Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 18x^{8} + 117x^{6} + 333x^{4} + 396x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.7 | ||
Root | \(1.36629i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.w.4049.4 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.36629i | 0.788825i | 0.918933 | + | 0.394413i | \(0.129052\pi\) | ||||
−0.918933 | + | 0.394413i | \(0.870948\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.28093i | 1.24008i | 0.784572 | + | 0.620038i | \(0.212883\pi\) | ||||
−0.784572 | + | 0.620038i | \(0.787117\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.13327 | 0.377755 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.49709 | 1.05441 | 0.527207 | − | 0.849737i | \(-0.323239\pi\) | ||||
0.527207 | + | 0.849737i | \(0.323239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41420i | 0.946928i | 0.880813 | + | 0.473464i | \(0.156997\pi\) | ||||
−0.880813 | + | 0.473464i | \(0.843003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.46023i | 1.80937i | 0.426080 | + | 0.904685i | \(0.359894\pi\) | ||||
−0.426080 | + | 0.904685i | \(0.640106\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.49709 | −0.802288 | −0.401144 | − | 0.916015i | \(-0.631387\pi\) | ||||
−0.401144 | + | 0.916015i | \(0.631387\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.48269 | −0.978203 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64722i | 1.08681i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.46268 | 0.643004 | 0.321502 | − | 0.946909i | \(-0.395812\pi\) | ||||
0.321502 | + | 0.946909i | \(0.395812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.01105 | 0.361195 | 0.180597 | − | 0.983557i | \(-0.442197\pi\) | ||||
0.180597 | + | 0.983557i | \(0.442197\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.77803i | 0.831748i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 0.511497i | − 0.0840896i | −0.999116 | − | 0.0420448i | \(-0.986613\pi\) | ||||
0.999116 | − | 0.0420448i | \(-0.0133872\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.66477 | −0.746961 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.07954 | −1.10564 | −0.552819 | − | 0.833301i | \(-0.686448\pi\) | ||||
−0.552819 | + | 0.833301i | \(0.686448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.76452i | − 0.421586i | −0.977531 | − | 0.210793i | \(-0.932395\pi\) | ||||
0.977531 | − | 0.210793i | \(-0.0676046\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.889198i | 0.129703i | 0.997895 | + | 0.0648514i | \(0.0206573\pi\) | ||||
−0.997895 | + | 0.0648514i | \(0.979343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.76452 | −0.537789 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.1928 | −1.42728 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 14.2383i | − 1.95577i | −0.209132 | − | 0.977887i | \(-0.567064\pi\) | ||||
0.209132 | − | 0.977887i | \(-0.432936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 4.77803i | − 0.632865i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.71325 | 0.613613 | 0.306807 | − | 0.951772i | \(-0.400739\pi\) | ||||
0.306807 | + | 0.951772i | \(0.400739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4769 | 1.72554 | 0.862769 | − | 0.505599i | \(-0.168728\pi\) | ||||
0.862769 | + | 0.505599i | \(0.168728\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.71817i | 0.468445i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.30025i | 0.281020i | 0.990079 | + | 0.140510i | \(0.0448743\pi\) | ||||
−0.990079 | + | 0.140510i | \(0.955126\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.36629 | −0.164481 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6214 | −1.26053 | −0.630264 | − | 0.776381i | \(-0.717053\pi\) | ||||
−0.630264 | + | 0.776381i | \(0.717053\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.70765i | 0.433948i | 0.976177 | + | 0.216974i | \(0.0696186\pi\) | ||||
−0.976177 | + | 0.216974i | \(0.930381\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.4737i | 1.30755i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.97978 | 0.897796 | 0.448898 | − | 0.893583i | \(-0.351817\pi\) | ||||
0.448898 | + | 0.893583i | \(0.351817\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.31592 | −0.479546 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.42336i | 1.03435i | 0.855880 | + | 0.517174i | \(0.173016\pi\) | ||||
−0.855880 | + | 0.517174i | \(0.826984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.73101i | 0.507218i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.801390 | −0.0849471 | −0.0424736 | − | 0.999098i | \(-0.513524\pi\) | ||||
−0.0424736 | + | 0.999098i | \(0.513524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.2018 | −1.17426 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.74766i | 0.284919i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 11.7722i | − 1.19529i | −0.801762 | − | 0.597644i | \(-0.796104\pi\) | ||||
0.801762 | − | 0.597644i | \(-0.203896\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.96313 | 0.398310 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1559 | 1.11006 | 0.555028 | − | 0.831831i | \(-0.312707\pi\) | ||||
0.555028 | + | 0.831831i | \(0.312707\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.28585i | 0.126698i | 0.997991 | + | 0.0633491i | \(0.0201782\pi\) | ||||
−0.997991 | + | 0.0633491i | \(0.979822\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8975i | 1.34352i | 0.740770 | + | 0.671759i | \(0.234461\pi\) | ||||
−0.740770 | + | 0.671759i | \(0.765539\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.77713 | 0.361783 | 0.180892 | − | 0.983503i | \(-0.442102\pi\) | ||||
