Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(449,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, 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("2240.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.g (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20x^{10} + 148x^{8} + 494x^{6} + 708x^{4} + 304x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.6 | ||
Root | \(-2.64856i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.449 |
Dual form | 2240.2.g.p.449.7 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 0.321637i | − | 0.185697i | −0.995680 | − | 0.0928487i | \(-0.970403\pi\) | ||
0.995680 | − | 0.0928487i | \(-0.0295973\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.10909 | + | 0.742782i | −0.943215 | + | 0.332182i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.89655 | 0.965517 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.37985 | 1.32057 | 0.660287 | − | 0.751013i | \(-0.270434\pi\) | ||||
0.660287 | + | 0.751013i | \(0.270434\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.86542i | − | 1.62677i | −0.581723 | − | 0.813387i | \(-0.697621\pi\) | ||
0.581723 | − | 0.813387i | \(-0.302379\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.238906 | + | 0.678363i | 0.0616853 | + | 0.175153i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.85766i | 1.17816i | 0.808076 | + | 0.589078i | \(0.200509\pi\) | ||||
−0.808076 | + | 0.589078i | \(0.799491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.75195 | −1.77842 | −0.889210 | − | 0.457500i | \(-0.848745\pi\) | ||||
−0.889210 | + | 0.457500i | \(0.848745\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.321637 | −0.0701870 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.35673i | − | 0.282897i | −0.989946 | − | 0.141448i | \(-0.954824\pi\) | ||
0.989946 | − | 0.141448i | \(-0.0451759\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.89655 | − | 3.13319i | 0.779310 | − | 0.626639i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.89655i | − | 0.364991i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.539824 | −0.100243 | −0.0501214 | − | 0.998743i | \(-0.515961\pi\) | ||||
−0.0501214 | + | 0.998743i | \(0.515961\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.97113 | 0.533630 | 0.266815 | − | 0.963748i | \(-0.414029\pi\) | ||||
0.266815 | + | 0.963748i | \(0.414029\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.40872i | − | 0.245227i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.742782 | + | 2.10909i | 0.125553 | + | 0.356502i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.26639i | 1.03019i | 0.857134 | + | 0.515094i | \(0.172243\pi\) | ||||
−0.857134 | + | 0.515094i | \(0.827757\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.88654 | −0.302087 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.64327 | 0.412810 | 0.206405 | − | 0.978467i | \(-0.433824\pi\) | ||||
0.206405 | + | 0.978467i | \(0.433824\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.64327i | − | 0.708093i | −0.935228 | − | 0.354046i | \(-0.884806\pi\) | ||
0.935228 | − | 0.354046i | \(-0.115194\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.10909 | + | 2.15151i | −0.910690 | + | 0.320727i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.3329i | − | 1.50721i | −0.657327 | − | 0.753606i | \(-0.728313\pi\) | ||
0.657327 | − | 0.753606i | \(-0.271687\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.56241 | 0.218781 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.477813i | 0.0656326i | 0.999461 | + | 0.0328163i | \(0.0104476\pi\) | ||||
−0.999461 | + | 0.0328163i | \(0.989552\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.23752 | + | 3.25328i | −1.24559 | + | 0.438672i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.49332i | 0.330248i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.75195 | 1.00922 | 0.504609 | − | 0.863348i | \(-0.331637\pi\) | ||||
0.504609 | + | 0.863348i | \(0.331637\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.57491 | −0.969868 | −0.484934 | − | 0.874551i | \(-0.661156\pi\) | ||||
−0.484934 | + | 0.874551i | \(0.661156\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.89655i | − | 0.364931i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.35673 | + | 12.3707i | 0.540385 | + | 1.53440i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.79310i | − | 0.463401i | −0.972787 | − | 0.231700i | \(-0.925571\pi\) | ||
0.972787 | − | 0.231700i | \(-0.0744289\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.436373 | −0.0525332 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.23752 | 1.09629 | 0.548146 | − | 0.836383i | \(-0.315334\pi\) | ||||
0.548146 | + | 0.836383i | \(0.315334\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.477813i | 0.0559237i | 0.999609 | + | 0.0279619i | \(0.00890170\pi\) | ||||
−0.999609 | + | 0.0279619i | \(0.991098\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00775 | − | 1.25328i | −0.116365 | − | 0.144716i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.37985i | − | 0.499130i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.88654 | 0.212252 | 0.106126 | − | 0.994353i | \(-0.466155\pi\) | ||||
0.106126 | + | 0.994353i | \(0.466155\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.07965 | 0.897739 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 15.2978i | − | 1.67916i | −0.543240 | − | 0.839578i | \(-0.682802\pi\) | ||
0.543240 | − | 0.839578i | \(-0.317198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.60819 | − | 10.2453i | −0.391363 | − | 1.11126i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.173627i | 0.0186148i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.86542 | −0.614863 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.955625i | − | 0.0990937i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.3496 | − | 5.75801i | 1.67743 | − | 0.590759i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.6174i | − | 1.38263i | −0.722552 | − | 0.691317i | \(-0.757031\pi\) | ||
0.722552 | − | 0.691317i | \(-0.242969\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.6865 | 1.27504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.28836 | −0.625716 | −0.312858 | − | 0.949800i | \(-0.601286\pi\) | ||||
−0.312858 | + | 0.949800i | \(0.601286\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.25328i | − | 0.911752i | −0.890043 | − | 0.455876i | \(-0.849326\pi\) | ||
0.890043 | − | 0.455876i | \(-0.150674\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.678363 | − | 0.238906i | 0.0662014 | − | 0.0233149i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.5862i | − | 1.50677i | −0.657577 | − | 0.753387i | \(-0.728419\pi\) | ||
0.657577 | − | 0.753387i | \(-0.271581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.2533 | 1.07787 | 0.538934 | − | 0.842348i | \(-0.318827\pi\) | ||||
0.538934 | + | 0.842348i | \(0.318827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.01550 | 0.191303 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.2086i | − | 1.14849i | −0.818683 | − | 0.574246i | \(-0.805295\pi\) | ||
