Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.a (trivial) |
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: | yes |
Analytic conductor: | \(27.5483886973\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 690) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.622216 | −0.235175 | −0.117588 | − | 0.993063i | \(-0.537516\pi\) | ||||
−0.117588 | + | 0.993063i | \(0.537516\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.42864 | 1.33529 | 0.667643 | − | 0.744482i | \(-0.267303\pi\) | ||||
0.667643 | + | 0.744482i | \(0.267303\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.37778 | −0.382129 | −0.191064 | − | 0.981578i | \(-0.561194\pi\) | ||||
−0.191064 | + | 0.981578i | \(0.561194\pi\) | |||||||
\(14\) | 0.622216 | 0.166294 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.42864 | −1.55917 | −0.779587 | − | 0.626294i | \(-0.784571\pi\) | ||||
−0.779587 | + | 0.626294i | \(0.784571\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.37778 | −0.316085 | −0.158043 | − | 0.987432i | \(-0.550518\pi\) | ||||
−0.158043 | + | 0.987432i | \(0.550518\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.622216 | −0.135779 | ||||||||
\(22\) | −4.42864 | −0.944189 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.37778 | 0.270206 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.622216 | −0.117588 | ||||||||
\(29\) | −4.23506 | −0.786432 | −0.393216 | − | 0.919446i | \(-0.628637\pi\) | ||||
−0.393216 | + | 0.919446i | \(0.628637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.42864 | 0.770927 | ||||||||
\(34\) | 6.42864 | 1.10250 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −11.8064 | −1.94096 | −0.970482 | − | 0.241173i | \(-0.922468\pi\) | ||||
−0.970482 | + | 0.241173i | \(0.922468\pi\) | |||||||
\(38\) | 1.37778 | 0.223506 | ||||||||
\(39\) | −1.37778 | −0.220622 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8573 | −1.69562 | −0.847811 | − | 0.530298i | \(-0.822080\pi\) | ||||
−0.847811 | + | 0.530298i | \(0.822080\pi\) | |||||||
\(42\) | 0.622216 | 0.0960100 | ||||||||
\(43\) | 1.05086 | 0.160254 | 0.0801270 | − | 0.996785i | \(-0.474467\pi\) | ||||
0.0801270 | + | 0.996785i | \(0.474467\pi\) | |||||||
\(44\) | 4.42864 | 0.667643 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 11.6128 | 1.69391 | 0.846954 | − | 0.531666i | \(-0.178434\pi\) | ||||
0.846954 | + | 0.531666i | \(0.178434\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.61285 | −0.944693 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.42864 | −0.900190 | ||||||||
\(52\) | −1.37778 | −0.191064 | ||||||||
\(53\) | −3.37778 | −0.463974 | −0.231987 | − | 0.972719i | \(-0.574523\pi\) | ||||
−0.231987 | + | 0.972719i | \(0.574523\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.622216 | 0.0831471 | ||||||||
\(57\) | −1.37778 | −0.182492 | ||||||||
\(58\) | 4.23506 | 0.556091 | ||||||||
\(59\) | 9.61285 | 1.25149 | 0.625743 | − | 0.780029i | \(-0.284796\pi\) | ||||
0.625743 | + | 0.780029i | \(0.284796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.66370 | 1.10927 | 0.554637 | − | 0.832093i | \(-0.312857\pi\) | ||||
0.554637 | + | 0.832093i | \(0.312857\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | −0.622216 | −0.0783918 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.42864 | −0.545128 | ||||||||
\(67\) | −11.8064 | −1.44238 | −0.721192 | − | 0.692735i | \(-0.756406\pi\) | ||||
−0.721192 | + | 0.692735i | \(0.756406\pi\) | |||||||
\(68\) | −6.42864 | −0.779587 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.99063 | −0.829635 | −0.414818 | − | 0.909905i | \(-0.636155\pi\) | ||||
−0.414818 | + | 0.909905i | \(0.636155\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.75557 | −0.322515 | −0.161257 | − | 0.986912i | \(-0.551555\pi\) | ||||
−0.161257 | + | 0.986912i | \(0.551555\pi\) | |||||||
\(74\) | 11.8064 | 1.37247 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.37778 | −0.158043 | ||||||||
\(77\) | −2.75557 | −0.314026 | ||||||||
\(78\) | 1.37778 | 0.156003 | ||||||||
\(79\) | 12.0415 | 1.35477 | 0.677387 | − | 0.735627i | \(-0.263112\pi\) | ||||
0.677387 | + | 0.735627i | \(0.263112\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.8573 | 1.19899 | ||||||||
\(83\) | −2.19358 | −0.240776 | −0.120388 | − | 0.992727i | \(-0.538414\pi\) | ||||
−0.120388 | + | 0.992727i | \(0.538414\pi\) | |||||||
\(84\) | −0.622216 | −0.0678893 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.05086 | −0.113317 | ||||||||
\(87\) | −4.23506 | −0.454046 | ||||||||
\(88\) | −4.42864 | −0.472095 | ||||||||
\(89\) | 2.75557 | 0.292090 | 0.146045 | − | 0.989278i | \(-0.453346\pi\) | ||||
0.146045 | + | 0.989278i | \(0.453346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.857279 | 0.0898673 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −4.00000 | −0.414781 | ||||||||
\(94\) | −11.6128 | −1.19777 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 2.13335 | 0.216609 | 0.108305 | − | 0.994118i | \(-0.465458\pi\) | ||||
0.108305 | + | 0.994118i | \(0.465458\pi\) | |||||||
\(98\) | 6.61285 | 0.667998 | ||||||||
\(99\) | 4.42864 | 0.445095 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.2351 | 1.61545 | 0.807725 | − | 0.589560i | \(-0.200699\pi\) | ||||
0.807725 | + | 0.589560i | \(0.200699\pi\) | |||||||
\(102\) | 6.42864 | 0.636530 | ||||||||
\(103\) | −12.2351 | −1.20556 | −0.602778 | − | 0.797909i | \(-0.705940\pi\) | ||||
−0.602778 | + | 0.797909i | \(0.705940\pi\) | |||||||
\(104\) | 1.37778 | 0.135103 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.37778 | 0.328079 | ||||||||
\(107\) | 10.6637 | 1.03090 | 0.515450 | − | 0.856920i | \(-0.327625\pi\) | ||||
0.515450 | + | 0.856920i | \(0.327625\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −15.1526 | −1.45135 | −0.725676 | − | 0.688036i | \(-0.758473\pi\) | ||||
−0.725676 | + | 0.688036i | \(0.758473\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.8064 | −1.12062 | ||||||||
\(112\) | −0.622216 | −0.0587939 | ||||||||
\(113\) | −14.4286 | −1.35733 | −0.678666 | − | 0.734447i | \(-0.737442\pi\) | ||||
−0.678666 | + | 0.734447i | \(0.737442\pi\) | |||||||
\(114\) | 1.37778 | 0.129041 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.23506 | −0.393216 | ||||||||
\(117\) | −1.37778 | −0.127376 | ||||||||
\(118\) | −9.61285 | −0.884934 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.61285 | 0.782986 | ||||||||
\(122\) | −8.66370 | −0.784375 | ||||||||
\(123\) | −10.8573 | −0.978968 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.622216 | 0.0554314 | ||||||||
\(127\) | 4.99063 | 0.442847 | 0.221423 | − | 0.975178i | \(-0.428930\pi\) | ||||
