Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(1,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, 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("845.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.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: | \(6.74735897080\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.80194 | 1.27416 | 0.637081 | − | 0.770797i | \(-0.280142\pi\) | ||||
0.637081 | + | 0.770797i | \(0.280142\pi\) | |||||||
\(3\) | −1.55496 | −0.897755 | −0.448878 | − | 0.893593i | \(-0.648176\pi\) | ||||
−0.448878 | + | 0.893593i | \(0.648176\pi\) | |||||||
\(4\) | 1.24698 | 0.623490 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.80194 | −1.14389 | ||||||||
\(7\) | 1.55496 | 0.587719 | 0.293859 | − | 0.955849i | \(-0.405060\pi\) | ||||
0.293859 | + | 0.955849i | \(0.405060\pi\) | |||||||
\(8\) | −1.35690 | −0.479735 | ||||||||
\(9\) | −0.582105 | −0.194035 | ||||||||
\(10\) | −1.80194 | −0.569823 | ||||||||
\(11\) | −0.356896 | −0.107608 | −0.0538041 | − | 0.998552i | \(-0.517135\pi\) | ||||
−0.0538041 | + | 0.998552i | \(0.517135\pi\) | |||||||
\(12\) | −1.93900 | −0.559741 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.80194 | 0.748849 | ||||||||
\(15\) | 1.55496 | 0.401488 | ||||||||
\(16\) | −4.93900 | −1.23475 | ||||||||
\(17\) | −1.33513 | −0.323816 | −0.161908 | − | 0.986806i | \(-0.551765\pi\) | ||||
−0.161908 | + | 0.986806i | \(0.551765\pi\) | |||||||
\(18\) | −1.04892 | −0.247232 | ||||||||
\(19\) | −8.65279 | −1.98509 | −0.992543 | − | 0.121892i | \(-0.961104\pi\) | ||||
−0.992543 | + | 0.121892i | \(0.961104\pi\) | |||||||
\(20\) | −1.24698 | −0.278833 | ||||||||
\(21\) | −2.41789 | −0.527628 | ||||||||
\(22\) | −0.643104 | −0.137110 | ||||||||
\(23\) | −8.00969 | −1.67014 | −0.835068 | − | 0.550147i | \(-0.814572\pi\) | ||||
−0.835068 | + | 0.550147i | \(0.814572\pi\) | |||||||
\(24\) | 2.10992 | 0.430685 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.57002 | 1.07195 | ||||||||
\(28\) | 1.93900 | 0.366437 | ||||||||
\(29\) | 7.14675 | 1.32712 | 0.663559 | − | 0.748124i | \(-0.269045\pi\) | ||||
0.663559 | + | 0.748124i | \(0.269045\pi\) | |||||||
\(30\) | 2.80194 | 0.511562 | ||||||||
\(31\) | 5.43296 | 0.975788 | 0.487894 | − | 0.872903i | \(-0.337765\pi\) | ||||
0.487894 | + | 0.872903i | \(0.337765\pi\) | |||||||
\(32\) | −6.18598 | −1.09354 | ||||||||
\(33\) | 0.554958 | 0.0966058 | ||||||||
\(34\) | −2.40581 | −0.412594 | ||||||||
\(35\) | −1.55496 | −0.262836 | ||||||||
\(36\) | −0.725873 | −0.120979 | ||||||||
\(37\) | −4.60388 | −0.756872 | −0.378436 | − | 0.925627i | \(-0.623538\pi\) | ||||
−0.378436 | + | 0.925627i | \(0.623538\pi\) | |||||||
\(38\) | −15.5918 | −2.52932 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.35690 | 0.214544 | ||||||||
\(41\) | −8.58211 | −1.34030 | −0.670150 | − | 0.742226i | \(-0.733770\pi\) | ||||
−0.670150 | + | 0.742226i | \(0.733770\pi\) | |||||||
\(42\) | −4.35690 | −0.672284 | ||||||||
\(43\) | −9.24698 | −1.41015 | −0.705076 | − | 0.709132i | \(-0.749087\pi\) | ||||
−0.705076 | + | 0.709132i | \(0.749087\pi\) | |||||||
\(44\) | −0.445042 | −0.0670926 | ||||||||
\(45\) | 0.582105 | 0.0867751 | ||||||||
\(46\) | −14.4330 | −2.12802 | ||||||||
\(47\) | 3.41789 | 0.498551 | 0.249276 | − | 0.968433i | \(-0.419808\pi\) | ||||
0.249276 | + | 0.968433i | \(0.419808\pi\) | |||||||
\(48\) | 7.67994 | 1.10850 | ||||||||
\(49\) | −4.58211 | −0.654586 | ||||||||
\(50\) | 1.80194 | 0.254832 | ||||||||
