Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(1.52505\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52505 | 1.07837 | 0.539187 | − | 0.842186i | \(-0.318732\pi\) | ||||
0.539187 | + | 0.842186i | \(0.318732\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.325779 | 0.162890 | ||||||||
\(5\) | 1.71268 | 0.765933 | 0.382966 | − | 0.923762i | \(-0.374902\pi\) | ||||
0.382966 | + | 0.923762i | \(0.374902\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.55327 | −0.902718 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.61192 | 0.825962 | ||||||||
\(11\) | 1.69211 | 0.510191 | 0.255096 | − | 0.966916i | \(-0.417893\pi\) | ||||
0.255096 | + | 0.966916i | \(0.417893\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.16748 | −0.323801 | −0.161901 | − | 0.986807i | \(-0.551762\pi\) | ||||
−0.161901 | + | 0.986807i | \(0.551762\pi\) | |||||||
\(14\) | 1.52505 | 0.407587 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.54543 | −1.13636 | ||||||||
\(17\) | −5.50471 | −1.33509 | −0.667544 | − | 0.744570i | \(-0.732655\pi\) | ||||
−0.667544 | + | 0.744570i | \(0.732655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.828520 | −0.190075 | −0.0950377 | − | 0.995474i | \(-0.530297\pi\) | ||||
−0.0950377 | + | 0.995474i | \(0.530297\pi\) | |||||||
\(20\) | 0.557955 | 0.124762 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.58056 | 0.550177 | ||||||||
\(23\) | 6.42297 | 1.33928 | 0.669641 | − | 0.742685i | \(-0.266448\pi\) | ||||
0.669641 | + | 0.742685i | \(0.266448\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.06673 | −0.413347 | ||||||||
\(26\) | −1.78047 | −0.349179 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.325779 | 0.0615664 | ||||||||
\(29\) | 2.43481 | 0.452133 | 0.226066 | − | 0.974112i | \(-0.427413\pi\) | ||||
0.226066 | + | 0.974112i | \(0.427413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.583990 | −0.104888 | −0.0524438 | − | 0.998624i | \(-0.516701\pi\) | ||||
−0.0524438 | + | 0.998624i | \(0.516701\pi\) | |||||||
\(32\) | −1.82546 | −0.322699 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.39496 | −1.43972 | ||||||||
\(35\) | 1.71268 | 0.289495 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.0189 | 1.81150 | 0.905749 | − | 0.423814i | \(-0.139309\pi\) | ||||
0.905749 | + | 0.423814i | \(0.139309\pi\) | |||||||
\(38\) | −1.26353 | −0.204972 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.37293 | −0.691421 | ||||||||
\(41\) | 0.0442353 | 0.00690839 | 0.00345419 | − | 0.999994i | \(-0.498900\pi\) | ||||
0.00345419 | + | 0.999994i | \(0.498900\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.9529 | 1.97529 | 0.987647 | − | 0.156695i | \(-0.0500839\pi\) | ||||
0.987647 | + | 0.156695i | \(0.0500839\pi\) | |||||||
\(44\) | 0.551255 | 0.0831048 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.79535 | 1.44425 | ||||||||
\(47\) | −3.58595 | −0.523065 | −0.261533 | − | 0.965195i | \(-0.584228\pi\) | ||||
−0.261533 | + | 0.965195i | \(0.584228\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.15187 | −0.445742 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.380341 | −0.0527439 | ||||||||
\(53\) | 12.7616 | 1.75295 | 0.876473 | − | 0.481451i | \(-0.159890\pi\) | ||||
0.876473 | + | 0.481451i | \(0.159890\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.89805 | 0.390772 | ||||||||
\(56\) | −2.55327 | −0.341195 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.71321 | 0.487568 | ||||||||
\(59\) | −1.61982 | −0.210883 | −0.105442 | − | 0.994426i | \(-0.533626\pi\) | ||||
−0.105442 | + | 0.994426i | \(0.533626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.74621 | −0.735727 | −0.367864 | − | 0.929880i | \(-0.619911\pi\) | ||||
−0.367864 | + | 0.929880i | \(0.619911\pi\) | |||||||
\(62\) | −0.890614 | −0.113108 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.30693 | 0.788366 | ||||||||
\(65\) | −1.99952 | −0.248010 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.393750 | −0.0481042 | −0.0240521 | − | 0.999711i | \(-0.507657\pi\) | ||||
−0.0240521 | + | 0.999711i | \(0.507657\pi\) | |||||||
\(68\) | −1.79332 | −0.217472 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.61192 | 0.312184 | ||||||||
\(71\) | −10.0573 | −1.19358 | −0.596792 | − | 0.802396i | \(-0.703558\pi\) | ||||
−0.596792 | + | 0.802396i | \(0.703558\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.94732 | 0.930163 | 0.465081 | − | 0.885268i | \(-0.346025\pi\) | ||||
0.465081 | + | 0.885268i | \(0.346025\pi\) | |||||||
\(74\) | 16.8044 | 1.95347 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.269914 | −0.0309613 | ||||||||
\(77\) | 1.69211 | 0.192834 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.92230 | 0.441293 | 0.220647 | − | 0.975354i | \(-0.429183\pi\) | ||||
0.220647 | + | 0.975354i | \(0.429183\pi\) | |||||||
\(80\) | −7.78485 | −0.870373 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.0674610 | 0.00744982 | ||||||||
\(83\) | −6.36257 | −0.698382 | −0.349191 | − | 0.937051i | \(-0.613544\pi\) | ||||
−0.349191 | + | 0.937051i | \(0.613544\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.42780 | −1.02259 | ||||||||
\(86\) | 19.7538 | 2.13010 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.32042 | −0.460559 | ||||||||
\(89\) | 5.77339 | 0.611978 | 0.305989 | − | 0.952035i | \(-0.401013\pi\) | ||||
0.305989 | + | 0.952035i | \(0.401013\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.16748 | −0.122385 | ||||||||
\(92\) | 2.09247 | 0.218155 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.46876 | −0.564060 | ||||||||
\(95\) | −1.41899 | −0.145585 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.1754 | 1.54083 | 0.770415 | − | 0.637542i | \(-0.220049\pi\) | ||||
0.770415 | + | 0.637542i | \(0.220049\pi\) | |||||||
\(98\) | 1.52505 | 0.154053 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.673298 | −0.0673298 | ||||||||
\(101\) | 16.9988 | 1.69144 | 0.845722 | − | 0.533624i | \(-0.179170\pi\) | ||||
0.845722 | + | 0.533624i | \(0.179170\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.475453 | 0.0468478 | 0.0234239 | − | 0.999726i | \(-0.492543\pi\) | ||||
0.0234239 | + | 0.999726i | \(0.492543\pi\) | |||||||
\(104\) | 2.98090 | 0.292301 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.4621 | 1.89033 | ||||||||
\(107\) | 16.9210 | 1.63582 | 0.817908 | − | 0.575349i | \(-0.195134\pi\) | ||||
0.817908 | + | 0.575349i | \(0.195134\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.98507 | 0.381700 | 0.190850 | − | 0.981619i | \(-0.438876\pi\) | ||||
0.190850 | + | 0.981619i | \(0.438876\pi\) | |||||||
