Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | 10.10.52900342088704.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 18x^{8} + 123x^{6} - 390x^{4} + 548x^{2} - 241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 414) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.32333\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.24774 | −1.89964 | −0.949822 | − | 0.312790i | \(-0.898737\pi\) | ||||
−0.949822 | + | 0.312790i | \(0.898737\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.296223 | 0.111962 | 0.0559808 | − | 0.998432i | \(-0.482171\pi\) | ||||
0.0559808 | + | 0.998432i | \(0.482171\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.24774 | −1.34325 | ||||||||
\(11\) | −2.39725 | −0.722799 | −0.361400 | − | 0.932411i | \(-0.617701\pi\) | ||||
−0.361400 | + | 0.932411i | \(0.617701\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51372 | 0.697181 | 0.348590 | − | 0.937275i | \(-0.386660\pi\) | ||||
0.348590 | + | 0.937275i | \(0.386660\pi\) | |||||||
\(14\) | 0.296223 | 0.0791688 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.50912 | −1.09362 | −0.546811 | − | 0.837256i | \(-0.684158\pi\) | ||||
−0.546811 | + | 0.837256i | \(0.684158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.13579 | −0.260569 | −0.130285 | − | 0.991477i | \(-0.541589\pi\) | ||||
−0.130285 | + | 0.991477i | \(0.541589\pi\) | |||||||
\(20\) | −4.24774 | −0.949822 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.39725 | −0.511096 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.0433 | 2.60865 | ||||||||
\(26\) | 2.51372 | 0.492981 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.296223 | 0.0559808 | ||||||||
\(29\) | 0.957087 | 0.177727 | 0.0888633 | − | 0.996044i | \(-0.471677\pi\) | ||||
0.0888633 | + | 0.996044i | \(0.471677\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.24911 | 1.48158 | 0.740792 | − | 0.671735i | \(-0.234451\pi\) | ||||
0.740792 | + | 0.671735i | \(0.234451\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.50912 | −0.773308 | ||||||||
\(35\) | −1.25827 | −0.212687 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.34724 | 1.37228 | 0.686139 | − | 0.727470i | \(-0.259304\pi\) | ||||
0.686139 | + | 0.727470i | \(0.259304\pi\) | |||||||
\(38\) | −1.13579 | −0.184250 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.24774 | −0.671626 | ||||||||
\(41\) | 4.10669 | 0.641357 | 0.320678 | − | 0.947188i | \(-0.396089\pi\) | ||||
0.320678 | + | 0.947188i | \(0.396089\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.86276 | 0.589066 | 0.294533 | − | 0.955641i | \(-0.404836\pi\) | ||||
0.294533 | + | 0.955641i | \(0.404836\pi\) | |||||||
\(44\) | −2.39725 | −0.361400 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.35841 | 0.489874 | 0.244937 | − | 0.969539i | \(-0.421233\pi\) | ||||
0.244937 | + | 0.969539i | \(0.421233\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91225 | −0.987465 | ||||||||
\(50\) | 13.0433 | 1.84459 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.51372 | 0.348590 | ||||||||
\(53\) | 4.84637 | 0.665701 | 0.332850 | − | 0.942980i | \(-0.391990\pi\) | ||||
0.332850 | + | 0.942980i | \(0.391990\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1829 | 1.37306 | ||||||||
\(56\) | 0.296223 | 0.0395844 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.957087 | 0.125672 | ||||||||
\(59\) | −11.3103 | −1.47248 | −0.736240 | − | 0.676720i | \(-0.763401\pi\) | ||||
−0.736240 | + | 0.676720i | \(0.763401\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.76531 | −0.994246 | −0.497123 | − | 0.867680i | \(-0.665610\pi\) | ||||
−0.497123 | + | 0.867680i | \(0.665610\pi\) | |||||||
\(62\) | 8.24911 | 1.04764 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.6776 | −1.32440 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.1030 | 1.72296 | 0.861478 | − | 0.507795i | \(-0.169539\pi\) | ||||
0.861478 | + | 0.507795i | \(0.169539\pi\) | |||||||
\(68\) | −4.50912 | −0.546811 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.25827 | −0.150393 | ||||||||
\(71\) | −14.7692 | −1.75279 | −0.876393 | − | 0.481597i | \(-0.840057\pi\) | ||||
−0.876393 | + | 0.481597i | \(0.840057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1912 | −1.30983 | −0.654915 | − | 0.755703i | \(-0.727296\pi\) | ||||
−0.654915 | + | 0.755703i | \(0.727296\pi\) | |||||||
\(74\) | 8.34724 | 0.970347 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.13579 | −0.130285 | ||||||||
\(77\) | −0.710121 | −0.0809258 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0724 | −1.35826 | −0.679128 | − | 0.734020i | \(-0.737642\pi\) | ||||
−0.679128 | + | 0.734020i | \(0.737642\pi\) | |||||||
\(80\) | −4.24774 | −0.474911 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.10669 | 0.453508 | ||||||||
\(83\) | −2.12541 | −0.233295 | −0.116647 | − | 0.993173i | \(-0.537215\pi\) | ||||
−0.116647 | + | 0.993173i | \(0.537215\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.1536 | 2.07749 | ||||||||
\(86\) | 3.86276 | 0.416532 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.39725 | −0.255548 | ||||||||
\(89\) | 11.4844 | 1.21735 | 0.608673 | − | 0.793421i | \(-0.291702\pi\) | ||||
0.608673 | + | 0.793421i | \(0.291702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.744621 | 0.0780575 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.35841 | 0.346393 | ||||||||
\(95\) | 4.82455 | 0.494989 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.795359 | 0.0807565 | 0.0403782 | − | 0.999184i | \(-0.487144\pi\) | ||||
0.0403782 | + | 0.999184i | \(0.487144\pi\) | |||||||
\(98\) | −6.91225 | −0.698243 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.0433 | 1.30433 | ||||||||
\(101\) | −9.35035 | −0.930395 | −0.465197 | − | 0.885207i | \(-0.654017\pi\) | ||||
−0.465197 | + | 0.885207i | \(0.654017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.90643 | −0.976109 | −0.488055 | − | 0.872813i | \(-0.662293\pi\) | ||||
−0.488055 | + | 0.872813i | \(0.662293\pi\) | |||||||
\(104\) | 2.51372 | 0.246491 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.84637 | 0.470722 | ||||||||
\(107\) | 18.4893 | 1.78743 | 0.893714 | − | 0.448637i | \(-0.148090\pi\) | ||||
0.893714 | + | 0.448637i | \(0.148090\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.4814 | −1.57863 | −0.789314 | − | 0.613990i | \(-0.789564\pi\) | ||||
−0.789314 | + | 0.613990i | \(0.789564\pi\) | |||||||
\(110\) | 10.1829 | 0.970901 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.296223 | 0.0279904 | ||||||||
\(113\) | 4.27218 | 0.401893 | 0.200946 | − | 0.979602i | \(-0.435598\pi\) | ||||