0.180892 | + | 0.983503i | \(0.442102\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.698851 | 0.0663320 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 19.3111i | − 1.81663i | −0.418282 | − | 0.908317i | \(-0.637368\pi\) | ||||
0.418282 | − | 0.908317i | \(-0.362632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.86919i | 0.357707i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.4765 | −2.24376 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.22966 | 0.111788 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 9.67267i | − 0.872155i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7612i | 1.22111i | 0.791975 | + | 0.610553i | \(0.209053\pi\) | ||||
−0.791975 | + | 0.610553i | \(0.790947\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.77713 | 0.332558 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.41665 | −0.647996 | −0.323998 | − | 0.946058i | \(-0.605027\pi\) | ||||
−0.323998 | + | 0.946058i | \(0.605027\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 11.4737i | − 0.994899i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 20.5502i | − 1.75573i | −0.478912 | − | 0.877863i | \(-0.658969\pi\) | ||||
0.478912 | − | 0.877863i | \(-0.341031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.49652 | 0.466209 | 0.233104 | − | 0.972452i | \(-0.425112\pi\) | ||||
0.233104 | + | 0.972452i | \(0.425112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.21490 | −0.102313 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.9398i | 0.998454i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 5.14341i | − 0.424221i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.80139 | −0.393345 | −0.196673 | − | 0.980469i | \(-0.563014\pi\) | ||||
−0.196673 | + | 0.980469i | \(0.563014\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.26862 | −0.265997 | −0.132998 | − | 0.991116i | \(-0.542461\pi\) | ||||
−0.132998 | + | 0.991116i | \(0.542461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.45441i | 0.683499i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.8392i | 1.74296i | 0.490430 | + | 0.871480i | \(0.336840\pi\) | ||||
−0.490430 | + | 0.871480i | \(0.663160\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.4535 | 1.54276 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.28093 | −0.258574 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 23.2435i | − 1.82057i | −0.413982 | − | 0.910285i | \(-0.635862\pi\) | ||||
0.413982 | − | 0.910285i | \(-0.364138\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 4.13179i | − 0.319728i | −0.987139 | − | 0.159864i | \(-0.948894\pi\) | ||||
0.987139 | − | 0.159864i | \(-0.0511055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.34325 | 0.103327 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.96313 | −0.303068 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 5.88548i | − 0.447465i | −0.974651 | − | 0.223732i | \(-0.928176\pi\) | ||||
0.974651 | − | 0.223732i | \(-0.0718241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.43965i | 0.484034i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.85789 | 0.512583 | 0.256292 | − | 0.966600i | \(-0.417499\pi\) | ||||
0.256292 | + | 0.966600i | \(0.417499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.29042 | −0.170246 | −0.0851229 | − | 0.996370i | \(-0.527128\pi\) | ||||
−0.0851229 | + | 0.996370i | \(0.527128\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.4133i | 1.36115i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.0891i | 1.90782i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.5281 | −1.34772 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.58748 | −0.693725 | −0.346863 | − | 0.937916i | \(-0.612753\pi\) | ||||
−0.346863 | + | 0.937916i | \(0.612753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 13.9410i | − 1.00350i | −0.865013 | − | 0.501749i | \(-0.832690\pi\) | ||||
0.865013 | − | 0.501749i | \(-0.167310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1011i | 1.07591i | 0.842974 | + | 0.537954i | \(0.180803\pi\) | ||||
−0.842974 | + | 0.537954i | \(0.819197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5128 | −1.02879 | −0.514394 | − | 0.857554i | \(-0.671983\pi\) | ||||
−0.514394 | + | 0.857554i | \(0.671983\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.14280 | −0.221676 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.3608i | 0.797374i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.13327i | 0.0787674i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.2297 | −0.845944 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4846 | −1.61674 | −0.808372 | − | 0.588672i | \(-0.799651\pi\) | ||||
−0.808372 | + | 0.588672i | \(0.799651\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 14.5119i | − 0.994336i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.59811i | 0.447909i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.06571 | −0.342309 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.4707 | −1.71334 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.20720i | 0.549595i | 0.961502 | + | 0.274797i | \(0.0886108\pi\) | ||||
−0.961502 | + | 0.274797i | \(0.911389\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9942i | 1.12794i | 0.825794 | + | 0.563972i | \(0.190727\pi\) | ||||
−0.825794 | + | 0.563972i | \(0.809273\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.6818 | −1.30061 | −0.650306 | − | 0.759672i | \(-0.725359\pi\) | ||||
−0.650306 | + | 0.759672i | \(0.725359\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.6764 | −1.03143 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 24.8799i | − 1.62993i | −0.579507 | − | 0.814967i | \(-0.696755\pi\) | ||||