0.221423 | + | 0.975178i | \(0.428930\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.05086 | 0.0925226 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.755569 | 0.0660143 | 0.0330072 | − | 0.999455i | \(-0.489492\pi\) | ||||
0.0330072 | + | 0.999455i | \(0.489492\pi\) | |||||||
\(132\) | 4.42864 | 0.385464 | ||||||||
\(133\) | 0.857279 | 0.0743355 | ||||||||
\(134\) | 11.8064 | 1.01992 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.42864 | 0.551251 | ||||||||
\(137\) | −12.9175 | −1.10362 | −0.551808 | − | 0.833971i | \(-0.686062\pi\) | ||||
−0.551808 | + | 0.833971i | \(0.686062\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −14.1017 | −1.19609 | −0.598046 | − | 0.801462i | \(-0.704056\pi\) | ||||
−0.598046 | + | 0.801462i | \(0.704056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.6128 | 0.977978 | ||||||||
\(142\) | 6.99063 | 0.586641 | ||||||||
\(143\) | −6.10171 | −0.510251 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.75557 | 0.228052 | ||||||||
\(147\) | −6.61285 | −0.545418 | ||||||||
\(148\) | −11.8064 | −0.970482 | ||||||||
\(149\) | 12.4286 | 1.01819 | 0.509097 | − | 0.860709i | \(-0.329979\pi\) | ||||
0.509097 | + | 0.860709i | \(0.329979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.85728 | −0.395280 | −0.197640 | − | 0.980275i | \(-0.563328\pi\) | ||||
−0.197640 | + | 0.980275i | \(0.563328\pi\) | |||||||
\(152\) | 1.37778 | 0.111753 | ||||||||
\(153\) | −6.42864 | −0.519725 | ||||||||
\(154\) | 2.75557 | 0.222050 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.37778 | −0.110311 | ||||||||
\(157\) | 9.90813 | 0.790755 | 0.395378 | − | 0.918519i | \(-0.370614\pi\) | ||||
0.395378 | + | 0.918519i | \(0.370614\pi\) | |||||||
\(158\) | −12.0415 | −0.957969 | ||||||||
\(159\) | −3.37778 | −0.267876 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.622216 | 0.0490375 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −10.1017 | −0.791227 | −0.395614 | − | 0.918417i | \(-0.629468\pi\) | ||||
−0.395614 | + | 0.918417i | \(0.629468\pi\) | |||||||
\(164\) | −10.8573 | −0.847811 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.19358 | 0.170255 | ||||||||
\(167\) | −1.89829 | −0.146894 | −0.0734470 | − | 0.997299i | \(-0.523400\pi\) | ||||
−0.0734470 | + | 0.997299i | \(0.523400\pi\) | |||||||
\(168\) | 0.622216 | 0.0480050 | ||||||||
\(169\) | −11.1017 | −0.853978 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.37778 | −0.105362 | ||||||||
\(172\) | 1.05086 | 0.0801270 | ||||||||
\(173\) | −21.2257 | −1.61376 | −0.806880 | − | 0.590716i | \(-0.798846\pi\) | ||||
−0.806880 | + | 0.590716i | \(0.798846\pi\) | |||||||
\(174\) | 4.23506 | 0.321059 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.42864 | 0.333821 | ||||||||
\(177\) | 9.61285 | 0.722546 | ||||||||
\(178\) | −2.75557 | −0.206539 | ||||||||
\(179\) | 0.488863 | 0.0365393 | 0.0182697 | − | 0.999833i | \(-0.494184\pi\) | ||||
0.0182697 | + | 0.999833i | \(0.494184\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.9304 | −1.55575 | −0.777873 | − | 0.628422i | \(-0.783701\pi\) | ||||
−0.777873 | + | 0.628422i | \(0.783701\pi\) | |||||||
\(182\) | −0.857279 | −0.0635457 | ||||||||
\(183\) | 8.66370 | 0.640439 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | −28.4701 | −2.08194 | ||||||||
\(188\) | 11.6128 | 0.846954 | ||||||||
\(189\) | −0.622216 | −0.0452595 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9590 | 1.37182 | 0.685912 | − | 0.727684i | \(-0.259403\pi\) | ||||
0.685912 | + | 0.727684i | \(0.259403\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 1.24443 | 0.0895761 | 0.0447881 | − | 0.998997i | \(-0.485739\pi\) | ||||
0.0447881 | + | 0.998997i | \(0.485739\pi\) | |||||||
\(194\) | −2.13335 | −0.153166 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.61285 | −0.472346 | ||||||||
\(197\) | 15.2444 | 1.08612 | 0.543060 | − | 0.839694i | \(-0.317265\pi\) | ||||
0.543060 | + | 0.839694i | \(0.317265\pi\) | |||||||
\(198\) | −4.42864 | −0.314730 | ||||||||
\(199\) | −14.5303 | −1.03003 | −0.515015 | − | 0.857181i | \(-0.672214\pi\) | ||||
−0.515015 | + | 0.857181i | \(0.672214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.8064 | −0.832761 | ||||||||
\(202\) | −16.2351 | −1.14230 | ||||||||
\(203\) | 2.63512 | 0.184949 | ||||||||
\(204\) | −6.42864 | −0.450095 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.2351 | 0.852457 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −1.37778 | −0.0955322 | ||||||||
\(209\) | −6.10171 | −0.422064 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.266706 | 0.0183608 | 0.00918041 | − | 0.999958i | \(-0.497078\pi\) | ||||
0.00918041 | + | 0.999958i | \(0.497078\pi\) | |||||||
\(212\) | −3.37778 | −0.231987 | ||||||||
\(213\) | −6.99063 | −0.478990 | ||||||||
\(214\) | −10.6637 | −0.728956 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 2.48886 | 0.168955 | ||||||||
\(218\) | 15.1526 | 1.02626 | ||||||||
\(219\) | −2.75557 | −0.186204 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.85728 | 0.595805 | ||||||||
\(222\) | 11.8064 | 0.792395 | ||||||||
\(223\) | 0.990632 | 0.0663376 | 0.0331688 | − | 0.999450i | \(-0.489440\pi\) | ||||
0.0331688 | + | 0.999450i | \(0.489440\pi\) | |||||||
\(224\) | 0.622216 | 0.0415735 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.4286 | 0.959779 | ||||||||
\(227\) | 17.1526 | 1.13846 | 0.569228 | − | 0.822180i | \(-0.307242\pi\) | ||||
0.569228 | + | 0.822180i | \(0.307242\pi\) | |||||||
\(228\) | −1.37778 | −0.0912460 | ||||||||
\(229\) | 7.15257 | 0.472655 | 0.236327 | − | 0.971673i | \(-0.424056\pi\) | ||||
0.236327 | + | 0.971673i | \(0.424056\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.75557 | −0.181303 | ||||||||
\(232\) | 4.23506 | 0.278046 | ||||||||
\(233\) | 3.71456 | 0.243349 | 0.121674 | − | 0.992570i | \(-0.461174\pi\) | ||||
0.121674 | + | 0.992570i | \(0.461174\pi\) | |||||||
\(234\) | 1.37778 | 0.0900686 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.61285 | 0.625743 | ||||||||
\(237\) | 12.0415 | 0.782179 | ||||||||
\(238\) | −4.00000 | −0.259281 | ||||||||
\(239\) | 27.8479 | 1.80133 | 0.900666 | − | 0.434512i | \(-0.143079\pi\) | ||||
0.900666 | + | 0.434512i | \(0.143079\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.12399 | −0.458896 | −0.229448 | − | 0.973321i | \(-0.573692\pi\) | ||||
−0.229448 | + | 0.973321i | \(0.573692\pi\) | |||||||
\(242\) | −8.61285 | −0.553655 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 8.66370 | 0.554637 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.8573 | 0.692235 | ||||||||
\(247\) | 1.89829 | 0.120785 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −2.19358 | −0.139012 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.4099 | −1.41450 | −0.707250 | − | 0.706963i | \(-0.750065\pi\) | ||||