0.200946 | + | 0.979602i | \(0.435598\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.957087 | 0.0888633 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.3103 | −1.04120 | ||||||||
\(119\) | −1.33570 | −0.122444 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.25317 | −0.477561 | ||||||||
\(122\) | −7.76531 | −0.703038 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.24911 | 0.740792 | ||||||||
\(125\) | −34.1656 | −3.05586 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.5281 | −1.20042 | −0.600210 | − | 0.799842i | \(-0.704917\pi\) | ||||
−0.600210 | + | 0.799842i | \(0.704917\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.6776 | −0.936489 | ||||||||
\(131\) | −13.1098 | −1.14541 | −0.572706 | − | 0.819761i | \(-0.694106\pi\) | ||||
−0.572706 | + | 0.819761i | \(0.694106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.336448 | −0.0291737 | ||||||||
\(134\) | 14.1030 | 1.21831 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.50912 | −0.386654 | ||||||||
\(137\) | −1.26947 | −0.108458 | −0.0542291 | − | 0.998529i | \(-0.517270\pi\) | ||||
−0.0542291 | + | 0.998529i | \(0.517270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.5662 | −1.32031 | −0.660155 | − | 0.751129i | \(-0.729509\pi\) | ||||
−0.660155 | + | 0.751129i | \(0.729509\pi\) | |||||||
\(140\) | −1.25827 | −0.106344 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.7692 | −1.23941 | ||||||||
\(143\) | −6.02603 | −0.503922 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.06545 | −0.337617 | ||||||||
\(146\) | −11.1912 | −0.926189 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.34724 | 0.686139 | ||||||||
\(149\) | −13.6820 | −1.12087 | −0.560435 | − | 0.828198i | \(-0.689366\pi\) | ||||
−0.560435 | + | 0.828198i | \(0.689366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.65087 | 0.622619 | 0.311309 | − | 0.950309i | \(-0.399232\pi\) | ||||
0.311309 | + | 0.950309i | \(0.399232\pi\) | |||||||
\(152\) | −1.13579 | −0.0921251 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.710121 | −0.0572232 | ||||||||
\(155\) | −35.0400 | −2.81448 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.27528 | −0.580631 | −0.290315 | − | 0.956931i | \(-0.593760\pi\) | ||||
−0.290315 | + | 0.956931i | \(0.593760\pi\) | |||||||
\(158\) | −12.0724 | −0.960433 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.24774 | −0.335813 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6142 | 1.37965 | 0.689824 | − | 0.723977i | \(-0.257688\pi\) | ||||
0.689824 | + | 0.723977i | \(0.257688\pi\) | |||||||
\(164\) | 4.10669 | 0.320678 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.12541 | −0.164964 | ||||||||
\(167\) | 12.8331 | 0.993054 | 0.496527 | − | 0.868021i | \(-0.334608\pi\) | ||||
0.496527 | + | 0.868021i | \(0.334608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.68121 | −0.513939 | ||||||||
\(170\) | 19.1536 | 1.46901 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.86276 | 0.294533 | ||||||||
\(173\) | −9.24925 | −0.703208 | −0.351604 | − | 0.936149i | \(-0.614364\pi\) | ||||
−0.351604 | + | 0.936149i | \(0.614364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.86371 | 0.292069 | ||||||||
\(176\) | −2.39725 | −0.180700 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.4844 | 0.860793 | ||||||||
\(179\) | −18.9994 | −1.42008 | −0.710042 | − | 0.704160i | \(-0.751324\pi\) | ||||
−0.710042 | + | 0.704160i | \(0.751324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.61367 | −0.194272 | −0.0971362 | − | 0.995271i | \(-0.530968\pi\) | ||||
−0.0971362 | + | 0.995271i | \(0.530968\pi\) | |||||||
\(182\) | 0.744621 | 0.0551950 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −35.4569 | −2.60684 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8095 | 0.790470 | ||||||||
\(188\) | 3.35841 | 0.244937 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.82455 | 0.350010 | ||||||||
\(191\) | −5.90298 | −0.427125 | −0.213562 | − | 0.976929i | \(-0.568507\pi\) | ||||
−0.213562 | + | 0.976929i | \(0.568507\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.350668 | 0.0252416 | 0.0126208 | − | 0.999920i | \(-0.495983\pi\) | ||||
0.0126208 | + | 0.999920i | \(0.495983\pi\) | |||||||
\(194\) | 0.795359 | 0.0571035 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.91225 | −0.493732 | ||||||||
\(197\) | 18.8533 | 1.34324 | 0.671621 | − | 0.740895i | \(-0.265598\pi\) | ||||
0.671621 | + | 0.740895i | \(0.265598\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.3425 | 1.15849 | 0.579243 | − | 0.815155i | \(-0.303348\pi\) | ||||
0.579243 | + | 0.815155i | \(0.303348\pi\) | |||||||
\(200\) | 13.0433 | 0.922297 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.35035 | −0.657888 | ||||||||
\(203\) | 0.283511 | 0.0198986 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.4441 | −1.21835 | ||||||||
\(206\) | −9.90643 | −0.690213 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.51372 | 0.174295 | ||||||||
\(209\) | 2.72279 | 0.188339 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8129 | 0.950918 | 0.475459 | − | 0.879738i | \(-0.342282\pi\) | ||||
0.475459 | + | 0.879738i | \(0.342282\pi\) | |||||||
\(212\) | 4.84637 | 0.332850 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.4893 | 1.26390 | ||||||||
\(215\) | −16.4080 | −1.11902 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.44357 | 0.165880 | ||||||||
\(218\) | −16.4814 | −1.11626 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.1829 | 0.686531 | ||||||||
\(221\) | −11.3347 | −0.762453 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.66413 | 0.245368 | 0.122684 | − | 0.992446i | \(-0.460850\pi\) | ||||
0.122684 | + | 0.992446i | \(0.460850\pi\) | |||||||
\(224\) | 0.296223 | 0.0197922 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.27218 | 0.284181 | ||||||||
\(227\) | −0.0570530 | −0.00378674 | −0.00189337 | − | 0.999998i | \(-0.500603\pi\) | ||||
−0.00189337 | + | 0.999998i | \(0.500603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.13532 | −0.405433 | −0.202717 | − | 0.979237i | \(-0.564977\pi\) | ||||
−0.202717 | + | 0.979237i | \(0.564977\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.957087 | 0.0628358 | ||||||||
\(233\) | 20.3085 | 1.33045 | 0.665227 | − | 0.746641i | \(-0.268335\pi\) | ||||
0.665227 | + | 0.746641i | \(0.268335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.2656 | −0.930586 | ||||||||
\(236\) | −11.3103 | −0.736240 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.33570 | −0.0865808 | ||||||||
