Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(811,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.811");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.c (of order \(2\), degree \(1\), 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: | \(10.0611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 811.4 | ||
Root | \(1.10145 + 0.887017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.811 |
Dual form | 1260.2.c.e.811.3 |
$q$-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 \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10145 | + | 0.887017i | −0.778846 | + | 0.627216i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.426402 | − | 1.95402i | 0.213201 | − | 0.977008i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.391948 | − | 2.61656i | −0.148142 | − | 0.988966i | ||||
\(8\) | 1.26358 | + | 2.53049i | 0.446744 | + | 0.894662i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.887017 | − | 1.10145i | −0.280499 | − | 0.348310i | ||||
\(11\) | − | 0.770756i | − | 0.232392i | −0.993226 | − | 0.116196i | \(-0.962930\pi\) | ||
0.993226 | − | 0.116196i | \(-0.0370700\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.60576i | 1.55476i | 0.629032 | + | 0.777379i | \(0.283451\pi\) | ||||
−0.629032 | + | 0.777379i | \(0.716549\pi\) | |||||||
\(14\) | 2.75264 | + | 2.53435i | 0.735675 | + | 0.677335i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.63636 | − | 1.66639i | −0.909091 | − | 0.416598i | ||||
\(17\) | − | 0.503042i | − | 0.122005i | −0.998138 | − | 0.0610027i | \(-0.980570\pi\) | ||
0.998138 | − | 0.0610027i | \(-0.0194298\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.63506 | −0.375109 | −0.187554 | − | 0.982254i | \(-0.560056\pi\) | ||||
−0.187554 | + | 0.982254i | \(0.560056\pi\) | |||||||
\(20\) | 1.95402 | + | 0.426402i | 0.436931 | + | 0.0953464i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.683673 | + | 0.848952i | 0.145760 | + | 0.180997i | ||||
\(23\) | 1.42475i | 0.297082i | 0.988906 | + | 0.148541i | \(0.0474577\pi\) | ||||
−0.988906 | + | 0.148541i | \(0.952542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −4.97240 | − | 6.17449i | −0.975169 | − | 1.21092i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.27993 | − | 0.349833i | −0.997812 | − | 0.0661123i | ||||
\(29\) | −5.03595 | −0.935152 | −0.467576 | − | 0.883953i | \(-0.654873\pi\) | ||||
−0.467576 | + | 0.883953i | \(0.654873\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.23212 | 1.47853 | 0.739266 | − | 0.673414i | \(-0.235173\pi\) | ||||
0.739266 | + | 0.673414i | \(0.235173\pi\) | |||||||
\(32\) | 5.48341 | − | 1.39006i | 0.969338 | − | 0.245730i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.446206 | + | 0.554077i | 0.0765238 | + | 0.0950235i | ||||
\(35\) | 2.61656 | − | 0.391948i | 0.442279 | − | 0.0662513i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.1403 | 1.66706 | 0.833530 | − | 0.552475i | \(-0.186316\pi\) | ||||
0.833530 | + | 0.552475i | \(0.186316\pi\) | |||||||
\(38\) | 1.80094 | − | 1.45033i | 0.292152 | − | 0.235274i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.53049 | + | 1.26358i | −0.400105 | + | 0.199790i | ||||
\(41\) | 5.07885i | 0.793184i | 0.917995 | + | 0.396592i | \(0.129807\pi\) | ||||
−0.917995 | + | 0.396592i | \(0.870193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.06204i | 1.38195i | 0.722880 | + | 0.690974i | \(0.242818\pi\) | ||||
−0.722880 | + | 0.690974i | \(0.757182\pi\) | |||||||
\(44\) | −1.50607 | − | 0.328652i | −0.227049 | − | 0.0495461i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.26378 | − | 1.56930i | −0.186334 | − | 0.231381i | ||||
\(47\) | 4.64967 | 0.678223 | 0.339112 | − | 0.940746i | \(-0.389874\pi\) | ||||
0.339112 | + | 0.940746i | \(0.389874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.69275 | + | 2.05111i | −0.956108 | + | 0.293016i | ||||
\(50\) | 1.10145 | − | 0.887017i | 0.155769 | − | 0.125443i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.9537 | + | 2.39031i | 1.51901 | + | 0.331476i | ||||
\(53\) | −0.455805 | −0.0626096 | −0.0313048 | − | 0.999510i | \(-0.509966\pi\) | ||||
−0.0313048 | + | 0.999510i | \(0.509966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.770756 | 0.103929 | ||||||||
\(56\) | 6.12590 | − | 4.29806i | 0.818608 | − | 0.574352i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.54687 | − | 4.46697i | 0.728339 | − | 0.586542i | ||||
\(59\) | 10.4908 | 1.36578 | 0.682890 | − | 0.730521i | \(-0.260723\pi\) | ||||
0.682890 | + | 0.730521i | \(0.260723\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.32394i | 0.425587i | 0.977097 | + | 0.212794i | \(0.0682562\pi\) | ||||
−0.977097 | + | 0.212794i | \(0.931744\pi\) | |||||||
\(62\) | −9.06730 | + | 7.30202i | −1.15155 | + | 0.927358i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.80671 | + | 6.39496i | −0.600839 | + | 0.799370i | ||||
\(65\) | −5.60576 | −0.695309 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.70791i | 1.06384i | 0.846794 | + | 0.531920i | \(0.178529\pi\) | ||||
−0.846794 | + | 0.531920i | \(0.821471\pi\) | |||||||
\(68\) | −0.982952 | − | 0.214498i | −0.119200 | − | 0.0260117i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.53435 | + | 2.75264i | −0.302913 | + | 0.329004i | ||||
\(71\) | − | 10.8176i | − | 1.28382i | −0.766781 | − | 0.641909i | \(-0.778143\pi\) | ||
0.766781 | − | 0.641909i | \(-0.221857\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.29564i | − | 0.268685i | −0.990935 | − | 0.134342i | \(-0.957108\pi\) | ||
0.990935 | − | 0.134342i | \(-0.0428922\pi\) | |||||||
\(74\) | −11.1691 | + | 8.99464i | −1.29838 | + | 1.04561i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.697193 | + | 3.19494i | −0.0799736 | + | 0.366484i | ||||
\(77\) | −2.01673 | + | 0.302096i | −0.229827 | + | 0.0344270i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.56336i | − | 0.288400i | −0.989549 | − | 0.144200i | \(-0.953939\pi\) | ||
0.989549 | − | 0.144200i | \(-0.0460609\pi\) | |||||||
\(80\) | 1.66639 | − | 3.63636i | 0.186309 | − | 0.406558i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.50503 | − | 5.59412i | −0.497497 | − | 0.617768i | ||||
\(83\) | 13.9979 | 1.53646 | 0.768232 | − | 0.640171i | \(-0.221137\pi\) | ||||
0.768232 | + | 0.640171i | \(0.221137\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.503042 | 0.0545625 | ||||||||
\(86\) | −8.03818 | − | 9.98142i | −0.866779 | − | 1.07632i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.95039 | − | 0.973914i | 0.207912 | − | 0.103820i | ||||
\(89\) | 2.98877i | 0.316809i | 0.987374 | + | 0.158404i | \(0.0506349\pi\) | ||||
−0.987374 | + | 0.158404i | \(0.949365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.6678 | − | 2.19717i | 1.53760 | − | 0.230326i | ||||
\(92\) | 2.78399 | + | 0.607518i | 0.290251 | + | 0.0633382i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.12139 | + | 4.12433i | −0.528231 | + | 0.425392i | ||||
\(95\) | − | 1.63506i | − | 0.167754i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.5818i | 1.58209i | 0.611756 | + | 0.791046i | \(0.290463\pi\) | ||||
−0.611756 | + | 0.791046i | \(0.709537\pi\) | |||||||
\(98\) | 5.55239 | − | 8.19579i | 0.560876 | − | 0.827900i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.426402 | + | 1.95402i | −0.0426402 | + | 0.195402i | ||||
\(101\) | 18.9661i | 1.88719i | 0.331097 | + | 0.943597i | \(0.392581\pi\) | ||||
−0.331097 | + | 0.943597i | \(0.607419\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.23760 | −0.811675 | −0.405837 | − | 0.913945i | \(-0.633020\pi\) | ||||
−0.405837 | + | 0.913945i | \(0.633020\pi\) | |||||||
\(104\) | −14.1853 | + | 7.08335i | −1.39098 | + | 0.694579i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.502048 | − | 0.404306i | 0.0487632 | − | 0.0392697i | ||||
\(107\) | 11.8042i | 1.14115i | 0.821244 | + | 0.570577i | \(0.193280\pi\) | ||||
−0.821244 | + | 0.570577i | \(0.806720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.80783 | −0.939419 | −0.469710 | − | 0.882821i | \(-0.655641\pi\) | ||||
−0.469710 | + | 0.882821i | \(0.655641\pi\) | |||||||
\(110\) | −0.848952 | + | 0.683673i | −0.0809444 | + | 0.0651857i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.93495 | + | 10.1679i | −0.277327 | + | 0.960776i | ||||