−0.707250 | + | 0.706963i | \(0.750065\pi\) | |||||||
\(252\) | −0.622216 | −0.0391959 | ||||||||
\(253\) | −4.42864 | −0.278426 | ||||||||
\(254\) | −4.99063 | −0.313140 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.7146 | −0.730734 | −0.365367 | − | 0.930864i | \(-0.619057\pi\) | ||||
−0.365367 | + | 0.930864i | \(0.619057\pi\) | |||||||
\(258\) | −1.05086 | −0.0654234 | ||||||||
\(259\) | 7.34614 | 0.456467 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.23506 | −0.262144 | ||||||||
\(262\) | −0.755569 | −0.0466792 | ||||||||
\(263\) | −8.47013 | −0.522290 | −0.261145 | − | 0.965300i | \(-0.584100\pi\) | ||||
−0.261145 | + | 0.965300i | \(0.584100\pi\) | |||||||
\(264\) | −4.42864 | −0.272564 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.857279 | −0.0525631 | ||||||||
\(267\) | 2.75557 | 0.168638 | ||||||||
\(268\) | −11.8064 | −0.721192 | ||||||||
\(269\) | 28.8256 | 1.75753 | 0.878765 | − | 0.477255i | \(-0.158368\pi\) | ||||
0.878765 | + | 0.477255i | \(0.158368\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8350 | −0.840417 | −0.420208 | − | 0.907428i | \(-0.638043\pi\) | ||||
−0.420208 | + | 0.907428i | \(0.638043\pi\) | |||||||
\(272\) | −6.42864 | −0.389794 | ||||||||
\(273\) | 0.857279 | 0.0518849 | ||||||||
\(274\) | 12.9175 | 0.780375 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 2.88892 | 0.173578 | 0.0867892 | − | 0.996227i | \(-0.472339\pi\) | ||||
0.0867892 | + | 0.996227i | \(0.472339\pi\) | |||||||
\(278\) | 14.1017 | 0.845764 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.51114 | 0.328767 | 0.164383 | − | 0.986397i | \(-0.447437\pi\) | ||||
0.164383 | + | 0.986397i | \(0.447437\pi\) | |||||||
\(282\) | −11.6128 | −0.691535 | ||||||||
\(283\) | 8.19358 | 0.487058 | 0.243529 | − | 0.969894i | \(-0.421695\pi\) | ||||
0.243529 | + | 0.969894i | \(0.421695\pi\) | |||||||
\(284\) | −6.99063 | −0.414818 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.10171 | 0.360802 | ||||||||
\(287\) | 6.75557 | 0.398769 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 24.3274 | 1.43102 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.13335 | 0.125059 | ||||||||
\(292\) | −2.75557 | −0.161257 | ||||||||
\(293\) | 12.6222 | 0.737398 | 0.368699 | − | 0.929549i | \(-0.379803\pi\) | ||||
0.368699 | + | 0.929549i | \(0.379803\pi\) | |||||||
\(294\) | 6.61285 | 0.385669 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.8064 | 0.686234 | ||||||||
\(297\) | 4.42864 | 0.256976 | ||||||||
\(298\) | −12.4286 | −0.719972 | ||||||||
\(299\) | 1.37778 | 0.0796793 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.653858 | −0.0376878 | ||||||||
\(302\) | 4.85728 | 0.279505 | ||||||||
\(303\) | 16.2351 | 0.932680 | ||||||||
\(304\) | −1.37778 | −0.0790214 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.42864 | 0.367501 | ||||||||
\(307\) | −0.653858 | −0.0373177 | −0.0186588 | − | 0.999826i | \(-0.505940\pi\) | ||||
−0.0186588 | + | 0.999826i | \(0.505940\pi\) | |||||||
\(308\) | −2.75557 | −0.157013 | ||||||||
\(309\) | −12.2351 | −0.696028 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0923 | −0.742399 | −0.371199 | − | 0.928553i | \(-0.621053\pi\) | ||||
−0.371199 | + | 0.928553i | \(0.621053\pi\) | |||||||
\(312\) | 1.37778 | 0.0780017 | ||||||||
\(313\) | 11.2573 | 0.636302 | 0.318151 | − | 0.948040i | \(-0.396938\pi\) | ||||
0.318151 | + | 0.948040i | \(0.396938\pi\) | |||||||
\(314\) | −9.90813 | −0.559148 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0415 | 0.677387 | ||||||||
\(317\) | −22.4701 | −1.26205 | −0.631024 | − | 0.775763i | \(-0.717365\pi\) | ||||
−0.631024 | + | 0.775763i | \(0.717365\pi\) | |||||||
\(318\) | 3.37778 | 0.189417 | ||||||||
\(319\) | −18.7556 | −1.05011 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.6637 | 0.595190 | ||||||||
\(322\) | −0.622216 | −0.0346747 | ||||||||
\(323\) | 8.85728 | 0.492832 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.1017 | 0.559482 | ||||||||
\(327\) | −15.1526 | −0.837939 | ||||||||
\(328\) | 10.8573 | 0.599493 | ||||||||
\(329\) | −7.22570 | −0.398365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.4479 | −1.61860 | −0.809300 | − | 0.587395i | \(-0.800153\pi\) | ||||
−0.809300 | + | 0.587395i | \(0.800153\pi\) | |||||||
\(332\) | −2.19358 | −0.120388 | ||||||||
\(333\) | −11.8064 | −0.646988 | ||||||||
\(334\) | 1.89829 | 0.103870 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.622216 | −0.0339446 | ||||||||
\(337\) | −24.6222 | −1.34126 | −0.670629 | − | 0.741793i | \(-0.733976\pi\) | ||||
−0.670629 | + | 0.741793i | \(0.733976\pi\) | |||||||
\(338\) | 11.1017 | 0.603853 | ||||||||
\(339\) | −14.4286 | −0.783656 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.7146 | −0.959297 | ||||||||
\(342\) | 1.37778 | 0.0745020 | ||||||||
\(343\) | 8.47013 | 0.457344 | ||||||||
\(344\) | −1.05086 | −0.0566583 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.2257 | 1.14110 | ||||||||
\(347\) | 26.1017 | 1.40121 | 0.700607 | − | 0.713548i | \(-0.252913\pi\) | ||||
0.700607 | + | 0.713548i | \(0.252913\pi\) | |||||||
\(348\) | −4.23506 | −0.227023 | ||||||||
\(349\) | −21.2257 | −1.13619 | −0.568093 | − | 0.822965i | \(-0.692319\pi\) | ||||
−0.568093 | + | 0.822965i | \(0.692319\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.37778 | −0.0735407 | ||||||||
\(352\) | −4.42864 | −0.236047 | ||||||||
\(353\) | −4.28544 | −0.228091 | −0.114046 | − | 0.993476i | \(-0.536381\pi\) | ||||
−0.114046 | + | 0.993476i | \(0.536381\pi\) | |||||||
\(354\) | −9.61285 | −0.510917 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.75557 | 0.146045 | ||||||||
\(357\) | 4.00000 | 0.211702 | ||||||||
\(358\) | −0.488863 | −0.0258372 | ||||||||
\(359\) | −4.65386 | −0.245621 | −0.122811 | − | 0.992430i | \(-0.539191\pi\) | ||||
−0.122811 | + | 0.992430i | \(0.539191\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1017 | −0.900090 | ||||||||
\(362\) | 20.9304 | 1.10008 | ||||||||
\(363\) | 8.61285 | 0.452057 | ||||||||
\(364\) | 0.857279 | 0.0449336 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.66370 | −0.452859 | ||||||||
\(367\) | 4.88892 | 0.255200 | 0.127600 | − | 0.991826i | \(-0.459273\pi\) | ||||
0.127600 | + | 0.991826i | \(0.459273\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −10.8573 | −0.565207 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.10171 | 0.109115 | ||||||||
\(372\) | −4.00000 | −0.207390 | ||||||||
\(373\) | 23.4193 | 1.21260 | 0.606302 | − | 0.795235i | \(-0.292652\pi\) | ||||
0.606302 | + | 0.795235i | \(0.292652\pi\) | |||||||