\(239\) | −3.65555 | −0.236458 | −0.118229 | − | 0.992986i | \(-0.537722\pi\) | ||||
−0.118229 | + | 0.992986i | \(0.537722\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7513 | 0.756970 | 0.378485 | − | 0.925607i | \(-0.376445\pi\) | ||||
0.378485 | + | 0.925607i | \(0.376445\pi\) | |||||||
\(242\) | −5.25317 | −0.337687 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.76531 | −0.497123 | ||||||||
\(245\) | 29.3614 | 1.87583 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.85507 | −0.181664 | ||||||||
\(248\) | 8.24911 | 0.523819 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −34.1656 | −2.16082 | ||||||||
\(251\) | 1.89694 | 0.119734 | 0.0598668 | − | 0.998206i | \(-0.480932\pi\) | ||||
0.0598668 | + | 0.998206i | \(0.480932\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.5281 | −0.848826 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.43775 | 0.339198 | 0.169599 | − | 0.985513i | \(-0.445753\pi\) | ||||
0.169599 | + | 0.985513i | \(0.445753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.47264 | 0.153642 | ||||||||
\(260\) | −10.6776 | −0.662198 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.1098 | −0.809928 | ||||||||
\(263\) | −23.1887 | −1.42988 | −0.714940 | − | 0.699186i | \(-0.753546\pi\) | ||||
−0.714940 | + | 0.699186i | \(0.753546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.5861 | −1.26460 | ||||||||
\(266\) | −0.336448 | −0.0206289 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.1030 | 0.861478 | ||||||||
\(269\) | 5.34716 | 0.326022 | 0.163011 | − | 0.986624i | \(-0.447879\pi\) | ||||
0.163011 | + | 0.986624i | \(0.447879\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0856 | −0.977128 | −0.488564 | − | 0.872528i | \(-0.662479\pi\) | ||||
−0.488564 | + | 0.872528i | \(0.662479\pi\) | |||||||
\(272\) | −4.50912 | −0.273406 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.26947 | −0.0766915 | ||||||||
\(275\) | −31.2680 | −1.88553 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.44954 | 0.207263 | 0.103631 | − | 0.994616i | \(-0.466954\pi\) | ||||
0.103631 | + | 0.994616i | \(0.466954\pi\) | |||||||
\(278\) | −15.5662 | −0.933600 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.25827 | −0.0751963 | ||||||||
\(281\) | 6.43983 | 0.384168 | 0.192084 | − | 0.981378i | \(-0.438475\pi\) | ||||
0.192084 | + | 0.981378i | \(0.438475\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.6630 | −0.693292 | −0.346646 | − | 0.937996i | \(-0.612679\pi\) | ||||
−0.346646 | + | 0.937996i | \(0.612679\pi\) | |||||||
\(284\) | −14.7692 | −0.876393 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.02603 | −0.356326 | ||||||||
\(287\) | 1.21649 | 0.0718073 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.33217 | 0.196010 | ||||||||
\(290\) | −4.06545 | −0.238732 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.1912 | −0.654915 | ||||||||
\(293\) | −5.15331 | −0.301059 | −0.150530 | − | 0.988605i | \(-0.548098\pi\) | ||||
−0.150530 | + | 0.988605i | \(0.548098\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 48.0433 | 2.79719 | ||||||||
\(296\) | 8.34724 | 0.485174 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.6820 | −0.792575 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.14424 | 0.0659527 | ||||||||
\(302\) | 7.65087 | 0.440258 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.13579 | −0.0651423 | ||||||||
\(305\) | 32.9850 | 1.88871 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5307 | −0.886382 | −0.443191 | − | 0.896427i | \(-0.646154\pi\) | ||||
−0.443191 | + | 0.896427i | \(0.646154\pi\) | |||||||
\(308\) | −0.710121 | −0.0404629 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −35.0400 | −1.99014 | ||||||||
\(311\) | 7.59667 | 0.430767 | 0.215384 | − | 0.976529i | \(-0.430900\pi\) | ||||
0.215384 | + | 0.976529i | \(0.430900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.1607 | −1.47869 | −0.739344 | − | 0.673328i | \(-0.764864\pi\) | ||||
−0.739344 | + | 0.673328i | \(0.764864\pi\) | |||||||
\(314\) | −7.27528 | −0.410568 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0724 | −0.679128 | ||||||||
\(317\) | 24.2042 | 1.35944 | 0.679720 | − | 0.733471i | \(-0.262101\pi\) | ||||
0.679720 | + | 0.733471i | \(0.262101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.29438 | −0.128461 | ||||||||
\(320\) | −4.24774 | −0.237456 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.12143 | 0.284964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 32.7871 | 1.81870 | ||||||||
\(326\) | 17.6142 | 0.975559 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.10669 | 0.226754 | ||||||||
\(329\) | 0.994835 | 0.0548470 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.4228 | −1.72716 | −0.863578 | − | 0.504216i | \(-0.831782\pi\) | ||||
−0.863578 | + | 0.504216i | \(0.831782\pi\) | |||||||
\(332\) | −2.12541 | −0.116647 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.8331 | 0.702195 | ||||||||
\(335\) | −59.9058 | −3.27300 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.72615 | −0.311923 | −0.155962 | − | 0.987763i | \(-0.549848\pi\) | ||||
−0.155962 | + | 0.987763i | \(0.549848\pi\) | |||||||
\(338\) | −6.68121 | −0.363410 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.1536 | 1.03875 | ||||||||
\(341\) | −19.7752 | −1.07089 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.12112 | −0.222520 | ||||||||
\(344\) | 3.86276 | 0.208266 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.24925 | −0.497243 | ||||||||
\(347\) | −19.6762 | −1.05628 | −0.528138 | − | 0.849159i | \(-0.677110\pi\) | ||||
−0.528138 | + | 0.849159i | \(0.677110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.20578 | 0.118073 | 0.0590364 | − | 0.998256i | \(-0.481197\pi\) | ||||
0.0590364 | + | 0.998256i | \(0.481197\pi\) | |||||||
\(350\) | 3.86371 | 0.206524 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.39725 | −0.127774 | ||||||||
\(353\) | −11.8417 | −0.630269 | −0.315134 | − | 0.949047i | \(-0.602050\pi\) | ||||
−0.315134 | + | 0.949047i | \(0.602050\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 62.7358 | 3.32967 | ||||||||
\(356\) | 11.4844 | 0.608673 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.9994 | −1.00415 | ||||||||
\(359\) | 22.8264 | 1.20473 | 0.602367 | − | 0.798219i | \(-0.294224\pi\) | ||||
0.602367 | + | 0.798219i | \(0.294224\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7100 | −0.932104 | ||||||||
\(362\) | −2.61367 | −0.137371 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.744621 | 0.0390287 | ||||||||