0.579507 | − | 0.814967i | \(-0.303245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.9027i | 0.708204i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.0718483 | 0.00464748 | 0.00232374 | − | 0.999997i | \(-0.499260\pi\) | ||||
0.00232374 | + | 0.999997i | \(0.499260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50658 | −0.547957 | −0.273979 | − | 0.961736i | \(-0.588340\pi\) | ||||
−0.273979 | + | 0.961736i | \(0.588340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0449i | 0.708530i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 11.9398i | − 0.759709i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.8750 | −0.815920 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.8858 | −1.25518 | −0.627591 | − | 0.778543i | \(-0.715959\pi\) | ||||
−0.627591 | + | 0.778543i | \(0.715959\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.49709i | 0.219860i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 11.4062i | − 0.711498i | −0.934582 | − | 0.355749i | \(-0.884226\pi\) | ||||
0.934582 | − | 0.355749i | \(-0.115774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.67819 | 0.104277 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.92414 | 0.242898 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3903i | 0.825679i | 0.910804 | + | 0.412840i | \(0.135463\pi\) | ||||
−0.910804 | + | 0.412840i | \(0.864537\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.09493i | − 0.0670084i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.8103 | −0.842027 | −0.421014 | − | 0.907054i | \(-0.638326\pi\) | ||||
−0.421014 | + | 0.907054i | \(0.638326\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.7574 | 1.62540 | 0.812699 | − | 0.582683i | \(-0.197997\pi\) | ||||
0.812699 | + | 0.582683i | \(0.197997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 15.3048i | − 0.926288i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.80667i | − 0.108552i | −0.998526 | − | 0.0542760i | \(-0.982715\pi\) | ||||
0.998526 | − | 0.0542760i | \(-0.0172851\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.27905 | 0.136443 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.1348 | 1.61873 | 0.809364 | − | 0.587308i | \(-0.199812\pi\) | ||||
0.809364 | + | 0.587308i | \(0.199812\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 20.9875i | − 1.24758i | −0.781594 | − | 0.623788i | \(-0.785593\pi\) | ||||
0.781594 | − | 0.623788i | \(-0.214407\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 23.2275i | − 1.37108i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38.6550 | −2.27382 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.0842 | 0.942873 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 0.00671252i | 0 0.000392149i | −1.00000 | 0.000196075i | \(-0.999938\pi\) | |||||
1.00000 | 0.000196075i | \(-6.24125e-5\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.7489i | 1.14594i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.41420 | −0.197448 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.07022 | 0.522799 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.2422i | 0.875641i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 19.9767i | − 1.14013i | −0.821598 | − | 0.570067i | \(-0.806917\pi\) | ||||
0.821598 | − | 0.570067i | \(-0.193083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.75683 | −0.0999427 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8601 | 1.35298 | 0.676491 | − | 0.736451i | \(-0.263500\pi\) | ||||
0.676491 | + | 0.736451i | \(0.263500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4406i | 0.985803i | 0.870085 | + | 0.492901i | \(0.164064\pi\) | ||||
−0.870085 | + | 0.492901i | \(0.835936\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.35581i | 0.0761499i | 0.999275 | + | 0.0380750i | \(0.0121226\pi\) | ||||
−0.999275 | + | 0.0380750i | \(0.987877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.1093 | 0.677992 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.9879 | −1.05980 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 26.0891i | − 1.45164i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.16063i | 0.285384i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.91740 | −0.160841 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.4050 | 0.956667 | 0.478333 | − | 0.878178i | \(-0.341241\pi\) | ||||
0.478333 | + | 0.878178i | \(0.341241\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 0.579662i | − 0.0317653i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.4648i | 1.22373i | 0.790961 | + | 0.611867i | \(0.209581\pi\) | ||||
−0.790961 | + | 0.611867i | \(0.790419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.3845 | 1.43301 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.03282 | 0.380849 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.6154i | 0.573177i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.97296i | 0.159597i | 0.996811 | + | 0.0797984i | \(0.0254277\pi\) | ||||
−0.996811 | + | 0.0797984i | \(0.974572\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.36975 | 0.233908 | 0.116954 | − | 0.993137i | \(-0.462687\pi\) | ||||
0.116954 | + | 0.993137i | \(0.462687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.2807 | −1.02913 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 31.4419i | − 1.67348i | −0.547598 | − | 0.836742i | \(-0.684458\pi\) | ||||
0.547598 | − | 0.836742i | \(-0.315542\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 33.4419i | − 1.76993i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.7912 | −1.46676 | −0.733381 | − | 0.679818i | \(-0.762059\pi\) | ||||