\(374\) | 28.4701 | 1.47216 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.6128 | −0.598887 | ||||||||
\(377\) | 5.83500 | 0.300518 | ||||||||
\(378\) | 0.622216 | 0.0320033 | ||||||||
\(379\) | −4.90766 | −0.252089 | −0.126045 | − | 0.992025i | \(-0.540228\pi\) | ||||
−0.126045 | + | 0.992025i | \(0.540228\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.99063 | 0.255678 | ||||||||
\(382\) | −18.9590 | −0.970026 | ||||||||
\(383\) | −19.8796 | −1.01580 | −0.507899 | − | 0.861417i | \(-0.669578\pi\) | ||||
−0.507899 | + | 0.861417i | \(0.669578\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.24443 | −0.0633399 | ||||||||
\(387\) | 1.05086 | 0.0534180 | ||||||||
\(388\) | 2.13335 | 0.108305 | ||||||||
\(389\) | −0.161933 | −0.00821034 | −0.00410517 | − | 0.999992i | \(-0.501307\pi\) | ||||
−0.00410517 | + | 0.999992i | \(0.501307\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.42864 | 0.325110 | ||||||||
\(392\) | 6.61285 | 0.333999 | ||||||||
\(393\) | 0.755569 | 0.0381134 | ||||||||
\(394\) | −15.2444 | −0.768003 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.42864 | 0.222548 | ||||||||
\(397\) | 1.76494 | 0.0885796 | 0.0442898 | − | 0.999019i | \(-0.485898\pi\) | ||||
0.0442898 | + | 0.999019i | \(0.485898\pi\) | |||||||
\(398\) | 14.5303 | 0.728341 | ||||||||
\(399\) | 0.857279 | 0.0429176 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.3461 | −1.56535 | −0.782676 | − | 0.622430i | \(-0.786146\pi\) | ||||
−0.782676 | + | 0.622430i | \(0.786146\pi\) | |||||||
\(402\) | 11.8064 | 0.588851 | ||||||||
\(403\) | 5.51114 | 0.274529 | ||||||||
\(404\) | 16.2351 | 0.807725 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.63512 | −0.130779 | ||||||||
\(407\) | −52.2864 | −2.59174 | ||||||||
\(408\) | 6.42864 | 0.318265 | ||||||||
\(409\) | −3.51114 | −0.173615 | −0.0868073 | − | 0.996225i | \(-0.527666\pi\) | ||||
−0.0868073 | + | 0.996225i | \(0.527666\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.9175 | −0.637173 | ||||||||
\(412\) | −12.2351 | −0.602778 | ||||||||
\(413\) | −5.98126 | −0.294319 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.37778 | 0.0675514 | ||||||||
\(417\) | −14.1017 | −0.690564 | ||||||||
\(418\) | 6.10171 | 0.298444 | ||||||||
\(419\) | −19.7748 | −0.966061 | −0.483031 | − | 0.875603i | \(-0.660464\pi\) | ||||
−0.483031 | + | 0.875603i | \(0.660464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.8064 | 0.575410 | 0.287705 | − | 0.957719i | \(-0.407108\pi\) | ||||
0.287705 | + | 0.957719i | \(0.407108\pi\) | |||||||
\(422\) | −0.266706 | −0.0129831 | ||||||||
\(423\) | 11.6128 | 0.564636 | ||||||||
\(424\) | 3.37778 | 0.164040 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.99063 | 0.338697 | ||||||||
\(427\) | −5.39069 | −0.260874 | ||||||||
\(428\) | 10.6637 | 0.515450 | ||||||||
\(429\) | −6.10171 | −0.294593 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.9403 | 1.20133 | 0.600665 | − | 0.799501i | \(-0.294903\pi\) | ||||
0.600665 | + | 0.799501i | \(0.294903\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −32.0513 | −1.54029 | −0.770144 | − | 0.637870i | \(-0.779816\pi\) | ||||
−0.770144 | + | 0.637870i | \(0.779816\pi\) | |||||||
\(434\) | −2.48886 | −0.119469 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.1526 | −0.725676 | ||||||||
\(437\) | 1.37778 | 0.0659084 | ||||||||
\(438\) | 2.75557 | 0.131666 | ||||||||
\(439\) | 0.470127 | 0.0224379 | 0.0112190 | − | 0.999937i | \(-0.496429\pi\) | ||||
0.0112190 | + | 0.999937i | \(0.496429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.61285 | −0.314898 | ||||||||
\(442\) | −8.85728 | −0.421298 | ||||||||
\(443\) | −0.653858 | −0.0310658 | −0.0155329 | − | 0.999879i | \(-0.504944\pi\) | ||||
−0.0155329 | + | 0.999879i | \(0.504944\pi\) | |||||||
\(444\) | −11.8064 | −0.560308 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.990632 | −0.0469078 | ||||||||
\(447\) | 12.4286 | 0.587854 | ||||||||
\(448\) | −0.622216 | −0.0293969 | ||||||||
\(449\) | 17.1427 | 0.809015 | 0.404508 | − | 0.914535i | \(-0.367443\pi\) | ||||
0.404508 | + | 0.914535i | \(0.367443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.0830 | −2.26414 | ||||||||
\(452\) | −14.4286 | −0.678666 | ||||||||
\(453\) | −4.85728 | −0.228215 | ||||||||
\(454\) | −17.1526 | −0.805010 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.37778 | 0.0645207 | ||||||||
\(457\) | 1.00937 | 0.0472162 | 0.0236081 | − | 0.999721i | \(-0.492485\pi\) | ||||
0.0236081 | + | 0.999721i | \(0.492485\pi\) | |||||||
\(458\) | −7.15257 | −0.334217 | ||||||||
\(459\) | −6.42864 | −0.300063 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.3180 | 0.946305 | 0.473153 | − | 0.880980i | \(-0.343116\pi\) | ||||
0.473153 | + | 0.880980i | \(0.343116\pi\) | |||||||
\(462\) | 2.75557 | 0.128201 | ||||||||
\(463\) | 12.4572 | 0.578936 | 0.289468 | − | 0.957188i | \(-0.406522\pi\) | ||||
0.289468 | + | 0.957188i | \(0.406522\pi\) | |||||||
\(464\) | −4.23506 | −0.196608 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.71456 | −0.172074 | ||||||||
\(467\) | −15.7877 | −0.730567 | −0.365284 | − | 0.930896i | \(-0.619028\pi\) | ||||
−0.365284 | + | 0.930896i | \(0.619028\pi\) | |||||||
\(468\) | −1.37778 | −0.0636881 | ||||||||
\(469\) | 7.34614 | 0.339213 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.90813 | 0.456543 | ||||||||
\(472\) | −9.61285 | −0.442467 | ||||||||
\(473\) | 4.65386 | 0.213985 | ||||||||
\(474\) | −12.0415 | −0.553084 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | −3.37778 | −0.154658 | ||||||||
\(478\) | −27.8479 | −1.27373 | ||||||||
\(479\) | 5.12399 | 0.234121 | 0.117060 | − | 0.993125i | \(-0.462653\pi\) | ||||
0.117060 | + | 0.993125i | \(0.462653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.2667 | 0.741698 | ||||||||
\(482\) | 7.12399 | 0.324489 | ||||||||
\(483\) | 0.622216 | 0.0283118 | ||||||||
\(484\) | 8.61285 | 0.391493 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −23.2128 | −1.05187 | −0.525936 | − | 0.850524i | \(-0.676285\pi\) | ||||
−0.525936 | + | 0.850524i | \(0.676285\pi\) | |||||||
\(488\) | −8.66370 | −0.392187 | ||||||||
\(489\) | −10.1017 | −0.456815 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40.1847 | −1.81351 | −0.906755 | − | 0.421658i | \(-0.861448\pi\) | ||||
−0.906755 | + | 0.421658i | \(0.861448\pi\) | |||||||
\(492\) | −10.8573 | −0.489484 | ||||||||
\(493\) | 27.2257 | 1.22618 | ||||||||
\(494\) | −1.89829 | −0.0854081 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 4.34968 | 0.195110 | ||||||||
\(498\) | 2.19358 | 0.0982965 | ||||||||
\(499\) | 30.5718 | 1.36858 | 0.684292 | − | 0.729208i | \(-0.260112\pi\) | ||||