\(365\) | 47.5372 | 2.48821 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.0634 | 1.56930 | 0.784649 | − | 0.619941i | \(-0.212843\pi\) | ||||
0.784649 | + | 0.619941i | \(0.212843\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −35.4569 | −1.84331 | ||||||||
\(371\) | 1.43561 | 0.0745329 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.5853 | −1.63543 | −0.817713 | − | 0.575625i | \(-0.804759\pi\) | ||||
−0.817713 | + | 0.575625i | \(0.804759\pi\) | |||||||
\(374\) | 10.8095 | 0.558946 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.35841 | 0.173197 | ||||||||
\(377\) | 2.40585 | 0.123908 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.6283 | 1.31644 | 0.658218 | − | 0.752828i | \(-0.271311\pi\) | ||||
0.658218 | + | 0.752828i | \(0.271311\pi\) | |||||||
\(380\) | 4.82455 | 0.247494 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.90298 | −0.302023 | ||||||||
\(383\) | 22.8494 | 1.16755 | 0.583774 | − | 0.811916i | \(-0.301575\pi\) | ||||
0.583774 | + | 0.811916i | \(0.301575\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.01640 | 0.153730 | ||||||||
\(386\) | 0.350668 | 0.0178485 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.795359 | 0.0403782 | ||||||||
\(389\) | −16.2740 | −0.825124 | −0.412562 | − | 0.910930i | \(-0.635366\pi\) | ||||
−0.412562 | + | 0.910930i | \(0.635366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.91225 | −0.349121 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.8533 | 0.949816 | ||||||||
\(395\) | 51.2806 | 2.58021 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.21827 | −0.261897 | −0.130949 | − | 0.991389i | \(-0.541802\pi\) | ||||
−0.130949 | + | 0.991389i | \(0.541802\pi\) | |||||||
\(398\) | 16.3425 | 0.819173 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.0433 | 0.652163 | ||||||||
\(401\) | −8.21417 | −0.410196 | −0.205098 | − | 0.978741i | \(-0.565751\pi\) | ||||
−0.205098 | + | 0.978741i | \(0.565751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.7360 | 1.03293 | ||||||||
\(404\) | −9.35035 | −0.465197 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.283511 | 0.0140704 | ||||||||
\(407\) | −20.0105 | −0.991882 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.9872 | −1.68056 | −0.840280 | − | 0.542153i | \(-0.817609\pi\) | ||||
−0.840280 | + | 0.542153i | \(0.817609\pi\) | |||||||
\(410\) | −17.4441 | −0.861504 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.90643 | −0.488055 | ||||||||
\(413\) | −3.35038 | −0.164861 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.02820 | 0.443177 | ||||||||
\(416\) | 2.51372 | 0.123245 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.72279 | 0.133176 | ||||||||
\(419\) | −22.8282 | −1.11523 | −0.557615 | − | 0.830100i | \(-0.688283\pi\) | ||||
−0.557615 | + | 0.830100i | \(0.688283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6661 | −0.812256 | −0.406128 | − | 0.913816i | \(-0.633121\pi\) | ||||
−0.406128 | + | 0.913816i | \(0.633121\pi\) | |||||||
\(422\) | 13.8129 | 0.672400 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.84637 | 0.235361 | ||||||||
\(425\) | −58.8136 | −2.85288 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.30026 | −0.111317 | ||||||||
\(428\) | 18.4893 | 0.893714 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.4080 | −0.791264 | ||||||||
\(431\) | −20.3455 | −0.980008 | −0.490004 | − | 0.871720i | \(-0.663005\pi\) | ||||
−0.490004 | + | 0.871720i | \(0.663005\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.1178 | 1.39931 | 0.699655 | − | 0.714481i | \(-0.253337\pi\) | ||||
0.699655 | + | 0.714481i | \(0.253337\pi\) | |||||||
\(434\) | 2.44357 | 0.117295 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.4814 | −0.789314 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.6105 | −0.935957 | −0.467979 | − | 0.883740i | \(-0.655018\pi\) | ||||
−0.467979 | + | 0.883740i | \(0.655018\pi\) | |||||||
\(440\) | 10.1829 | 0.485451 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.3347 | −0.539135 | ||||||||
\(443\) | −8.63954 | −0.410477 | −0.205238 | − | 0.978712i | \(-0.565797\pi\) | ||||
−0.205238 | + | 0.978712i | \(0.565797\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.7828 | −2.31252 | ||||||||
\(446\) | 3.66413 | 0.173502 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.296223 | 0.0139952 | ||||||||
\(449\) | 22.2983 | 1.05232 | 0.526161 | − | 0.850385i | \(-0.323631\pi\) | ||||
0.526161 | + | 0.850385i | \(0.323631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.84477 | −0.463572 | ||||||||
\(452\) | 4.27218 | 0.200946 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.0570530 | −0.00267763 | ||||||||
\(455\) | −3.16295 | −0.148281 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.42721 | −0.160318 | −0.0801591 | − | 0.996782i | \(-0.525543\pi\) | ||||
−0.0801591 | + | 0.996782i | \(0.525543\pi\) | |||||||
\(458\) | −6.13532 | −0.286685 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.9575 | −1.34869 | −0.674344 | − | 0.738418i | \(-0.735573\pi\) | ||||
−0.674344 | + | 0.738418i | \(0.735573\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.09325 | 0.422599 | 0.211299 | − | 0.977421i | \(-0.432230\pi\) | ||||
0.211299 | + | 0.977421i | \(0.432230\pi\) | |||||||
\(464\) | 0.957087 | 0.0444317 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.3085 | 0.940773 | ||||||||
\(467\) | −20.9454 | −0.969238 | −0.484619 | − | 0.874725i | \(-0.661042\pi\) | ||||
−0.484619 | + | 0.874725i | \(0.661042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.17763 | 0.192905 | ||||||||
\(470\) | −14.2656 | −0.658024 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.3103 | −0.520601 | ||||||||
\(473\) | −9.26002 | −0.425776 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.8145 | −0.679734 | ||||||||
\(476\) | −1.33570 | −0.0612219 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.65555 | −0.167201 | ||||||||
\(479\) | 9.92872 | 0.453655 | 0.226827 | − | 0.973935i | \(-0.427165\pi\) | ||||
0.226827 | + | 0.973935i | \(0.427165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.9826 | 0.956726 | ||||||||
\(482\) | 11.7513 | 0.535259 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.25317 | −0.238781 | ||||||||
\(485\) | −3.37848 | −0.153409 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.0194 | −0.680595 | −0.340298 | − | 0.940318i | \(-0.610528\pi\) | ||||
−0.340298 | + | 0.940318i | \(0.610528\pi\) | |||||||
\(488\) | −7.76531 | −0.351519 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 29.3614 | 1.32641 | ||||||||