−0.733381 | + | 0.679818i | \(0.762059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.77034 | −0.356333 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.68007i | 0.0881809i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.9061i | 0.725890i | 0.931811 | + | 0.362945i | \(0.118229\pi\) | ||||
−0.931811 | + | 0.362945i | \(0.881771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.02299 | −0.417660 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.7148 | 2.42531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.2799i | 1.36072i | 0.732876 | + | 0.680362i | \(0.238177\pi\) | ||||
−0.732876 | + | 0.680362i | \(0.761823\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.8223i | 0.608879i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.06792 | 0.157588 | 0.0787942 | − | 0.996891i | \(-0.474893\pi\) | ||||
0.0787942 | + | 0.996891i | \(0.474893\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.8017 | −0.963239 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 28.8872i | − 1.47607i | −0.674763 | − | 0.738034i | \(-0.735754\pi\) | ||||
0.674763 | − | 0.738034i | \(-0.264246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3.13294i | − 0.159256i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.4697 | −1.24066 | −0.620331 | − | 0.784340i | \(-0.713002\pi\) | ||||
−0.620331 | + | 0.784340i | \(0.713002\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.46023 | −0.377280 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 10.1333i | − 0.511156i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8.44828i | − 0.424007i | −0.977269 | − | 0.212004i | \(-0.932001\pi\) | ||||
0.977269 | − | 0.212004i | \(-0.0679988\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.6764 | 0.784801 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.3352 | 1.01549 | 0.507746 | − | 0.861507i | \(-0.330479\pi\) | ||||
0.507746 | + | 0.861507i | \(0.330479\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.86611i | 0.342025i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.78875i | − 0.0886652i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.05655 | −0.299477 | −0.149738 | − | 0.988726i | \(-0.547843\pi\) | ||||
−0.149738 | + | 0.988726i | \(0.547843\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.0775 | 1.38496 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.4639i | 0.760927i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.50982i | 0.367757i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.02434 | −0.343162 | −0.171581 | − | 0.985170i | \(-0.554887\pi\) | ||||
−0.171581 | + | 0.985170i | \(0.554887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.17652 | 0.349762 | 0.174881 | − | 0.984590i | \(-0.444046\pi\) | ||||
0.174881 | + | 0.984590i | \(0.444046\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.00770i | 0.0489959i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44.2167i | 2.13980i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.3131 | −0.787605 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.2944 | 0.544034 | 0.272017 | − | 0.962292i | \(-0.412309\pi\) | ||||
0.272017 | + | 0.962292i | \(0.412309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.2266i | 1.06814i | 0.845439 | + | 0.534072i | \(0.179339\pi\) | ||||
−0.845439 | + | 0.534072i | \(0.820661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.49709i | − 0.167289i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.2573 | 1.44410 | 0.722052 | − | 0.691839i | \(-0.243199\pi\) | ||||
0.722052 | + | 0.691839i | \(0.243199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.26620 | −0.203153 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 14.0307i | − 0.666620i | −0.942817 | − | 0.333310i | \(-0.891834\pi\) | ||||
0.942817 | − | 0.333310i | \(-0.108166\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 6.56007i | − 0.310281i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.70110 | −0.410630 | −0.205315 | − | 0.978696i | \(-0.565822\pi\) | ||||
−0.205315 | + | 0.978696i | \(0.565822\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.7578 | −1.16580 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 4.46587i | − 0.209825i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 33.8379i | − 1.58287i | −0.611255 | − | 0.791434i | \(-0.709335\pi\) | ||||
0.611255 | − | 0.791434i | \(-0.290665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −42.1295 | −1.96644 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.6512 | 1.84674 | 0.923370 | − | 0.383912i | \(-0.125423\pi\) | ||||
0.923370 | + | 0.383912i | \(0.125423\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.8490i | 1.61957i | 0.586727 | + | 0.809784i | \(0.300416\pi\) | ||||
−0.586727 | + | 0.809784i | \(0.699584\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.9442i | 0.645258i | 0.946525 | + | 0.322629i | \(0.104567\pi\) | ||||
−0.946525 | + | 0.322629i | \(0.895433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.54697 | −0.348486 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.8386 | −1.37489 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.66780i | − 0.444526i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 16.1357i | − 0.738804i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.4103 | 1.48086 | 0.740432 | − | 0.672131i | \(-0.234621\pi\) | ||||
0.740432 | + | 0.672131i | \(0.234621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.74635 | 0.0796268 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.48269i | − 0.203969i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1999i | 1.14192i | 0.820979 | + | 0.570959i | \(0.193428\pi\) | ||||