\(110\) | 4.41967 | 0.421399 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.54543 | −0.429502 | ||||||||
\(113\) | 18.6198 | 1.75160 | 0.875802 | − | 0.482670i | \(-0.160333\pi\) | ||||
0.875802 | + | 0.482670i | \(0.160333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.0005 | 1.02580 | ||||||||
\(116\) | 0.793210 | 0.0736477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.47031 | −0.227411 | ||||||||
\(119\) | −5.50471 | −0.504616 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.13675 | −0.739705 | ||||||||
\(122\) | −8.76327 | −0.793389 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.190252 | −0.0170851 | ||||||||
\(125\) | −12.1030 | −1.08253 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 13.2693 | 1.17285 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.04937 | −0.267448 | ||||||||
\(131\) | 10.2394 | 0.894622 | 0.447311 | − | 0.894379i | \(-0.352382\pi\) | ||||
0.447311 | + | 0.894379i | \(0.352382\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.828520 | −0.0718418 | ||||||||
\(134\) | −0.600488 | −0.0518743 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.0550 | 1.20521 | ||||||||
\(137\) | −14.4173 | −1.23175 | −0.615874 | − | 0.787844i | \(-0.711197\pi\) | ||||
−0.615874 | + | 0.787844i | \(0.711197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.41938 | 0.205209 | 0.102605 | − | 0.994722i | \(-0.467282\pi\) | ||||
0.102605 | + | 0.994722i | \(0.467282\pi\) | |||||||
\(140\) | 0.557955 | 0.0471558 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.3379 | −1.28713 | ||||||||
\(143\) | −1.97551 | −0.165201 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.17004 | 0.346303 | ||||||||
\(146\) | 12.1201 | 1.00306 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.58973 | 0.295074 | ||||||||
\(149\) | −13.8882 | −1.13776 | −0.568882 | − | 0.822419i | \(-0.692624\pi\) | ||||
−0.568882 | + | 0.822419i | \(0.692624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.9548 | 1.29839 | 0.649193 | − | 0.760624i | \(-0.275107\pi\) | ||||
0.649193 | + | 0.760624i | \(0.275107\pi\) | |||||||
\(152\) | 2.11544 | 0.171584 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.58056 | 0.207947 | ||||||||
\(155\) | −1.00019 | −0.0803369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.84694 | −0.706063 | −0.353031 | − | 0.935611i | \(-0.614849\pi\) | ||||
−0.353031 | + | 0.935611i | \(0.614849\pi\) | |||||||
\(158\) | 5.98171 | 0.475879 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.12643 | −0.247166 | ||||||||
\(161\) | 6.42297 | 0.506201 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.1224 | −1.10615 | −0.553077 | − | 0.833130i | \(-0.686547\pi\) | ||||
−0.553077 | + | 0.833130i | \(0.686547\pi\) | |||||||
\(164\) | 0.0144109 | 0.00112530 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.70323 | −0.753117 | ||||||||
\(167\) | 18.7284 | 1.44925 | 0.724624 | − | 0.689144i | \(-0.242013\pi\) | ||||
0.724624 | + | 0.689144i | \(0.242013\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6370 | −0.895153 | ||||||||
\(170\) | −14.3779 | −1.10273 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.21977 | 0.321755 | ||||||||
\(173\) | 22.7424 | 1.72907 | 0.864535 | − | 0.502573i | \(-0.167613\pi\) | ||||
0.864535 | + | 0.502573i | \(0.167613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.06673 | −0.156230 | ||||||||
\(176\) | −7.69138 | −0.579759 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.80471 | 0.659941 | ||||||||
\(179\) | −4.09159 | −0.305820 | −0.152910 | − | 0.988240i | \(-0.548864\pi\) | ||||
−0.152910 | + | 0.988240i | \(0.548864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.9770 | −1.78220 | −0.891099 | − | 0.453810i | \(-0.850065\pi\) | ||||
−0.891099 | + | 0.453810i | \(0.850065\pi\) | |||||||
\(182\) | −1.78047 | −0.131977 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.3996 | −1.20899 | ||||||||
\(185\) | 18.8719 | 1.38749 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.31460 | −0.681151 | ||||||||
\(188\) | −1.16823 | −0.0852018 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.16403 | −0.156995 | ||||||||
\(191\) | 5.39625 | 0.390459 | 0.195229 | − | 0.980758i | \(-0.437455\pi\) | ||||
0.195229 | + | 0.980758i | \(0.437455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.73030 | −0.700402 | −0.350201 | − | 0.936675i | \(-0.613887\pi\) | ||||
−0.350201 | + | 0.936675i | \(0.613887\pi\) | |||||||
\(194\) | 23.1433 | 1.66159 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.325779 | 0.0232699 | ||||||||
\(197\) | 0.142596 | 0.0101595 | 0.00507976 | − | 0.999987i | \(-0.498383\pi\) | ||||
0.00507976 | + | 0.999987i | \(0.498383\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8974 | −0.843386 | −0.421693 | − | 0.906739i | \(-0.638564\pi\) | ||||
−0.421693 | + | 0.906739i | \(0.638564\pi\) | |||||||
\(200\) | 5.27693 | 0.373135 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 25.9240 | 1.82401 | ||||||||
\(203\) | 2.43481 | 0.170890 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0757608 | 0.00529136 | ||||||||
\(206\) | 0.725090 | 0.0505194 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.30671 | 0.367954 | ||||||||
\(209\) | −1.40195 | −0.0969748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.02643 | 0.483720 | 0.241860 | − | 0.970311i | \(-0.422243\pi\) | ||||
0.241860 | + | 0.970311i | \(0.422243\pi\) | |||||||
\(212\) | 4.15747 | 0.285537 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.8054 | 1.76402 | ||||||||
\(215\) | 22.1841 | 1.51294 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.583990 | −0.0396438 | ||||||||
\(218\) | 6.07743 | 0.411615 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.944122 | 0.0636527 | ||||||||
\(221\) | 6.42666 | 0.432304 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.33132 | −0.557907 | −0.278953 | − | 0.960305i | \(-0.589987\pi\) | ||||
−0.278953 | + | 0.960305i | \(0.589987\pi\) | |||||||
\(224\) | −1.82546 | −0.121969 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 28.3961 | 1.88888 | ||||||||
\(227\) | −7.54679 | −0.500898 | −0.250449 | − | 0.968130i | \(-0.580578\pi\) | ||||
−0.250449 | + | 0.968130i | \(0.580578\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.3110 | −0.879614 | −0.439807 | − | 0.898092i | \(-0.644953\pi\) | ||||
−0.439807 | + | 0.898092i | \(0.644953\pi\) | |||||||
\(230\) | 16.7763 | 1.10620 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.21673 | −0.408148 | ||||||||
\(233\) | −26.4435 | −1.73237 | −0.866187 | − | 0.499720i | \(-0.833436\pi\) | ||||
−0.866187 | + | 0.499720i | \(0.833436\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.14159 | −0.400633 | ||||||||