\(113\) | 10.0104 | 0.941702 | 0.470851 | − | 0.882213i | \(-0.343947\pi\) | ||||
0.470851 | + | 0.882213i | \(0.343947\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.42475 | −0.132859 | ||||||||
\(116\) | −2.14734 | + | 9.84033i | −0.199376 | + | 0.913652i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.5551 | + | 9.30548i | −1.06373 | + | 0.856638i | ||||
\(119\) | −1.31624 | + | 0.197166i | −0.120659 | + | 0.0180742i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4059 | 0.945994 | ||||||||
\(122\) | −2.94839 | − | 3.66117i | −0.266935 | − | 0.331467i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.51019 | − | 16.0857i | 0.315225 | − | 1.44454i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.09530i | − | 0.274663i | −0.990525 | − | 0.137332i | \(-0.956147\pi\) | ||
0.990525 | − | 0.137332i | \(-0.0438526\pi\) | |||||||
\(128\) | −0.378061 | − | 11.3074i | −0.0334162 | − | 0.999442i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.17449 | − | 4.97240i | 0.541538 | − | 0.436109i | ||||
\(131\) | −17.5001 | −1.52899 | −0.764495 | − | 0.644630i | \(-0.777011\pi\) | ||||
−0.764495 | + | 0.644630i | \(0.777011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.640859 | + | 4.27823i | 0.0555695 | + | 0.370970i | ||||
\(134\) | −7.72407 | − | 9.59137i | −0.667258 | − | 0.828568i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.27294 | − | 0.635635i | 0.109154 | − | 0.0545052i | ||||
\(137\) | 15.6542 | 1.33742 | 0.668712 | − | 0.743521i | \(-0.266846\pi\) | ||||
0.668712 | + | 0.743521i | \(0.266846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.13095 | −0.0959261 | −0.0479630 | − | 0.998849i | \(-0.515273\pi\) | ||||
−0.0479630 | + | 0.998849i | \(0.515273\pi\) | |||||||
\(140\) | 0.349833 | − | 5.27993i | 0.0295663 | − | 0.446235i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.59542 | + | 11.9151i | 0.805230 | + | 0.999895i | ||||
\(143\) | 4.32067 | 0.361313 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.03595i | − | 0.418213i | ||||||
\(146\) | 2.03627 | + | 2.52855i | 0.168523 | + | 0.209264i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.32386 | − | 19.8144i | 0.355419 | − | 1.62873i | ||||
\(149\) | −21.3643 | −1.75023 | −0.875117 | − | 0.483911i | \(-0.839216\pi\) | ||||
−0.875117 | + | 0.483911i | \(0.839216\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.83045i | − | 0.230339i | −0.993346 | − | 0.115169i | \(-0.963259\pi\) | ||
0.993346 | − | 0.115169i | \(-0.0367411\pi\) | |||||||
\(152\) | −2.06604 | − | 4.13750i | −0.167578 | − | 0.335595i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.95337 | − | 2.12162i | 0.157407 | − | 0.170965i | ||||
\(155\) | 8.23212i | 0.661219i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.7903i | 1.49963i | 0.661649 | + | 0.749814i | \(0.269857\pi\) | ||||
−0.661649 | + | 0.749814i | \(0.730143\pi\) | |||||||
\(158\) | 2.27374 | + | 2.82342i | 0.180889 | + | 0.224619i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.39006 | + | 5.48341i | 0.109894 | + | 0.433501i | ||||
\(161\) | 3.72795 | − | 0.558430i | 0.293804 | − | 0.0440104i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.40744i | − | 0.580195i | −0.956997 | − | 0.290098i | \(-0.906312\pi\) | ||
0.956997 | − | 0.290098i | \(-0.0936878\pi\) | |||||||
\(164\) | 9.92417 | + | 2.16563i | 0.774947 | + | 0.169108i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.4180 | + | 12.4163i | −1.19667 | + | 0.963694i | ||||
\(167\) | −2.96147 | −0.229165 | −0.114583 | − | 0.993414i | \(-0.536553\pi\) | ||||
−0.114583 | + | 0.993414i | \(0.536553\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.4246 | −1.41727 | ||||||||
\(170\) | −0.554077 | + | 0.446206i | −0.0424958 | + | 0.0342225i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.7074 | + | 3.86407i | 1.35017 | + | 0.294633i | ||||
\(173\) | 15.0215i | 1.14206i | 0.820928 | + | 0.571031i | \(0.193457\pi\) | ||||
−0.820928 | + | 0.571031i | \(0.806543\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.391948 | + | 2.61656i | 0.0296285 | + | 0.197793i | ||||
\(176\) | −1.28438 | + | 2.80275i | −0.0968140 | + | 0.211265i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.65109 | − | 3.29199i | −0.198707 | − | 0.246745i | ||||
\(179\) | − | 4.82936i | − | 0.360963i | −0.983578 | − | 0.180482i | \(-0.942234\pi\) | ||
0.983578 | − | 0.180482i | \(-0.0577656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.2050i | − | 1.35316i | −0.736367 | − | 0.676582i | \(-0.763460\pi\) | ||
0.736367 | − | 0.676582i | \(-0.236540\pi\) | |||||||
\(182\) | −14.2070 | + | 15.4307i | −1.05309 | + | 1.14380i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.60532 | + | 1.80030i | −0.265788 | + | 0.132720i | ||||
\(185\) | 10.1403i | 0.745532i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.387722 | −0.0283531 | ||||||||
\(188\) | 1.98263 | − | 9.08552i | 0.144598 | − | 0.662630i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.45033 | + | 1.80094i | 0.105218 | + | 0.130654i | ||||
\(191\) | 5.65184i | 0.408953i | 0.978871 | + | 0.204476i | \(0.0655492\pi\) | ||||
−0.978871 | + | 0.204476i | \(0.934451\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0978 | −1.15874 | −0.579372 | − | 0.815063i | \(-0.696702\pi\) | ||||
−0.579372 | + | 0.815063i | \(0.696702\pi\) | |||||||
\(194\) | −13.8213 | − | 17.1626i | −0.992313 | − | 1.23221i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.15410 | + | 13.9523i | 0.0824355 | + | 0.996596i | ||||
\(197\) | 12.2972 | 0.876141 | 0.438071 | − | 0.898941i | \(-0.355662\pi\) | ||||
0.438071 | + | 0.898941i | \(0.355662\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.8234 | 1.19258 | 0.596290 | − | 0.802769i | \(-0.296641\pi\) | ||||
0.596290 | + | 0.802769i | \(0.296641\pi\) | |||||||
\(200\) | −1.26358 | − | 2.53049i | −0.0893488 | − | 0.178932i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −16.8232 | − | 20.8902i | −1.18368 | − | 1.46983i | ||||
\(203\) | 1.97383 | + | 13.1769i | 0.138536 | + | 0.924834i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.07885 | −0.354723 | ||||||||
\(206\) | 9.07333 | − | 7.30689i | 0.632169 | − | 0.509095i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.34141 | − | 20.3846i | 0.647710 | − | 1.41342i | ||||
\(209\) | 1.26023i | 0.0871721i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.19446i | − | 0.632973i | −0.948597 | − | 0.316486i | \(-0.897497\pi\) | ||
0.948597 | − | 0.316486i | \(-0.102503\pi\) | |||||||
\(212\) | −0.194356 | + | 0.890650i | −0.0133484 | + | 0.0611701i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.4705 | − | 13.0018i | −0.715749 | − | 0.888782i | ||||
\(215\) | −9.06204 | −0.618026 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.22656 | − | 21.5398i | −0.219033 | − | 1.46222i | ||||
\(218\) | 10.8029 | − | 8.69971i | 0.731663 | − | 0.589219i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.328652 | − | 1.50607i | 0.0221577 | − | 0.101539i | ||||
\(221\) | 2.81993 | 0.189689 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.8560 | −1.53055 | −0.765275 | − | 0.643704i | \(-0.777397\pi\) | ||||
−0.765275 | + | 0.643704i | \(0.777397\pi\) | |||||||
\(224\) | −5.78638 | − | 13.8028i | −0.386619 | − | 0.922240i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.0260 | + | 8.87942i | −0.733440 | + | 0.590650i | ||||
\(227\) | 17.4680 | 1.15939 | 0.579697 | − | 0.814832i | \(-0.303171\pi\) | ||||
0.579697 | + | 0.814832i | \(0.303171\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6233i | 0.834169i | 0.908868 | + | 0.417085i | \(0.136948\pi\) | ||||
−0.908868 | + | 0.417085i | \(0.863052\pi\) | |||||||
\(230\) | 1.56930 | − | 1.26378i | 0.103477 | − | 0.0833313i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.36334 | − | 12.7434i | −0.417774 | − | 0.836645i | ||||
\(233\) | 3.89410 | 0.255111 | 0.127555 | − | 0.991831i | \(-0.459287\pi\) | ||||
0.127555 | + | 0.991831i | \(0.459287\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.64967i | 0.303311i | ||||||||
\(236\) | 4.47328 | − | 20.4991i | 0.291186 | − | 1.33438i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.27489 | − | 1.38469i | 0.0826386 | − | 0.0897564i | ||||