0.818683 | − | 0.574246i | \(-0.194705\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00775 | + | 2.86146i | 0.0939733 | + | 0.266833i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 16.9895i | − | 1.57068i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.85766 | 0.445301 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.18310 | 0.743918 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.850175i | − | 0.0766577i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.89091 | + | 9.50248i | −0.526899 | + | 0.849928i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.14982i | − | 0.811916i | −0.913892 | − | 0.405958i | \(-0.866938\pi\) | ||
0.913892 | − | 0.405958i | \(-0.133062\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.49345 | −0.131491 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5117 | 1.44263 | 0.721315 | − | 0.692607i | \(-0.243538\pi\) | ||||
0.721315 | + | 0.692607i | \(0.243538\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.75195i | 0.672179i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.40872 | + | 4.00000i | 0.121244 | + | 0.344265i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.75970i | 0.748392i | 0.927350 | + | 0.374196i | \(0.122081\pi\) | ||||
−0.927350 | + | 0.374196i | \(0.877919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.76745 | 0.828465 | 0.414232 | − | 0.910171i | \(-0.364050\pi\) | ||||
0.414232 | + | 0.910171i | \(0.364050\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.32345 | −0.279885 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 25.6896i | − | 2.14828i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.13854 | − | 0.400972i | 0.0945505 | − | 0.0332989i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.321637i | 0.0265282i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.8727 | 1.87381 | 0.936904 | − | 0.349586i | \(-0.113678\pi\) | ||||
0.936904 | + | 0.349586i | \(0.113678\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.1107 | −1.31107 | −0.655534 | − | 0.755165i | \(-0.727557\pi\) | ||||
−0.655534 | + | 0.755165i | \(0.727557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.0705i | 1.13753i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.26639 | + | 2.20690i | −0.503328 | + | 0.177263i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.529939i | 0.0422937i | 0.999776 | + | 0.0211469i | \(0.00673176\pi\) | ||||
−0.999776 | + | 0.0211469i | \(0.993268\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.153682 | 0.0121878 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.35673 | −0.106925 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21.5160i | − | 1.68526i | −0.538489 | − | 0.842632i | \(-0.681005\pi\) | ||
0.538489 | − | 0.842632i | \(-0.318995\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.04637 | + | 2.97113i | 0.0814601 | + | 0.231302i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.5398i | 0.815596i | 0.913072 | + | 0.407798i | \(0.133703\pi\) | ||||
−0.913072 | + | 0.407798i | \(0.866297\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.4031 | −1.64639 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.4539 | −1.71709 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8077i | 0.897721i | 0.893602 | + | 0.448860i | \(0.148170\pi\) | ||||
−0.893602 | + | 0.448860i | \(0.851830\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.13319 | − | 3.89655i | −0.236847 | − | 0.294551i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.49332i | − | 0.187409i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.4750 | −1.38089 | −0.690444 | − | 0.723386i | \(-0.742585\pi\) | ||||
−0.690444 | + | 0.723386i | \(0.742585\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.86146 | −0.361350 | −0.180675 | − | 0.983543i | \(-0.557828\pi\) | ||||
−0.180675 | + | 0.983543i | \(0.557828\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.43637i | 0.180102i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.65456 | − | 13.2164i | −0.342210 | − | 0.971689i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.2758i | 1.55584i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.89655 | −0.137954 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.6329 | −1.13115 | −0.565577 | − | 0.824695i | \(-0.691347\pi\) | ||||
−0.565577 | + | 0.824695i | \(0.691347\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.9683i | 1.50933i | 0.656108 | + | 0.754667i | \(0.272202\pi\) | ||||
−0.656108 | + | 0.754667i | \(0.727798\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.97888 | − | 1.40128i | 0.284934 | − | 0.100348i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1798i | 1.08151i | 0.841179 | + | 0.540757i | \(0.181862\pi\) | ||||
−0.841179 | + | 0.540757i | \(0.818138\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7308 | 0.831577 | 0.415788 | − | 0.909461i | \(-0.363506\pi\) | ||||
0.415788 | + | 0.909461i | \(0.363506\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.22000 | −0.0860523 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.539824i | 0.0378882i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.57491 | + | 1.96338i | −0.389369 | + | 0.137128i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3.92982i | − | 0.273142i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −33.9524 | −2.34854 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.40872 | −0.0969805 | −0.0484902 | − | 0.998824i | \(-0.515441\pi\) | ||||
−0.0484902 | + | 0.998824i | \(0.515441\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 2.97113i | − | 0.203578i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.44894 | + | 9.79310i | 0.235216 | + | 0.667884i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.97113i | − | 0.201693i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.153682 | 0.0103849 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.4922 | 1.91659 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.61000i | 0.308708i | 0.988016 | + | 0.154354i | \(0.0493297\pi\) | ||||
−0.988016 | + | 0.154354i | \(0.950670\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.2865 | − | 9.07545i | 0.752437 | − | 0.605030i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.74854i | 0.381544i | 0.981634 | + | 0.190772i | \(0.0610991\pi\) | ||||
−0.981634 | + | 0.190772i | \(0.938901\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.5047 | 1.15675 | 0.578373 | − | 0.815773i | \(-0.303688\pi\) | ||||
0.578373 | + | 0.815773i | \(0.303688\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.40872 | −0.0926872 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18.4750i | − | 1.21034i | −0.796096 | − | 0.605170i | \(-0.793105\pi\) | ||
0.796096 | − | 0.605170i | \(-0.206895\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.67511 | + | 21.7931i | 0.500669 | + | 1.42163i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 0.606780i | − | 0.0394146i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.35098 | −0.475495 | −0.237748 | − | 0.971327i | \(-0.576409\pi\) | ||||