\(236\) | −0.527705 | −0.0343506 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.39496 | −0.544165 | ||||||||
\(239\) | −13.5322 | −0.875328 | −0.437664 | − | 0.899139i | \(-0.644194\pi\) | ||||
−0.437664 | + | 0.899139i | \(0.644194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.26598 | 0.274796 | 0.137398 | − | 0.990516i | \(-0.456126\pi\) | ||||
0.137398 | + | 0.990516i | \(0.456126\pi\) | |||||||
\(242\) | −12.4090 | −0.797678 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.87200 | −0.119842 | ||||||||
\(245\) | 1.71268 | 0.109419 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.967283 | 0.0615467 | ||||||||
\(248\) | 1.49108 | 0.0946840 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −18.4577 | −1.16737 | ||||||||
\(251\) | −11.6345 | −0.734363 | −0.367182 | − | 0.930149i | \(-0.619677\pi\) | ||||
−0.367182 | + | 0.930149i | \(0.619677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8684 | 0.683290 | ||||||||
\(254\) | 1.52505 | 0.0956902 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.62251 | 0.476407 | ||||||||
\(257\) | 21.3143 | 1.32955 | 0.664774 | − | 0.747044i | \(-0.268528\pi\) | ||||
0.664774 | + | 0.747044i | \(0.268528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.0189 | 0.684682 | ||||||||
\(260\) | −0.651402 | −0.0403983 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.6156 | 0.964737 | ||||||||
\(263\) | 18.8019 | 1.15938 | 0.579688 | − | 0.814839i | \(-0.303175\pi\) | ||||
0.579688 | + | 0.814839i | \(0.303175\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.8566 | 1.34264 | ||||||||
\(266\) | −1.26353 | −0.0774723 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.128275 | −0.00783566 | ||||||||
\(269\) | 19.1251 | 1.16608 | 0.583038 | − | 0.812445i | \(-0.301864\pi\) | ||||
0.583038 | + | 0.812445i | \(0.301864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.9073 | −1.51301 | −0.756507 | − | 0.653986i | \(-0.773095\pi\) | ||||
−0.756507 | + | 0.653986i | \(0.773095\pi\) | |||||||
\(272\) | 25.0213 | 1.51714 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.9870 | −1.32829 | ||||||||
\(275\) | −3.49715 | −0.210886 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.2979 | 0.979245 | 0.489623 | − | 0.871934i | \(-0.337135\pi\) | ||||
0.489623 | + | 0.871934i | \(0.337135\pi\) | |||||||
\(278\) | 3.68968 | 0.221292 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.37293 | −0.261333 | ||||||||
\(281\) | −18.9557 | −1.13080 | −0.565401 | − | 0.824816i | \(-0.691279\pi\) | ||||
−0.565401 | + | 0.824816i | \(0.691279\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.71943 | −0.161654 | −0.0808268 | − | 0.996728i | \(-0.525756\pi\) | ||||
−0.0808268 | + | 0.996728i | \(0.525756\pi\) | |||||||
\(284\) | −3.27646 | −0.194422 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.01276 | −0.178148 | ||||||||
\(287\) | 0.0442353 | 0.00261113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.3019 | 0.782462 | ||||||||
\(290\) | 6.35953 | 0.373444 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.58907 | 0.151514 | ||||||||
\(293\) | 1.50441 | 0.0878883 | 0.0439442 | − | 0.999034i | \(-0.486008\pi\) | ||||
0.0439442 | + | 0.999034i | \(0.486008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.77424 | −0.161522 | ||||||||
\(296\) | −28.1343 | −1.63527 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.1802 | −1.22693 | ||||||||
\(299\) | −7.49870 | −0.433661 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.9529 | 0.746591 | ||||||||
\(302\) | 24.3319 | 1.40015 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.76597 | 0.215993 | ||||||||
\(305\) | −9.84142 | −0.563518 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.8091 | −0.845197 | −0.422599 | − | 0.906317i | \(-0.638882\pi\) | ||||
−0.422599 | + | 0.906317i | \(0.638882\pi\) | |||||||
\(308\) | 0.551255 | 0.0314107 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.52534 | −0.0866332 | ||||||||
\(311\) | −18.8186 | −1.06711 | −0.533554 | − | 0.845766i | \(-0.679144\pi\) | ||||
−0.533554 | + | 0.845766i | \(0.679144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.1089 | −0.740961 | −0.370480 | − | 0.928840i | \(-0.620807\pi\) | ||||
−0.370480 | + | 0.928840i | \(0.620807\pi\) | |||||||
\(314\) | −13.4920 | −0.761400 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.27780 | 0.0718820 | ||||||||
\(317\) | 26.8211 | 1.50642 | 0.753210 | − | 0.657780i | \(-0.228504\pi\) | ||||
0.753210 | + | 0.657780i | \(0.228504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.11997 | 0.230674 | ||||||||
\(320\) | 10.8017 | 0.603836 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.79535 | 0.545873 | ||||||||
\(323\) | 4.56076 | 0.253768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41288 | 0.133842 | ||||||||
\(326\) | −21.5374 | −1.19285 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.112945 | −0.00623633 | ||||||||
\(329\) | −3.58595 | −0.197700 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.70474 | 0.0937009 | 0.0468505 | − | 0.998902i | \(-0.485082\pi\) | ||||
0.0468505 | + | 0.998902i | \(0.485082\pi\) | |||||||
\(332\) | −2.07279 | −0.113759 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 28.5618 | 1.56283 | ||||||||
\(335\) | −0.674366 | −0.0368446 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.03114 | 0.219590 | 0.109795 | − | 0.993954i | \(-0.464981\pi\) | ||||
0.109795 | + | 0.993954i | \(0.464981\pi\) | |||||||
\(338\) | −17.7470 | −0.965309 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.07138 | −0.166569 | ||||||||
\(341\) | −0.988177 | −0.0535128 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −33.0722 | −1.78313 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 34.6833 | 1.86458 | ||||||||
\(347\) | 28.9241 | 1.55272 | 0.776362 | − | 0.630287i | \(-0.217063\pi\) | ||||
0.776362 | + | 0.630287i | \(0.217063\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.0120 | −1.49945 | −0.749723 | − | 0.661752i | \(-0.769813\pi\) | ||||
−0.749723 | + | 0.661752i | \(0.769813\pi\) | |||||||
\(350\) | −3.15187 | −0.168475 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.08889 | −0.164638 | ||||||||
\(353\) | 13.4125 | 0.713874 | 0.356937 | − | 0.934129i | \(-0.383821\pi\) | ||||
0.356937 | + | 0.934129i | \(0.383821\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.2249 | −0.914205 | ||||||||
\(356\) | 1.88085 | 0.0996848 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.23988 | −0.329788 | ||||||||
\(359\) | 14.1328 | 0.745901 | 0.372951 | − | 0.927851i | \(-0.378346\pi\) | ||||
0.372951 | + | 0.927851i | \(0.378346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3136 | −0.963871 | ||||||||