\(51\) | 2.07606 | 0.290707 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.24698 | −0.308646 | −0.154323 | − | 0.988020i | \(-0.549320\pi\) | ||||
−0.154323 | + | 0.988020i | \(0.549320\pi\) | |||||||
\(54\) | 10.0368 | 1.36584 | ||||||||
\(55\) | 0.356896 | 0.0481238 | ||||||||
\(56\) | −2.10992 | −0.281949 | ||||||||
\(57\) | 13.4547 | 1.78212 | ||||||||
\(58\) | 12.8780 | 1.69096 | ||||||||
\(59\) | 0.506041 | 0.0658809 | 0.0329404 | − | 0.999457i | \(-0.489513\pi\) | ||||
0.0329404 | + | 0.999457i | \(0.489513\pi\) | |||||||
\(60\) | 1.93900 | 0.250324 | ||||||||
\(61\) | −7.24698 | −0.927881 | −0.463940 | − | 0.885866i | \(-0.653565\pi\) | ||||
−0.463940 | + | 0.885866i | \(0.653565\pi\) | |||||||
\(62\) | 9.78986 | 1.24331 | ||||||||
\(63\) | −0.905149 | −0.114038 | ||||||||
\(64\) | −1.26875 | −0.158594 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 4.48188 | 0.547548 | 0.273774 | − | 0.961794i | \(-0.411728\pi\) | ||||
0.273774 | + | 0.961794i | \(0.411728\pi\) | |||||||
\(68\) | −1.66487 | −0.201896 | ||||||||
\(69\) | 12.4547 | 1.49937 | ||||||||
\(70\) | −2.80194 | −0.334896 | ||||||||
\(71\) | 6.39373 | 0.758796 | 0.379398 | − | 0.925233i | \(-0.376131\pi\) | ||||
0.379398 | + | 0.925233i | \(0.376131\pi\) | |||||||
\(72\) | 0.789856 | 0.0930854 | ||||||||
\(73\) | 15.5254 | 1.81711 | 0.908556 | − | 0.417762i | \(-0.137186\pi\) | ||||
0.908556 | + | 0.417762i | \(0.137186\pi\) | |||||||
\(74\) | −8.29590 | −0.964378 | ||||||||
\(75\) | −1.55496 | −0.179551 | ||||||||
\(76\) | −10.7899 | −1.23768 | ||||||||
\(77\) | −0.554958 | −0.0632433 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.65519 | −0.523749 | −0.261875 | − | 0.965102i | \(-0.584341\pi\) | ||||
−0.261875 | + | 0.965102i | \(0.584341\pi\) | |||||||
\(80\) | 4.93900 | 0.552197 | ||||||||
\(81\) | −6.91484 | −0.768315 | ||||||||
\(82\) | −15.4644 | −1.70776 | ||||||||
\(83\) | 5.48427 | 0.601977 | 0.300988 | − | 0.953628i | \(-0.402683\pi\) | ||||
0.300988 | + | 0.953628i | \(0.402683\pi\) | |||||||
\(84\) | −3.01507 | −0.328971 | ||||||||
\(85\) | 1.33513 | 0.144815 | ||||||||
\(86\) | −16.6625 | −1.79676 | ||||||||
\(87\) | −11.1129 | −1.19143 | ||||||||
\(88\) | 0.484271 | 0.0516234 | ||||||||
\(89\) | 16.5797 | 1.75745 | 0.878723 | − | 0.477332i | \(-0.158396\pi\) | ||||
0.878723 | + | 0.477332i | \(0.158396\pi\) | |||||||
\(90\) | 1.04892 | 0.110566 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.98792 | −1.04131 | ||||||||
\(93\) | −8.44803 | −0.876019 | ||||||||
\(94\) | 6.15883 | 0.635235 | ||||||||
\(95\) | 8.65279 | 0.887758 | ||||||||
\(96\) | 9.61894 | 0.981729 | ||||||||
\(97\) | 10.4330 | 1.05931 | 0.529653 | − | 0.848214i | \(-0.322322\pi\) | ||||
0.529653 | + | 0.848214i | \(0.322322\pi\) | |||||||
\(98\) | −8.25667 | −0.834049 | ||||||||
\(99\) | 0.207751 | 0.0208798 | ||||||||
\(100\) | 1.24698 | 0.124698 | ||||||||
\(101\) | 1.62565 | 0.161758 | 0.0808789 | − | 0.996724i | \(-0.474227\pi\) | ||||
0.0808789 | + | 0.996724i | \(0.474227\pi\) | |||||||
\(102\) | 3.74094 | 0.370408 | ||||||||
\(103\) | −9.33513 | −0.919817 | −0.459909 | − | 0.887966i | \(-0.652118\pi\) | ||||
−0.459909 | + | 0.887966i | \(0.652118\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.41789 | 0.235962 | ||||||||
\(106\) | −4.04892 | −0.393266 | ||||||||
\(107\) | 16.2228 | 1.56832 | 0.784159 | − | 0.620559i | \(-0.213094\pi\) | ||||
0.784159 | + | 0.620559i | \(0.213094\pi\) | |||||||
\(108\) | 6.94571 | 0.668351 | ||||||||
\(109\) | −5.06638 | −0.485271 | −0.242635 | − | 0.970118i | \(-0.578012\pi\) | ||||