−0.820979 | + | 0.570959i | \(0.806572\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.7572 | 1.43611 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.9247 | −1.48587 | −0.742936 | − | 0.669363i | \(-0.766567\pi\) | ||||
−0.742936 | + | 0.669363i | \(0.766567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.8324i | 1.16343i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 34.8481i | − 1.56315i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4047 | −0.555309 | −0.277654 | − | 0.960681i | \(-0.589557\pi\) | ||||
−0.277654 | + | 0.960681i | \(0.589557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.64521 | 0.252209 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.74517i | 0.166989i | 0.996508 | + | 0.0834945i | \(0.0266081\pi\) | ||||
−0.996508 | + | 0.0834945i | \(0.973392\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.83526i | 0.0815069i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.84783 | 0.259201 | 0.129600 | − | 0.991566i | \(-0.458631\pi\) | ||||
0.129600 | + | 0.991566i | \(0.458631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.1646 | −0.538128 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 19.7489i | − 0.871933i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.10961i | 0.136760i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.04124 | 0.352971 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.3808 | 0.805278 | 0.402639 | − | 0.915359i | \(-0.368093\pi\) | ||||
0.402639 | + | 0.915359i | \(0.368093\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 23.4541i | − 1.02558i | −0.858515 | − | 0.512789i | \(-0.828612\pi\) | ||||
0.858515 | − | 0.512789i | \(-0.171388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.0029i | 0.653535i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.34137 | 0.231796 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 24.1710i | − 1.04696i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.36984i | 0.404338i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.1649 | −0.567052 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.03474 | 0.130474 | 0.0652368 | − | 0.997870i | \(-0.479220\pi\) | ||||
0.0652368 | + | 0.997870i | \(0.479220\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 3.12937i | − 0.134294i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4383i | 0.702851i | 0.936216 | + | 0.351426i | \(0.114303\pi\) | ||||
−0.936216 | + | 0.351426i | \(0.885697\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.2729 | 0.651830 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.1093 | −0.515875 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.1811i | 1.11334i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 6.72395i | − 0.284903i | −0.989802 | − | 0.142451i | \(-0.954502\pi\) | ||||
0.989802 | − | 0.142451i | \(-0.0454985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.43863 | 0.399212 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.6452 | −1.50494 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.0044i | 1.77027i | 0.465331 | + | 0.885137i | \(0.345935\pi\) | ||||
−0.465331 | + | 0.885137i | \(0.654065\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 14.1602i | − 0.594674i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.1152 | 1.63980 | 0.819898 | − | 0.572510i | \(-0.194030\pi\) | ||||
0.819898 | + | 0.572510i | \(0.194030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.2607 | −0.554944 | −0.277472 | − | 0.960734i | \(-0.589497\pi\) | ||||
−0.277472 | + | 0.960734i | \(0.589497\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 13.0992i | − 0.547228i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.31588i | 0.387825i | 0.981019 | + | 0.193913i | \(0.0621178\pi\) | ||||
−0.981019 | + | 0.193913i | \(0.937882\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.0474 | 0.791584 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.9174 | −1.28267 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 49.7925i | − 2.06220i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.80336i | 0.322079i | 0.986948 | + | 0.161040i | \(0.0514847\pi\) | ||||
−0.986948 | + | 0.161040i | \(0.948515\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.03282 | −0.289782 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.6324 | −0.848704 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 12.8383i | − 0.527204i | −0.964632 | − | 0.263602i | \(-0.915089\pi\) | ||||
0.964632 | − | 0.263602i | \(-0.0849106\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 19.8287i | − 0.811534i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.4957 | 0.428843 | 0.214422 | − | 0.976741i | \(-0.431213\pi\) | ||||
0.214422 | + | 0.976741i | \(0.431213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.1978 | −1.15021 | −0.575106 | − | 0.818079i | \(-0.695039\pi\) | ||||
−0.575106 | + | 0.818079i | \(0.695039\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.60679i | 0.106157i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 46.5662i | − 1.89007i | −0.326976 | − | 0.945033i | \(-0.606030\pi\) | ||||
0.326976 | − | 0.945033i | \(-0.393970\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.5221 | −0.628989 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.03590 | −0.122819 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.3120i | 1.22429i | 0.790746 | + | 0.612145i | \(0.209693\pi\) | ||||
−0.790746 | + | 0.612145i | \(0.790307\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 24.1879i | − 0.973768i | −0.873467 | − | 0.486884i | \(-0.838134\pi\) | ||||