\(362\) | −36.5662 | −1.92187 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.380341 | −0.0199353 | ||||||||
\(365\) | 13.6112 | 0.712442 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.149960 | −0.00782787 | −0.00391393 | − | 0.999992i | \(-0.501246\pi\) | ||||
−0.00391393 | + | 0.999992i | \(0.501246\pi\) | |||||||
\(368\) | −29.1951 | −1.52190 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 28.7805 | 1.49623 | ||||||||
\(371\) | 12.7616 | 0.662551 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.4335 | 1.67934 | 0.839672 | − | 0.543093i | \(-0.182747\pi\) | ||||
0.839672 | + | 0.543093i | \(0.182747\pi\) | |||||||
\(374\) | −14.2052 | −0.734535 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.15592 | 0.472180 | ||||||||
\(377\) | −2.84260 | −0.146401 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.44284 | −0.176847 | −0.0884234 | − | 0.996083i | \(-0.528183\pi\) | ||||
−0.0884234 | + | 0.996083i | \(0.528183\pi\) | |||||||
\(380\) | −0.462276 | −0.0237143 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.22955 | 0.421060 | ||||||||
\(383\) | 33.4195 | 1.70766 | 0.853828 | − | 0.520556i | \(-0.174275\pi\) | ||||
0.853828 | + | 0.520556i | \(0.174275\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.89805 | 0.147698 | ||||||||
\(386\) | −14.8392 | −0.755295 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.94383 | 0.250985 | ||||||||
\(389\) | 29.8748 | 1.51471 | 0.757356 | − | 0.653002i | \(-0.226491\pi\) | ||||
0.757356 | + | 0.653002i | \(0.226491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.3566 | −1.78806 | ||||||||
\(392\) | −2.55327 | −0.128960 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.217466 | 0.0109558 | ||||||||
\(395\) | 6.71764 | 0.338001 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.8790 | 1.04788 | 0.523942 | − | 0.851754i | \(-0.324461\pi\) | ||||
0.523942 | + | 0.851754i | \(0.324461\pi\) | |||||||
\(398\) | −18.1442 | −0.909486 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.39418 | 0.469709 | ||||||||
\(401\) | 26.7500 | 1.33583 | 0.667915 | − | 0.744237i | \(-0.267187\pi\) | ||||
0.667915 | + | 0.744237i | \(0.267187\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.681798 | 0.0339628 | ||||||||
\(404\) | 5.53785 | 0.275518 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.71321 | 0.184283 | ||||||||
\(407\) | 18.6453 | 0.924211 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3447 | 0.956535 | 0.478267 | − | 0.878214i | \(-0.341265\pi\) | ||||
0.478267 | + | 0.878214i | \(0.341265\pi\) | |||||||
\(410\) | 0.115539 | 0.00570607 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.154893 | 0.00763101 | ||||||||
\(413\) | −1.61982 | −0.0797063 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.8970 | −0.534914 | ||||||||
\(416\) | 2.13119 | 0.104490 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.13804 | −0.104575 | ||||||||
\(419\) | 2.14664 | 0.104870 | 0.0524351 | − | 0.998624i | \(-0.483302\pi\) | ||||
0.0524351 | + | 0.998624i | \(0.483302\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.674689 | −0.0328823 | −0.0164412 | − | 0.999865i | \(-0.505234\pi\) | ||||
−0.0164412 | + | 0.999865i | \(0.505234\pi\) | |||||||
\(422\) | 10.7157 | 0.521630 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −32.5839 | −1.58242 | ||||||||
\(425\) | 11.3768 | 0.551855 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.74621 | −0.278079 | ||||||||
\(428\) | 5.51251 | 0.266457 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.8319 | 1.63152 | ||||||||
\(431\) | −7.06226 | −0.340177 | −0.170089 | − | 0.985429i | \(-0.554405\pi\) | ||||
−0.170089 | + | 0.985429i | \(0.554405\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.73974 | 0.323891 | 0.161946 | − | 0.986800i | \(-0.448223\pi\) | ||||
0.161946 | + | 0.986800i | \(0.448223\pi\) | |||||||
\(434\) | −0.890614 | −0.0427508 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.29825 | 0.0621749 | ||||||||
\(437\) | −5.32155 | −0.254564 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.65835 | 0.126876 | 0.0634380 | − | 0.997986i | \(-0.479793\pi\) | ||||
0.0634380 | + | 0.997986i | \(0.479793\pi\) | |||||||
\(440\) | −7.39950 | −0.352757 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.80098 | 0.466185 | ||||||||
\(443\) | −5.02361 | −0.238679 | −0.119339 | − | 0.992854i | \(-0.538078\pi\) | ||||
−0.119339 | + | 0.992854i | \(0.538078\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.88795 | 0.468734 | ||||||||
\(446\) | −12.7057 | −0.601632 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.30693 | 0.297975 | ||||||||
\(449\) | −16.7743 | −0.791626 | −0.395813 | − | 0.918331i | \(-0.629537\pi\) | ||||
−0.395813 | + | 0.918331i | \(0.629537\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0748511 | 0.00352460 | ||||||||
\(452\) | 6.06594 | 0.285318 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.5092 | −0.540155 | ||||||||
\(455\) | −1.99952 | −0.0937391 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6220 | −0.824320 | −0.412160 | − | 0.911111i | \(-0.635226\pi\) | ||||
−0.412160 | + | 0.911111i | \(0.635226\pi\) | |||||||
\(458\) | −20.2999 | −0.948552 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.58372 | 0.167092 | ||||||||
\(461\) | 0.380299 | 0.0177123 | 0.00885614 | − | 0.999961i | \(-0.497181\pi\) | ||||
0.00885614 | + | 0.999961i | \(0.497181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.78153 | −0.408112 | −0.204056 | − | 0.978959i | \(-0.565413\pi\) | ||||
−0.204056 | + | 0.978959i | \(0.565413\pi\) | |||||||
\(464\) | −11.0672 | −0.513784 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −40.3277 | −1.86815 | ||||||||
\(467\) | 19.8468 | 0.918400 | 0.459200 | − | 0.888333i | \(-0.348136\pi\) | ||||
0.459200 | + | 0.888333i | \(0.348136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.393750 | −0.0181817 | ||||||||
\(470\) | −9.36623 | −0.432032 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.13585 | 0.190368 | ||||||||
\(473\) | 21.9177 | 1.00778 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.71233 | 0.0785671 | ||||||||
\(476\) | −1.79332 | −0.0821967 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.6374 | −0.943930 | ||||||||
\(479\) | −1.39194 | −0.0635993 | −0.0317997 | − | 0.999494i | \(-0.510124\pi\) | ||||
−0.0317997 | + | 0.999494i | \(0.510124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.8644 | −0.586566 | ||||||||
\(482\) | 6.50584 | 0.296333 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.65078 | −0.120490 | ||||||||
\(485\) | 25.9906 | 1.18017 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.98929 | −0.271401 | −0.135700 | − | 0.990750i | \(-0.543328\pi\) | ||||