−0.242635 | + | 0.970118i | \(0.578012\pi\) | |||||||
\(110\) | 0.643104 | 0.0613176 | ||||||||
\(111\) | 7.15883 | 0.679486 | ||||||||
\(112\) | −7.67994 | −0.725686 | ||||||||
\(113\) | 10.1153 | 0.951567 | 0.475783 | − | 0.879562i | \(-0.342165\pi\) | ||||
0.475783 | + | 0.879562i | \(0.342165\pi\) | |||||||
\(114\) | 24.2446 | 2.27071 | ||||||||
\(115\) | 8.00969 | 0.746907 | ||||||||
\(116\) | 8.91185 | 0.827445 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.911854 | 0.0839430 | ||||||||
\(119\) | −2.07606 | −0.190313 | ||||||||
\(120\) | −2.10992 | −0.192608 | ||||||||
\(121\) | −10.8726 | −0.988420 | ||||||||
\(122\) | −13.0586 | −1.18227 | ||||||||
\(123\) | 13.3448 | 1.20326 | ||||||||
\(124\) | 6.77479 | 0.608394 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.63102 | −0.145303 | ||||||||
\(127\) | −6.02715 | −0.534823 | −0.267411 | − | 0.963582i | \(-0.586168\pi\) | ||||
−0.267411 | + | 0.963582i | \(0.586168\pi\) | |||||||
\(128\) | 10.0858 | 0.891463 | ||||||||
\(129\) | 14.3787 | 1.26597 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.1075 | −0.883098 | −0.441549 | − | 0.897237i | \(-0.645571\pi\) | ||||
−0.441549 | + | 0.897237i | \(0.645571\pi\) | |||||||
\(132\) | 0.692021 | 0.0602327 | ||||||||
\(133\) | −13.4547 | −1.16667 | ||||||||
\(134\) | 8.07606 | 0.697666 | ||||||||
\(135\) | −5.57002 | −0.479391 | ||||||||
\(136\) | 1.81163 | 0.155346 | ||||||||
\(137\) | 4.96077 | 0.423827 | 0.211914 | − | 0.977288i | \(-0.432030\pi\) | ||||
0.211914 | + | 0.977288i | \(0.432030\pi\) | |||||||
\(138\) | 22.4426 | 1.91045 | ||||||||
\(139\) | −9.02177 | −0.765217 | −0.382608 | − | 0.923911i | \(-0.624974\pi\) | ||||
−0.382608 | + | 0.923911i | \(0.624974\pi\) | |||||||
\(140\) | −1.93900 | −0.163876 | ||||||||
\(141\) | −5.31468 | −0.447577 | ||||||||
\(142\) | 11.5211 | 0.966830 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.87502 | 0.239585 | ||||||||
\(145\) | −7.14675 | −0.593505 | ||||||||
\(146\) | 27.9758 | 2.31530 | ||||||||
\(147\) | 7.12498 | 0.587659 | ||||||||
\(148\) | −5.74094 | −0.471902 | ||||||||
\(149\) | −18.1957 | −1.49065 | −0.745324 | − | 0.666703i | \(-0.767705\pi\) | ||||
−0.745324 | + | 0.666703i | \(0.767705\pi\) | |||||||
\(150\) | −2.80194 | −0.228777 | ||||||||
\(151\) | −7.22521 | −0.587979 | −0.293990 | − | 0.955809i | \(-0.594983\pi\) | ||||
−0.293990 | + | 0.955809i | \(0.594983\pi\) | |||||||
\(152\) | 11.7409 | 0.952316 | ||||||||
\(153\) | 0.777184 | 0.0628316 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | −5.43296 | −0.436386 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.79954 | −0.702280 | −0.351140 | − | 0.936323i | \(-0.614206\pi\) | ||||
−0.351140 | + | 0.936323i | \(0.614206\pi\) | |||||||
\(158\) | −8.38835 | −0.667342 | ||||||||
\(159\) | 3.49396 | 0.277089 | ||||||||
\(160\) | 6.18598 | 0.489045 | ||||||||
\(161\) | −12.4547 | −0.981570 | ||||||||
\(162\) | −12.4601 | −0.978958 | ||||||||
\(163\) | 5.91723 | 0.463473 | 0.231737 | − | 0.972779i | \(-0.425559\pi\) | ||||
0.231737 | + | 0.972779i | \(0.425559\pi\) | |||||||
\(164\) | −10.7017 | −0.835663 | ||||||||
\(165\) | −0.554958 | −0.0432034 | ||||||||
\(166\) | 9.88231 | 0.767016 | ||||||||
\(167\) | −6.00431 | −0.464628 | −0.232314 | − | 0.972641i | \(-0.574630\pi\) | ||||
−0.232314 | + | 0.972641i | \(0.574630\pi\) | |||||||
\(168\) | 3.28083 | 0.253122 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.40581 | 0.184517 | ||||||||
\(171\) | 5.03684 | 0.385176 | ||||||||
\(172\) | −11.5308 | −0.879215 | ||||||||