\(239\) | 11.6497i | 0.753559i | 0.926303 | + | 0.376779i | \(0.122968\pi\) | ||||
−0.926303 | + | 0.376779i | \(0.877032\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 21.0259i | − | 1.35440i | −0.735799 | − | 0.677200i | \(-0.763193\pi\) | ||
0.735799 | − | 0.677200i | \(-0.236807\pi\) | |||||||
\(242\) | −11.4617 | + | 9.23024i | −0.736783 | + | 0.593342i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.49504 | + | 1.41734i | 0.415802 | + | 0.0907357i | ||||
\(245\) | −2.05111 | − | 6.69275i | −0.131041 | − | 0.427584i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 9.16576i | − | 0.583203i | ||||||
\(248\) | 10.4020 | + | 20.8312i | 0.660525 | + | 1.32279i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.887017 | + | 1.10145i | 0.0560999 | + | 0.0696621i | ||||
\(251\) | 1.36484 | 0.0861478 | 0.0430739 | − | 0.999072i | \(-0.486285\pi\) | ||||
0.0430739 | + | 0.999072i | \(0.486285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.09814 | 0.0690393 | ||||||||
\(254\) | 2.74558 | + | 3.40933i | 0.172273 | + | 0.213920i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.4463 | + | 12.1192i | 0.652891 | + | 0.757452i | ||||
\(257\) | − | 4.44214i | − | 0.277093i | −0.990356 | − | 0.138547i | \(-0.955757\pi\) | ||
0.990356 | − | 0.138547i | \(-0.0442431\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.97448 | − | 26.5328i | −0.246962 | − | 1.64866i | ||||
\(260\) | −2.39031 | + | 10.9537i | −0.148241 | + | 0.679323i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.2755 | − | 15.5229i | 1.19085 | − | 0.959006i | ||||
\(263\) | − | 4.92839i | − | 0.303898i | −0.988388 | − | 0.151949i | \(-0.951445\pi\) | ||
0.988388 | − | 0.151949i | \(-0.0485549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.455805i | − | 0.0279999i | ||||||
\(266\) | −4.50074 | − | 4.14382i | −0.275958 | − | 0.254074i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 17.0154 | + | 3.71307i | 1.03938 | + | 0.226812i | ||||
\(269\) | − | 25.0193i | − | 1.52546i | −0.646719 | − | 0.762728i | \(-0.723859\pi\) | ||
0.646719 | − | 0.762728i | \(-0.276141\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.1353 | −0.737170 | −0.368585 | − | 0.929594i | \(-0.620158\pi\) | ||||
−0.368585 | + | 0.929594i | \(0.620158\pi\) | |||||||
\(272\) | −0.838265 | + | 1.82924i | −0.0508273 | + | 0.110914i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.2423 | + | 13.8855i | −1.04165 | + | 0.838854i | ||||
\(275\) | 0.770756i | 0.0464783i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.4692 | 1.16979 | 0.584896 | − | 0.811108i | \(-0.301135\pi\) | ||||
0.584896 | + | 0.811108i | \(0.301135\pi\) | |||||||
\(278\) | 1.24569 | − | 1.00317i | 0.0747116 | − | 0.0601663i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.29806 | + | 6.12590i | 0.256858 | + | 0.366093i | ||||
\(281\) | 17.7452 | 1.05859 | 0.529296 | − | 0.848437i | \(-0.322456\pi\) | ||||
0.529296 | + | 0.848437i | \(0.322456\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.4942 | 1.75325 | 0.876623 | − | 0.481177i | \(-0.159791\pi\) | ||||
0.876623 | + | 0.481177i | \(0.159791\pi\) | |||||||
\(284\) | −21.1378 | − | 4.61266i | −1.25430 | − | 0.273711i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.75902 | + | 3.83251i | −0.281407 | + | 0.226621i | ||||
\(287\) | 13.2891 | − | 1.99065i | 0.784432 | − | 0.117504i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7469 | 0.985115 | ||||||||
\(290\) | 4.46697 | + | 5.54687i | 0.262310 | + | 0.325723i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.48573 | − | 0.978867i | −0.262507 | − | 0.0572839i | ||||
\(293\) | − | 19.8780i | − | 1.16129i | −0.814158 | − | 0.580643i | \(-0.802801\pi\) | ||
0.814158 | − | 0.580643i | \(-0.197199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.4908i | 0.610795i | ||||||||
\(296\) | 12.8131 | + | 25.6599i | 0.744749 | + | 1.49145i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 23.5318 | − | 18.9505i | 1.36316 | − | 1.09777i | ||||
\(299\) | −7.98683 | −0.461890 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.7114 | − | 3.55185i | 1.36670 | − | 0.204725i | ||||
\(302\) | 2.51065 | + | 3.11761i | 0.144472 | + | 0.179398i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.94567 | + | 2.72466i | 0.341008 | + | 0.156270i | ||||
\(305\) | −3.32394 | −0.190328 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.12425 | −0.121238 | −0.0606188 | − | 0.998161i | \(-0.519307\pi\) | ||||
−0.0606188 | + | 0.998161i | \(0.519307\pi\) | |||||||
\(308\) | −0.269636 | + | 4.06953i | −0.0153639 | + | 0.231883i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.30202 | − | 9.06730i | −0.414727 | − | 0.514988i | ||||
\(311\) | 10.2870 | 0.583323 | 0.291661 | − | 0.956522i | \(-0.405792\pi\) | ||||
0.291661 | + | 0.956522i | \(0.405792\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.8800i | − | 1.01064i | −0.862932 | − | 0.505320i | \(-0.831374\pi\) | ||
0.862932 | − | 0.505320i | \(-0.168626\pi\) | |||||||
\(314\) | −16.6673 | − | 20.6966i | −0.940590 | − | 1.16798i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.00884 | − | 1.09302i | −0.281769 | − | 0.0614872i | ||||
\(317\) | −12.3840 | −0.695557 | −0.347778 | − | 0.937577i | \(-0.613064\pi\) | ||||
−0.347778 | + | 0.937577i | \(0.613064\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.88149i | 0.217322i | ||||||||
\(320\) | −6.39496 | − | 4.80671i | −0.357489 | − | 0.268703i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.61083 | + | 3.92184i | −0.201224 | + | 0.218556i | ||||
\(323\) | 0.822503i | 0.0457653i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.60576i | − | 0.310952i | ||||||
\(326\) | 6.57052 | + | 8.15895i | 0.363908 | + | 0.451883i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.8520 | + | 6.41756i | −0.709631 | + | 0.354350i | ||||
\(329\) | −1.82243 | − | 12.1661i | −0.100474 | − | 0.670740i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.3000i | − | 1.17075i | −0.810762 | − | 0.585376i | \(-0.800947\pi\) | ||
0.810762 | − | 0.585376i | \(-0.199053\pi\) | |||||||
\(332\) | 5.96872 | − | 27.3520i | 0.327576 | − | 1.50114i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.26192 | − | 2.62687i | 0.178484 | − | 0.143736i | ||||
\(335\) | −8.70791 | −0.475764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.875789 | −0.0477073 | −0.0238536 | − | 0.999715i | \(-0.507594\pi\) | ||||
−0.0238536 | + | 0.999715i | \(0.507594\pi\) | |||||||
\(338\) | 20.2938 | − | 16.3429i | 1.10384 | − | 0.888936i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.214498 | − | 0.982952i | 0.0116328 | − | 0.0533080i | ||||
\(341\) | − | 6.34495i | − | 0.343598i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.99006 | + | 16.7081i | 0.431423 | + | 0.902150i | ||||
\(344\) | −22.9314 | + | 11.4506i | −1.23638 | + | 0.617377i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.3243 | − | 16.5455i | −0.716320 | − | 0.889491i | ||||
\(347\) | − | 34.9081i | − | 1.87396i | −0.349379 | − | 0.936981i | \(-0.613608\pi\) | ||
0.349379 | − | 0.936981i | \(-0.386392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 21.1880i | − | 1.13417i | −0.823660 | − | 0.567084i | \(-0.808071\pi\) | ||
0.823660 | − | 0.567084i | \(-0.191929\pi\) | |||||||
\(350\) | −2.75264 | − | 2.53435i | −0.147135 | − | 0.135467i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.07140 | − | 4.22637i | −0.0571056 | − | 0.225266i | ||||
\(353\) | 7.69915i | 0.409785i | 0.978785 | + | 0.204892i | \(0.0656844\pi\) | ||||
−0.978785 | + | 0.204892i | \(0.934316\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8176 | 0.574140 | ||||||||
\(356\) | 5.84010 | + | 1.27442i | 0.309525 | + | 0.0675439i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.28372 | + | 5.31931i | 0.226402 | + | 0.281134i | ||||
\(359\) | − | 2.14821i | − | 0.113378i | −0.998392 | − | 0.0566890i | \(-0.981946\pi\) | ||
0.998392 | − | 0.0566890i | \(-0.0180543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3266 | −0.859294 | ||||||||
\(362\) | 16.1481 | + | 20.0519i | 0.848726 | + | 1.05391i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.96108 | − | 29.5980i | 0.102789 | − | 1.55136i | ||||