−0.135700 | + | 0.990750i | \(0.543328\pi\) | |||||||
\(488\) | 14.6716 | 0.664154 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.61192 | 0.117995 | ||||||||
\(491\) | 1.88645 | 0.0851344 | 0.0425672 | − | 0.999094i | \(-0.486446\pi\) | ||||
0.0425672 | + | 0.999094i | \(0.486446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.4029 | −0.603637 | ||||||||
\(494\) | 1.47515 | 0.0663703 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.65448 | 0.119190 | ||||||||
\(497\) | −10.0573 | −0.451132 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0508 | 0.808066 | 0.404033 | − | 0.914744i | \(-0.367608\pi\) | ||||
0.404033 | + | 0.914744i | \(0.367608\pi\) | |||||||
\(500\) | −3.94292 | −0.176333 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.7432 | −0.791918 | ||||||||
\(503\) | −40.4303 | −1.80270 | −0.901348 | − | 0.433095i | \(-0.857421\pi\) | ||||
−0.901348 | + | 0.433095i | \(0.857421\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.1135 | 1.29553 | ||||||||
\(506\) | 16.5748 | 0.736841 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.325779 | 0.0144541 | ||||||||
\(509\) | 28.8945 | 1.28072 | 0.640362 | − | 0.768073i | \(-0.278784\pi\) | ||||
0.640362 | + | 0.768073i | \(0.278784\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.94732 | 0.351569 | ||||||||
\(512\) | −14.9139 | −0.659108 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.5054 | 1.43375 | ||||||||
\(515\) | 0.814298 | 0.0358823 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.06784 | −0.266863 | ||||||||
\(518\) | 16.8044 | 0.738343 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.10532 | 0.223883 | ||||||||
\(521\) | 11.5348 | 0.505348 | 0.252674 | − | 0.967551i | \(-0.418690\pi\) | ||||
0.252674 | + | 0.967551i | \(0.418690\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.32409 | 0.363987 | 0.181993 | − | 0.983300i | \(-0.441745\pi\) | ||||
0.181993 | + | 0.983300i | \(0.441745\pi\) | |||||||
\(524\) | 3.33579 | 0.145725 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.6739 | 1.25024 | ||||||||
\(527\) | 3.21470 | 0.140034 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.2545 | 0.793674 | ||||||||
\(530\) | 33.3324 | 1.44787 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.269914 | −0.0117023 | ||||||||
\(533\) | −0.0516439 | −0.00223695 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.9803 | 1.25293 | ||||||||
\(536\) | 1.00535 | 0.0434245 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.1667 | 1.25746 | ||||||||
\(539\) | 1.69211 | 0.0728845 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.0228 | 1.20479 | 0.602396 | − | 0.798197i | \(-0.294213\pi\) | ||||
0.602396 | + | 0.798197i | \(0.294213\pi\) | |||||||
\(542\) | −37.9850 | −1.63159 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.0486 | 0.430832 | ||||||||
\(545\) | 6.82514 | 0.292357 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.859530 | 0.0367509 | 0.0183754 | − | 0.999831i | \(-0.494151\pi\) | ||||
0.0183754 | + | 0.999831i | \(0.494151\pi\) | |||||||
\(548\) | −4.69684 | −0.200639 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.33333 | −0.227414 | ||||||||
\(551\) | −2.01729 | −0.0859393 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.92230 | 0.166793 | ||||||||
\(554\) | 24.8551 | 1.05599 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.788183 | 0.0334264 | ||||||||
\(557\) | 34.8987 | 1.47871 | 0.739354 | − | 0.673317i | \(-0.235131\pi\) | ||||
0.739354 | + | 0.673317i | \(0.235131\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.1223 | −0.639603 | ||||||||
\(560\) | −7.78485 | −0.328970 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.9084 | −1.21943 | ||||||||
\(563\) | −13.3554 | −0.562865 | −0.281432 | − | 0.959581i | \(-0.590810\pi\) | ||||
−0.281432 | + | 0.959581i | \(0.590810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.8897 | 1.34161 | ||||||||
\(566\) | −4.14727 | −0.174323 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.6790 | 1.07747 | ||||||||
\(569\) | 3.71560 | 0.155766 | 0.0778831 | − | 0.996962i | \(-0.475184\pi\) | ||||
0.0778831 | + | 0.996962i | \(0.475184\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.10153 | −0.213492 | −0.106746 | − | 0.994286i | \(-0.534043\pi\) | ||||
−0.106746 | + | 0.994286i | \(0.534043\pi\) | |||||||
\(572\) | −0.643581 | −0.0269095 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.0674610 | 0.00281577 | ||||||||
\(575\) | −13.2746 | −0.553587 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.8444 | −0.576349 | −0.288174 | − | 0.957578i | \(-0.593048\pi\) | ||||
−0.288174 | + | 0.957578i | \(0.593048\pi\) | |||||||
\(578\) | 20.2860 | 0.843786 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.35851 | 0.0564092 | ||||||||
\(581\) | −6.36257 | −0.263964 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.5941 | 0.894338 | ||||||||
\(584\) | −20.2917 | −0.839675 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.29429 | 0.0947764 | ||||||||
\(587\) | 42.5391 | 1.75578 | 0.877888 | − | 0.478866i | \(-0.158952\pi\) | ||||
0.877888 | + | 0.478866i | \(0.158952\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.483847 | 0.0199366 | ||||||||
\(590\) | −4.23085 | −0.174181 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −50.0857 | −2.05851 | ||||||||
\(593\) | −14.6580 | −0.601933 | −0.300966 | − | 0.953635i | \(-0.597309\pi\) | ||||
−0.300966 | + | 0.953635i | \(0.597309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.42780 | −0.386502 | ||||||||
\(596\) | −4.52448 | −0.185330 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.4359 | −0.467649 | ||||||||
\(599\) | −40.4992 | −1.65475 | −0.827377 | − | 0.561647i | \(-0.810168\pi\) | ||||
−0.827377 | + | 0.561647i | \(0.810168\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.8489 | 0.564908 | 0.282454 | − | 0.959281i | \(-0.408851\pi\) | ||||
0.282454 | + | 0.959281i | \(0.408851\pi\) | |||||||
\(602\) | 19.7538 | 0.805104 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.19775 | 0.211494 | ||||||||
\(605\) | −13.9356 | −0.566564 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.2955 | −1.75731 | −0.878656 | − | 0.477456i | \(-0.841559\pi\) | ||||
−0.878656 | + | 0.477456i | \(0.841559\pi\) | |||||||
\(608\) | 1.51243 | 0.0613372 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.0087 | −0.607683 | ||||||||
\(611\) | 4.18654 | 0.169369 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6948 | −0.431959 | −0.215980 | − | 0.976398i | \(-0.569295\pi\) | ||||
−0.215980 | + | 0.976398i | \(0.569295\pi\) | |||||||