−0.237748 | + | 0.971327i | \(0.576409\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.51602 | −0.226487 | −0.113243 | − | 0.993567i | \(-0.536124\pi\) | ||||
−0.113243 | + | 0.993567i | \(0.536124\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 8.28836i | − | 0.531699i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.10909 | − | 0.742782i | 0.134745 | − | 0.0474546i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 45.4684i | 2.89309i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.92035 | −0.311815 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.73645 | −0.362081 | −0.181041 | − | 0.983476i | \(-0.557947\pi\) | ||||
−0.181041 | + | 0.983476i | \(0.557947\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.94226i | − | 0.373586i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.29526 | + | 1.16053i | −0.206357 | + | 0.0726750i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.9972i | − | 1.12264i | −0.827600 | − | 0.561318i | \(-0.810295\pi\) | ||
0.827600 | − | 0.561318i | \(-0.189705\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.26639 | 0.389374 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.56363 | −0.0967861 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.8727i | − | 1.04042i | −0.854039 | − | 0.520209i | \(-0.825854\pi\) | ||
0.854039 | − | 0.520209i | \(-0.174146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.354911 | − | 1.00775i | −0.0218020 | − | 0.0619057i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.92982i | 0.118103i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.8746 | 1.57760 | 0.788800 | − | 0.614650i | \(-0.210703\pi\) | ||||
0.788800 | + | 0.614650i | \(0.210703\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.2347 | 1.65439 | 0.827196 | − | 0.561913i | \(-0.189935\pi\) | ||||
0.827196 | + | 0.561913i | \(0.189935\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.88654i | 0.114178i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.0663 | − | 13.7229i | 1.02914 | − | 0.827523i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.9395i | 1.43838i | 0.694812 | + | 0.719192i | \(0.255488\pi\) | ||||
−0.694812 | + | 0.719192i | \(0.744512\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.60602 | 0.515229 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.5493 | −1.16621 | −0.583107 | − | 0.812396i | \(-0.698163\pi\) | ||||
−0.583107 | + | 0.812396i | \(0.698163\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.9173i | 1.83784i | 0.394440 | + | 0.918922i | \(0.370938\pi\) | ||||
−0.394440 | + | 0.918922i | \(0.629062\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.85199 | − | 5.25864i | −0.109702 | − | 0.311495i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.64327i | − | 0.156028i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.59690 | −0.388053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.37985 | −0.256751 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.63849i | − | 0.563086i | −0.959549 | − | 0.281543i | \(-0.909154\pi\) | ||
0.959549 | − | 0.281543i | \(-0.0908463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.3496 | + | 5.75801i | −0.951910 | + | 0.335244i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 8.30661i | − | 0.481998i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.95776 | −0.460209 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.64327 | −0.267634 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.02257i | 0.116194i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.9762 | − | 5.62651i | 0.914794 | − | 0.322173i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8282i | 0.617997i | 0.951062 | + | 0.308999i | \(0.0999939\pi\) | ||||
−0.951062 | + | 0.308999i | \(0.900006\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.97620 | −0.169310 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.71533 | −0.550906 | −0.275453 | − | 0.961315i | \(-0.588828\pi\) | ||||
−0.275453 | + | 0.961315i | \(0.588828\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.85766i | 0.274571i | 0.990531 | + | 0.137286i | \(0.0438378\pi\) | ||||
−0.990531 | + | 0.137286i | \(0.956162\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.15151 | + | 6.10909i | 0.121224 | + | 0.344208i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 20.8147i | − | 1.16907i | −0.811369 | − | 0.584534i | \(-0.801277\pi\) | ||
0.811369 | − | 0.584534i | \(-0.198723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.36435 | −0.132378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.01310 | −0.279804 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 37.6564i | − | 2.09526i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.3775 | − | 22.8549i | −1.01940 | − | 1.26776i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3.61947i | − | 0.200157i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.3329 | −0.569672 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.4595 | 0.904697 | 0.452349 | − | 0.891841i | \(-0.350586\pi\) | ||||
0.452349 | + | 0.891841i | \(0.350586\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.1509i | 0.994663i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.81745 | + | 8.00000i | 0.153934 | + | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.5011i | 1.82492i | 0.409163 | + | 0.912461i | \(0.365821\pi\) | ||||
−0.409163 | + | 0.912461i | \(0.634179\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.92675 | −0.213272 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.0131 | 0.704699 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.920352 | − | 0.324130i | 0.0495501 | − | 0.0174506i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.7360i | 1.43526i | 0.696422 | + | 0.717632i | \(0.254774\pi\) | ||||
−0.696422 | + | 0.717632i | \(0.745226\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0113 | −0.642949 | −0.321475 | − | 0.946918i | \(-0.604179\pi\) | ||||
−0.321475 | + | 0.946918i | \(0.604179\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.1241 | −0.593758 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.70398i | 0.250368i | 0.992134 | + | 0.125184i | \(0.0399521\pi\) | ||||
−0.992134 | + | 0.125184i | \(0.960048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.4828 | + | 6.86146i | −1.03404 | + | 0.364169i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1.56241i | − | 0.0826913i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4173 | −1.28870 | −0.644348 | − | 0.764733i | \(-0.722871\pi\) | ||||
−0.644348 | + | 0.764733i | \(0.722871\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.0927 | 2.16278 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.63199i | − | 0.138144i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.354911 | − | 1.00775i | −0.0185769 | − | 0.0527481i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.18310i | − | 0.166156i | −0.996543 | − | 0.0830782i | \(-0.973525\pi\) | ||