0.873467 | − | 0.486884i | \(-0.161866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.29534 | 0.172644 | 0.0863221 | − | 0.996267i | \(-0.472489\pi\) | ||||
0.0863221 | + | 0.996267i | \(0.472489\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.64722 | −0.226615 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.62931i | − 0.105341i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 16.7092i | − 0.667301i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.81588 | 0.152149 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.3857 | 0.493066 | 0.246533 | − | 0.969134i | \(-0.420709\pi\) | ||||
0.246533 | + | 0.969134i | \(0.420709\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 32.0866i | − 1.27533i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 12.8528i | − 0.509248i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0369 | −0.476171 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.21653 | −0.206041 | −0.103020 | − | 0.994679i | \(-0.532851\pi\) | ||||
−0.103020 | + | 0.994679i | \(0.532851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.5639i | 0.495471i | 0.968828 | + | 0.247735i | \(0.0796863\pi\) | ||||
−0.968828 | + | 0.247735i | \(0.920314\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.7423i | 0.894094i | 0.894510 | + | 0.447047i | \(0.147524\pi\) | ||||
−0.894510 | + | 0.447047i | \(0.852476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.4827 | 0.647002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.01490 | −0.353322 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.36997i | 0.366675i | 0.983050 | + | 0.183338i | \(0.0586902\pi\) | ||||
−0.983050 | + | 0.183338i | \(0.941310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.20175i | 0.163926i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.4086 | 0.600235 | 0.300117 | − | 0.953902i | \(-0.402974\pi\) | ||||
0.300117 | + | 0.953902i | \(0.402974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.1386 | 1.67790 | 0.838948 | − | 0.544211i | \(-0.183171\pi\) | ||||
0.838948 | + | 0.544211i | \(0.183171\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 34.8002i | − 1.35153i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.46268i | 0.134076i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.2134 | −0.433534 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47.1299 | 1.81943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 12.6356i | − 0.487066i | −0.969893 | − | 0.243533i | \(-0.921694\pi\) | ||||
0.969893 | − | 0.243533i | \(-0.0783065\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 10.9139i | − 0.419454i | −0.977760 | − | 0.209727i | \(-0.932742\pi\) | ||||
0.977760 | − | 0.209727i | \(-0.0672575\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.6238 | 1.48225 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.2189 | −0.889750 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.5334i | 0.670896i | 0.942059 | + | 0.335448i | \(0.108888\pi\) | ||||
−0.942059 | + | 0.335448i | \(0.891112\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 26.8910i | − 1.02596i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 48.6122 | 1.85198 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −52.2318 | −1.98699 | −0.993496 | − | 0.113871i | \(-0.963675\pi\) | ||||
−0.993496 | + | 0.113871i | \(0.963675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.0028i | 0.493935i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 52.8150i | − 2.00051i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.9930 | 1.28573 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0270 | 0.983026 | 0.491513 | − | 0.870870i | \(-0.336444\pi\) | ||||
0.491513 | + | 0.870870i | \(0.336444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.78875i | 0.0674641i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.6019i | 1.37655i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.7971 | 1.30683 | 0.653415 | − | 0.757000i | \(-0.273336\pi\) | ||||
0.653415 | + | 0.757000i | \(0.273336\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.04321 | 0.339147 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.01105i | 0.0753143i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.0981652i | 0.00366605i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.40110 | −0.164133 | −0.0820667 | − | 0.996627i | \(-0.526152\pi\) | ||||
−0.0820667 | + | 0.996627i | \(0.526152\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.21878 | −0.157115 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 11.6224i | − 0.432242i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.744921i | 0.0276276i | 0.999905 | + | 0.0138138i | \(0.00439721\pi\) | ||||
−0.999905 | + | 0.0138138i | \(0.995603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.0382 | −1.03845 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.6240 | 0.762805 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.35631i | 0.271711i | 0.990729 | + | 0.135856i | \(0.0433784\pi\) | ||||
−0.990729 | + | 0.135856i | \(0.956622\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.04419i | 0.296311i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.2496 | −0.487394 | −0.243697 | − | 0.969851i | \(-0.578360\pi\) | ||||
−0.243697 | + | 0.969851i | \(0.578360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.3131 | 0.599278 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.8314i | 1.05772i | 0.848708 | + | 0.528861i | \(0.177381\pi\) | ||||
−0.848708 | + | 0.528861i | \(0.822619\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.6792i | 0.390730i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −45.5966 | −1.66607 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.3962 | −0.890228 | −0.445114 | − | 0.895474i | \(-0.646837\pi\) | ||||