\(614\) | −22.5846 | −0.911439 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.32042 | −0.174075 | ||||||||
\(617\) | −14.2139 | −0.572230 | −0.286115 | − | 0.958195i | \(-0.592364\pi\) | ||||
−0.286115 | + | 0.958195i | \(0.592364\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.95554 | −0.199180 | −0.0995899 | − | 0.995029i | \(-0.531753\pi\) | ||||
−0.0995899 | + | 0.995029i | \(0.531753\pi\) | |||||||
\(620\) | −0.325840 | −0.0130860 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.6994 | −1.15074 | ||||||||
\(623\) | 5.77339 | 0.231306 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.3949 | −0.415798 | ||||||||
\(626\) | −19.9918 | −0.799032 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.88215 | −0.115010 | ||||||||
\(629\) | −60.6560 | −2.41851 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.86390 | 0.392675 | 0.196338 | − | 0.980536i | \(-0.437095\pi\) | ||||
0.196338 | + | 0.980536i | \(0.437095\pi\) | |||||||
\(632\) | −10.0147 | −0.398363 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 40.9035 | 1.62448 | ||||||||
\(635\) | 1.71268 | 0.0679656 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.16748 | −0.0462574 | ||||||||
\(638\) | 6.28317 | 0.248753 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 22.7261 | 0.898326 | ||||||||
\(641\) | −22.0104 | −0.869358 | −0.434679 | − | 0.900585i | \(-0.643138\pi\) | ||||
−0.434679 | + | 0.900585i | \(0.643138\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.9113 | 1.37677 | 0.688383 | − | 0.725347i | \(-0.258321\pi\) | ||||
0.688383 | + | 0.725347i | \(0.258321\pi\) | |||||||
\(644\) | 2.09247 | 0.0824548 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.95539 | 0.273656 | ||||||||
\(647\) | −5.34394 | −0.210092 | −0.105046 | − | 0.994467i | \(-0.533499\pi\) | ||||
−0.105046 | + | 0.994467i | \(0.533499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.74093 | −0.107591 | ||||||||
\(650\) | 3.67976 | 0.144332 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.60079 | −0.180181 | ||||||||
\(653\) | −17.7216 | −0.693500 | −0.346750 | − | 0.937958i | \(-0.612715\pi\) | ||||
−0.346750 | + | 0.937958i | \(0.612715\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.5368 | 0.685220 | ||||||||
\(656\) | −0.201068 | −0.00785039 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.46876 | −0.213195 | ||||||||
\(659\) | −47.9307 | −1.86711 | −0.933557 | − | 0.358429i | \(-0.883312\pi\) | ||||
−0.933557 | + | 0.358429i | \(0.883312\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.4838 | −1.30237 | −0.651184 | − | 0.758920i | \(-0.725727\pi\) | ||||
−0.651184 | + | 0.758920i | \(0.725727\pi\) | |||||||
\(662\) | 2.59981 | 0.101045 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.2454 | 0.630442 | ||||||||
\(665\) | −1.41899 | −0.0550260 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.6387 | 0.605533 | ||||||||
\(668\) | 6.10133 | 0.236067 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.02844 | −0.0397322 | ||||||||
\(671\) | −9.72325 | −0.375362 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.9171 | −0.999031 | −0.499515 | − | 0.866305i | \(-0.666489\pi\) | ||||
−0.499515 | + | 0.866305i | \(0.666489\pi\) | |||||||
\(674\) | 6.14769 | 0.236800 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.79109 | −0.145811 | ||||||||
\(677\) | −42.5126 | −1.63389 | −0.816946 | − | 0.576714i | \(-0.804335\pi\) | ||||
−0.816946 | + | 0.576714i | \(0.804335\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.1754 | 0.582379 | ||||||||
\(680\) | 24.0717 | 0.923109 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.50702 | −0.0577068 | ||||||||
\(683\) | 33.7802 | 1.29257 | 0.646283 | − | 0.763098i | \(-0.276323\pi\) | ||||
0.646283 | + | 0.763098i | \(0.276323\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.6921 | −0.943437 | ||||||||
\(686\) | 1.52505 | 0.0582267 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −58.8763 | −2.24464 | ||||||||
\(689\) | −14.8990 | −0.567607 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.2866 | 0.657611 | 0.328806 | − | 0.944398i | \(-0.393354\pi\) | ||||
0.328806 | + | 0.944398i | \(0.393354\pi\) | |||||||
\(692\) | 7.40899 | 0.281647 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44.1106 | 1.67442 | ||||||||
\(695\) | 4.14362 | 0.157176 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.243502 | −0.00922331 | ||||||||
\(698\) | −42.7196 | −1.61696 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.673298 | −0.0254483 | ||||||||
\(701\) | −10.5109 | −0.396991 | −0.198495 | − | 0.980102i | \(-0.563605\pi\) | ||||
−0.198495 | + | 0.980102i | \(0.563605\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.12939 | −0.344321 | ||||||||
\(704\) | 10.6720 | 0.402218 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.4547 | 0.769823 | ||||||||
\(707\) | 16.9988 | 0.639306 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.557852 | −0.0209506 | −0.0104753 | − | 0.999945i | \(-0.503334\pi\) | ||||
−0.0104753 | + | 0.999945i | \(0.503334\pi\) | |||||||
\(710\) | −26.2689 | −0.985854 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.7410 | −0.552443 | ||||||||
\(713\) | −3.75095 | −0.140474 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.38342 | −0.126533 | ||||||||
\(716\) | −1.33295 | −0.0498148 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.5532 | 0.804360 | ||||||||
\(719\) | −31.7055 | −1.18242 | −0.591209 | − | 0.806519i | \(-0.701349\pi\) | ||||
−0.591209 | + | 0.806519i | \(0.701349\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.475453 | 0.0177068 | ||||||||
\(722\) | −27.9291 | −1.03941 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.81121 | −0.290301 | ||||||||
\(725\) | −5.03210 | −0.186888 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.0045 | −0.853190 | −0.426595 | − | 0.904443i | \(-0.640287\pi\) | ||||
−0.426595 | + | 0.904443i | \(0.640287\pi\) | |||||||
\(728\) | 2.98090 | 0.110480 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 20.7578 | 0.768279 | ||||||||
\(731\) | −71.3018 | −2.63719 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.5374 | −1.31260 | −0.656302 | − | 0.754498i | \(-0.727880\pi\) | ||||
−0.656302 | + | 0.754498i | \(0.727880\pi\) | |||||||
\(734\) | −0.228697 | −0.00844136 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.7249 | −0.432185 | ||||||||
\(737\) | −0.666269 | −0.0245423 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.4169 | 1.11890 | 0.559451 | − | 0.828863i | \(-0.311012\pi\) | ||||
0.559451 | + | 0.828863i | \(0.311012\pi\) | |||||||
\(740\) | 6.14806 | 0.226007 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.4621 | 0.714478 | ||||||||