\(173\) | 17.7506 | 1.34956 | 0.674778 | − | 0.738021i | \(-0.264240\pi\) | ||||
0.674778 | + | 0.738021i | \(0.264240\pi\) | |||||||
\(174\) | −20.0248 | −1.51807 | ||||||||
\(175\) | 1.55496 | 0.117544 | ||||||||
\(176\) | 1.76271 | 0.132869 | ||||||||
\(177\) | −0.786872 | −0.0591449 | ||||||||
\(178\) | 29.8756 | 2.23927 | ||||||||
\(179\) | −16.5550 | −1.23738 | −0.618688 | − | 0.785637i | \(-0.712335\pi\) | ||||
−0.618688 | + | 0.785637i | \(0.712335\pi\) | |||||||
\(180\) | 0.725873 | 0.0541034 | ||||||||
\(181\) | 11.1739 | 0.830549 | 0.415275 | − | 0.909696i | \(-0.363685\pi\) | ||||
0.415275 | + | 0.909696i | \(0.363685\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2687 | 0.833010 | ||||||||
\(184\) | 10.8683 | 0.801223 | ||||||||
\(185\) | 4.60388 | 0.338484 | ||||||||
\(186\) | −15.2228 | −1.11619 | ||||||||
\(187\) | 0.476501 | 0.0348452 | ||||||||
\(188\) | 4.26205 | 0.310842 | ||||||||
\(189\) | 8.66115 | 0.630006 | ||||||||
\(190\) | 15.5918 | 1.13115 | ||||||||
\(191\) | −8.03684 | −0.581525 | −0.290763 | − | 0.956795i | \(-0.593909\pi\) | ||||
−0.290763 | + | 0.956795i | \(0.593909\pi\) | |||||||
\(192\) | 1.97285 | 0.142378 | ||||||||
\(193\) | −15.8931 | −1.14401 | −0.572004 | − | 0.820251i | \(-0.693834\pi\) | ||||
−0.572004 | + | 0.820251i | \(0.693834\pi\) | |||||||
\(194\) | 18.7995 | 1.34973 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.71379 | −0.408128 | ||||||||
\(197\) | −20.1715 | −1.43716 | −0.718580 | − | 0.695444i | \(-0.755208\pi\) | ||||
−0.718580 | + | 0.695444i | \(0.755208\pi\) | |||||||
\(198\) | 0.374354 | 0.0266042 | ||||||||
\(199\) | −11.8116 | −0.837304 | −0.418652 | − | 0.908147i | \(-0.637497\pi\) | ||||
−0.418652 | + | 0.908147i | \(0.637497\pi\) | |||||||
\(200\) | −1.35690 | −0.0959470 | ||||||||
\(201\) | −6.96913 | −0.491565 | ||||||||
\(202\) | 2.92931 | 0.206106 | ||||||||
\(203\) | 11.1129 | 0.779973 | ||||||||
\(204\) | 2.58881 | 0.181253 | ||||||||
\(205\) | 8.58211 | 0.599400 | ||||||||
\(206\) | −16.8213 | −1.17200 | ||||||||
\(207\) | 4.66248 | 0.324065 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.08815 | 0.213612 | ||||||||
\(210\) | 4.35690 | 0.300654 | ||||||||
\(211\) | −24.0978 | −1.65896 | −0.829482 | − | 0.558534i | \(-0.811364\pi\) | ||||
−0.829482 | + | 0.558534i | \(0.811364\pi\) | |||||||
\(212\) | −2.80194 | −0.192438 | ||||||||
\(213\) | −9.94198 | −0.681214 | ||||||||
\(214\) | 29.2325 | 1.99829 | ||||||||
\(215\) | 9.24698 | 0.630639 | ||||||||
\(216\) | −7.55794 | −0.514253 | ||||||||
\(217\) | 8.44803 | 0.573489 | ||||||||
\(218\) | −9.12929 | −0.618314 | ||||||||
\(219\) | −24.1414 | −1.63132 | ||||||||
\(220\) | 0.445042 | 0.0300047 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 12.8998 | 0.865776 | ||||||||
\(223\) | 10.2034 | 0.683273 | 0.341636 | − | 0.939832i | \(-0.389019\pi\) | ||||
0.341636 | + | 0.939832i | \(0.389019\pi\) | |||||||
\(224\) | −9.61894 | −0.642693 | ||||||||
\(225\) | −0.582105 | −0.0388070 | ||||||||
\(226\) | 18.2271 | 1.21245 | ||||||||
\(227\) | −7.83446 | −0.519991 | −0.259996 | − | 0.965610i | \(-0.583721\pi\) | ||||
−0.259996 | + | 0.965610i | \(0.583721\pi\) | |||||||
\(228\) | 16.7778 | 1.11114 | ||||||||
\(229\) | 6.61596 | 0.437195 | 0.218597 | − | 0.975815i | \(-0.429852\pi\) | ||||
0.218597 | + | 0.975815i | \(0.429852\pi\) | |||||||
\(230\) | 14.4330 | 0.951681 | ||||||||
\(231\) | 0.862937 | 0.0567771 | ||||||||
\(232\) | −9.69740 | −0.636665 | ||||||||
\(233\) | 1.37196 | 0.0898802 | 0.0449401 | − | 0.998990i | \(-0.485690\pi\) | ||||