\(365\) | 2.29564 | 0.120159 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.6962 | −1.39353 | −0.696764 | − | 0.717300i | \(-0.745378\pi\) | ||||
−0.696764 | + | 0.717300i | \(0.745378\pi\) | |||||||
\(368\) | 2.37420 | − | 5.18092i | 0.123764 | − | 0.270074i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.99464 | − | 11.1691i | −0.467609 | − | 0.580654i | ||||
\(371\) | 0.178652 | + | 1.19264i | 0.00927513 | + | 0.0619187i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.51430 | −0.440854 | −0.220427 | − | 0.975403i | \(-0.570745\pi\) | ||||
−0.220427 | + | 0.975403i | \(0.570745\pi\) | |||||||
\(374\) | 0.427058 | − | 0.343916i | 0.0220826 | − | 0.0177835i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.87524 | + | 11.7659i | 0.302992 | + | 0.606781i | ||||
\(377\) | − | 28.2303i | − | 1.45394i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.1693i | 1.60106i | 0.599295 | + | 0.800529i | \(0.295448\pi\) | ||||
−0.599295 | + | 0.800529i | \(0.704552\pi\) | |||||||
\(380\) | −3.19494 | − | 0.697193i | −0.163897 | − | 0.0357653i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.01328 | − | 6.22524i | −0.256502 | − | 0.318511i | ||||
\(383\) | −33.7311 | −1.72358 | −0.861788 | − | 0.507268i | \(-0.830655\pi\) | ||||
−0.861788 | + | 0.507268i | \(0.830655\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.302096 | − | 2.01673i | −0.0153962 | − | 0.102782i | ||||
\(386\) | 17.7310 | − | 14.2790i | 0.902483 | − | 0.726783i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30.4471 | + | 6.64412i | 1.54572 | + | 0.337304i | ||||
\(389\) | −25.9912 | −1.31780 | −0.658902 | − | 0.752228i | \(-0.728979\pi\) | ||||
−0.658902 | + | 0.752228i | \(0.728979\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.716711 | 0.0362456 | ||||||||
\(392\) | −13.6472 | − | 14.3442i | −0.689285 | − | 0.724490i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.5448 | + | 10.9078i | −0.682379 | + | 0.549529i | ||||
\(395\) | 2.56336 | 0.128977 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.63535i | − | 0.0820760i | −0.999158 | − | 0.0410380i | \(-0.986934\pi\) | ||
0.999158 | − | 0.0410380i | \(-0.0130665\pi\) | |||||||
\(398\) | −18.5302 | + | 14.9226i | −0.928835 | + | 0.748004i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.63636 | + | 1.66639i | 0.181818 | + | 0.0833197i | ||||
\(401\) | 11.7906 | 0.588797 | 0.294398 | − | 0.955683i | \(-0.404881\pi\) | ||||
0.294398 | + | 0.955683i | \(0.404881\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 46.1473i | 2.29876i | ||||||||
\(404\) | 37.0600 | + | 8.08717i | 1.84380 | + | 0.402352i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.8622 | − | 12.7629i | −0.687968 | − | 0.633411i | ||||
\(407\) | − | 7.81571i | − | 0.387411i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.74926i | 0.482070i | 0.970516 | + | 0.241035i | \(0.0774868\pi\) | ||||
−0.970516 | + | 0.241035i | \(0.922513\pi\) | |||||||
\(410\) | 5.59412 | − | 4.50503i | 0.276274 | − | 0.222488i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.51253 | + | 16.0964i | −0.173050 | + | 0.793013i | ||||
\(413\) | −4.11183 | − | 27.4497i | −0.202330 | − | 1.35071i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.9979i | 0.687128i | ||||||||
\(416\) | 7.79233 | + | 30.7387i | 0.382051 | + | 1.50709i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.11785 | − | 1.38809i | −0.0546757 | − | 0.0678936i | ||||
\(419\) | 15.3501 | 0.749902 | 0.374951 | − | 0.927045i | \(-0.377659\pi\) | ||||
0.374951 | + | 0.927045i | \(0.377659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.0738 | 1.75813 | 0.879064 | − | 0.476703i | \(-0.158168\pi\) | ||||
0.879064 | + | 0.476703i | \(0.158168\pi\) | |||||||
\(422\) | 8.15564 | + | 10.1273i | 0.397011 | + | 0.492988i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.575947 | − | 1.15341i | −0.0279705 | − | 0.0560144i | ||||
\(425\) | 0.503042i | 0.0244011i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.69729 | − | 1.30281i | 0.420891 | − | 0.0630475i | ||||
\(428\) | 23.0656 | + | 5.03333i | 1.11492 | + | 0.243295i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.98142 | − | 8.03818i | 0.481347 | − | 0.387635i | ||||
\(431\) | − | 20.9842i | − | 1.01077i | −0.862893 | − | 0.505387i | \(-0.831350\pi\) | ||
0.862893 | − | 0.505387i | \(-0.168650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.4424i | − | 0.501828i | −0.968009 | − | 0.250914i | \(-0.919269\pi\) | ||
0.968009 | − | 0.250914i | \(-0.0807312\pi\) | |||||||
\(434\) | 22.6601 | + | 20.8631i | 1.08772 | + | 1.00146i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.18208 | + | 19.1647i | −0.200285 | + | 0.917821i | ||||
\(437\) | − | 2.32956i | − | 0.111438i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.2996 | −1.73249 | −0.866243 | − | 0.499624i | \(-0.833472\pi\) | ||||
−0.866243 | + | 0.499624i | \(0.833472\pi\) | |||||||
\(440\) | 0.973914 | + | 1.95039i | 0.0464295 | + | 0.0929810i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.10602 | + | 2.50133i | −0.147738 | + | 0.118976i | ||||
\(443\) | − | 3.71212i | − | 0.176368i | −0.996104 | − | 0.0881842i | \(-0.971894\pi\) | ||
0.996104 | − | 0.0881842i | \(-0.0281064\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.98877 | −0.141681 | ||||||||
\(446\) | 25.1748 | − | 20.2736i | 1.19206 | − | 0.959985i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.6168 | + | 10.0706i | 0.879559 | + | 0.475789i | ||||
\(449\) | −8.56515 | −0.404215 | −0.202107 | − | 0.979363i | \(-0.564779\pi\) | ||||
−0.202107 | + | 0.979363i | \(0.564779\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.91456 | 0.184329 | ||||||||
\(452\) | 4.26847 | − | 19.5605i | 0.200772 | − | 0.920051i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.2402 | + | 15.4944i | −0.902989 | + | 0.727190i | ||||
\(455\) | 2.19717 | + | 14.6678i | 0.103005 | + | 0.687637i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.6705 | −0.686259 | −0.343129 | − | 0.939288i | \(-0.611487\pi\) | ||||
−0.343129 | + | 0.939288i | \(0.611487\pi\) | |||||||
\(458\) | −11.1971 | − | 13.9040i | −0.523204 | − | 0.649689i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.607518 | + | 2.78399i | −0.0283257 | + | 0.129804i | ||||
\(461\) | 19.3683i | 0.902072i | 0.892506 | + | 0.451036i | \(0.148945\pi\) | ||||
−0.892506 | + | 0.451036i | \(0.851055\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.34277i | − | 0.201826i | −0.994895 | − | 0.100913i | \(-0.967824\pi\) | ||
0.994895 | − | 0.100913i | \(-0.0321763\pi\) | |||||||
\(464\) | 18.3125 | + | 8.39188i | 0.850138 | + | 0.389583i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.28917 | + | 3.45413i | −0.198692 | + | 0.160009i | ||||
\(467\) | −15.4501 | −0.714943 | −0.357472 | − | 0.933924i | \(-0.616361\pi\) | ||||
−0.357472 | + | 0.933924i | \(0.616361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.7848 | − | 3.41305i | 1.05210 | − | 0.157600i | ||||
\(470\) | −4.12433 | − | 5.12139i | −0.190241 | − | 0.236232i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.2559 | + | 26.5467i | 0.610154 | + | 1.22191i | ||||
\(473\) | 6.98462 | 0.321153 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.63506 | 0.0750217 | ||||||||
\(476\) | −0.175981 | + | 2.65602i | −0.00806606 | + | 0.121739i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.3335 | − | 12.8316i | −0.472644 | − | 0.586906i | ||||
\(479\) | −22.4129 | −1.02407 | −0.512035 | − | 0.858964i | \(-0.671108\pi\) | ||||
−0.512035 | + | 0.858964i | \(0.671108\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.8442i | 2.59187i | ||||||||
\(482\) | 18.6504 | + | 23.1591i | 0.849501 | + | 1.05487i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.43711 | − | 20.3334i | 0.201687 | − | 0.924244i | ||||
\(485\) | −15.5818 | −0.707533 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14.7901i | − | 0.670202i | −0.942182 | − | 0.335101i | \(-0.891230\pi\) | ||
0.942182 | − | 0.335101i | \(-0.108770\pi\) | |||||||
\(488\) | −8.41119 | + | 4.20008i | −0.380757 | + | 0.190129i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.19579 | + | 5.55239i | 0.370248 | + | 0.250832i | ||||