\(743\) | −43.1393 | −1.58263 | −0.791313 | − | 0.611411i | \(-0.790602\pi\) | ||||
−0.791313 | + | 0.611411i | \(0.790602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.7860 | −0.871451 | ||||||||
\(746\) | 49.4628 | 1.81096 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.03450 | −0.110952 | ||||||||
\(749\) | 16.9210 | 0.618280 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.1332 | −1.31852 | −0.659260 | − | 0.751915i | \(-0.729130\pi\) | ||||
−0.659260 | + | 0.751915i | \(0.729130\pi\) | |||||||
\(752\) | 16.2997 | 0.594389 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.33511 | −0.157875 | ||||||||
\(755\) | 27.3255 | 0.994477 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.0480 | −1.23750 | −0.618748 | − | 0.785590i | \(-0.712360\pi\) | ||||
−0.618748 | + | 0.785590i | \(0.712360\pi\) | |||||||
\(758\) | −5.25050 | −0.190707 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.62306 | 0.131422 | ||||||||
\(761\) | −49.9432 | −1.81044 | −0.905219 | − | 0.424945i | \(-0.860293\pi\) | ||||
−0.905219 | + | 0.424945i | \(0.860293\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.98507 | 0.144269 | ||||||||
\(764\) | 1.75798 | 0.0636016 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50.9664 | 1.84149 | ||||||||
\(767\) | 1.89112 | 0.0682843 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.4520 | −1.45874 | −0.729368 | − | 0.684121i | \(-0.760186\pi\) | ||||
−0.729368 | + | 0.684121i | \(0.760186\pi\) | |||||||
\(770\) | 4.41967 | 0.159274 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.16993 | −0.114088 | ||||||||
\(773\) | 27.5266 | 0.990063 | 0.495032 | − | 0.868875i | \(-0.335156\pi\) | ||||
0.495032 | + | 0.868875i | \(0.335156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.20695 | 0.0433550 | ||||||||
\(776\) | −38.7470 | −1.39094 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 45.5606 | 1.63343 | ||||||||
\(779\) | −0.0366498 | −0.00131312 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0181 | −0.608956 | ||||||||
\(782\) | −53.9206 | −1.92820 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.54543 | −0.162337 | ||||||||
\(785\) | −15.1520 | −0.540797 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.4724 | −1.44269 | −0.721343 | − | 0.692578i | \(-0.756475\pi\) | ||||
−0.721343 | + | 0.692578i | \(0.756475\pi\) | |||||||
\(788\) | 0.0464547 | 0.00165488 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.2447 | 0.364491 | ||||||||
\(791\) | 18.6198 | 0.662044 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.70861 | 0.238230 | ||||||||
\(794\) | 31.8415 | 1.13001 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.87593 | −0.137379 | ||||||||
\(797\) | 42.8646 | 1.51834 | 0.759170 | − | 0.650892i | \(-0.225605\pi\) | ||||
0.759170 | + | 0.650892i | \(0.225605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.7396 | 0.698338 | ||||||||
\(800\) | 3.77274 | 0.133387 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.7951 | 1.44052 | ||||||||
\(803\) | 13.4478 | 0.474561 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.0005 | 0.387716 | ||||||||
\(806\) | 1.03978 | 0.0366246 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −43.4025 | −1.52690 | ||||||||
\(809\) | 24.1197 | 0.848003 | 0.424001 | − | 0.905662i | \(-0.360625\pi\) | ||||
0.424001 | + | 0.905662i | \(0.360625\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.65144 | −0.163334 | −0.0816670 | − | 0.996660i | \(-0.526024\pi\) | ||||
−0.0816670 | + | 0.996660i | \(0.526024\pi\) | |||||||
\(812\) | 0.793210 | 0.0278362 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 28.4350 | 0.996645 | ||||||||
\(815\) | −24.1872 | −0.847240 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.7317 | −0.375455 | ||||||||
\(818\) | 29.5017 | 1.03150 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0246813 | 0.000861908 0 | ||||||||
\(821\) | −11.1947 | −0.390697 | −0.195349 | − | 0.980734i | \(-0.562584\pi\) | ||||
−0.195349 | + | 0.980734i | \(0.562584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.6002 | 1.65924 | 0.829619 | − | 0.558330i | \(-0.188558\pi\) | ||||
0.829619 | + | 0.558330i | \(0.188558\pi\) | |||||||
\(824\) | −1.21396 | −0.0422903 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.47031 | −0.0859532 | ||||||||
\(827\) | 32.7249 | 1.13796 | 0.568979 | − | 0.822352i | \(-0.307339\pi\) | ||||
0.568979 | + | 0.822352i | \(0.307339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.8180 | 1.10508 | 0.552542 | − | 0.833485i | \(-0.313658\pi\) | ||||
0.552542 | + | 0.833485i | \(0.313658\pi\) | |||||||
\(830\) | −16.6185 | −0.576837 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.36323 | −0.255274 | ||||||||
\(833\) | −5.50471 | −0.190727 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0758 | 1.11003 | ||||||||
\(836\) | −0.456726 | −0.0157962 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.27374 | 0.113089 | ||||||||
\(839\) | 4.50320 | 0.155468 | 0.0777338 | − | 0.996974i | \(-0.475232\pi\) | ||||
0.0777338 | + | 0.996974i | \(0.475232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0717 | −0.795576 | ||||||||
\(842\) | −1.02894 | −0.0354594 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.28906 | 0.0787928 | ||||||||
\(845\) | −19.9304 | −0.685627 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.13675 | −0.279582 | ||||||||
\(848\) | −58.0071 | −1.99197 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.3502 | 0.595105 | ||||||||
\(851\) | 70.7741 | 2.42611 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.9321 | −1.50421 | −0.752103 | − | 0.659046i | \(-0.770960\pi\) | ||||
−0.752103 | + | 0.659046i | \(0.770960\pi\) | |||||||
\(854\) | −8.76327 | −0.299873 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −43.2039 | −1.47668 | ||||||||
\(857\) | 8.78489 | 0.300086 | 0.150043 | − | 0.988679i | \(-0.452059\pi\) | ||||
0.150043 | + | 0.988679i | \(0.452059\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0693 | 1.36715 | 0.683573 | − | 0.729883i | \(-0.260425\pi\) | ||||
0.683573 | + | 0.729883i | \(0.260425\pi\) | |||||||
\(860\) | 7.22711 | 0.246443 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.7703 | −0.366838 | ||||||||
\(863\) | −38.3279 | −1.30470 | −0.652348 | − | 0.757919i | \(-0.726216\pi\) | ||||
−0.652348 | + | 0.757919i | \(0.726216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.9504 | 1.32435 | ||||||||
\(866\) | 10.2784 | 0.349276 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.190252 | −0.00645756 | ||||||||
\(869\) | 6.63698 | 0.225144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.459696 | 0.0155762 | ||||||||