\(491\) | 4.08834 | 0.184504 | 0.0922522 | − | 0.995736i | \(-0.470593\pi\) | ||||
0.0922522 | + | 0.995736i | \(0.470593\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.31562 | −0.194366 | ||||||||
\(494\) | −2.85507 | −0.128456 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.24911 | 0.370396 | ||||||||
\(497\) | −4.37498 | −0.196245 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.0954 | −0.675763 | −0.337881 | − | 0.941189i | \(-0.609710\pi\) | ||||
−0.337881 | + | 0.941189i | \(0.609710\pi\) | |||||||
\(500\) | −34.1656 | −1.52793 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.89694 | 0.0846644 | ||||||||
\(503\) | −33.3581 | −1.48736 | −0.743681 | − | 0.668534i | \(-0.766922\pi\) | ||||
−0.743681 | + | 0.668534i | \(0.766922\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.7178 | 1.76742 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.5281 | −0.600210 | ||||||||
\(509\) | 33.1267 | 1.46832 | 0.734158 | − | 0.678979i | \(-0.237577\pi\) | ||||
0.734158 | + | 0.678979i | \(0.237577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.31508 | −0.146651 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.43775 | 0.239849 | ||||||||
\(515\) | 42.0799 | 1.85426 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.05095 | −0.354080 | ||||||||
\(518\) | 2.47264 | 0.108642 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.6776 | −0.468245 | ||||||||
\(521\) | −13.8143 | −0.605214 | −0.302607 | − | 0.953115i | \(-0.597857\pi\) | ||||
−0.302607 | + | 0.953115i | \(0.597857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.0204 | −0.700524 | −0.350262 | − | 0.936652i | \(-0.613907\pi\) | ||||
−0.350262 | + | 0.936652i | \(0.613907\pi\) | |||||||
\(524\) | −13.1098 | −0.572706 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.1887 | −1.01108 | ||||||||
\(527\) | −37.1962 | −1.62029 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −20.5861 | −0.894204 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.336448 | −0.0145869 | ||||||||
\(533\) | 10.3231 | 0.447142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −78.5377 | −3.39548 | ||||||||
\(536\) | 14.1030 | 0.609157 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.34716 | 0.230532 | ||||||||
\(539\) | 16.5704 | 0.713739 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.0153 | −0.516579 | −0.258289 | − | 0.966068i | \(-0.583159\pi\) | ||||
−0.258289 | + | 0.966068i | \(0.583159\pi\) | |||||||
\(542\) | −16.0856 | −0.690934 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.50912 | −0.193327 | ||||||||
\(545\) | 70.0084 | 2.99883 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.6869 | 1.26932 | 0.634661 | − | 0.772791i | \(-0.281140\pi\) | ||||
0.634661 | + | 0.772791i | \(0.281140\pi\) | |||||||
\(548\) | −1.26947 | −0.0542291 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −31.2680 | −1.33327 | ||||||||
\(551\) | −1.08705 | −0.0463101 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.57613 | −0.152073 | ||||||||
\(554\) | 3.44954 | 0.146557 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.5662 | −0.660155 | ||||||||
\(557\) | −30.1816 | −1.27883 | −0.639417 | − | 0.768860i | \(-0.720824\pi\) | ||||
−0.639417 | + | 0.768860i | \(0.720824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.70991 | 0.410685 | ||||||||
\(560\) | −1.25827 | −0.0531718 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.43983 | 0.271648 | ||||||||
\(563\) | −2.17257 | −0.0915630 | −0.0457815 | − | 0.998951i | \(-0.514578\pi\) | ||||
−0.0457815 | + | 0.998951i | \(0.514578\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.1471 | −0.763454 | ||||||||
\(566\) | −11.6630 | −0.490231 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.7692 | −0.619703 | ||||||||
\(569\) | −2.10059 | −0.0880614 | −0.0440307 | − | 0.999030i | \(-0.514020\pi\) | ||||
−0.0440307 | + | 0.999030i | \(0.514020\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.2711 | −1.39235 | −0.696177 | − | 0.717871i | \(-0.745117\pi\) | ||||
−0.696177 | + | 0.717871i | \(0.745117\pi\) | |||||||
\(572\) | −6.02603 | −0.251961 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.21649 | 0.0507754 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.58875 | −0.149402 | −0.0747008 | − | 0.997206i | \(-0.523800\pi\) | ||||
−0.0747008 | + | 0.997206i | \(0.523800\pi\) | |||||||
\(578\) | 3.33217 | 0.138600 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.06545 | −0.168809 | ||||||||
\(581\) | −0.629596 | −0.0261200 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.6180 | −0.481168 | ||||||||
\(584\) | −11.1912 | −0.463095 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.15331 | −0.212881 | ||||||||
\(587\) | −37.5313 | −1.54908 | −0.774541 | − | 0.632524i | \(-0.782019\pi\) | ||||
−0.774541 | + | 0.632524i | \(0.782019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.36929 | −0.386055 | ||||||||
\(590\) | 48.0433 | 1.97791 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.34724 | 0.343069 | ||||||||
\(593\) | 20.9062 | 0.858515 | 0.429258 | − | 0.903182i | \(-0.358775\pi\) | ||||
0.429258 | + | 0.903182i | \(0.358775\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.67371 | 0.232600 | ||||||||
\(596\) | −13.6820 | −0.560435 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.81949 | 0.115201 | 0.0576007 | − | 0.998340i | \(-0.481655\pi\) | ||||
0.0576007 | + | 0.998340i | \(0.481655\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.7258 | 1.21254 | 0.606269 | − | 0.795259i | \(-0.292665\pi\) | ||||
0.606269 | + | 0.795259i | \(0.292665\pi\) | |||||||
\(602\) | 1.14424 | 0.0466356 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.65087 | 0.311309 | ||||||||
\(605\) | 22.3141 | 0.907197 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.9379 | −0.931021 | −0.465511 | − | 0.885042i | \(-0.654129\pi\) | ||||
−0.465511 | + | 0.885042i | \(0.654129\pi\) | |||||||
\(608\) | −1.13579 | −0.0460625 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.9850 | 1.33552 | ||||||||
\(611\) | 8.44209 | 0.341531 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.7781 | 1.08156 | 0.540779 | − | 0.841164i | \(-0.318129\pi\) | ||||
0.540779 | + | 0.841164i | \(0.318129\pi\) | |||||||
\(614\) | −15.5307 | −0.626766 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.710121 | −0.0286116 | ||||||||
\(617\) | 34.1884 | 1.37637 | 0.688187 | − | 0.725533i | \(-0.258407\pi\) | ||||
0.688187 | + | 0.725533i | \(0.258407\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.18439 | −0.328958 | −0.164479 | − | 0.986381i | \(-0.552594\pi\) | ||||