0.0449401 | + | 0.998990i | \(0.485690\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.41789 | −0.222959 | ||||||||
\(236\) | 0.631023 | 0.0410761 | ||||||||
\(237\) | 7.23862 | 0.470199 | ||||||||
\(238\) | −3.74094 | −0.242489 | ||||||||
\(239\) | −2.10454 | −0.136131 | −0.0680657 | − | 0.997681i | \(-0.521683\pi\) | ||||
−0.0680657 | + | 0.997681i | \(0.521683\pi\) | |||||||
\(240\) | −7.67994 | −0.495738 | ||||||||
\(241\) | 19.1890 | 1.23607 | 0.618035 | − | 0.786151i | \(-0.287929\pi\) | ||||
0.618035 | + | 0.786151i | \(0.287929\pi\) | |||||||
\(242\) | −19.5918 | −1.25941 | ||||||||
\(243\) | −5.95779 | −0.382192 | ||||||||
\(244\) | −9.03684 | −0.578524 | ||||||||
\(245\) | 4.58211 | 0.292740 | ||||||||
\(246\) | 24.0465 | 1.53315 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.37196 | −0.468120 | ||||||||
\(249\) | −8.52781 | −0.540428 | ||||||||
\(250\) | −1.80194 | −0.113965 | ||||||||
\(251\) | −10.0653 | −0.635317 | −0.317658 | − | 0.948205i | \(-0.602897\pi\) | ||||
−0.317658 | + | 0.948205i | \(0.602897\pi\) | |||||||
\(252\) | −1.12870 | −0.0711016 | ||||||||
\(253\) | 2.85862 | 0.179720 | ||||||||
\(254\) | −10.8605 | −0.681451 | ||||||||
\(255\) | −2.07606 | −0.130008 | ||||||||
\(256\) | 20.7114 | 1.29446 | ||||||||
\(257\) | 10.9095 | 0.680513 | 0.340257 | − | 0.940333i | \(-0.389486\pi\) | ||||
0.340257 | + | 0.940333i | \(0.389486\pi\) | |||||||
\(258\) | 25.9095 | 1.61305 | ||||||||
\(259\) | −7.15883 | −0.444828 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.16016 | −0.257508 | ||||||||
\(262\) | −18.2131 | −1.12521 | ||||||||
\(263\) | −8.41789 | −0.519070 | −0.259535 | − | 0.965734i | \(-0.583569\pi\) | ||||
−0.259535 | + | 0.965734i | \(0.583569\pi\) | |||||||
\(264\) | −0.753020 | −0.0463452 | ||||||||
\(265\) | 2.24698 | 0.138031 | ||||||||
\(266\) | −24.2446 | −1.48653 | ||||||||
\(267\) | −25.7808 | −1.57776 | ||||||||
\(268\) | 5.58881 | 0.341391 | ||||||||
\(269\) | 19.3991 | 1.18278 | 0.591392 | − | 0.806384i | \(-0.298579\pi\) | ||||
0.591392 | + | 0.806384i | \(0.298579\pi\) | |||||||
\(270\) | −10.0368 | −0.610822 | ||||||||
\(271\) | 3.10023 | 0.188325 | 0.0941627 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941627 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(272\) | 6.59419 | 0.399831 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.93900 | 0.540025 | ||||||||
\(275\) | −0.356896 | −0.0215216 | ||||||||
\(276\) | 15.5308 | 0.934844 | ||||||||
\(277\) | 7.10752 | 0.427050 | 0.213525 | − | 0.976938i | \(-0.431506\pi\) | ||||
0.213525 | + | 0.976938i | \(0.431506\pi\) | |||||||
\(278\) | −16.2567 | −0.975010 | ||||||||
\(279\) | −3.16255 | −0.189337 | ||||||||
\(280\) | 2.10992 | 0.126092 | ||||||||
\(281\) | −8.80492 | −0.525258 | −0.262629 | − | 0.964897i | \(-0.584589\pi\) | ||||
−0.262629 | + | 0.964897i | \(0.584589\pi\) | |||||||
\(282\) | −9.57673 | −0.570286 | ||||||||
\(283\) | −7.59419 | −0.451428 | −0.225714 | − | 0.974194i | \(-0.572471\pi\) | ||||
−0.225714 | + | 0.974194i | \(0.572471\pi\) | |||||||
\(284\) | 7.97285 | 0.473102 | ||||||||
\(285\) | −13.4547 | −0.796989 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.3448 | −0.787719 | ||||||||
\(288\) | 3.60089 | 0.212185 | ||||||||
\(289\) | −15.2174 | −0.895144 | ||||||||
\(290\) | −12.8780 | −0.756222 | ||||||||
\(291\) | −16.2228 | −0.950998 | ||||||||
\(292\) | 19.3599 | 1.13295 | ||||||||
\(293\) | 6.96615 | 0.406967 | 0.203483 | − | 0.979078i | \(-0.434774\pi\) | ||||
0.203483 | + | 0.979078i | \(0.434774\pi\) | |||||||