\(491\) | − | 18.0235i | − | 0.813388i | −0.913565 | − | 0.406694i | \(-0.866682\pi\) | ||
0.913565 | − | 0.406694i | \(-0.133318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.53329i | 0.114094i | ||||||||
\(494\) | 8.13018 | + | 10.0957i | 0.365794 | + | 0.454225i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.9350 | − | 13.7179i | −1.34412 | − | 0.615954i | ||||
\(497\) | −28.3050 | + | 4.23995i | −1.26965 | + | 0.190188i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.6272i | 0.610036i | 0.952347 | + | 0.305018i | \(0.0986625\pi\) | ||||
−0.952347 | + | 0.305018i | \(0.901338\pi\) | |||||||
\(500\) | −1.95402 | − | 0.426402i | −0.0873863 | − | 0.0190693i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.50331 | + | 1.21063i | −0.0670959 | + | 0.0540333i | ||||
\(503\) | −23.8378 | −1.06287 | −0.531436 | − | 0.847098i | \(-0.678348\pi\) | ||||
−0.531436 | + | 0.847098i | \(0.678348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.9661 | −0.843979 | ||||||||
\(506\) | −1.20955 | + | 0.974067i | −0.0537710 | + | 0.0433025i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.04827 | − | 1.31984i | −0.268348 | − | 0.0585585i | ||||
\(509\) | 35.2475i | 1.56232i | 0.624332 | + | 0.781159i | \(0.285371\pi\) | ||||
−0.624332 | + | 0.781159i | \(0.714629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00668 | + | 0.899773i | −0.265720 | + | 0.0398036i | ||||
\(512\) | −22.2560 | − | 4.08276i | −0.983587 | − | 0.180434i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.94026 | + | 4.89282i | 0.173797 | + | 0.215813i | ||||
\(515\) | − | 8.23760i | − | 0.362992i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.58376i | − | 0.157613i | ||||||
\(518\) | 27.9127 | + | 25.6992i | 1.22641 | + | 1.12916i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.08335 | − | 14.1853i | −0.310625 | − | 0.622066i | ||||
\(521\) | − | 5.38270i | − | 0.235820i | −0.993024 | − | 0.117910i | \(-0.962381\pi\) | ||
0.993024 | − | 0.117910i | \(-0.0376195\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.0967711 | −0.00423150 | −0.00211575 | − | 0.999998i | \(-0.500673\pi\) | ||||
−0.00211575 | + | 0.999998i | \(0.500673\pi\) | |||||||
\(524\) | −7.46207 | + | 34.1954i | −0.325982 | + | 1.49384i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.37156 | + | 5.42839i | 0.190609 | + | 0.236689i | ||||
\(527\) | − | 4.14110i | − | 0.180389i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.9701 | 0.911742 | ||||||||
\(530\) | 0.404306 | + | 0.502048i | 0.0175619 | + | 0.0218076i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.63300 | + | 0.571999i | 0.374288 | + | 0.0247993i | ||||
\(533\) | −28.4708 | −1.23321 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.8042 | −0.510339 | ||||||||
\(536\) | −22.0352 | + | 11.0032i | −0.951778 | + | 0.475265i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.1926 | + | 27.5577i | 0.956790 | + | 1.18810i | ||||
\(539\) | 1.58090 | + | 5.15848i | 0.0680944 | + | 0.222191i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.76915 | 0.119055 | 0.0595275 | − | 0.998227i | \(-0.481041\pi\) | ||||
0.0595275 | + | 0.998227i | \(0.481041\pi\) | |||||||
\(542\) | 13.3665 | − | 10.7643i | 0.574141 | − | 0.462364i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.699257 | − | 2.75838i | −0.0299804 | − | 0.118265i | ||||
\(545\) | − | 9.80783i | − | 0.420121i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.1688i | − | 1.07614i | −0.842900 | − | 0.538071i | \(-0.819153\pi\) | ||
0.842900 | − | 0.538071i | \(-0.180847\pi\) | |||||||
\(548\) | 6.67497 | − | 30.5885i | 0.285140 | − | 1.30668i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.683673 | − | 0.848952i | −0.0291519 | − | 0.0361994i | ||||
\(551\) | 8.23408 | 0.350784 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.70717 | + | 1.00470i | −0.285218 | + | 0.0427243i | ||||
\(554\) | −21.4445 | + | 17.2695i | −0.911088 | + | 0.733712i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.482240 | + | 2.20990i | −0.0204515 | + | 0.0937206i | ||||
\(557\) | 39.1885 | 1.66047 | 0.830235 | − | 0.557413i | \(-0.188206\pi\) | ||||
0.830235 | + | 0.557413i | \(0.188206\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −50.7996 | −2.14859 | ||||||||
\(560\) | −10.1679 | − | 2.93495i | −0.429672 | − | 0.124024i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.5455 | + | 15.7403i | −0.824479 | + | 0.663965i | ||||
\(563\) | −23.3400 | −0.983665 | −0.491832 | − | 0.870690i | \(-0.663673\pi\) | ||||
−0.491832 | + | 0.870690i | \(0.663673\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0104i | 0.421142i | ||||||||
\(566\) | −32.4865 | + | 26.1618i | −1.36551 | + | 1.09966i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 27.3739 | − | 13.6690i | 1.14858 | − | 0.573538i | ||||
\(569\) | 35.0677 | 1.47011 | 0.735057 | − | 0.678005i | \(-0.237155\pi\) | ||||
0.735057 | + | 0.678005i | \(0.237155\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 8.01227i | − | 0.335303i | −0.985846 | − | 0.167651i | \(-0.946382\pi\) | ||
0.985846 | − | 0.167651i | \(-0.0536183\pi\) | |||||||
\(572\) | 1.84234 | − | 8.44266i | 0.0770323 | − | 0.353006i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.8716 | + | 13.9803i | −0.537251 | + | 0.583525i | ||||
\(575\) | − | 1.42475i | − | 0.0594164i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.1156i | 1.12884i | 0.825489 | + | 0.564418i | \(0.190900\pi\) | ||||
−0.825489 | + | 0.564418i | \(0.809100\pi\) | |||||||
\(578\) | −18.4460 | + | 14.8548i | −0.767252 | + | 0.617879i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.84033 | − | 2.14734i | −0.408598 | − | 0.0891634i | ||||
\(581\) | −5.48643 | − | 36.6262i | −0.227615 | − | 1.51951i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.351314i | 0.0145499i | ||||||||
\(584\) | 5.80909 | − | 2.90074i | 0.240382 | − | 0.120033i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.6321 | + | 21.8947i | 0.728377 | + | 0.904463i | ||||
\(587\) | −44.6409 | −1.84253 | −0.921264 | − | 0.388939i | \(-0.872842\pi\) | ||||
−0.921264 | + | 0.388939i | \(0.872842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.4600 | −0.554610 | ||||||||
\(590\) | −9.30548 | − | 11.5551i | −0.383100 | − | 0.475715i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −36.8739 | − | 16.8978i | −1.51551 | − | 0.694494i | ||||
\(593\) | 42.8848i | 1.76107i | 0.473984 | + | 0.880534i | \(0.342816\pi\) | ||||
−0.473984 | + | 0.880534i | \(0.657184\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.197166 | − | 1.31624i | −0.00808302 | − | 0.0539605i | ||||
\(596\) | −9.10980 | + | 41.7463i | −0.373152 | + | 1.70999i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.79713 | − | 7.08445i | 0.359741 | − | 0.289705i | ||||
\(599\) | 17.8050i | 0.727492i | 0.931498 | + | 0.363746i | \(0.118502\pi\) | ||||
−0.931498 | + | 0.363746i | \(0.881498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.15463i | 0.291843i | 0.989296 | + | 0.145922i | \(0.0466148\pi\) | ||||
−0.989296 | + | 0.145922i | \(0.953385\pi\) | |||||||
\(602\) | −22.9664 | + | 24.9446i | −0.936041 | + | 1.01666i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.53074 | − | 1.20691i | −0.225043 | − | 0.0491084i | ||||
\(605\) | 10.4059i | 0.423061i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8573 | −0.481272 | −0.240636 | − | 0.970615i | \(-0.577356\pi\) | ||||
−0.240636 | + | 0.970615i | \(0.577356\pi\) | |||||||
\(608\) | −8.96570 | + | 2.27283i | −0.363607 | + | 0.0921754i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.66117 | − | 2.94839i | 0.148236 | − | 0.119377i | ||||
\(611\) | 26.0649i | 1.05447i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.6111 | −0.913254 | −0.456627 | − | 0.889658i | \(-0.650943\pi\) | ||||
−0.456627 | + | 0.889658i | \(0.650943\pi\) | |||||||
\(614\) | 2.33977 | − | 1.88425i | 0.0944254 | − | 0.0760421i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.31275 | − | 4.72158i | −0.133475 | − | 0.190238i | ||||
\(617\) | −18.4097 | −0.741146 | −0.370573 | − | 0.928803i | \(-0.620839\pi\) | ||||
−0.370573 | + | 0.928803i | \(0.620839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.4715 | 1.34533 | 0.672667 | − | 0.739946i | \(-0.265149\pi\) | ||||