−0.164479 | + | 0.986381i | \(0.552594\pi\) | |||||||
\(620\) | −35.0400 | −1.40724 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.59667 | 0.304599 | ||||||||
\(623\) | 3.40194 | 0.136296 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 79.9102 | 3.19641 | ||||||||
\(626\) | −26.1607 | −1.04559 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.27528 | −0.290315 | ||||||||
\(629\) | −37.6387 | −1.50075 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.1546 | −1.47910 | −0.739550 | − | 0.673102i | \(-0.764962\pi\) | ||||
−0.739550 | + | 0.673102i | \(0.764962\pi\) | |||||||
\(632\) | −12.0724 | −0.480216 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.2042 | 0.961270 | ||||||||
\(635\) | 57.4636 | 2.28037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.3755 | −0.688441 | ||||||||
\(638\) | −2.29438 | −0.0908354 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.24774 | −0.167906 | ||||||||
\(641\) | −2.08457 | −0.0823357 | −0.0411679 | − | 0.999152i | \(-0.513108\pi\) | ||||
−0.0411679 | + | 0.999152i | \(0.513108\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.7677 | −1.52885 | −0.764424 | − | 0.644713i | \(-0.776977\pi\) | ||||
−0.764424 | + | 0.644713i | \(0.776977\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.12143 | 0.201500 | ||||||||
\(647\) | 7.60261 | 0.298889 | 0.149445 | − | 0.988770i | \(-0.452251\pi\) | ||||
0.149445 | + | 0.988770i | \(0.452251\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.1138 | 1.06431 | ||||||||
\(650\) | 32.7871 | 1.28602 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.6142 | 0.689824 | ||||||||
\(653\) | 9.86403 | 0.386009 | 0.193005 | − | 0.981198i | \(-0.438177\pi\) | ||||
0.193005 | + | 0.981198i | \(0.438177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 55.6871 | 2.17587 | ||||||||
\(656\) | 4.10669 | 0.160339 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.994835 | 0.0387827 | ||||||||
\(659\) | 18.2003 | 0.708981 | 0.354491 | − | 0.935060i | \(-0.384654\pi\) | ||||
0.354491 | + | 0.935060i | \(0.384654\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.1697 | 0.434451 | 0.217226 | − | 0.976121i | \(-0.430299\pi\) | ||||
0.217226 | + | 0.976121i | \(0.430299\pi\) | |||||||
\(662\) | −31.4228 | −1.22128 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.12541 | −0.0824821 | ||||||||
\(665\) | 1.42914 | 0.0554197 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 12.8331 | 0.496527 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −59.9058 | −2.31436 | ||||||||
\(671\) | 18.6154 | 0.718640 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.7021 | 1.53040 | 0.765201 | − | 0.643792i | \(-0.222640\pi\) | ||||
0.765201 | + | 0.643792i | \(0.222640\pi\) | |||||||
\(674\) | −5.72615 | −0.220563 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.68121 | −0.256970 | ||||||||
\(677\) | 7.95806 | 0.305853 | 0.152926 | − | 0.988238i | \(-0.451130\pi\) | ||||
0.152926 | + | 0.988238i | \(0.451130\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.235603 | 0.00904162 | ||||||||
\(680\) | 19.1536 | 0.734505 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −19.7752 | −0.757232 | ||||||||
\(683\) | −17.4650 | −0.668280 | −0.334140 | − | 0.942523i | \(-0.608446\pi\) | ||||
−0.334140 | + | 0.942523i | \(0.608446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.39237 | 0.206032 | ||||||||
\(686\) | −4.12112 | −0.157345 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.86276 | 0.147266 | ||||||||
\(689\) | 12.1824 | 0.464114 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.4115 | −0.548240 | −0.274120 | − | 0.961696i | \(-0.588386\pi\) | ||||
−0.274120 | + | 0.961696i | \(0.588386\pi\) | |||||||
\(692\) | −9.24925 | −0.351604 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.6762 | −0.746900 | ||||||||
\(695\) | 66.1212 | 2.50812 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.5175 | −0.701402 | ||||||||
\(698\) | 2.20578 | 0.0834901 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.86371 | 0.146034 | ||||||||
\(701\) | −27.1514 | −1.02550 | −0.512748 | − | 0.858539i | \(-0.671372\pi\) | ||||
−0.512748 | + | 0.858539i | \(0.671372\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.48075 | −0.357573 | ||||||||
\(704\) | −2.39725 | −0.0903499 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.8417 | −0.445667 | ||||||||
\(707\) | −2.76978 | −0.104168 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.8838 | −0.558972 | −0.279486 | − | 0.960150i | \(-0.590164\pi\) | ||||
−0.279486 | + | 0.960150i | \(0.590164\pi\) | |||||||
\(710\) | 62.7358 | 2.35443 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.4844 | 0.430397 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.5970 | 0.957272 | ||||||||
\(716\) | −18.9994 | −0.710042 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.8264 | 0.851876 | ||||||||
\(719\) | 3.29160 | 0.122756 | 0.0613780 | − | 0.998115i | \(-0.480450\pi\) | ||||
0.0613780 | + | 0.998115i | \(0.480450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.93451 | −0.109287 | ||||||||
\(722\) | −17.7100 | −0.659097 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.61367 | −0.0971362 | ||||||||
\(725\) | 12.4835 | 0.463627 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.1610 | 1.19279 | 0.596393 | − | 0.802693i | \(-0.296600\pi\) | ||||
0.596393 | + | 0.802693i | \(0.296600\pi\) | |||||||
\(728\) | 0.744621 | 0.0275975 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 47.5372 | 1.75943 | ||||||||
\(731\) | −17.4177 | −0.644216 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.0402 | 1.92215 | 0.961074 | − | 0.276291i | \(-0.0891054\pi\) | ||||
0.961074 | + | 0.276291i | \(0.0891054\pi\) | |||||||
\(734\) | 30.0634 | 1.10966 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.8085 | −1.24535 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5749 | −0.609717 | −0.304859 | − | 0.952398i | \(-0.598609\pi\) | ||||
−0.304859 | + | 0.952398i | \(0.598609\pi\) | |||||||
\(740\) | −35.4569 | −1.30342 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.43561 | 0.0527027 | ||||||||
\(743\) | −9.13697 | −0.335203 | −0.167601 | − | 0.985855i | \(-0.553602\pi\) | ||||
−0.167601 | + | 0.985855i | \(0.553602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 58.1173 | 2.12925 | ||||||||
\(746\) | −31.5853 | −1.15642 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.8095 | 0.395235 | ||||||||
\(749\) | 5.47695 | 0.200123 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.0794 | 1.53550 | 0.767750 | − | 0.640750i | \(-0.221376\pi\) | ||||