0.996543 | − | 0.0830782i | \(-0.0264751\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.65638 | 0.398575 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.477813 | 0.0248068 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.42007i | 0.332419i | 0.986090 | + | 0.166209i | \(0.0531527\pi\) | ||||
−0.986090 | + | 0.166209i | \(0.946847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.05635 | + | 1.89473i | 0.157829 | + | 0.0978437i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.16629i | 0.163072i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3884 | −1.40685 | −0.703424 | − | 0.710770i | \(-0.748347\pi\) | ||||
−0.703424 | + | 0.710770i | \(0.748347\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.94292 | −0.150771 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 27.0095i | − | 1.38012i | −0.723752 | − | 0.690060i | \(-0.757584\pi\) | ||
0.723752 | − | 0.690060i | \(-0.242416\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.25328 | + | 9.23752i | 0.165802 | + | 0.470787i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 13.4495i | − | 0.683675i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.1129 | 0.766256 | 0.383128 | − | 0.923695i | \(-0.374847\pi\) | ||||
0.383128 | + | 0.923695i | \(0.374847\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.59052 | 0.333297 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.31076i | − | 0.267892i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.97888 | + | 1.40128i | −0.200199 | + | 0.0705063i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5652i | 0.680820i | 0.940277 | + | 0.340410i | \(0.110566\pi\) | ||||
−0.940277 | + | 0.340410i | \(0.889434\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.49332 | 0.124822 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.4031 | −0.819132 | −0.409566 | − | 0.912281i | \(-0.634320\pi\) | ||||
−0.409566 | + | 0.912281i | \(0.634320\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 17.4269i | − | 0.868096i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.0407 | + | 6.00142i | −0.846761 | + | 0.298213i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.4458i | 1.36044i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.07018 | −0.399045 | −0.199522 | − | 0.979893i | \(-0.563939\pi\) | ||||
−0.199522 | + | 0.979893i | \(0.563939\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.81745 | 0.138974 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 7.75195i | − | 0.381449i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.3630 | + | 32.2646i | 0.557786 | + | 1.58381i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.14158i | − | 0.153844i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.82520 | −0.186873 | −0.0934366 | − | 0.995625i | \(-0.529785\pi\) | ||||
−0.0934366 | + | 0.995625i | \(0.529785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5304 | −0.659429 | −0.329715 | − | 0.944081i | \(-0.606952\pi\) | ||||
−0.329715 | + | 0.944081i | \(0.606952\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 29.9298i | − | 1.45524i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.2200 | + | 18.9281i | 0.738279 | + | 0.918149i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.57491i | 0.366576i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.26275 | −0.398929 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.0529 | 1.06225 | 0.531126 | − | 0.847293i | \(-0.321769\pi\) | ||||
0.531126 | + | 0.847293i | \(0.321769\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 32.5455i | − | 1.56404i | −0.623255 | − | 0.782018i | \(-0.714190\pi\) | ||
0.623255 | − | 0.782018i | \(-0.285810\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.128967 | − | 0.366196i | −0.00618351 | − | 0.0175578i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.5173i | 0.503109i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.6442 | −0.985295 | −0.492647 | − | 0.870229i | \(-0.663971\pi\) | ||||
−0.492647 | + | 0.870229i | \(0.663971\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.89655 | −0.137931 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 10.5066i | − | 0.499181i | −0.968351 | − | 0.249591i | \(-0.919704\pi\) | ||
0.968351 | − | 0.249591i | \(-0.0802961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.6546 | − | 4.45669i | 0.599884 | − | 0.211267i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 7.35673i | − | 0.347961i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.76930 | −0.413849 | −0.206924 | − | 0.978357i | \(-0.566345\pi\) | ||||
−0.206924 | + | 0.978357i | \(0.566345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.5771 | 0.545147 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.18179i | 0.243462i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.3707 | − | 4.35673i | 0.579948 | − | 0.204246i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.1509i | 0.849063i | 0.905413 | + | 0.424532i | \(0.139561\pi\) | ||||
−0.905413 | + | 0.424532i | \(0.860439\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.21280 | 0.430017 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.22766 | −0.150327 | −0.0751635 | − | 0.997171i | \(-0.523948\pi\) | ||||
−0.0751635 | + | 0.997171i | \(0.523948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.7931i | 0.919863i | 0.887954 | + | 0.459932i | \(0.152126\pi\) | ||||
−0.887954 | + | 0.459932i | \(0.847874\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.709821 | + | 2.01550i | 0.0329172 | + | 0.0934667i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.3918i | 0.665974i | 0.942931 | + | 0.332987i | \(0.108056\pi\) | ||||
−0.942931 | + | 0.332987i | \(0.891944\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.79310 | −0.175149 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.170448 | 0.00785383 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 20.3369i | − | 0.935089i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −30.2059 | + | 24.2884i | −1.38594 | + | 1.11443i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.38401i | 0.0633694i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.92675 | 0.179418 | 0.0897090 | − | 0.995968i | \(-0.471406\pi\) | ||||
0.0897090 | + | 0.995968i | \(0.471406\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.7550 | 1.67588 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.436373i | 0.0198557i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.1147 | + | 28.7203i | 0.459287 | + | 1.30412i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.4364i | 0.472917i | 0.971642 | + | 0.236459i | \(0.0759868\pi\) | ||||
−0.971642 | + | 0.236459i | \(0.924013\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.92035 | −0.312949 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.6435 | 1.29266 | 0.646331 | − | 0.763058i | \(-0.276303\pi\) | ||||