0.684292 | + | 0.729208i | \(0.260112\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.89829 | −0.0848093 | ||||||||
\(502\) | 22.4099 | 1.00020 | ||||||||
\(503\) | −23.4291 | −1.04465 | −0.522326 | − | 0.852746i | \(-0.674936\pi\) | ||||
−0.522326 | + | 0.852746i | \(0.674936\pi\) | |||||||
\(504\) | 0.622216 | 0.0277157 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.42864 | 0.196877 | ||||||||
\(507\) | −11.1017 | −0.493044 | ||||||||
\(508\) | 4.99063 | 0.221423 | ||||||||
\(509\) | −17.2128 | −0.762943 | −0.381472 | − | 0.924381i | \(-0.624583\pi\) | ||||
−0.381472 | + | 0.924381i | \(0.624583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.71456 | 0.0758476 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.37778 | −0.0608307 | ||||||||
\(514\) | 11.7146 | 0.516707 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.05086 | 0.0462613 | ||||||||
\(517\) | 51.4291 | 2.26185 | ||||||||
\(518\) | −7.34614 | −0.322771 | ||||||||
\(519\) | −21.2257 | −0.931705 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.3684 | 0.979978 | 0.489989 | − | 0.871729i | \(-0.337001\pi\) | ||||
0.489989 | + | 0.871729i | \(0.337001\pi\) | |||||||
\(522\) | 4.23506 | 0.185364 | ||||||||
\(523\) | 30.2953 | 1.32472 | 0.662360 | − | 0.749186i | \(-0.269555\pi\) | ||||
0.662360 | + | 0.749186i | \(0.269555\pi\) | |||||||
\(524\) | 0.755569 | 0.0330072 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.47013 | 0.369315 | ||||||||
\(527\) | 25.7146 | 1.12014 | ||||||||
\(528\) | 4.42864 | 0.192732 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.61285 | 0.417162 | ||||||||
\(532\) | 0.857279 | 0.0371678 | ||||||||
\(533\) | 14.9590 | 0.647946 | ||||||||
\(534\) | −2.75557 | −0.119245 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.8064 | 0.509960 | ||||||||
\(537\) | 0.488863 | 0.0210960 | ||||||||
\(538\) | −28.8256 | −1.24276 | ||||||||
\(539\) | −29.2859 | −1.26143 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.4479 | 1.35205 | 0.676024 | − | 0.736879i | \(-0.263701\pi\) | ||||
0.676024 | + | 0.736879i | \(0.263701\pi\) | |||||||
\(542\) | 13.8350 | 0.594264 | ||||||||
\(543\) | −20.9304 | −0.898210 | ||||||||
\(544\) | 6.42864 | 0.275626 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.857279 | −0.0366882 | ||||||||
\(547\) | 20.8573 | 0.891793 | 0.445896 | − | 0.895085i | \(-0.352885\pi\) | ||||
0.445896 | + | 0.895085i | \(0.352885\pi\) | |||||||
\(548\) | −12.9175 | −0.551808 | ||||||||
\(549\) | 8.66370 | 0.369758 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.83500 | 0.248580 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −7.49240 | −0.318609 | ||||||||
\(554\) | −2.88892 | −0.122739 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.1017 | −0.598046 | ||||||||
\(557\) | 36.3180 | 1.53884 | 0.769422 | − | 0.638740i | \(-0.220544\pi\) | ||||
0.769422 | + | 0.638740i | \(0.220544\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | −1.44785 | −0.0612376 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.4701 | −1.20201 | ||||||||
\(562\) | −5.51114 | −0.232473 | ||||||||
\(563\) | 2.58073 | 0.108765 | 0.0543824 | − | 0.998520i | \(-0.482681\pi\) | ||||
0.0543824 | + | 0.998520i | \(0.482681\pi\) | |||||||
\(564\) | 11.6128 | 0.488989 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.19358 | −0.344402 | ||||||||
\(567\) | −0.622216 | −0.0261306 | ||||||||
\(568\) | 6.99063 | 0.293320 | ||||||||
\(569\) | −36.3497 | −1.52386 | −0.761929 | − | 0.647661i | \(-0.775747\pi\) | ||||
−0.761929 | + | 0.647661i | \(0.775747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.9309 | −1.92215 | −0.961074 | − | 0.276292i | \(-0.910894\pi\) | ||||
−0.961074 | + | 0.276292i | \(0.910894\pi\) | |||||||
\(572\) | −6.10171 | −0.255125 | ||||||||
\(573\) | 18.9590 | 0.792023 | ||||||||
\(574\) | −6.75557 | −0.281972 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 4.00000 | 0.166522 | 0.0832611 | − | 0.996528i | \(-0.473466\pi\) | ||||
0.0832611 | + | 0.996528i | \(0.473466\pi\) | |||||||
\(578\) | −24.3274 | −1.01189 | ||||||||
\(579\) | 1.24443 | 0.0517168 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.36488 | 0.0566247 | ||||||||
\(582\) | −2.13335 | −0.0884303 | ||||||||
\(583\) | −14.9590 | −0.619538 | ||||||||
\(584\) | 2.75557 | 0.114026 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.6222 | −0.521419 | ||||||||
\(587\) | 42.1847 | 1.74115 | 0.870574 | − | 0.492037i | \(-0.163748\pi\) | ||||
0.870574 | + | 0.492037i | \(0.163748\pi\) | |||||||
\(588\) | −6.61285 | −0.272709 | ||||||||
\(589\) | 5.51114 | 0.227082 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.2444 | 0.627072 | ||||||||
\(592\) | −11.8064 | −0.485241 | ||||||||
\(593\) | 18.7368 | 0.769430 | 0.384715 | − | 0.923036i | \(-0.374300\pi\) | ||||
0.384715 | + | 0.923036i | \(0.374300\pi\) | |||||||
\(594\) | −4.42864 | −0.181709 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.4286 | 0.509097 | ||||||||
\(597\) | −14.5303 | −0.594688 | ||||||||
\(598\) | −1.37778 | −0.0563418 | ||||||||
\(599\) | −41.5625 | −1.69820 | −0.849098 | − | 0.528235i | \(-0.822854\pi\) | ||||
−0.849098 | + | 0.528235i | \(0.822854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7146 | 0.967337 | 0.483668 | − | 0.875251i | \(-0.339304\pi\) | ||||
0.483668 | + | 0.875251i | \(0.339304\pi\) | |||||||
\(602\) | 0.653858 | 0.0266493 | ||||||||
\(603\) | −11.8064 | −0.480795 | ||||||||
\(604\) | −4.85728 | −0.197640 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.2351 | −0.659504 | ||||||||
\(607\) | 2.74266 | 0.111321 | 0.0556606 | − | 0.998450i | \(-0.482274\pi\) | ||||
0.0556606 | + | 0.998450i | \(0.482274\pi\) | |||||||
\(608\) | 1.37778 | 0.0558765 | ||||||||
\(609\) | 2.63512 | 0.106781 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.0000 | −0.647291 | ||||||||
\(612\) | −6.42864 | −0.259862 | ||||||||
\(613\) | −24.0731 | −0.972305 | −0.486152 | − | 0.873874i | \(-0.661600\pi\) | ||||
−0.486152 | + | 0.873874i | \(0.661600\pi\) | |||||||
\(614\) | 0.653858 | 0.0263876 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.75557 | 0.111025 | ||||||||
\(617\) | −39.4893 | −1.58978 | −0.794890 | − | 0.606753i | \(-0.792472\pi\) | ||||
−0.794890 | + | 0.606753i | \(0.792472\pi\) | |||||||
\(618\) | 12.2351 | 0.492166 | ||||||||
\(619\) | −22.6222 | −0.909264 | −0.454632 | − | 0.890679i | \(-0.650229\pi\) | ||||
−0.454632 | + | 0.890679i | \(0.650229\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 13.0923 | 0.524955 | ||||||||
\(623\) | −1.71456 | −0.0686923 | ||||||||
\(624\) | −1.37778 | −0.0551555 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.2573 | −0.449934 | ||||||||