0.767750 | + | 0.640750i | \(0.221376\pi\) | |||||||
\(752\) | 3.35841 | 0.122468 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.40585 | 0.0876159 | ||||||||
\(755\) | −32.4989 | −1.18275 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.58553 | 0.275701 | 0.137850 | − | 0.990453i | \(-0.455981\pi\) | ||||
0.137850 | + | 0.990453i | \(0.455981\pi\) | |||||||
\(758\) | 25.6283 | 0.930860 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.82455 | 0.175005 | ||||||||
\(761\) | −46.0739 | −1.67018 | −0.835089 | − | 0.550115i | \(-0.814584\pi\) | ||||
−0.835089 | + | 0.550115i | \(0.814584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.88215 | −0.176746 | ||||||||
\(764\) | −5.90298 | −0.213562 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.8494 | 0.825581 | ||||||||
\(767\) | −28.4310 | −1.02659 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.3780 | −0.446364 | −0.223182 | − | 0.974777i | \(-0.571644\pi\) | ||||
−0.223182 | + | 0.974777i | \(0.571644\pi\) | |||||||
\(770\) | 3.01640 | 0.108704 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.350668 | 0.0126208 | ||||||||
\(773\) | −46.1635 | −1.66038 | −0.830192 | − | 0.557477i | \(-0.811769\pi\) | ||||
−0.830192 | + | 0.557477i | \(0.811769\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 107.595 | 3.86493 | ||||||||
\(776\) | 0.795359 | 0.0285517 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.2740 | −0.583451 | ||||||||
\(779\) | −4.66435 | −0.167118 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.4056 | 1.26691 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.91225 | −0.246866 | ||||||||
\(785\) | 30.9035 | 1.10299 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.7894 | −0.455893 | −0.227946 | − | 0.973674i | \(-0.573201\pi\) | ||||
−0.227946 | + | 0.973674i | \(0.573201\pi\) | |||||||
\(788\) | 18.8533 | 0.671621 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 51.2806 | 1.82448 | ||||||||
\(791\) | 1.26552 | 0.0449966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.5198 | −0.693169 | ||||||||
\(794\) | −5.21827 | −0.185189 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.3425 | 0.579243 | ||||||||
\(797\) | −17.8798 | −0.633334 | −0.316667 | − | 0.948537i | \(-0.602564\pi\) | ||||
−0.316667 | + | 0.948537i | \(0.602564\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.1435 | −0.535737 | ||||||||
\(800\) | 13.0433 | 0.461149 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.21417 | −0.290052 | ||||||||
\(803\) | 26.8281 | 0.946744 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.7360 | 0.730393 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.35035 | −0.328944 | ||||||||
\(809\) | 37.7595 | 1.32755 | 0.663776 | − | 0.747931i | \(-0.268953\pi\) | ||||
0.663776 | + | 0.747931i | \(0.268953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.3002 | 0.747950 | 0.373975 | − | 0.927439i | \(-0.377995\pi\) | ||||
0.373975 | + | 0.927439i | \(0.377995\pi\) | |||||||
\(812\) | 0.283511 | 0.00994928 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.0105 | −0.701366 | ||||||||
\(815\) | −74.8204 | −2.62084 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.38730 | −0.153492 | ||||||||
\(818\) | −33.9872 | −1.18834 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.4441 | −0.609175 | ||||||||
\(821\) | 7.82220 | 0.272997 | 0.136498 | − | 0.990640i | \(-0.456415\pi\) | ||||
0.136498 | + | 0.990640i | \(0.456415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0399456 | 0.00139242 | 0.000696208 | − | 1.00000i | \(-0.499778\pi\) | ||||
0.000696208 | 1.00000i | \(0.499778\pi\) | ||||||||
\(824\) | −9.90643 | −0.345107 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.35038 | −0.116575 | ||||||||
\(827\) | −35.9303 | −1.24942 | −0.624710 | − | 0.780857i | \(-0.714783\pi\) | ||||
−0.624710 | + | 0.780857i | \(0.714783\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7357 | 0.407597 | 0.203799 | − | 0.979013i | \(-0.434671\pi\) | ||||
0.203799 | + | 0.979013i | \(0.434671\pi\) | |||||||
\(830\) | 9.02820 | 0.313373 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.51372 | 0.0871476 | ||||||||
\(833\) | 31.1682 | 1.07991 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54.5115 | −1.88645 | ||||||||
\(836\) | 2.72279 | 0.0941696 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.8282 | −0.788586 | ||||||||
\(839\) | 54.3029 | 1.87475 | 0.937373 | − | 0.348328i | \(-0.113251\pi\) | ||||
0.937373 | + | 0.348328i | \(0.113251\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0840 | −0.968413 | ||||||||
\(842\) | −16.6661 | −0.574352 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.8129 | 0.475459 | ||||||||
\(845\) | 28.3800 | 0.976302 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.55611 | −0.0534685 | ||||||||
\(848\) | 4.84637 | 0.166425 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −58.8136 | −2.01729 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.1406 | 1.51135 | 0.755673 | − | 0.654949i | \(-0.227310\pi\) | ||||
0.755673 | + | 0.654949i | \(0.227310\pi\) | |||||||
\(854\) | −2.30026 | −0.0787132 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.4893 | 0.631951 | ||||||||
\(857\) | −25.1720 | −0.859860 | −0.429930 | − | 0.902862i | \(-0.641462\pi\) | ||||
−0.429930 | + | 0.902862i | \(0.641462\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.2254 | 0.587722 | 0.293861 | − | 0.955848i | \(-0.405060\pi\) | ||||
0.293861 | + | 0.955848i | \(0.405060\pi\) | |||||||
\(860\) | −16.4080 | −0.559508 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.3455 | −0.692971 | ||||||||
\(863\) | 37.7817 | 1.28610 | 0.643052 | − | 0.765823i | \(-0.277668\pi\) | ||||
0.643052 | + | 0.765823i | \(0.277668\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.2884 | 1.33585 | ||||||||
\(866\) | 29.1178 | 0.989462 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.44357 | 0.0829402 | ||||||||
\(869\) | 28.9407 | 0.981747 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.4510 | 1.20121 | ||||||||
\(872\) | −16.4814 | −0.558129 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1206 | −0.342139 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.5016 | −1.94169 | −0.970845 | − | 0.239708i | \(-0.922948\pi\) | ||||
−0.970845 | + | 0.239708i | \(0.922948\pi\) | |||||||
\(878\) | −19.6105 | −0.661822 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.1829 | 0.343265 | ||||||||
\(881\) | −33.9249 | −1.14296 | −0.571479 | − | 0.820616i | \(-0.693630\pi\) | ||||