0.646331 | + | 0.763058i | \(0.276303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.62228i | − | 0.118102i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −26.7569 | + | 9.42327i | −1.20263 | + | 0.423545i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 9.23752i | − | 0.414359i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.5857 | 1.54827 | 0.774135 | − | 0.633021i | \(-0.218185\pi\) | ||||
0.774135 | + | 0.633021i | \(0.218185\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.39000 | 0.151454 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.5624i | 0.827656i | 0.910355 | + | 0.413828i | \(0.135809\pi\) | ||||
−0.910355 | + | 0.413828i | \(0.864191\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.2627 | − | 4.67088i | 0.590184 | − | 0.207852i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.88403i | 0.305731i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.5975 | 1.22324 | 0.611618 | − | 0.791153i | \(-0.290519\pi\) | ||||
0.611618 | + | 0.791153i | \(0.290519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.477813 | 0.0211372 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.7020i | 0.649107i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.87317 | + | 19.5160i | 0.302868 | + | 0.859979i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 45.2567i | − | 1.99039i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.79779 | 0.166704 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0095 | −0.920442 | −0.460221 | − | 0.887804i | \(-0.652230\pi\) | ||||
−0.460221 | + | 0.887804i | \(0.652230\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.1706i | 1.40672i | 0.710833 | + | 0.703361i | \(0.248318\pi\) | ||||
−0.710833 | + | 0.703361i | \(0.751682\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.25328 | + | 1.00775i | −0.0546974 | + | 0.0439819i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.4327i | 0.628700i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1593 | 0.919969 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.4539 | 0.974417 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 15.5039i | − | 0.671549i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.5771 | + | 32.8727i | 0.500524 | + | 1.42121i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.94226i | 0.256427i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.37985 | −0.188654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.3424 | −1.51949 | −0.759744 | − | 0.650222i | \(-0.774676\pi\) | ||||
−0.759744 | + | 0.650222i | \(0.774676\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.56363i | 0.0671016i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.7342 | + | 8.35873i | −1.01666 | + | 0.358049i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.3567i | 0.827634i | 0.910360 | + | 0.413817i | \(0.135805\pi\) | ||||
−0.910360 | + | 0.413817i | \(0.864195\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.9411 | −0.936424 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.18469 | 0.178274 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.88654i | − | 0.0802237i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.25088 | + | 1.49708i | −0.180440 | + | 0.0635475i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15.8280i | − | 0.670655i | −0.942102 | − | 0.335328i | \(-0.891153\pi\) | ||
0.942102 | − | 0.335328i | \(-0.108847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.2347 | −1.15191 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.84310 | 0.288916 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.5749i | 1.07785i | 0.842352 | + | 0.538927i | \(0.181170\pi\) | ||||
−0.842352 | + | 0.538927i | \(0.818830\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.06836 | + | 25.7492i | 0.381509 | + | 1.08328i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 8.07965i | − | 0.339313i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.3662 | 0.769951 | 0.384976 | − | 0.922927i | \(-0.374210\pi\) | ||||
0.384976 | + | 0.922927i | \(0.374210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.9078 | −1.87933 | −0.939667 | − | 0.342091i | \(-0.888865\pi\) | ||||
−0.939667 | + | 0.342091i | \(0.888865\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.02811i | 0.210052i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.25088 | − | 5.28655i | −0.177274 | − | 0.220464i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.84216i | − | 0.118321i | −0.998248 | − | 0.0591604i | \(-0.981158\pi\) | ||
0.998248 | − | 0.0591604i | \(-0.0188423\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.74420 | 0.280279 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.2978 | −0.634661 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.09275i | 0.0866728i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.6195 | + | 35.8324i | 0.521751 | + | 1.48149i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 9.16111i | − | 0.378119i | −0.981966 | − | 0.189060i | \(-0.939456\pi\) | ||
0.981966 | − | 0.189060i | \(-0.0605440\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.0320 | −0.949019 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.88238 | 0.200834 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.8676i | 1.76036i | 0.474639 | + | 0.880181i | \(0.342579\pi\) | ||||
−0.474639 | + | 0.880181i | \(0.657421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.2453 | + | 3.60819i | −0.420015 | + | 0.147921i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 3.77307i | − | 0.154422i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.6019 | 0.474039 | 0.237020 | − | 0.971505i | \(-0.423829\pi\) | ||||
0.237020 | + | 0.971505i | \(0.423829\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.5066 | 1.65230 | 0.826148 | − | 0.563453i | \(-0.190527\pi\) | ||||
0.826148 | + | 0.563453i | \(0.190527\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 10.9869i | − | 0.447421i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.2589 | + | 6.07826i | −0.701675 | + | 0.247116i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.10345i | − | 0.0853764i | −0.999088 | − | 0.0426882i | \(-0.986408\pi\) | ||
0.999088 | − | 0.0426882i | \(-0.0135922\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.173627 | 0.00703574 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −60.6069 | −2.45189 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 44.1721i | − | 1.78409i | −0.451943 | − | 0.892047i | \(-0.649269\pi\) | ||
0.451943 | − | 0.892047i | \(-0.350731\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.631495 | + | 1.79310i | 0.0254643 | + | 0.0723047i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 33.5011i | − | 1.34870i | −0.738410 | − | 0.674352i | \(-0.764423\pi\) | ||
0.738410 | − | 0.674352i | \(-0.235577\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.4117 | −1.22235 | −0.611174 | − | 0.791496i | \(-0.709302\pi\) | ||||