\(627\) | −6.10171 | −0.243679 | ||||||||
\(628\) | 9.90813 | 0.395378 | ||||||||
\(629\) | 75.8992 | 3.02630 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.93978 | 0.236459 | 0.118229 | − | 0.992986i | \(-0.462278\pi\) | ||||
0.118229 | + | 0.992986i | \(0.462278\pi\) | |||||||
\(632\) | −12.0415 | −0.478985 | ||||||||
\(633\) | 0.266706 | 0.0106006 | ||||||||
\(634\) | 22.4701 | 0.892403 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.37778 | −0.133938 | ||||||||
\(637\) | 9.11108 | 0.360994 | ||||||||
\(638\) | 18.7556 | 0.742540 | ||||||||
\(639\) | −6.99063 | −0.276545 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.8163 | 0.782696 | 0.391348 | − | 0.920243i | \(-0.372009\pi\) | ||||
0.391348 | + | 0.920243i | \(0.372009\pi\) | |||||||
\(642\) | −10.6637 | −0.420863 | ||||||||
\(643\) | 44.7467 | 1.76464 | 0.882318 | − | 0.470653i | \(-0.155982\pi\) | ||||
0.882318 | + | 0.470653i | \(0.155982\pi\) | |||||||
\(644\) | 0.622216 | 0.0245187 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.85728 | −0.348485 | ||||||||
\(647\) | 32.9403 | 1.29501 | 0.647507 | − | 0.762059i | \(-0.275811\pi\) | ||||
0.647507 | + | 0.762059i | \(0.275811\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 42.5718 | 1.67109 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.48886 | 0.0975462 | ||||||||
\(652\) | −10.1017 | −0.395614 | ||||||||
\(653\) | 37.2257 | 1.45675 | 0.728377 | − | 0.685177i | \(-0.240275\pi\) | ||||
0.728377 | + | 0.685177i | \(0.240275\pi\) | |||||||
\(654\) | 15.1526 | 0.592512 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.8573 | −0.423906 | ||||||||
\(657\) | −2.75557 | −0.107505 | ||||||||
\(658\) | 7.22570 | 0.281687 | ||||||||
\(659\) | 24.6953 | 0.961994 | 0.480997 | − | 0.876722i | \(-0.340275\pi\) | ||||
0.480997 | + | 0.876722i | \(0.340275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8287 | −0.576770 | −0.288385 | − | 0.957515i | \(-0.593118\pi\) | ||||
−0.288385 | + | 0.957515i | \(0.593118\pi\) | |||||||
\(662\) | 29.4479 | 1.14452 | ||||||||
\(663\) | 8.85728 | 0.343988 | ||||||||
\(664\) | 2.19358 | 0.0851273 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.8064 | 0.457490 | ||||||||
\(667\) | 4.23506 | 0.163982 | ||||||||
\(668\) | −1.89829 | −0.0734470 | ||||||||
\(669\) | 0.990632 | 0.0383000 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.3684 | 1.48120 | ||||||||
\(672\) | 0.622216 | 0.0240025 | ||||||||
\(673\) | 8.77430 | 0.338225 | 0.169112 | − | 0.985597i | \(-0.445910\pi\) | ||||
0.169112 | + | 0.985597i | \(0.445910\pi\) | |||||||
\(674\) | 24.6222 | 0.948412 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.1017 | −0.426989 | ||||||||
\(677\) | −12.8256 | −0.492929 | −0.246465 | − | 0.969152i | \(-0.579269\pi\) | ||||
−0.246465 | + | 0.969152i | \(0.579269\pi\) | |||||||
\(678\) | 14.4286 | 0.554129 | ||||||||
\(679\) | −1.32741 | −0.0509412 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.1526 | 0.657288 | ||||||||
\(682\) | 17.7146 | 0.678325 | ||||||||
\(683\) | 8.47013 | 0.324100 | 0.162050 | − | 0.986783i | \(-0.448189\pi\) | ||||
0.162050 | + | 0.986783i | \(0.448189\pi\) | |||||||
\(684\) | −1.37778 | −0.0526809 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.47013 | −0.323391 | ||||||||
\(687\) | 7.15257 | 0.272887 | ||||||||
\(688\) | 1.05086 | 0.0400635 | ||||||||
\(689\) | 4.65386 | 0.177298 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.7975 | 0.981384 | 0.490692 | − | 0.871333i | \(-0.336744\pi\) | ||||
0.490692 | + | 0.871333i | \(0.336744\pi\) | |||||||
\(692\) | −21.2257 | −0.806880 | ||||||||
\(693\) | −2.75557 | −0.104675 | ||||||||
\(694\) | −26.1017 | −0.990807 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.23506 | 0.160530 | ||||||||
\(697\) | 69.7975 | 2.64377 | ||||||||
\(698\) | 21.2257 | 0.803404 | ||||||||
\(699\) | 3.71456 | 0.140497 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.45091 | 0.281417 | 0.140709 | − | 0.990051i | \(-0.455062\pi\) | ||||
0.140709 | + | 0.990051i | \(0.455062\pi\) | |||||||
\(702\) | 1.37778 | 0.0520011 | ||||||||
\(703\) | 16.2667 | 0.613510 | ||||||||
\(704\) | 4.42864 | 0.166911 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.28544 | 0.161285 | ||||||||
\(707\) | −10.1017 | −0.379914 | ||||||||
\(708\) | 9.61285 | 0.361273 | ||||||||
\(709\) | 13.2543 | 0.497775 | 0.248887 | − | 0.968532i | \(-0.419935\pi\) | ||||
0.248887 | + | 0.968532i | \(0.419935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0415 | 0.451591 | ||||||||
\(712\) | −2.75557 | −0.103269 | ||||||||
\(713\) | 4.00000 | 0.149801 | ||||||||
\(714\) | −4.00000 | −0.149696 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.488863 | 0.0182697 | ||||||||
\(717\) | 27.8479 | 1.04000 | ||||||||
\(718\) | 4.65386 | 0.173680 | ||||||||
\(719\) | −2.33677 | −0.0871469 | −0.0435735 | − | 0.999050i | \(-0.513874\pi\) | ||||
−0.0435735 | + | 0.999050i | \(0.513874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.61285 | 0.283517 | ||||||||
\(722\) | 17.1017 | 0.636460 | ||||||||
\(723\) | −7.12399 | −0.264944 | ||||||||
\(724\) | −20.9304 | −0.777873 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.61285 | −0.319653 | ||||||||
\(727\) | −3.37778 | −0.125275 | −0.0626375 | − | 0.998036i | \(-0.519951\pi\) | ||||
−0.0626375 | + | 0.998036i | \(0.519951\pi\) | |||||||
\(728\) | −0.857279 | −0.0317729 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.75557 | −0.249864 | ||||||||
\(732\) | 8.66370 | 0.320220 | ||||||||
\(733\) | 21.0509 | 0.777531 | 0.388766 | − | 0.921337i | \(-0.372902\pi\) | ||||
0.388766 | + | 0.921337i | \(0.372902\pi\) | |||||||
\(734\) | −4.88892 | −0.180453 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −52.2864 | −1.92599 | ||||||||
\(738\) | 10.8573 | 0.399662 | ||||||||
\(739\) | −22.6351 | −0.832646 | −0.416323 | − | 0.909217i | \(-0.636682\pi\) | ||||
−0.416323 | + | 0.909217i | \(0.636682\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.89829 | 0.0697354 | ||||||||
\(742\) | −2.10171 | −0.0771562 | ||||||||
\(743\) | −3.87955 | −0.142327 | −0.0711635 | − | 0.997465i | \(-0.522671\pi\) | ||||
−0.0711635 | + | 0.997465i | \(0.522671\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.4193 | −0.857440 | ||||||||
\(747\) | −2.19358 | −0.0802588 | ||||||||
\(748\) | −28.4701 | −1.04097 | ||||||||
\(749\) | −6.63512 | −0.242442 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.7748 | 0.721592 | 0.360796 | − | 0.932645i | \(-0.382505\pi\) | ||||
0.360796 | + | 0.932645i | \(0.382505\pi\) | |||||||
\(752\) | 11.6128 | 0.423477 | ||||||||
\(753\) | −22.4099 | −0.816662 | ||||||||