\(294\) | 12.8388 | 0.748772 | ||||||||
\(295\) | −0.506041 | −0.0294628 | ||||||||
\(296\) | 6.24698 | 0.363098 | ||||||||
\(297\) | −1.98792 | −0.115351 | ||||||||
\(298\) | −32.7875 | −1.89933 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.93900 | −0.111948 | ||||||||
\(301\) | −14.3787 | −0.828773 | ||||||||
\(302\) | −13.0194 | −0.749181 | ||||||||
\(303\) | −2.52781 | −0.145219 | ||||||||
\(304\) | 42.7362 | 2.45109 | ||||||||
\(305\) | 7.24698 | 0.414961 | ||||||||
\(306\) | 1.40044 | 0.0800576 | ||||||||
\(307\) | −21.3153 | −1.21653 | −0.608263 | − | 0.793735i | \(-0.708134\pi\) | ||||
−0.608263 | + | 0.793735i | \(0.708134\pi\) | |||||||
\(308\) | −0.692021 | −0.0394316 | ||||||||
\(309\) | 14.5157 | 0.825771 | ||||||||
\(310\) | −9.78986 | −0.556026 | ||||||||
\(311\) | −29.3672 | −1.66526 | −0.832630 | − | 0.553830i | \(-0.813166\pi\) | ||||
−0.832630 | + | 0.553830i | \(0.813166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.09246 | 0.118273 | 0.0591364 | − | 0.998250i | \(-0.481165\pi\) | ||||
0.0591364 | + | 0.998250i | \(0.481165\pi\) | |||||||
\(314\) | −15.8562 | −0.894819 | ||||||||
\(315\) | 0.905149 | 0.0509994 | ||||||||
\(316\) | −5.80492 | −0.326552 | ||||||||
\(317\) | 10.1981 | 0.572780 | 0.286390 | − | 0.958113i | \(-0.407545\pi\) | ||||
0.286390 | + | 0.958113i | \(0.407545\pi\) | |||||||
\(318\) | 6.29590 | 0.353056 | ||||||||
\(319\) | −2.55065 | −0.142809 | ||||||||
\(320\) | 1.26875 | 0.0709253 | ||||||||
\(321\) | −25.2258 | −1.40797 | ||||||||
\(322\) | −22.4426 | −1.25068 | ||||||||
\(323\) | 11.5526 | 0.642802 | ||||||||
\(324\) | −8.62266 | −0.479037 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.6625 | 0.590540 | ||||||||
\(327\) | 7.87800 | 0.435655 | ||||||||
\(328\) | 11.6450 | 0.642989 | ||||||||
\(329\) | 5.31468 | 0.293008 | ||||||||
\(330\) | −1.00000 | −0.0550482 | ||||||||
\(331\) | −15.2282 | −0.837017 | −0.418509 | − | 0.908213i | \(-0.637447\pi\) | ||||
−0.418509 | + | 0.908213i | \(0.637447\pi\) | |||||||
\(332\) | 6.83877 | 0.375326 | ||||||||
\(333\) | 2.67994 | 0.146860 | ||||||||
\(334\) | −10.8194 | −0.592011 | ||||||||
\(335\) | −4.48188 | −0.244871 | ||||||||
\(336\) | 11.9420 | 0.651489 | ||||||||
\(337\) | −0.869641 | −0.0473724 | −0.0236862 | − | 0.999719i | \(-0.507540\pi\) | ||||
−0.0236862 | + | 0.999719i | \(0.507540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.7289 | −0.854274 | ||||||||
\(340\) | 1.66487 | 0.0902905 | ||||||||
\(341\) | −1.93900 | −0.105003 | ||||||||
\(342\) | 9.07606 | 0.490777 | ||||||||
\(343\) | −18.0097 | −0.972432 | ||||||||
\(344\) | 12.5472 | 0.676499 | ||||||||
\(345\) | −12.4547 | −0.670540 | ||||||||
\(346\) | 31.9855 | 1.71955 | ||||||||
\(347\) | −16.7614 | −0.899798 | −0.449899 | − | 0.893079i | \(-0.648540\pi\) | ||||
−0.449899 | + | 0.893079i | \(0.648540\pi\) | |||||||
\(348\) | −13.8576 | −0.742843 | ||||||||
\(349\) | −23.3381 | −1.24926 | −0.624630 | − | 0.780921i | \(-0.714750\pi\) | ||||
−0.624630 | + | 0.780921i | \(0.714750\pi\) | |||||||
\(350\) | 2.80194 | 0.149770 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.20775 | 0.117674 | ||||||||
\(353\) | 30.5870 | 1.62798 | 0.813991 | − | 0.580877i | \(-0.197290\pi\) | ||||
0.813991 | + | 0.580877i | \(0.197290\pi\) | |||||||
\(354\) | −1.41789 | −0.0753603 | ||||||||
\(355\) | −6.39373 | −0.339344 | ||||||||
\(356\) | 20.6746 | 1.09575 | ||||||||
\(357\) | 3.22819 | 0.170854 | ||||||||
\(358\) | −29.8310 | −1.57662 | ||||||||
\(359\) | −12.3418 | −0.651377 | −0.325688 | − | 0.945477i | \(-0.605596\pi\) | ||||