\(872\) | −10.1750 | −0.344567 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.11564 | −0.274516 | ||||||||
\(875\) | −12.1030 | −0.409157 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.4617 | 0.792245 | 0.396122 | − | 0.918198i | \(-0.370356\pi\) | ||||
0.396122 | + | 0.918198i | \(0.370356\pi\) | |||||||
\(878\) | 4.05412 | 0.136820 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.1729 | −0.444057 | ||||||||
\(881\) | 38.6863 | 1.30338 | 0.651688 | − | 0.758487i | \(-0.274061\pi\) | ||||
0.651688 | + | 0.758487i | \(0.274061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.55080 | −0.287757 | −0.143879 | − | 0.989595i | \(-0.545958\pi\) | ||||
−0.143879 | + | 0.989595i | \(0.545958\pi\) | |||||||
\(884\) | 2.09367 | 0.0704177 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.66126 | −0.257385 | ||||||||
\(887\) | −53.2942 | −1.78944 | −0.894722 | − | 0.446623i | \(-0.852627\pi\) | ||||
−0.894722 | + | 0.446623i | \(0.852627\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 15.0796 | 0.505470 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.71417 | −0.0908772 | ||||||||
\(893\) | 2.97103 | 0.0994219 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.00758 | −0.234237 | ||||||||
\(896\) | 13.2693 | 0.443297 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.5816 | −0.853669 | ||||||||
\(899\) | −1.42190 | −0.0474231 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −70.2492 | −2.34034 | ||||||||
\(902\) | 0.114152 | 0.00380084 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47.5414 | −1.58120 | ||||||||
\(905\) | −41.0649 | −1.36504 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0792 | 0.799536 | 0.399768 | − | 0.916616i | \(-0.369091\pi\) | ||||
0.399768 | + | 0.916616i | \(0.369091\pi\) | |||||||
\(908\) | −2.45859 | −0.0815911 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.04937 | −0.101086 | ||||||||
\(911\) | 43.2252 | 1.43212 | 0.716058 | − | 0.698041i | \(-0.245945\pi\) | ||||
0.716058 | + | 0.698041i | \(0.245945\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.7662 | −0.356309 | ||||||||
\(914\) | −26.8744 | −0.888925 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.33644 | −0.143280 | ||||||||
\(917\) | 10.2394 | 0.338135 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.5792 | 1.37157 | 0.685786 | − | 0.727803i | \(-0.259459\pi\) | ||||
0.685786 | + | 0.727803i | \(0.259459\pi\) | |||||||
\(920\) | −28.0872 | −0.926007 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.579975 | 0.0191005 | ||||||||
\(923\) | 11.7417 | 0.386484 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.7732 | −0.748777 | ||||||||
\(926\) | −13.3923 | −0.440098 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.44465 | −0.145903 | ||||||||
\(929\) | 0.613766 | 0.0201370 | 0.0100685 | − | 0.999949i | \(-0.496795\pi\) | ||||
0.0100685 | + | 0.999949i | \(0.496795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.828520 | −0.0271536 | ||||||||
\(932\) | −8.61475 | −0.282185 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.2674 | 0.990378 | ||||||||
\(935\) | −15.9529 | −0.521716 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.1622 | 1.50805 | 0.754026 | − | 0.656845i | \(-0.228109\pi\) | ||||
0.754026 | + | 0.656845i | \(0.228109\pi\) | |||||||
\(938\) | −0.600488 | −0.0196066 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.00080 | −0.0652589 | ||||||||
\(941\) | −6.85694 | −0.223530 | −0.111765 | − | 0.993735i | \(-0.535650\pi\) | ||||
−0.111765 | + | 0.993735i | \(0.535650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.284122 | 0.00925227 | ||||||||
\(944\) | 7.36279 | 0.239638 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 33.4256 | 1.08676 | ||||||||
\(947\) | −15.9566 | −0.518519 | −0.259259 | − | 0.965808i | \(-0.583478\pi\) | ||||
−0.259259 | + | 0.965808i | \(0.583478\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.27835 | −0.301188 | ||||||||
\(950\) | 2.61139 | 0.0847246 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 14.0550 | 0.455526 | ||||||||
\(953\) | −3.19350 | −0.103447 | −0.0517237 | − | 0.998661i | \(-0.516472\pi\) | ||||
−0.0517237 | + | 0.998661i | \(0.516472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.24203 | 0.299065 | ||||||||
\(956\) | −4.40852 | −0.142582 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.12278 | −0.0685838 | ||||||||
\(959\) | −14.4173 | −0.465557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6590 | −0.988999 | ||||||||
\(962\) | −19.6189 | −0.632537 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.38977 | 0.0447614 | ||||||||
\(965\) | −16.6649 | −0.536461 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.8839 | −1.05747 | −0.528737 | − | 0.848786i | \(-0.677334\pi\) | ||||
−0.528737 | + | 0.848786i | \(0.677334\pi\) | |||||||
\(968\) | 20.7753 | 0.667745 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 39.6370 | 1.27267 | ||||||||
\(971\) | 49.2552 | 1.58068 | 0.790338 | − | 0.612671i | \(-0.209905\pi\) | ||||
0.790338 | + | 0.612671i | \(0.209905\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.41938 | 0.0775618 | ||||||||
\(974\) | −9.13397 | −0.292671 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.1190 | 0.836049 | ||||||||
\(977\) | 16.7606 | 0.536220 | 0.268110 | − | 0.963388i | \(-0.413601\pi\) | ||||
0.268110 | + | 0.963388i | \(0.413601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.76923 | 0.312226 | ||||||||
\(980\) | 0.557955 | 0.0178232 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.87694 | 0.0918067 | ||||||||
\(983\) | 49.5398 | 1.58007 | 0.790037 | − | 0.613059i | \(-0.210061\pi\) | ||||
0.790037 | + | 0.613059i | \(0.210061\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.244221 | 0.00778151 | ||||||||
\(986\) | −20.4401 | −0.650946 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.315120 | 0.0100253 | ||||||||
\(989\) | 83.1958 | 2.64547 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.0914 | −0.987652 | −0.493826 | − | 0.869561i | \(-0.664402\pi\) | ||||
−0.493826 | + | 0.869561i | \(0.664402\pi\) | |||||||
\(992\) | 1.06605 | 0.0338471 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.3379 | −0.486489 | ||||||||
\(995\) | −20.3765 | −0.645977 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.4798 | −1.69372 | −0.846861 | − | 0.531814i | \(-0.821510\pi\) | ||||
−0.846861 | + | 0.531814i | \(0.821510\pi\) | |||||||
\(998\) | 27.5284 | 0.871397 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.u.1.12 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.7 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.7 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.12 | 18 | 1.1 | even | 1 | trivial |