.479510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.66025 | + | 1.53590i | −0.0860838 | + | 0.0497005i | ||||
\(956\) | −11.9545 | + | 6.90192i | −0.386636 | + | 0.223224i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.6962 | − | 27.1865i | −0.507120 | − | 0.878357i | ||||
\(959\) | −7.73205 | + | 13.3923i | −0.249681 | + | 0.432460i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6795 | −0.892887 | ||||||||
\(962\) | 3.29423 | − | 3.16987i | 0.106210 | − | 0.102201i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.0718 | − | 6.39230i | −0.356599 | − | 0.205882i | ||||
\(965\) | −6.29423 | + | 10.9019i | −0.202618 | + | 0.350945i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.0000i | 1.15768i | 0.815440 | + | 0.578841i | \(0.196495\pi\) | ||||
−0.815440 | + | 0.578841i | \(0.803505\pi\) | |||||||
\(968\) | −2.53590 | + | 1.46410i | −0.0815069 | + | 0.0470580i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 0.535898i | − | 0.0172067i | ||||||
\(971\) | 22.1244 | + | 38.3205i | 0.710004 | + | 1.22976i | 0.964855 | + | 0.262783i | \(0.0846404\pi\) |
−0.254851 | + | 0.966980i | \(0.582026\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.6962 | + | 9.06218i | 0.503196 | + | 0.290520i | ||||
\(974\) | 21.1962 | 0.679169 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.7321 | −0.375534 | ||||||||
\(977\) | −15.8038 | − | 9.12436i | −0.505610 | − | 0.291914i | 0.225417 | − | 0.974262i | \(-0.427625\pi\) |
−0.731027 | + | 0.682348i | \(0.760959\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0622 | − | 20.8923i | −0.385509 | − | 0.667721i | ||||
\(980\) | − | 0.732051i | − | 0.0233845i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.3923 | + | 18.1244i | −1.00177 | + | 0.578371i | ||||
\(983\) | 28.1436i | 0.897641i | 0.893622 | + | 0.448821i | \(0.148156\pi\) | ||||
−0.893622 | + | 0.448821i | \(0.851844\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.830127 | + | 1.43782i | −0.0264500 | + | 0.0458128i | ||||
\(986\) | 0.696152 | + | 0.401924i | 0.0221700 | + | 0.0127999i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.46410 | − | 15.4641i | 0.142022 | − | 0.491979i | ||||
\(989\) | −2.53590 | −0.0806369 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.30385 | − | 3.99038i | 0.0731841 | − | 0.126759i | −0.827111 | − | 0.562039i | \(-0.810017\pi\) |
0.900295 | + | 0.435280i | \(0.143351\pi\) | |||||||
\(992\) | 3.83013 | + | 6.63397i | 0.121607 | + | 0.210629i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.90192 | + | 1.09808i | −0.0603254 | + | 0.0348289i | ||||
\(995\) | −2.66025 | + | 1.53590i | −0.0843357 | + | 0.0486913i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.1147 | − | 36.5718i | −0.668710 | − | 1.15824i | −0.978265 | − | 0.207359i | \(-0.933513\pi\) |
0.309555 | − | 0.950882i | \(-0.399820\pi\) | |||||||
\(998\) | 6.49038 | − | 11.2417i | 0.205449 | − | 0.355849i | ||||
\(999\) | 0 | 0 |
(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 | 1638.2.bj.d.1135.2 | 4 | ||
3.2 | odd | 2 | 546.2.s.d.43.1 | ✓ | 4 | ||
13.10 | even | 6 | inner | 1638.2.bj.d.127.2 | 4 | ||
39.20 | even | 12 | 7098.2.a.bj.1.1 | 2 | |||
39.23 | odd | 6 | 546.2.s.d.127.1 | yes | 4 | ||
39.32 | even | 12 | 7098.2.a.bs.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.d.43.1 | ✓ | 4 | 3.2 | odd | 2 | ||
546.2.s.d.127.1 | yes | 4 | 39.23 | odd | 6 | ||
1638.2.bj.d.127.2 | 4 | 13.10 | even | 6 | inner | ||
1638.2.bj.d.1135.2 | 4 | 1.1 | even | 1 | trivial | ||
7098.2.a.bj.1.1 | 2 | 39.20 | even | 12 | |||
7098.2.a.bs.1.2 | 2 | 39.32 | even | 12 |