−0.325688 | + | 0.945477i | \(0.605596\pi\) | |||||||
\(360\) | −0.789856 | −0.0416291 | ||||||||
\(361\) | 55.8708 | 2.94057 | ||||||||
\(362\) | 20.1347 | 1.05825 | ||||||||
\(363\) | 16.9065 | 0.887360 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.5254 | −0.812638 | ||||||||
\(366\) | 20.3056 | 1.06139 | ||||||||
\(367\) | 18.5569 | 0.968661 | 0.484331 | − | 0.874885i | \(-0.339063\pi\) | ||||
0.484331 | + | 0.874885i | \(0.339063\pi\) | |||||||
\(368\) | 39.5599 | 2.06220 | ||||||||
\(369\) | 4.99569 | 0.260065 | ||||||||
\(370\) | 8.29590 | 0.431283 | ||||||||
\(371\) | −3.49396 | −0.181397 | ||||||||
\(372\) | −10.5345 | −0.546189 | ||||||||
\(373\) | −23.9245 | −1.23877 | −0.619383 | − | 0.785089i | \(-0.712617\pi\) | ||||
−0.619383 | + | 0.785089i | \(0.712617\pi\) | |||||||
\(374\) | 0.858625 | 0.0443984 | ||||||||
\(375\) | 1.55496 | 0.0802977 | ||||||||
\(376\) | −4.63773 | −0.239173 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 15.6069 | 0.802730 | ||||||||
\(379\) | −7.85623 | −0.403548 | −0.201774 | − | 0.979432i | \(-0.564671\pi\) | ||||
−0.201774 | + | 0.979432i | \(0.564671\pi\) | |||||||
\(380\) | 10.7899 | 0.553508 | ||||||||
\(381\) | 9.37196 | 0.480140 | ||||||||
\(382\) | −14.4819 | −0.740957 | ||||||||
\(383\) | −5.45473 | −0.278724 | −0.139362 | − | 0.990242i | \(-0.544505\pi\) | ||||
−0.139362 | + | 0.990242i | \(0.544505\pi\) | |||||||
\(384\) | −15.6829 | −0.800316 | ||||||||
\(385\) | 0.554958 | 0.0282833 | ||||||||
\(386\) | −28.6383 | −1.45765 | ||||||||
\(387\) | 5.38271 | 0.273619 | ||||||||
\(388\) | 13.0097 | 0.660467 | ||||||||
\(389\) | −18.0084 | −0.913060 | −0.456530 | − | 0.889708i | \(-0.650908\pi\) | ||||
−0.456530 | + | 0.889708i | \(0.650908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.6939 | 0.540816 | ||||||||
\(392\) | 6.21744 | 0.314028 | ||||||||
\(393\) | 15.7168 | 0.792806 | ||||||||
\(394\) | −36.3478 | −1.83118 | ||||||||
\(395\) | 4.65519 | 0.234228 | ||||||||
\(396\) | 0.259061 | 0.0130183 | ||||||||
\(397\) | −18.3080 | −0.918851 | −0.459426 | − | 0.888216i | \(-0.651945\pi\) | ||||
−0.459426 | + | 0.888216i | \(0.651945\pi\) | |||||||
\(398\) | −21.2838 | −1.06686 | ||||||||
\(399\) | 20.9215 | 1.04739 | ||||||||
\(400\) | −4.93900 | −0.246950 | ||||||||
\(401\) | 19.1728 | 0.957446 | 0.478723 | − | 0.877966i | \(-0.341100\pi\) | ||||
0.478723 | + | 0.877966i | \(0.341100\pi\) | |||||||
\(402\) | −12.5579 | −0.626333 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.02715 | 0.100854 | ||||||||
\(405\) | 6.91484 | 0.343601 | ||||||||
\(406\) | 20.0248 | 0.993812 | ||||||||
\(407\) | 1.64310 | 0.0814456 | ||||||||
\(408\) | −2.81700 | −0.139462 | ||||||||
\(409\) | 7.22223 | 0.357116 | 0.178558 | − | 0.983929i | \(-0.442857\pi\) | ||||
0.178558 | + | 0.983929i | \(0.442857\pi\) | |||||||
\(410\) | 15.4644 | 0.763733 | ||||||||
\(411\) | −7.71379 | −0.380493 | ||||||||
\(412\) | −11.6407 | −0.573497 | ||||||||
\(413\) | 0.786872 | 0.0387195 | ||||||||
\(414\) | 8.40150 | 0.412911 | ||||||||
\(415\) | −5.48427 | −0.269212 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.0285 | 0.686977 | ||||||||
\(418\) | 5.56465 | 0.272176 | ||||||||
\(419\) | 0.271143 | 0.0132462 | 0.00662310 | − | 0.999978i | \(-0.497892\pi\) | ||||
0.00662310 | + | 0.999978i | \(0.497892\pi\) | |||||||
\(420\) | 3.01507 | 0.147120 | ||||||||
\(421\) | 35.6286 | 1.73643 | 0.868217 | − | 0.496185i | \(-0.165266\pi\) | ||||
0.868217 | + | 0.496185i | \(0.165266\pi\) | |||||||