0.672667 | + | 0.739946i | \(0.265149\pi\) | |||||||
\(620\) | 16.0857 | + | 3.51019i | 0.646017 | + | 0.140973i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.3307 | + | 9.12475i | −0.454318 | + | 0.365869i | ||||
\(623\) | 7.82028 | − | 1.17144i | 0.313313 | − | 0.0469328i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 15.8599 | + | 19.6941i | 0.633889 | + | 0.787133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.7165 | + | 8.01221i | 1.46515 | + | 0.319722i | ||||
\(629\) | − | 5.10101i | − | 0.203390i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 43.0583i | − | 1.71412i | −0.515213 | − | 0.857062i | \(-0.672287\pi\) | ||
0.515213 | − | 0.857062i | \(-0.327713\pi\) | |||||||
\(632\) | 6.48654 | − | 3.23902i | 0.258021 | − | 0.128841i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.6404 | − | 10.9848i | 0.541731 | − | 0.436264i | ||||
\(635\) | 3.09530 | 0.122833 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.4980 | − | 37.5180i | −0.455568 | − | 1.48652i | ||||
\(638\) | −3.44294 | − | 4.27528i | −0.136307 | − | 0.169260i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.3074 | − | 0.378061i | 0.446964 | − | 0.0149442i | ||||
\(641\) | 12.3471 | 0.487681 | 0.243841 | − | 0.969815i | \(-0.421593\pi\) | ||||
0.243841 | + | 0.969815i | \(0.421593\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.21215 | 0.363292 | 0.181646 | − | 0.983364i | \(-0.441858\pi\) | ||||
0.181646 | + | 0.983364i | \(0.441858\pi\) | |||||||
\(644\) | 0.498427 | − | 7.52260i | 0.0196408 | − | 0.296432i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.729574 | − | 0.905950i | −0.0287047 | − | 0.0356441i | ||||
\(647\) | −19.8210 | −0.779243 | −0.389622 | − | 0.920975i | \(-0.627394\pi\) | ||||
−0.389622 | + | 0.920975i | \(0.627394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.08581i | − | 0.317396i | ||||||
\(650\) | 4.97240 | + | 6.17449i | 0.195034 | + | 0.242183i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.4743 | − | 3.15855i | −0.566856 | − | 0.123698i | ||||
\(653\) | 19.0538 | 0.745635 | 0.372817 | − | 0.927905i | \(-0.378392\pi\) | ||||
0.372817 | + | 0.927905i | \(0.378392\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 17.5001i | − | 0.683785i | ||||||
\(656\) | 8.46337 | − | 18.4686i | 0.330439 | − | 0.721076i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.7989 | + | 11.7839i | 0.498952 | + | 0.459384i | ||||
\(659\) | − | 10.4331i | − | 0.406416i | −0.979136 | − | 0.203208i | \(-0.934863\pi\) | ||
0.979136 | − | 0.203208i | \(-0.0651367\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 9.84122i | − | 0.382779i | −0.981514 | − | 0.191389i | \(-0.938701\pi\) | ||
0.981514 | − | 0.191389i | \(-0.0612994\pi\) | |||||||
\(662\) | 18.8934 | + | 23.4609i | 0.734314 | + | 0.911836i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.6875 | + | 35.4214i | 0.686406 | + | 1.37462i | ||||
\(665\) | −4.27823 | + | 0.640859i | −0.165903 | + | 0.0248514i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.17499i | − | 0.277817i | ||||||
\(668\) | −1.26278 | + | 5.78676i | −0.0488583 | + | 0.223896i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.59137 | − | 7.72407i | 0.370547 | − | 0.298407i | ||||
\(671\) | 2.56195 | 0.0989029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.51471 | 0.212577 | 0.106288 | − | 0.994335i | \(-0.466103\pi\) | ||||
0.106288 | + | 0.994335i | \(0.466103\pi\) | |||||||
\(674\) | 0.964641 | − | 0.776840i | 0.0371566 | − | 0.0299227i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.85627 | + | 36.0019i | −0.302164 | + | 1.38469i | ||||
\(677\) | 44.8711i | 1.72454i | 0.506451 | + | 0.862269i | \(0.330957\pi\) | ||||
−0.506451 | + | 0.862269i | \(0.669043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.7707 | − | 6.10726i | 1.56464 | − | 0.234375i | ||||
\(680\) | 0.635635 | + | 1.27294i | 0.0243755 | + | 0.0488150i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.62808 | + | 6.98867i | 0.215510 | + | 0.267610i | ||||
\(683\) | 34.0718i | 1.30372i | 0.758338 | + | 0.651862i | \(0.226012\pi\) | ||||
−0.758338 | + | 0.651862i | \(0.773988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.6542i | 0.598115i | ||||||||
\(686\) | −23.6210 | − | 11.3158i | −0.901854 | − | 0.432041i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.1009 | − | 32.9529i | 0.575717 | − | 1.25632i | ||||
\(689\) | − | 2.55513i | − | 0.0973428i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.264224 | 0.0100515 | 0.00502577 | − | 0.999987i | \(-0.498400\pi\) | ||||
0.00502577 | + | 0.999987i | \(0.498400\pi\) | |||||||
\(692\) | 29.3522 | + | 6.40520i | 1.11581 | + | 0.243489i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.9640 | + | 38.4496i | 1.17538 | + | 1.45953i | ||||
\(695\) | − | 1.13095i | − | 0.0428994i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.55487 | 0.0967728 | ||||||||
\(698\) | 18.7941 | + | 23.3376i | 0.711368 | + | 0.883342i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.27993 | + | 0.349833i | 0.199562 | + | 0.0132225i | ||||
\(701\) | −17.5109 | −0.661376 | −0.330688 | − | 0.943740i | \(-0.607281\pi\) | ||||
−0.330688 | + | 0.943740i | \(0.607281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.5800 | −0.625328 | ||||||||
\(704\) | 4.92895 | + | 3.70480i | 0.185767 | + | 0.139630i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.82928 | − | 8.48026i | −0.257023 | − | 0.319159i | ||||
\(707\) | 49.6258 | − | 7.43371i | 1.86637 | − | 0.279573i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0797 | −0.491219 | −0.245610 | − | 0.969369i | \(-0.578988\pi\) | ||||
−0.245610 | + | 0.969369i | \(0.578988\pi\) | |||||||
\(710\) | −11.9151 | + | 9.59542i | −0.447167 | + | 0.360110i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.56303 | + | 3.77656i | −0.283437 | + | 0.141532i | ||||
\(713\) | 11.7287i | 0.439245i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.32067i | 0.161584i | ||||||||
\(716\) | −9.43664 | − | 2.05925i | −0.352664 | − | 0.0769577i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.90549 | + | 2.36615i | 0.0711124 | + | 0.0883039i | ||||
\(719\) | −16.9650 | −0.632689 | −0.316345 | − | 0.948644i | \(-0.602456\pi\) | ||||
−0.316345 | + | 0.948644i | \(0.602456\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.22871 | + | 21.5542i | 0.120243 | + | 0.802719i | ||||
\(722\) | 17.9830 | − | 14.4819i | 0.669257 | − | 0.538962i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −35.5728 | − | 7.76264i | −1.32205 | − | 0.288496i | ||||
\(725\) | 5.03595 | 0.187030 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.4836 | 1.20475 | 0.602375 | − | 0.798213i | \(-0.294221\pi\) | ||||
0.602375 | + | 0.798213i | \(0.294221\pi\) | |||||||
\(728\) | 24.0939 | + | 34.3403i | 0.892979 | + | 1.27274i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.52855 | + | 2.03627i | −0.0935857 | + | 0.0753659i | ||||
\(731\) | 4.55858 | 0.168605 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.8223i | 1.32313i | 0.749890 | + | 0.661563i | \(0.230106\pi\) | ||||
−0.749890 | + | 0.661563i | \(0.769894\pi\) | |||||||
\(734\) | 29.4046 | − | 23.6799i | 1.08534 | − | 0.874043i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.98049 | + | 7.81251i | 0.0730019 | + | 0.287973i | ||||
\(737\) | 6.71167 | 0.247228 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 21.8037i | − | 0.802060i | −0.916065 | − | 0.401030i | \(-0.868652\pi\) | ||
0.916065 | − | 0.401030i | \(-0.131348\pi\) | |||||||
\(740\) | 19.8144 | + | 4.32386i | 0.728391 | + | 0.158948i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.25467 | − | 1.15517i | −0.0460603 | − | 0.0424076i | ||||
\(743\) | 23.4618i | 0.860731i | 0.902655 | + | 0.430365i | \(0.141615\pi\) | ||||
−0.902655 | + | 0.430365i | \(0.858385\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 21.3643i | − | 0.782729i | ||||||
\(746\) | 9.37811 | − | 7.55233i | 0.343357 | − | 0.276510i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.165326 | + | 0.757616i | −0.00604490 | + | 0.0277012i | ||||
\(749\) | 30.8863 | − | 4.62662i | 1.12856 | − | 0.169053i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9484i | 0.581965i | 0.956728 | + | 0.290983i | \(0.0939822\pi\) | ||||