−0.611174 | + | 0.791496i | \(0.709302\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.57310 | −0.103255 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.00000i | 0.240385i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.36620 | − | 24.4173i | 0.214648 | − | 0.976692i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.9204i | 0.436117i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.4400 | −1.21372 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.99798 | −0.398013 | −0.199007 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199007 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.453098i | 0.0180090i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.79633 | + | 19.2978i | 0.269704 | + | 0.765811i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.86542i | 0.232396i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.7569 | 1.05849 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.79310 | 0.307809 | 0.153904 | − | 0.988086i | \(-0.450815\pi\) | ||||
0.153904 | + | 0.988086i | \(0.450815\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 31.0351i | − | 1.22390i | −0.790895 | − | 0.611952i | \(-0.790384\pi\) | ||
0.790895 | − | 0.611952i | \(-0.209616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.14982 | − | 1.10931i | 0.124024 | − | 0.0436789i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.2771i | 0.875802i | 0.899023 | + | 0.437901i | \(0.144278\pi\) | ||||
−0.899023 | + | 0.437901i | \(0.855722\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.9524 | 1.33275 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.955625 | −0.0374539 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 7.47995i | − | 0.292713i | −0.989232 | − | 0.146356i | \(-0.953245\pi\) | ||
0.989232 | − | 0.146356i | \(-0.0467547\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.8246 | + | 12.2646i | −1.36071 | + | 0.479216i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.38401i | 0.0539953i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.54904 | 0.255114 | 0.127557 | − | 0.991831i | \(-0.459286\pi\) | ||||
0.127557 | + | 0.991831i | \(0.459286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.9637 | −1.47662 | −0.738308 | − | 0.674464i | \(-0.764375\pi\) | ||||
−0.738308 | + | 0.674464i | \(0.764375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 9.16416i | − | 0.355906i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.75801 | − | 16.3496i | −0.223286 | − | 0.634010i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.732393i | 0.0283584i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.48275 | 0.0573263 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.1770 | −1.28078 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.12481i | − | 0.120453i | −0.998185 | − | 0.0602263i | \(-0.980818\pi\) | ||
0.998185 | − | 0.0602263i | \(-0.0191822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.94226 | − | 7.39000i | −0.228718 | − | 0.284441i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.4137i | 0.784562i | 0.919845 | + | 0.392281i | \(0.128314\pi\) | ||||
−0.919845 | + | 0.392281i | \(0.871686\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.6174 | −0.522587 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.84894 | 0.0708517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 9.63380i | − | 0.368627i | −0.982867 | − | 0.184314i | \(-0.940994\pi\) | ||
0.982867 | − | 0.184314i | \(-0.0590062\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.50655 | − | 18.4750i | −0.248603 | − | 0.705895i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5.63017i | − | 0.214805i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.80257 | 0.106769 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.4384 | −0.777514 | −0.388757 | − | 0.921340i | \(-0.627095\pi\) | ||||
−0.388757 | + | 0.921340i | \(0.627095\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 12.6865i | − | 0.481919i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.6005 | + | 7.25509i | −0.781420 | + | 0.275201i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.8401i | 0.486355i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.94226 | −0.224757 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.4733 | −0.471109 | −0.235555 | − | 0.971861i | \(-0.575691\pi\) | ||||
−0.235555 | + | 0.971861i | \(0.575691\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 48.5767i | − | 1.83211i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.00947 | − | 2.46860i | 0.263992 | − | 0.0929729i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.28836i | 0.236498i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.7788 | 1.19348 | 0.596738 | − | 0.802436i | \(-0.296463\pi\) | ||||
0.596738 | + | 0.802436i | \(0.296463\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.46444 | 0.204933 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.03101i | − | 0.150962i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.0818 | + | 54.1819i | 0.713619 | + | 2.02629i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.36435i | 0.0882982i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.4905 | 0.764168 | 0.382084 | − | 0.924128i | \(-0.375207\pi\) | ||||
0.382084 | + | 0.924128i | \(0.375207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.25328 | −0.344610 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.13088i | 0.0420580i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.10345 | + | 1.69137i | −0.0781202 | + | 0.0628160i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8822i | 1.47915i | 0.673074 | + | 0.739575i | \(0.264973\pi\) | ||||
−0.673074 | + | 0.739575i | \(0.735027\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.5731 | 0.799004 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.5555 | 0.834244 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.4559i | − | 0.460070i | −0.973182 | − | 0.230035i | \(-0.926116\pi\) | ||
0.973182 | − | 0.230035i | \(-0.0738841\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.238906 | − | 0.678363i | −0.00881219 | − | 0.0250218i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 16.6132i | − | 0.611955i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.5258 | 1.23327 | 0.616634 | − | 0.787250i | \(-0.288496\pi\) | ||||
0.616634 | + | 0.787250i | \(0.288496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.6243 | 0.537238 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.72292i | − | 0.136581i | −0.997665 | − | 0.0682904i | \(-0.978246\pi\) | ||
0.997665 | − | 0.0682904i | \(-0.0217544\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.2408 | + | 16.9895i | −1.76740 | + | 0.622446i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 44.3109i | − | 1.62125i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.5862 | −0.569507 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.5991 | −1.08009 | −0.540043 | − | 0.841637i | \(-0.681592\pi\) | ||||
−0.540043 | + | 0.841637i | \(0.681592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.84506i | 0.0672375i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.9789 | − | 11.9667i | 1.23662 | − | 0.435514i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4.66250i | − | 0.169461i | −0.996404 | − | 0.0847307i | \(-0.972997\pi\) | ||