−0.571479 | + | 0.820616i | \(0.693630\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.3770 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(884\) | −11.3347 | −0.381226 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.63954 | −0.290251 | ||||||||
\(887\) | −7.10730 | −0.238640 | −0.119320 | − | 0.992856i | \(-0.538071\pi\) | ||||
−0.119320 | + | 0.992856i | \(0.538071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00732 | −0.134401 | ||||||||
\(890\) | −48.7828 | −1.63520 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.66413 | 0.122684 | ||||||||
\(893\) | −3.81446 | −0.127646 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 80.7045 | 2.69765 | ||||||||
\(896\) | 0.296223 | 0.00989610 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.2983 | 0.744104 | ||||||||
\(899\) | 7.89511 | 0.263317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.8529 | −0.728025 | ||||||||
\(902\) | −9.84477 | −0.327795 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.27218 | 0.142091 | ||||||||
\(905\) | 11.1022 | 0.369048 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.9535 | −0.961386 | −0.480693 | − | 0.876889i | \(-0.659615\pi\) | ||||
−0.480693 | + | 0.876889i | \(0.659615\pi\) | |||||||
\(908\) | −0.0570530 | −0.00189337 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.16295 | −0.104851 | ||||||||
\(911\) | 3.10995 | 0.103037 | 0.0515186 | − | 0.998672i | \(-0.483594\pi\) | ||||
0.0515186 | + | 0.998672i | \(0.483594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.09516 | 0.168625 | ||||||||
\(914\) | −3.42721 | −0.113362 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.13532 | −0.202717 | ||||||||
\(917\) | −3.88343 | −0.128242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.9768 | 0.494038 | 0.247019 | − | 0.969011i | \(-0.420549\pi\) | ||||
0.247019 | + | 0.969011i | \(0.420549\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.9575 | −0.953666 | ||||||||
\(923\) | −37.1257 | −1.22201 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 108.875 | 3.57979 | ||||||||
\(926\) | 9.09325 | 0.298823 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.957087 | 0.0314179 | ||||||||
\(929\) | 31.9251 | 1.04743 | 0.523715 | − | 0.851893i | \(-0.324546\pi\) | ||||
0.523715 | + | 0.851893i | \(0.324546\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.85090 | 0.257303 | ||||||||
\(932\) | 20.3085 | 0.665227 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.9454 | −0.685355 | ||||||||
\(935\) | −45.9159 | −1.50161 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.6312 | 0.706661 | 0.353330 | − | 0.935499i | \(-0.385049\pi\) | ||||
0.353330 | + | 0.935499i | \(0.385049\pi\) | |||||||
\(938\) | 4.17763 | 0.136404 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.2656 | −0.465293 | ||||||||
\(941\) | −2.95773 | −0.0964193 | −0.0482097 | − | 0.998837i | \(-0.515352\pi\) | ||||
−0.0482097 | + | 0.998837i | \(0.515352\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −11.3103 | −0.368120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.26002 | −0.301069 | ||||||||
\(947\) | −1.61057 | −0.0523364 | −0.0261682 | − | 0.999658i | \(-0.508331\pi\) | ||||
−0.0261682 | + | 0.999658i | \(0.508331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.1315 | −0.913188 | ||||||||
\(950\) | −14.8145 | −0.480644 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.33570 | −0.0432904 | ||||||||
\(953\) | 31.4202 | 1.01780 | 0.508899 | − | 0.860826i | \(-0.330053\pi\) | ||||
0.508899 | + | 0.860826i | \(0.330053\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.0743 | 0.811385 | ||||||||
\(956\) | −3.65555 | −0.118229 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.92872 | 0.320782 | ||||||||
\(959\) | −0.376046 | −0.0121431 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.0478 | 1.19509 | ||||||||
\(962\) | 20.9826 | 0.676507 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.7513 | 0.378485 | ||||||||
\(965\) | −1.48955 | −0.0479502 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2718 | 0.491108 | 0.245554 | − | 0.969383i | \(-0.421030\pi\) | ||||
0.245554 | + | 0.969383i | \(0.421030\pi\) | |||||||
\(968\) | −5.25317 | −0.168843 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.37848 | −0.108476 | ||||||||
\(971\) | 25.7653 | 0.826848 | 0.413424 | − | 0.910539i | \(-0.364333\pi\) | ||||
0.413424 | + | 0.910539i | \(0.364333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.61107 | −0.147824 | ||||||||
\(974\) | −15.0194 | −0.481253 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.76531 | −0.248561 | ||||||||
\(977\) | −8.88263 | −0.284180 | −0.142090 | − | 0.989854i | \(-0.545382\pi\) | ||||
−0.142090 | + | 0.989854i | \(0.545382\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.5311 | −0.879897 | ||||||||
\(980\) | 29.3614 | 0.937916 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.08834 | 0.130464 | ||||||||
\(983\) | −3.56769 | −0.113792 | −0.0568959 | − | 0.998380i | \(-0.518120\pi\) | ||||
−0.0568959 | + | 0.998380i | \(0.518120\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −80.0838 | −2.55168 | ||||||||
\(986\) | −4.31562 | −0.137437 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.85507 | −0.0908319 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.467875 | 0.0148625 | 0.00743127 | − | 0.999972i | \(-0.497635\pi\) | ||||
0.00743127 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(992\) | 8.24911 | 0.261909 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.37498 | −0.138766 | ||||||||
\(995\) | −69.4184 | −2.20071 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.2383 | 0.514273 | 0.257137 | − | 0.966375i | \(-0.417221\pi\) | ||||
0.257137 | + | 0.966375i | \(0.417221\pi\) | |||||||
\(998\) | −15.0954 | −0.477836 | ||||||||
\(999\) | 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 | 9522.2.a.ci.1.1 | 10 | ||
3.2 | odd | 2 | 9522.2.a.ch.1.10 | 10 | |||
23.11 | odd | 22 | 414.2.i.g.397.2 | yes | 20 | ||
23.21 | odd | 22 | 414.2.i.g.73.2 | ✓ | 20 | ||
23.22 | odd | 2 | 9522.2.a.cj.1.10 | 10 | |||
69.11 | even | 22 | 414.2.i.h.397.1 | yes | 20 | ||
69.44 | even | 22 | 414.2.i.h.73.1 | yes | 20 | ||
69.68 | even | 2 | 9522.2.a.cg.1.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.2.i.g.73.2 | ✓ | 20 | 23.21 | odd | 22 | ||
414.2.i.g.397.2 | yes | 20 | 23.11 | odd | 22 | ||
414.2.i.h.73.1 | yes | 20 | 69.44 | even | 22 | ||
414.2.i.h.397.1 | yes | 20 | 69.11 | even | 22 | ||
9522.2.a.cg.1.1 | 10 | 69.68 | even | 2 | |||
9522.2.a.ch.1.10 | 10 | 3.2 | odd | 2 | |||
9522.2.a.ci.1.1 | 10 | 1.1 | even | 1 | trivial | ||
9522.2.a.cj.1.10 | 10 | 23.22 | odd | 2 |