−0.956728 | + | 0.290983i | \(0.906018\pi\) | |||||||
\(752\) | −16.9079 | − | 7.74817i | −0.616567 | − | 0.282547i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25.0408 | + | 31.0944i | 0.911931 | + | 1.13239i | ||||
\(755\) | 2.83045 | 0.103011 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.9746 | 1.01675 | 0.508377 | − | 0.861135i | \(-0.330246\pi\) | ||||
0.508377 | + | 0.861135i | \(0.330246\pi\) | |||||||
\(758\) | −27.6477 | − | 34.3315i | −1.00421 | − | 1.24698i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.13750 | − | 2.06604i | 0.150083 | − | 0.0749430i | ||||
\(761\) | − | 17.5525i | − | 0.636277i | −0.948044 | − | 0.318138i | \(-0.896942\pi\) | ||
0.948044 | − | 0.318138i | \(-0.103058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.84416 | + | 25.6627i | 0.139168 | + | 0.929054i | ||||
\(764\) | 11.0438 | + | 2.40996i | 0.399550 | + | 0.0871892i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.1532 | − | 29.9200i | 1.34240 | − | 1.08105i | ||||
\(767\) | 58.8087i | 2.12346i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.74365i | − | 0.207121i | −0.994623 | − | 0.103561i | \(-0.966976\pi\) | ||
0.994623 | − | 0.103561i | \(-0.0330236\pi\) | |||||||
\(770\) | 2.12162 | + | 1.95337i | 0.0764577 | + | 0.0703945i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.86414 | + | 31.4554i | −0.247046 | + | 1.13210i | ||||
\(773\) | − | 46.0638i | − | 1.65680i | −0.560138 | − | 0.828399i | \(-0.689252\pi\) | ||
0.560138 | − | 0.828399i | \(-0.310748\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.23212 | −0.295706 | ||||||||
\(776\) | −39.4295 | + | 19.6889i | −1.41544 | + | 0.706791i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.6281 | − | 23.0546i | 1.02637 | − | 0.826548i | ||||
\(779\) | − | 8.30423i | − | 0.297530i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.33775 | −0.298348 | ||||||||
\(782\) | −0.789424 | + | 0.635734i | −0.0282297 | + | 0.0227338i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.7552 | + | 3.69419i | 0.991258 | + | 0.131935i | ||||
\(785\) | −18.7903 | −0.670654 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.5373 | 0.945951 | 0.472976 | − | 0.881075i | \(-0.343180\pi\) | ||||
0.472976 | + | 0.881075i | \(0.343180\pi\) | |||||||
\(788\) | 5.24356 | − | 24.0290i | 0.186794 | − | 0.855997i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.82342 | + | 2.27374i | −0.100453 | + | 0.0808961i | ||||
\(791\) | −3.92357 | − | 26.1929i | −0.139506 | − | 0.931311i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.6332 | −0.661685 | ||||||||
\(794\) | 1.45059 | + | 1.80127i | 0.0514794 | + | 0.0639245i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.17353 | − | 32.8732i | 0.254259 | − | 1.16516i | ||||
\(797\) | − | 29.3245i | − | 1.03873i | −0.854553 | − | 0.519364i | \(-0.826169\pi\) | ||
0.854553 | − | 0.519364i | \(-0.173831\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.33898i | − | 0.0827470i | ||||||
\(800\) | −5.48341 | + | 1.39006i | −0.193868 | + | 0.0491460i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.9869 | + | 10.4585i | −0.458582 | + | 0.369302i | ||||
\(803\) | −1.76938 | −0.0624401 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.558430 | + | 3.72795i | 0.0196821 | + | 0.131393i | ||||
\(806\) | −40.9334 | − | 50.8291i | −1.44182 | − | 1.79038i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −47.9933 | + | 23.9652i | −1.68840 | + | 0.843093i | ||||
\(809\) | 15.6127 | 0.548913 | 0.274456 | − | 0.961600i | \(-0.411502\pi\) | ||||
0.274456 | + | 0.961600i | \(0.411502\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.0925 | −0.846004 | −0.423002 | − | 0.906129i | \(-0.639024\pi\) | ||||
−0.423002 | + | 0.906129i | \(0.639024\pi\) | |||||||
\(812\) | 26.5894 | + | 1.76174i | 0.933107 | + | 0.0618251i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.93267 | + | 8.60865i | 0.242990 | + | 0.301733i | ||||
\(815\) | 7.40744 | 0.259471 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.8170i | − | 0.518381i | ||||||
\(818\) | −8.64776 | − | 10.7384i | −0.302362 | − | 0.375458i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.16563 | + | 9.92417i | −0.0756272 | + | 0.346567i | ||||
\(821\) | 47.2309 | 1.64837 | 0.824185 | − | 0.566321i | \(-0.191634\pi\) | ||||
0.824185 | + | 0.566321i | \(0.191634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0076i | 0.523133i | 0.965185 | + | 0.261566i | \(0.0842390\pi\) | ||||
−0.965185 | + | 0.261566i | \(0.915761\pi\) | |||||||
\(824\) | −10.4089 | − | 20.8451i | −0.362611 | − | 0.726174i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.8773 | + | 26.5873i | 1.00477 | + | 0.925090i | ||||
\(827\) | − | 8.53837i | − | 0.296908i | −0.988919 | − | 0.148454i | \(-0.952570\pi\) | ||
0.988919 | − | 0.148454i | \(-0.0474297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.3755i | 0.672941i | 0.941694 | + | 0.336470i | \(0.109233\pi\) | ||||
−0.941694 | + | 0.336470i | \(0.890767\pi\) | |||||||
\(830\) | −12.4163 | − | 15.4180i | −0.430977 | − | 0.535166i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −35.8486 | − | 26.9453i | −1.24283 | − | 0.934160i | ||||
\(833\) | 1.03179 | + | 3.36673i | 0.0357495 | + | 0.116650i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2.96147i | − | 0.102486i | ||||||
\(836\) | 2.46251 | + | 0.537366i | 0.0851679 | + | 0.0185852i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.9074 | + | 13.6158i | −0.584058 | + | 0.470350i | ||||
\(839\) | 33.8009 | 1.16693 | 0.583467 | − | 0.812137i | \(-0.301696\pi\) | ||||
0.583467 | + | 0.812137i | \(0.301696\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.63920 | −0.125490 | ||||||||
\(842\) | −39.7336 | + | 31.9981i | −1.36931 | + | 1.10273i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.9661 | − | 3.92054i | −0.618420 | − | 0.134951i | ||||
\(845\) | − | 18.4246i | − | 0.633824i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.07858 | − | 27.2277i | −0.140142 | − | 0.935556i | ||||
\(848\) | 1.65747 | + | 0.759550i | 0.0569178 | + | 0.0260831i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.446206 | − | 0.554077i | −0.0153048 | − | 0.0190047i | ||||
\(851\) | 14.4475i | 0.495253i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 20.5520i | − | 0.703688i | −0.936059 | − | 0.351844i | \(-0.885555\pi\) | ||
0.936059 | − | 0.351844i | \(-0.114445\pi\) | |||||||
\(854\) | −8.42405 | + | 9.14963i | −0.288265 | + | 0.313094i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −29.8703 | + | 14.9156i | −1.02095 | + | 0.509803i | ||||
\(857\) | 12.0420i | 0.411346i | 0.978621 | + | 0.205673i | \(0.0659384\pi\) | ||||
−0.978621 | + | 0.205673i | \(0.934062\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.0195 | 0.648938 | 0.324469 | − | 0.945896i | \(-0.394814\pi\) | ||||
0.324469 | + | 0.945896i | \(0.394814\pi\) | |||||||
\(860\) | −3.86407 | + | 17.7074i | −0.131764 | + | 0.603816i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.6133 | + | 23.1131i | 0.633973 | + | 0.787236i | ||||
\(863\) | − | 51.7910i | − | 1.76299i | −0.472198 | − | 0.881493i | \(-0.656539\pi\) | ||
0.472198 | − | 0.881493i | \(-0.343461\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0215 | −0.510746 | ||||||||
\(866\) | 9.26256 | + | 11.5018i | 0.314755 | + | 0.390847i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −43.4650 | − | 2.87987i | −1.47530 | − | 0.0977491i | ||||
\(869\) | −1.97572 | −0.0670218 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.8145 | −1.65402 | ||||||||
\(872\) | −12.3930 | − | 24.8186i | −0.419680 | − | 0.840463i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.06636 | + | 2.56590i | 0.0698956 | + | 0.0867930i | ||||
\(875\) | −2.61656 | + | 0.391948i | −0.0884558 | + | 0.0132503i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.5940 | −1.57337 | −0.786683 | − | 0.617357i | \(-0.788204\pi\) | ||||
−0.786683 | + | 0.617357i | \(0.788204\pi\) | |||||||
\(878\) | 39.9823 | − | 32.1984i | 1.34934 | − | 1.08664i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.80275 | − | 1.28438i | −0.0944806 | − | 0.0432965i | ||||