\(754\) | −5.83500 | −0.212498 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.622216 | −0.0226298 | ||||||||
\(757\) | 8.19358 | 0.297801 | 0.148900 | − | 0.988852i | \(-0.452427\pi\) | ||||
0.148900 | + | 0.988852i | \(0.452427\pi\) | |||||||
\(758\) | 4.90766 | 0.178254 | ||||||||
\(759\) | −4.42864 | −0.160749 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.1624 | −1.63714 | −0.818568 | − | 0.574410i | \(-0.805232\pi\) | ||||
−0.818568 | + | 0.574410i | \(0.805232\pi\) | |||||||
\(762\) | −4.99063 | −0.180792 | ||||||||
\(763\) | 9.42816 | 0.341322 | ||||||||
\(764\) | 18.9590 | 0.685912 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.8796 | 0.718277 | ||||||||
\(767\) | −13.2444 | −0.478229 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 29.4924 | 1.06352 | 0.531762 | − | 0.846894i | \(-0.321530\pi\) | ||||
0.531762 | + | 0.846894i | \(0.321530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.7146 | −0.421889 | ||||||||
\(772\) | 1.24443 | 0.0447881 | ||||||||
\(773\) | −41.0923 | −1.47799 | −0.738994 | − | 0.673712i | \(-0.764699\pi\) | ||||
−0.738994 | + | 0.673712i | \(0.764699\pi\) | |||||||
\(774\) | −1.05086 | −0.0377722 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.13335 | −0.0765829 | ||||||||
\(777\) | 7.34614 | 0.263541 | ||||||||
\(778\) | 0.161933 | 0.00580559 | ||||||||
\(779\) | 14.9590 | 0.535961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.9590 | −1.10780 | ||||||||
\(782\) | −6.42864 | −0.229888 | ||||||||
\(783\) | −4.23506 | −0.151349 | ||||||||
\(784\) | −6.61285 | −0.236173 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.755569 | −0.0269502 | ||||||||
\(787\) | 10.0919 | 0.359736 | 0.179868 | − | 0.983691i | \(-0.442433\pi\) | ||||
0.179868 | + | 0.983691i | \(0.442433\pi\) | |||||||
\(788\) | 15.2444 | 0.543060 | ||||||||
\(789\) | −8.47013 | −0.301544 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.97773 | 0.319211 | ||||||||
\(792\) | −4.42864 | −0.157365 | ||||||||
\(793\) | −11.9367 | −0.423885 | ||||||||
\(794\) | −1.76494 | −0.0626353 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.5303 | −0.515015 | ||||||||
\(797\) | −25.2958 | −0.896022 | −0.448011 | − | 0.894028i | \(-0.647867\pi\) | ||||
−0.448011 | + | 0.894028i | \(0.647867\pi\) | |||||||
\(798\) | −0.857279 | −0.0303473 | ||||||||
\(799\) | −74.6548 | −2.64110 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.75557 | 0.0973632 | ||||||||
\(802\) | 31.3461 | 1.10687 | ||||||||
\(803\) | −12.2034 | −0.430649 | ||||||||
\(804\) | −11.8064 | −0.416380 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.51114 | −0.194122 | ||||||||
\(807\) | 28.8256 | 1.01471 | ||||||||
\(808\) | −16.2351 | −0.571148 | ||||||||
\(809\) | 43.4479 | 1.52755 | 0.763773 | − | 0.645485i | \(-0.223345\pi\) | ||||
0.763773 | + | 0.645485i | \(0.223345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.65386 | −0.303878 | −0.151939 | − | 0.988390i | \(-0.548552\pi\) | ||||
−0.151939 | + | 0.988390i | \(0.548552\pi\) | |||||||
\(812\) | 2.63512 | 0.0924747 | ||||||||
\(813\) | −13.8350 | −0.485215 | ||||||||
\(814\) | 52.2864 | 1.83264 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.42864 | −0.225047 | ||||||||
\(817\) | −1.44785 | −0.0506539 | ||||||||
\(818\) | 3.51114 | 0.122764 | ||||||||
\(819\) | 0.857279 | 0.0299558 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.78721 | 0.0972744 | 0.0486372 | − | 0.998817i | \(-0.484512\pi\) | ||||
0.0486372 | + | 0.998817i | \(0.484512\pi\) | |||||||
\(822\) | 12.9175 | 0.450550 | ||||||||
\(823\) | 29.9684 | 1.04463 | 0.522316 | − | 0.852752i | \(-0.325068\pi\) | ||||
0.522316 | + | 0.852752i | \(0.325068\pi\) | |||||||
\(824\) | 12.2351 | 0.426229 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.98126 | 0.208115 | ||||||||
\(827\) | 47.2543 | 1.64319 | 0.821596 | − | 0.570070i | \(-0.193084\pi\) | ||||
0.821596 | + | 0.570070i | \(0.193084\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −53.1624 | −1.84641 | −0.923203 | − | 0.384312i | \(-0.874439\pi\) | ||||
−0.923203 | + | 0.384312i | \(0.874439\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.88892 | 0.100216 | ||||||||
\(832\) | −1.37778 | −0.0477661 | ||||||||
\(833\) | 42.5116 | 1.47294 | ||||||||
\(834\) | 14.1017 | 0.488302 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.10171 | −0.211032 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 19.7748 | 0.683108 | ||||||||
\(839\) | −17.3274 | −0.598208 | −0.299104 | − | 0.954220i | \(-0.596688\pi\) | ||||
−0.299104 | + | 0.954220i | \(0.596688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0642 | −0.381525 | ||||||||
\(842\) | −11.8064 | −0.406876 | ||||||||
\(843\) | 5.51114 | 0.189814 | ||||||||
\(844\) | 0.266706 | 0.00918041 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.6128 | −0.399258 | ||||||||
\(847\) | −5.35905 | −0.184139 | ||||||||
\(848\) | −3.37778 | −0.115994 | ||||||||
\(849\) | 8.19358 | 0.281203 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.8064 | 0.404719 | ||||||||
\(852\) | −6.99063 | −0.239495 | ||||||||
\(853\) | 17.7649 | 0.608260 | 0.304130 | − | 0.952631i | \(-0.401634\pi\) | ||||
0.304130 | + | 0.952631i | \(0.401634\pi\) | |||||||
\(854\) | 5.39069 | 0.184466 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.6637 | −0.364478 | ||||||||
\(857\) | 10.0830 | 0.344428 | 0.172214 | − | 0.985060i | \(-0.444908\pi\) | ||||
0.172214 | + | 0.985060i | \(0.444908\pi\) | |||||||
\(858\) | 6.10171 | 0.208309 | ||||||||
\(859\) | 5.12399 | 0.174828 | 0.0874141 | − | 0.996172i | \(-0.472140\pi\) | ||||
0.0874141 | + | 0.996172i | \(0.472140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.75557 | 0.230229 | ||||||||
\(862\) | −24.9403 | −0.849468 | ||||||||
\(863\) | 49.2070 | 1.67502 | 0.837512 | − | 0.546419i | \(-0.184009\pi\) | ||||
0.837512 | + | 0.546419i | \(0.184009\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 32.0513 | 1.08915 | ||||||||
\(867\) | 24.3274 | 0.826202 | ||||||||
\(868\) | 2.48886 | 0.0844775 | ||||||||
\(869\) | 53.3274 | 1.80901 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2667 | 0.551176 | ||||||||
\(872\) | 15.1526 | 0.513131 | ||||||||
\(873\) | 2.13335 | 0.0722031 | ||||||||
\(874\) | −1.37778 | −0.0466043 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.75557 | −0.0931020 | ||||||||
\(877\) | −9.11108 | −0.307659 | −0.153830 | − | 0.988097i | \(-0.549161\pi\) | ||||
−0.153830 | + | 0.988097i | \(0.549161\pi\) | |||||||
\(878\) | −0.470127 | −0.0158660 | ||||||||
\(879\) | 12.6222 | 0.425737 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.71456 | −0.327292 | −0.163646 | − | 0.986519i | \(-0.552325\pi\) | ||||
−0.163646 | + | 0.986519i | \(0.552325\pi\) | |||||||