0.996404 | − | 0.0847307i | \(-0.0270030\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.91125 | −0.0693740 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.5160 | −0.997455 | −0.498727 | − | 0.866759i | \(-0.666199\pi\) | ||||
−0.498727 | + | 0.866759i | \(0.666199\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 11.2533i | − | 0.407396i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.4513 | − | 29.6759i | −0.377867 | − | 1.07294i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 45.4684i | − | 1.64177i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.8026 | −0.605916 | −0.302958 | − | 0.953004i | \(-0.597974\pi\) | ||||
−0.302958 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.78857 | −0.208470 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.6695i | 0.491657i | 0.969313 | + | 0.245829i | \(0.0790601\pi\) | ||||
−0.969313 | + | 0.245829i | \(0.920940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.5771 | − | 9.30912i | 0.415863 | − | 0.334393i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.01550i | − | 0.0723058i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.4905 | −0.734150 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.4589 | 1.44773 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.02380i | 0.0365877i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.393629 | − | 1.11769i | −0.0140492 | − | 0.0398921i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 5.81509i | − | 0.207285i | −0.994615 | − | 0.103643i | \(-0.966950\pi\) | ||
0.994615 | − | 0.103643i | \(-0.0330499\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.42690 | −0.193203 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.2086 | −0.434089 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.4300i | 1.57776i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.324130 | + | 0.114152i | −0.0114957 | + | 0.00404857i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.6907i | 1.40592i | 0.711232 | + | 0.702958i | \(0.248138\pi\) | ||||
−0.711232 | + | 0.702958i | \(0.751862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.1939 | 1.77573 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.3793 | −0.614067 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.09275i | 0.0738515i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.86146 | − | 1.00775i | 0.100853 | − | 0.0355186i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 8.32222i | − | 0.292956i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.6765 | 0.586316 | 0.293158 | − | 0.956064i | \(-0.405294\pi\) | ||||
0.293158 | + | 0.956064i | \(0.405294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.2981 | 0.537189 | 0.268594 | − | 0.963253i | \(-0.413441\pi\) | ||||
0.268594 | + | 0.963253i | \(0.413441\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8.75970i | − | 0.307216i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.9817 | + | 45.3793i | 0.559815 | + | 1.58957i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.9944i | 1.25929i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.9895 | −0.593660 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.9097 | 0.729752 | 0.364876 | − | 0.931056i | \(-0.381111\pi\) | ||||
0.364876 | + | 0.931056i | \(0.381111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.9048i | 1.80929i | 0.426169 | + | 0.904644i | \(0.359863\pi\) | ||||
−0.426169 | + | 0.904644i | \(0.640137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.41380 | − | 5.48916i | −0.153669 | − | 0.191108i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.63380i | 0.195907i | 0.995191 | + | 0.0979533i | \(0.0312296\pi\) | ||||
−0.995191 | + | 0.0979533i | \(0.968770\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.8044 | −0.965686 | −0.482843 | − | 0.875707i | \(-0.660396\pi\) | ||||
−0.482843 | + | 0.875707i | \(0.660396\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.69983 | 0.267104 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4.85766i | − | 0.168308i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.82879 | − | 22.2295i | −0.270927 | − | 0.769283i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 5.63489i | − | 0.194770i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.61939 | −0.124955 | −0.0624776 | − | 0.998046i | \(-0.519900\pi\) | ||||
−0.0624776 | + | 0.998046i | \(0.519900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7086 | −0.989951 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.28778i | 0.216563i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.1411 | − | 15.8978i | 1.55290 | − | 0.546902i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.18310i | − | 0.281175i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.94415 | 0.341283 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.50177 | 0.291437 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 57.9705i | 1.98487i | 0.122758 | + | 0.992437i | \(0.460826\pi\) | ||||
−0.122758 | + | 0.992437i | \(0.539174\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 47.3574 | − | 16.6784i | 1.61959 | − | 0.570388i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.09720i | 0.139958i | 0.997548 | + | 0.0699789i | \(0.0222932\pi\) | ||||
−0.997548 | + | 0.0699789i | \(0.977707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.96551 | 0.305899 | 0.152950 | − | 0.988234i | \(-0.451123\pi\) | ||||
0.152950 | + | 0.988234i | \(0.451123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.850175 | −0.0289739 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 48.4589i | − | 1.64956i | −0.565453 | − | 0.824781i | \(-0.691298\pi\) | ||
0.565453 | − | 0.824781i | \(-0.308702\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.77053 | − | 24.9035i | −0.298207 | − | 0.846744i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.12181i | 0.0720604i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.26275 | 0.280294 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.2481 | −0.753848 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 39.4434i | − | 1.33496i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.50248 | + | 5.89091i | 0.321243 | + | 0.199149i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.5589i | 0.930597i | 0.885154 | + | 0.465298i | \(0.154053\pi\) | ||||
−0.885154 | + | 0.465298i | \(0.845947\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.10010 | −0.104564 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.2389 | −0.715558 | −0.357779 | − | 0.933806i | \(-0.616466\pi\) | ||||
−0.357779 | + | 0.933806i | \(0.616466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.9204i | − | 0.367499i | −0.982973 | − | 0.183750i | \(-0.941176\pi\) | ||
0.982973 | − | 0.183750i | \(-0.0588235\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.85199 | + | 5.25864i | 0.0622540 | + | 0.176767i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.5898i | 1.39645i | 0.715878 | + | 0.698225i | \(0.246026\pi\) | ||||