−0.445114 | + | 0.895474i | \(0.646837\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 27.1697i | − 0.990120i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9.49825i | − 0.345220i | −0.984990 | − | 0.172610i | \(-0.944780\pi\) | ||||
0.984990 | − | 0.172610i | \(-0.0552200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.77803 | −0.173431 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.43957 | −0.305934 | −0.152967 | − | 0.988231i | \(-0.548883\pi\) | ||||
−0.152967 | + | 0.988231i | \(0.548883\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.3925i | 0.448639i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.0920i | 0.581048i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.85911 | −0.319468 | −0.159734 | − | 0.987160i | \(-0.551064\pi\) | ||||
−0.159734 | + | 0.987160i | \(0.551064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.5841 | 0.561247 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.7351i | 1.17740i | 0.808352 | + | 0.588699i | \(0.200360\pi\) | ||||
−0.808352 | + | 0.588699i | \(0.799640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.29288i | 0.0822567i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.7578 | 0.887041 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −37.1440 | −1.32912 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.5545i | 0.698822i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 0.736862i | − 0.0262663i | −0.999914 | − | 0.0131331i | \(-0.995819\pi\) | ||||
0.999914 | − | 0.0131331i | \(-0.00418053\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.2949 | −0.651316 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.3584 | 2.25276 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.0127i | 1.63396i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.7353i | 1.47834i | 0.673519 | + | 0.739170i | \(0.264782\pi\) | ||||
−0.673519 | + | 0.739170i | \(0.735218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.63362 | −0.234681 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.908187 | −0.0320892 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.9660i | 0.457560i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 18.8688i | − 0.664212i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.3182 | −0.749506 | −0.374753 | − | 0.927125i | \(-0.622273\pi\) | ||||
−0.374753 | + | 0.927125i | \(0.622273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3126 | 0.853732 | 0.426866 | − | 0.904315i | \(-0.359618\pi\) | ||||
0.426866 | + | 0.904315i | \(0.359618\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 36.5583i | 1.28216i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.66780i | 0.338233i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.6946 | −0.443584 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.3157 | 1.72113 | 0.860566 | − | 0.509340i | \(-0.170110\pi\) | ||||
0.860566 | + | 0.509340i | \(0.170110\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.5427i | 1.44809i | 0.689755 | + | 0.724043i | \(0.257718\pi\) | ||||
−0.689755 | + | 0.724043i | \(0.742282\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.306510i | 0.0106584i | 0.999986 | + | 0.00532919i | \(0.00169634\pi\) | ||||
−0.999986 | + | 0.00532919i | \(0.998304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.5423 | −0.609268 | −0.304634 | − | 0.952469i | \(-0.598534\pi\) | ||||
−0.304634 | + | 0.952469i | \(0.598534\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.46842 | 0.0856285 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 28.0842i | − 0.973060i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.3568i | 0.392549i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.1480 | 1.52416 | 0.762078 | − | 0.647485i | \(-0.224179\pi\) | ||||
0.762078 | + | 0.647485i | \(0.224179\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0098 | −0.586546 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.0739i | 1.27689i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.03445i | 0.138625i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.6749 | 0.984119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.511497 | 0.0175339 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 41.2098i | − 1.41100i | −0.708711 | − | 0.705499i | \(-0.750723\pi\) | ||||
0.708711 | − | 0.705499i | \(-0.249277\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 19.3245i | − 0.660114i | −0.943961 | − | 0.330057i | \(-0.892932\pi\) | ||||
0.943961 | − | 0.330057i | \(-0.107068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2174 | 0.553330 | 0.276665 | − | 0.960966i | \(-0.410771\pi\) | ||||
0.276665 | + | 0.960966i | \(0.410771\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.7354 | 1.08154 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 56.9036i | − 1.93702i | −0.248974 | − | 0.968510i | \(-0.580093\pi\) | ||||
0.248974 | − | 0.968510i | \(-0.419907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 52.8137i | − 1.79365i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.9061 | 0.946648 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.85351 | −0.266106 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 13.3410i | − 0.451526i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 33.4569i | − 1.12976i | −0.825173 | − | 0.564880i | \(-0.808923\pi\) | ||||
0.825173 | − | 0.564880i | \(-0.191077\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.00917121 | 0.000309337 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.99700 | −0.202044 | −0.101022 | − | 0.994884i | \(-0.532211\pi\) | ||||