\(881\) | − | 53.7772i | − | 1.81180i | −0.423491 | − | 0.905901i | \(-0.639195\pi\) | ||
0.423491 | − | 0.905901i | \(-0.360805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.0329i | 0.573202i | 0.958050 | + | 0.286601i | \(0.0925255\pi\) | ||||
−0.958050 | + | 0.286601i | \(0.907475\pi\) | |||||||
\(884\) | 1.20242 | − | 5.51019i | 0.0404419 | − | 0.185328i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.29272 | + | 4.08873i | 0.110621 | + | 0.137364i | ||||
\(887\) | −47.8749 | −1.60748 | −0.803741 | − | 0.594980i | \(-0.797160\pi\) | ||||
−0.803741 | + | 0.594980i | \(0.797160\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.09903 | + | 1.21320i | −0.271633 | + | 0.0406893i | ||||
\(890\) | 3.29199 | − | 2.65109i | 0.110348 | − | 0.0888646i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.74584 | + | 44.6610i | −0.326315 | + | 1.49536i | ||||
\(893\) | −7.60249 | −0.254407 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.82936 | 0.161428 | ||||||||
\(896\) | −29.4383 | + | 5.42113i | −0.983463 | + | 0.181107i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.43412 | − | 7.59744i | 0.314821 | − | 0.253530i | ||||
\(899\) | −41.4565 | −1.38265 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.229289i | 0.00763871i | ||||||||
\(902\) | −4.31170 | + | 3.47228i | −0.143564 | + | 0.115614i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.6490 | + | 25.3312i | 0.420700 | + | 0.842505i | ||||
\(905\) | 18.2050 | 0.605154 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.5992i | 0.750395i | 0.926945 | + | 0.375197i | \(0.122425\pi\) | ||||
−0.926945 | + | 0.375197i | \(0.877575\pi\) | |||||||
\(908\) | 7.44841 | − | 34.1328i | 0.247184 | − | 1.13274i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15.4307 | − | 14.2070i | −0.511521 | − | 0.470957i | ||||
\(911\) | − | 38.2369i | − | 1.26685i | −0.773806 | − | 0.633423i | \(-0.781650\pi\) | ||
0.773806 | − | 0.633423i | \(-0.218350\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 10.7889i | − | 0.357061i | ||||||
\(914\) | 16.1589 | − | 13.0130i | 0.534490 | − | 0.430432i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.6661 | + | 5.38259i | 0.814990 | + | 0.177846i | ||||
\(917\) | 6.85912 | + | 45.7900i | 0.226508 | + | 1.51212i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0673i | 0.562999i | 0.959561 | + | 0.281500i | \(0.0908318\pi\) | ||||
−0.959561 | + | 0.281500i | \(0.909168\pi\) | |||||||
\(920\) | −1.80030 | − | 3.60532i | −0.0593540 | − | 0.118864i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.1800 | − | 21.3333i | −0.565794 | − | 0.702575i | ||||
\(923\) | 60.6411 | 1.99603 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.1403 | −0.333412 | ||||||||
\(926\) | 3.85211 | + | 4.78336i | 0.126588 | + | 0.157191i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −27.6142 | + | 7.00027i | −0.906479 | + | 0.229795i | ||||
\(929\) | 19.7796i | 0.648947i | 0.945895 | + | 0.324473i | \(0.105187\pi\) | ||||
−0.945895 | + | 0.324473i | \(0.894813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9431 | − | 3.35369i | 0.358644 | − | 0.109913i | ||||
\(932\) | 1.66045 | − | 7.60913i | 0.0543899 | − | 0.249245i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.0175 | − | 13.7045i | 0.556830 | − | 0.448424i | ||||
\(935\) | − | 0.387722i | − | 0.0126799i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.4491i | 0.700712i | 0.936617 | + | 0.350356i | \(0.113939\pi\) | ||||
−0.936617 | + | 0.350356i | \(0.886061\pi\) | |||||||
\(938\) | −22.0689 | + | 23.9698i | −0.720576 | + | 0.782641i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.08552 | + | 1.98263i | 0.296337 | + | 0.0646662i | ||||
\(941\) | 42.2481i | 1.37725i | 0.725119 | + | 0.688624i | \(0.241785\pi\) | ||||
−0.725119 | + | 0.688624i | \(0.758215\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.23612 | −0.235640 | ||||||||
\(944\) | −38.1482 | − | 17.4817i | −1.24162 | − | 0.568982i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.69324 | + | 6.19547i | −0.250129 | + | 0.201432i | ||||
\(947\) | 17.0774i | 0.554939i | 0.960734 | + | 0.277470i | \(0.0894958\pi\) | ||||
−0.960734 | + | 0.277470i | \(0.910504\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.8688 | 0.417740 | ||||||||
\(950\) | −1.80094 | + | 1.45033i | −0.0584303 | + | 0.0470548i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.16210 | − | 3.08158i | −0.0700741 | − | 0.0998747i | ||||
\(953\) | 9.75364 | 0.315951 | 0.157976 | − | 0.987443i | \(-0.449503\pi\) | ||||
0.157976 | + | 0.987443i | \(0.449503\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.65184 | −0.182889 | ||||||||
\(956\) | 22.7638 | + | 4.96747i | 0.736233 | + | 0.160659i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.6868 | − | 19.8806i | 0.797593 | − | 0.642313i | ||||
\(959\) | −6.13561 | − | 40.9600i | −0.198129 | − | 1.32267i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.7677 | 1.18606 | ||||||||
\(962\) | −50.4218 | − | 62.6113i | −1.62566 | − | 2.01867i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −41.0850 | − | 8.96551i | −1.32326 | − | 0.288759i | ||||
\(965\) | − | 16.0978i | − | 0.518206i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.1757i | 0.777437i | 0.921356 | + | 0.388719i | \(0.127082\pi\) | ||||
−0.921356 | + | 0.388719i | \(0.872918\pi\) | |||||||
\(968\) | 13.1488 | + | 26.3321i | 0.422617 | + | 0.846345i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.1626 | − | 13.8213i | 0.551059 | − | 0.443776i | ||||
\(971\) | 30.5804 | 0.981373 | 0.490686 | − | 0.871336i | \(-0.336746\pi\) | ||||
0.490686 | + | 0.871336i | \(0.336746\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.443274 | + | 2.95920i | 0.0142107 | + | 0.0948676i | ||||
\(974\) | 13.1190 | + | 16.2906i | 0.420361 | + | 0.521984i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.53900 | − | 12.0871i | 0.177299 | − | 0.386897i | ||||
\(977\) | −26.4757 | −0.847031 | −0.423516 | − | 0.905889i | \(-0.639204\pi\) | ||||
−0.423516 | + | 0.905889i | \(0.639204\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.30361 | 0.0736237 | ||||||||
\(980\) | −13.9523 | + | 1.15410i | −0.445691 | + | 0.0368663i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.9871 | + | 19.8520i | 0.510169 | + | 0.633503i | ||||
\(983\) | 1.44944 | 0.0462300 | 0.0231150 | − | 0.999733i | \(-0.492642\pi\) | ||||
0.0231150 | + | 0.999733i | \(0.492642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.2972i | 0.391822i | ||||||||
\(986\) | −2.24707 | − | 2.79031i | −0.0715614 | − | 0.0888614i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.9100 | − | 3.90830i | −0.569794 | − | 0.124340i | ||||
\(989\) | −12.9112 | −0.410552 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 43.1709i | − | 1.37137i | −0.727899 | − | 0.685684i | \(-0.759503\pi\) | ||
0.727899 | − | 0.685684i | \(-0.240497\pi\) | |||||||
\(992\) | 45.1400 | − | 11.4431i | 1.43320 | − | 0.363319i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 27.4157 | − | 29.7771i | 0.869574 | − | 0.944472i | ||||
\(995\) | 16.8234i | 0.533338i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 59.0825i | − | 1.87116i | −0.353114 | − | 0.935580i | \(-0.614877\pi\) | ||
0.353114 | − | 0.935580i | \(-0.385123\pi\) | |||||||
\(998\) | −12.0875 | − | 15.0097i | −0.382624 | − | 0.475124i | ||||
\(999\) | 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 | 1260.2.c.e.811.4 | 16 | ||
3.2 | odd | 2 | 420.2.c.b.391.13 | yes | 16 | ||
4.3 | odd | 2 | 1260.2.c.d.811.3 | 16 | |||
7.6 | odd | 2 | 1260.2.c.d.811.4 | 16 | |||
12.11 | even | 2 | 420.2.c.a.391.14 | yes | 16 | ||
21.20 | even | 2 | 420.2.c.a.391.13 | ✓ | 16 | ||
28.27 | even | 2 | inner | 1260.2.c.e.811.3 | 16 | ||
84.83 | odd | 2 | 420.2.c.b.391.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.c.a.391.13 | ✓ | 16 | 21.20 | even | 2 | ||
420.2.c.a.391.14 | yes | 16 | 12.11 | even | 2 | ||
420.2.c.b.391.13 | yes | 16 | 3.2 | odd | 2 | ||
420.2.c.b.391.14 | yes | 16 | 84.83 | odd | 2 | ||
1260.2.c.d.811.3 | 16 | 4.3 | odd | 2 | |||
1260.2.c.d.811.4 | 16 | 7.6 | odd | 2 | |||
1260.2.c.e.811.3 | 16 | 28.27 | even | 2 | inner | ||
1260.2.c.e.811.4 | 16 | 1.1 | even | 1 | trivial |