−0.715878 | + | 0.698225i | \(0.753974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.14982 | −0.306875 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.3877 | 1.18553 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 80.1003i | 2.68045i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.9656 | − | 13.7229i | 1.30248 | − | 0.458707i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.55951i | 0.0854596i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.60389 | −0.0534926 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.32105 | −0.0773255 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.49345i | 0.0496989i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.2533 | − | 3.61101i | 0.340830 | − | 0.120034i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 11.8596i | − | 0.393793i | −0.980424 | − | 0.196897i | \(-0.936914\pi\) | ||
0.980424 | − | 0.196897i | \(-0.0630863\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.2146 | −0.604139 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0522 | 0.995673 | 0.497837 | − | 0.867271i | \(-0.334128\pi\) | ||||
0.497837 | + | 0.867271i | \(0.334128\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 67.0022i | − | 2.21745i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.80969 | − | 5.13854i | −0.0598267 | − | 0.169875i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 16.5117i | − | 0.545263i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.5751 | −0.711698 | −0.355849 | − | 0.934544i | \(-0.615808\pi\) | ||||
−0.355849 | + | 0.934544i | \(0.615808\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.48275 | 0.114760 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 54.1819i | − | 1.78342i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.6338 | + | 24.4173i | 0.645555 | + | 0.802835i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 26.8026i | − | 0.880312i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.7229 | 0.778324 | 0.389162 | − | 0.921169i | \(-0.372765\pi\) | ||||
0.389162 | + | 0.921169i | \(0.372765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.75195 | 0.254060 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.12481i | 0.102302i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.8033 | − | 44.8727i | −0.516824 | − | 1.46750i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.8154i | 0.418662i | 0.977845 | + | 0.209331i | \(0.0671286\pi\) | ||||
−0.977845 | + | 0.209331i | \(0.932871\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.56241 | 0.0509872 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.0339 | 1.30507 | 0.652533 | − | 0.757760i | \(-0.273706\pi\) | ||||
0.652533 | + | 0.757760i | \(0.273706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.58620i | − | 0.116783i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00000 | − | 1.40872i | 0.130120 | − | 0.0458258i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.8822i | 1.03603i | 0.855371 | + | 0.518016i | \(0.173329\pi\) | ||||
−0.855371 | + | 0.518016i | \(0.826671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.80257 | 0.0909753 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.69477 | −0.217093 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.5138i | 1.73348i | 0.498757 | + | 0.866742i | \(0.333790\pi\) | ||||
−0.498757 | + | 0.866742i | \(0.666210\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.9712 | − | 11.6118i | 1.06692 | − | 0.375750i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.760462i | 0.0245823i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.75970 | 0.282866 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.1724 | −0.715239 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 45.1462i | − | 1.45482i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.5749 | − | 44.2242i | −0.501374 | − | 1.42363i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.2295i | − | 0.714852i | −0.933942 | − | 0.357426i | \(-0.883654\pi\) | ||
0.933942 | − | 0.357426i | \(-0.116346\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.1117 | −0.389084 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.0888 | −0.901413 | −0.450706 | − | 0.892672i | \(-0.648828\pi\) | ||||
−0.450706 | + | 0.892672i | \(0.648828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 9.76745i | − | 0.313130i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.35098 | + | 5.91088i | −0.235420 | + | 0.189300i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.75970i | 0.280248i | 0.990134 | + | 0.140124i | \(0.0447501\pi\) | ||||
−0.990134 | + | 0.140124i | \(0.955250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.2791 | −0.839884 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.5957 | 1.04070 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 34.7467i | − | 1.10825i | −0.832434 | − | 0.554124i | \(-0.813053\pi\) | ||
0.832434 | − | 0.554124i | \(-0.186947\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2753 | − | 32.0156i | −0.359260 | − | 1.02010i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.32345i | 0.105787i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.29965 | −0.200317 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.1798 | −0.482201 | −0.241101 | − | 0.970500i | \(-0.577508\pi\) | ||||
−0.241101 | + | 0.970500i | \(0.577508\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 5.29400i | − | 0.168000i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.7414 | + | 8.71345i | −0.784356 | + | 0.276235i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 55.3483i | − | 1.75290i | −0.481496 | − | 0.876448i | \(-0.659906\pi\) | ||
0.481496 | − | 0.876448i | \(-0.340094\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.8845 | 0.376009 |
(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 | 2240.2.g.p.449.6 | 12 | ||
4.3 | odd | 2 | inner | 2240.2.g.p.449.8 | 12 | ||
5.4 | even | 2 | inner | 2240.2.g.p.449.7 | 12 | ||
8.3 | odd | 2 | 1120.2.g.d.449.5 | ✓ | 12 | ||
8.5 | even | 2 | 1120.2.g.d.449.7 | yes | 12 | ||
20.19 | odd | 2 | inner | 2240.2.g.p.449.5 | 12 | ||
40.3 | even | 4 | 5600.2.a.bz.1.4 | 6 | |||
40.13 | odd | 4 | 5600.2.a.by.1.3 | 6 | |||
40.19 | odd | 2 | 1120.2.g.d.449.8 | yes | 12 | ||
40.27 | even | 4 | 5600.2.a.by.1.4 | 6 | |||
40.29 | even | 2 | 1120.2.g.d.449.6 | yes | 12 | ||
40.37 | odd | 4 | 5600.2.a.bz.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.g.d.449.5 | ✓ | 12 | 8.3 | odd | 2 | ||
1120.2.g.d.449.6 | yes | 12 | 40.29 | even | 2 | ||
1120.2.g.d.449.7 | yes | 12 | 8.5 | even | 2 | ||
1120.2.g.d.449.8 | yes | 12 | 40.19 | odd | 2 | ||
2240.2.g.p.449.5 | 12 | 20.19 | odd | 2 | inner | ||
2240.2.g.p.449.6 | 12 | 1.1 | even | 1 | trivial | ||
2240.2.g.p.449.7 | 12 | 5.4 | even | 2 | inner | ||
2240.2.g.p.449.8 | 12 | 4.3 | odd | 2 | inner | ||
5600.2.a.by.1.3 | 6 | 40.13 | odd | 4 | |||
5600.2.a.by.1.4 | 6 | 40.27 | even | 4 | |||
5600.2.a.bz.1.3 | 6 | 40.37 | odd | 4 | |||
5600.2.a.bz.1.4 | 6 | 40.3 | even | 4 |