−0.101022 | + | 0.994884i | \(0.532211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.3210i | 1.72709i | 0.504273 | + | 0.863544i | \(0.331761\pi\) | ||||
−0.504273 | + | 0.863544i | \(0.668239\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 27.1121i | − 0.910336i | −0.890405 | − | 0.455168i | \(-0.849579\pi\) | ||||
0.890405 | − | 0.455168i | \(-0.150421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.1495 | −1.51426 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.0932 | −0.505640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 3.10961i | − 0.104059i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 4.66477i | − 0.155752i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.96362 | 0.232250 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 106.221 | 3.53872 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.3925i | 0.412397i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 40.6194i | − 1.34875i | −0.738391 | − | 0.674373i | \(-0.764414\pi\) | ||||
0.738391 | − | 0.674373i | \(-0.235586\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.6426 | 0.419329 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.2475 | 1.06841 | 0.534203 | − | 0.845356i | \(-0.320612\pi\) | ||||
0.534203 | + | 0.845356i | \(0.320612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.9544i | 1.09063i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 24.3335i | − 0.803565i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.4042 | 1.00294 | 0.501470 | − | 0.865175i | \(-0.332793\pi\) | ||||
0.501470 | + | 0.865175i | \(0.332793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.2939 | 0.899366 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 36.2636i | − 1.19363i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.45720i | 0.0478609i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.2834 | 0.829520 | 0.414760 | − | 0.909931i | \(-0.363866\pi\) | ||||
0.414760 | + | 0.909931i | \(0.363866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1649 | 0.431462 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.5997i | 1.06727i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 22.1769i | − 0.724487i | −0.932084 | − | 0.362243i | \(-0.882011\pi\) | ||||
0.932084 | − | 0.362243i | \(-0.117989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.8289 | −0.777626 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.23228 | 0.137968 | 0.0689842 | − | 0.997618i | \(-0.478024\pi\) | ||||
0.0689842 | + | 0.997618i | \(0.478024\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 7.07954i | − 0.230542i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.2374i | 1.47002i | 0.678058 | + | 0.735009i | \(0.262822\pi\) | ||||
−0.678058 | + | 0.735009i | \(0.737178\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.6587 | −0.410917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.85242 | −0.0600690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.7170i | 1.41613i | 0.706146 | + | 0.708066i | \(0.250432\pi\) | ||||
−0.706146 | + | 0.708066i | \(0.749568\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.5448i | 0.534817i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 67.4240 | 2.17723 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.9557 | −0.869538 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.7495i | 0.507521i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 5.58482i | − 0.179596i | −0.995960 | − | 0.0897979i | \(-0.971378\pi\) | ||||
0.995960 | − | 0.0897979i | \(-0.0286221\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 35.6452 | 1.14509 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.1206 | 1.25544 | 0.627720 | − | 0.778439i | \(-0.283988\pi\) | ||||
0.627720 | + | 0.778439i | \(0.283988\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.0337i | 0.578135i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 52.3050i | − 1.67339i | −0.547672 | − | 0.836693i | \(-0.684486\pi\) | ||||
0.547672 | − | 0.836693i | \(-0.315514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.80253 | −0.0895694 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.28049 | 0.136665 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 22.4395i | − 0.715710i | −0.933777 | − | 0.357855i | \(-0.883508\pi\) | ||||
0.933777 | − | 0.357855i | \(-0.116492\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 3.98600i | − 0.126876i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.76452 | 0.0879067 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.851383 | −0.0270451 | −0.0135225 | − | 0.999909i | \(-0.504304\pi\) | ||||
−0.0135225 | + | 0.999909i | \(0.504304\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.7802i | 0.754643i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.1784i | 0.385693i | 0.981229 | + | 0.192846i | \(0.0617719\pi\) | ||||
−0.981229 | + | 0.192846i | \(0.938228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.88853 | 0.0913892 |
(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 | 4600.2.e.w.4049.7 | 10 | ||
5.2 | odd | 4 | 4600.2.a.bd.1.4 | ✓ | 5 | ||
5.3 | odd | 4 | 4600.2.a.bf.1.2 | yes | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.w.4049.4 | 10 | ||
20.3 | even | 4 | 9200.2.a.ct.1.4 | 5 | |||
20.7 | even | 4 | 9200.2.a.cv.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bd.1.4 | ✓ | 5 | 5.2 | odd | 4 | ||
4600.2.a.bf.1.2 | yes | 5 | 5.3 | odd | 4 | ||
4600.2.e.w.4049.4 | 10 | 5.4 | even | 2 | inner | ||
4600.2.e.w.4049.7 | 10 | 1.1 | even | 1 | trivial | ||
9200.2.a.ct.1.4 | 5 | 20.3 | even | 4 | |||
9200.2.a.cv.1.2 | 5 | 20.7 | even | 4 |