\(882\) | 6.61285 | 0.222666 | ||||||||
\(883\) | 33.3274 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(884\) | 8.85728 | 0.297903 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.653858 | 0.0219668 | ||||||||
\(887\) | 53.5941 | 1.79951 | 0.899757 | − | 0.436391i | \(-0.143744\pi\) | ||||
0.899757 | + | 0.436391i | \(0.143744\pi\) | |||||||
\(888\) | 11.8064 | 0.396198 | ||||||||
\(889\) | −3.10525 | −0.104147 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.42864 | 0.148365 | ||||||||
\(892\) | 0.990632 | 0.0331688 | ||||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | −12.4286 | −0.415676 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.622216 | 0.0207868 | ||||||||
\(897\) | 1.37778 | 0.0460029 | ||||||||
\(898\) | −17.1427 | −0.572060 | ||||||||
\(899\) | 16.9403 | 0.564989 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.7146 | 0.723417 | ||||||||
\(902\) | 48.0830 | 1.60099 | ||||||||
\(903\) | −0.653858 | −0.0217590 | ||||||||
\(904\) | 14.4286 | 0.479889 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.85728 | 0.161372 | ||||||||
\(907\) | −2.56199 | −0.0850696 | −0.0425348 | − | 0.999095i | \(-0.513543\pi\) | ||||
−0.0425348 | + | 0.999095i | \(0.513543\pi\) | |||||||
\(908\) | 17.1526 | 0.569228 | ||||||||
\(909\) | 16.2351 | 0.538483 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.47013 | 0.280628 | 0.140314 | − | 0.990107i | \(-0.455189\pi\) | ||||
0.140314 | + | 0.990107i | \(0.455189\pi\) | |||||||
\(912\) | −1.37778 | −0.0456230 | ||||||||
\(913\) | −9.71456 | −0.321505 | ||||||||
\(914\) | −1.00937 | −0.0333869 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.15257 | 0.236327 | ||||||||
\(917\) | −0.470127 | −0.0155250 | ||||||||
\(918\) | 6.42864 | 0.212177 | ||||||||
\(919\) | −36.8988 | −1.21718 | −0.608589 | − | 0.793486i | \(-0.708264\pi\) | ||||
−0.608589 | + | 0.793486i | \(0.708264\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.653858 | −0.0215454 | ||||||||
\(922\) | −20.3180 | −0.669139 | ||||||||
\(923\) | 9.63158 | 0.317027 | ||||||||
\(924\) | −2.75557 | −0.0906516 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.4572 | −0.409370 | ||||||||
\(927\) | −12.2351 | −0.401852 | ||||||||
\(928\) | 4.23506 | 0.139023 | ||||||||
\(929\) | −0.164996 | −0.00541334 | −0.00270667 | − | 0.999996i | \(-0.500862\pi\) | ||||
−0.00270667 | + | 0.999996i | \(0.500862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.11108 | 0.298604 | ||||||||
\(932\) | 3.71456 | 0.121674 | ||||||||
\(933\) | −13.0923 | −0.428624 | ||||||||
\(934\) | 15.7877 | 0.516589 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.37778 | 0.0450343 | ||||||||
\(937\) | 40.3180 | 1.31713 | 0.658566 | − | 0.752523i | \(-0.271163\pi\) | ||||
0.658566 | + | 0.752523i | \(0.271163\pi\) | |||||||
\(938\) | −7.34614 | −0.239860 | ||||||||
\(939\) | 11.2573 | 0.367369 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.3689 | 1.73978 | 0.869888 | − | 0.493249i | \(-0.164191\pi\) | ||||
0.869888 | + | 0.493249i | \(0.164191\pi\) | |||||||
\(942\) | −9.90813 | −0.322824 | ||||||||
\(943\) | 10.8573 | 0.353562 | ||||||||
\(944\) | 9.61285 | 0.312872 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.65386 | −0.151310 | ||||||||
\(947\) | −44.6735 | −1.45170 | −0.725848 | − | 0.687856i | \(-0.758552\pi\) | ||||
−0.725848 | + | 0.687856i | \(0.758552\pi\) | |||||||
\(948\) | 12.0415 | 0.391089 | ||||||||
\(949\) | 3.79658 | 0.123242 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.4701 | −0.728644 | ||||||||
\(952\) | −4.00000 | −0.129641 | ||||||||
\(953\) | 21.2672 | 0.688912 | 0.344456 | − | 0.938803i | \(-0.388063\pi\) | ||||
0.344456 | + | 0.938803i | \(0.388063\pi\) | |||||||
\(954\) | 3.37778 | 0.109360 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 27.8479 | 0.900666 | ||||||||
\(957\) | −18.7556 | −0.606281 | ||||||||
\(958\) | −5.12399 | −0.165548 | ||||||||
\(959\) | 8.03747 | 0.259543 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −16.2667 | −0.524460 | ||||||||
\(963\) | 10.6637 | 0.343633 | ||||||||
\(964\) | −7.12399 | −0.229448 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.622216 | −0.0200195 | ||||||||
\(967\) | −10.9461 | −0.352002 | −0.176001 | − | 0.984390i | \(-0.556316\pi\) | ||||
−0.176001 | + | 0.984390i | \(0.556316\pi\) | |||||||
\(968\) | −8.61285 | −0.276827 | ||||||||
\(969\) | 8.85728 | 0.284537 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.8988 | −0.542307 | −0.271154 | − | 0.962536i | \(-0.587405\pi\) | ||||
−0.271154 | + | 0.962536i | \(0.587405\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 8.77430 | 0.281291 | ||||||||
\(974\) | 23.2128 | 0.743786 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.66370 | 0.277318 | ||||||||
\(977\) | −59.2484 | −1.89553 | −0.947763 | − | 0.318976i | \(-0.896661\pi\) | ||||
−0.947763 | + | 0.318976i | \(0.896661\pi\) | |||||||
\(978\) | 10.1017 | 0.323017 | ||||||||
\(979\) | 12.2034 | 0.390023 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.1526 | −0.483784 | ||||||||
\(982\) | 40.1847 | 1.28234 | ||||||||
\(983\) | 23.8163 | 0.759621 | 0.379810 | − | 0.925064i | \(-0.375989\pi\) | ||||
0.379810 | + | 0.925064i | \(0.375989\pi\) | |||||||
\(984\) | 10.8573 | 0.346117 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −27.2257 | −0.867043 | ||||||||
\(987\) | −7.22570 | −0.229996 | ||||||||
\(988\) | 1.89829 | 0.0603926 | ||||||||
\(989\) | −1.05086 | −0.0334152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.7146 | 0.943914 | 0.471957 | − | 0.881622i | \(-0.343548\pi\) | ||||
0.471957 | + | 0.881622i | \(0.343548\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | −29.4479 | −0.934499 | ||||||||
\(994\) | −4.34968 | −0.137963 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.19358 | −0.0695061 | ||||||||
\(997\) | −22.7052 | −0.719081 | −0.359540 | − | 0.933130i | \(-0.617066\pi\) | ||||
−0.359540 | + | 0.933130i | \(0.617066\pi\) | |||||||
\(998\) | −30.5718 | −0.967735 | ||||||||
\(999\) | −11.8064 | −0.373539 |
(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 | 3450.2.a.bo.1.2 | 3 | ||
5.2 | odd | 4 | 690.2.d.c.139.3 | ✓ | 6 | ||
5.3 | odd | 4 | 690.2.d.c.139.6 | yes | 6 | ||
5.4 | even | 2 | 3450.2.a.bt.1.2 | 3 | |||
15.2 | even | 4 | 2070.2.d.e.829.4 | 6 | |||
15.8 | even | 4 | 2070.2.d.e.829.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.c.139.3 | ✓ | 6 | 5.2 | odd | 4 | ||
690.2.d.c.139.6 | yes | 6 | 5.3 | odd | 4 | ||
2070.2.d.e.829.1 | 6 | 15.8 | even | 4 | |||
2070.2.d.e.829.4 | 6 | 15.2 | even | 4 | |||
3450.2.a.bo.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3450.2.a.bt.1.2 | 3 | 5.4 | even | 2 |