\(422\) | −43.4228 | −2.11379 | ||||||||
\(423\) | −1.98957 | −0.0967364 | ||||||||
\(424\) | 3.04892 | 0.148069 | ||||||||
\(425\) | −1.33513 | −0.0647631 | ||||||||
\(426\) | −17.9148 | −0.867977 | ||||||||
\(427\) | −11.2687 | −0.545333 | ||||||||
\(428\) | 20.2295 | 0.977831 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.6625 | 0.803536 | ||||||||
\(431\) | 35.4959 | 1.70978 | 0.854888 | − | 0.518812i | \(-0.173626\pi\) | ||||
0.854888 | + | 0.518812i | \(0.173626\pi\) | |||||||
\(432\) | −27.5104 | −1.32359 | ||||||||
\(433\) | 15.8605 | 0.762209 | 0.381105 | − | 0.924532i | \(-0.375544\pi\) | ||||
0.381105 | + | 0.924532i | \(0.375544\pi\) | |||||||
\(434\) | 15.2228 | 0.730719 | ||||||||
\(435\) | 11.1129 | 0.532823 | ||||||||
\(436\) | −6.31767 | −0.302561 | ||||||||
\(437\) | 69.3062 | 3.31536 | ||||||||
\(438\) | −43.5013 | −2.07857 | ||||||||
\(439\) | −25.9312 | −1.23763 | −0.618815 | − | 0.785537i | \(-0.712387\pi\) | ||||
−0.618815 | + | 0.785537i | \(0.712387\pi\) | |||||||
\(440\) | −0.484271 | −0.0230867 | ||||||||
\(441\) | 2.66727 | 0.127013 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.2306 | −0.533581 | −0.266791 | − | 0.963755i | \(-0.585963\pi\) | ||||
−0.266791 | + | 0.963755i | \(0.585963\pi\) | |||||||
\(444\) | 8.92692 | 0.423653 | ||||||||
\(445\) | −16.5797 | −0.785954 | ||||||||
\(446\) | 18.3860 | 0.870601 | ||||||||
\(447\) | 28.2935 | 1.33824 | ||||||||
\(448\) | −1.97285 | −0.0932085 | ||||||||
\(449\) | −36.8471 | −1.73892 | −0.869462 | − | 0.494000i | \(-0.835534\pi\) | ||||
−0.869462 | + | 0.494000i | \(0.835534\pi\) | |||||||
\(450\) | −1.04892 | −0.0494464 | ||||||||
\(451\) | 3.06292 | 0.144227 | ||||||||
\(452\) | 12.6136 | 0.593292 | ||||||||
\(453\) | 11.2349 | 0.527862 | ||||||||
\(454\) | −14.1172 | −0.662554 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.2567 | −0.854947 | ||||||||
\(457\) | 21.9879 | 1.02855 | 0.514276 | − | 0.857625i | \(-0.328061\pi\) | ||||
0.514276 | + | 0.857625i | \(0.328061\pi\) | |||||||
\(458\) | 11.9215 | 0.557057 | ||||||||
\(459\) | −7.43668 | −0.347115 | ||||||||
\(460\) | 9.98792 | 0.465689 | ||||||||
\(461\) | −8.53750 | −0.397631 | −0.198816 | − | 0.980037i | \(-0.563709\pi\) | ||||
−0.198816 | + | 0.980037i | \(0.563709\pi\) | |||||||
\(462\) | 1.55496 | 0.0723432 | ||||||||
\(463\) | −20.9922 | −0.975592 | −0.487796 | − | 0.872958i | \(-0.662199\pi\) | ||||
−0.487796 | + | 0.872958i | \(0.662199\pi\) | |||||||
\(464\) | −35.2978 | −1.63866 | ||||||||
\(465\) | 8.44803 | 0.391768 | ||||||||
\(466\) | 2.47219 | 0.114522 | ||||||||
\(467\) | 13.9976 | 0.647732 | 0.323866 | − | 0.946103i | \(-0.395017\pi\) | ||||
0.323866 | + | 0.946103i | \(0.395017\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.96913 | 0.321805 | ||||||||
\(470\) | −6.15883 | −0.284086 | ||||||||
\(471\) | 13.6829 | 0.630476 | ||||||||
\(472\) | −0.686645 | −0.0316054 | ||||||||
\(473\) | 3.30021 | 0.151744 | ||||||||
\(474\) | 13.0435 | 0.599110 | ||||||||
\(475\) | −8.65279 | −0.397017 | ||||||||
\(476\) | −2.58881 | −0.118658 | ||||||||
\(477\) | 1.30798 | 0.0598882 | ||||||||
\(478\) | −3.79225 | −0.173453 | ||||||||
\(479\) | −14.6136 | −0.667711 | −0.333855 | − | 0.942624i | \(-0.608350\pi\) | ||||
−0.333855 | + | 0.942624i | \(0.608350\pi\) | |||||||
\(480\) | −9.61894 | −0.439043 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 34.5773 | 1.57495 | ||||||||
\(483\) | 19.3666 | 0.881210 | ||||||||
\(484\) | −13.5579 | −0.616270 | ||||||||
\(485\) | −10.4330 | −0.473736 | ||||||||
\(486\) | −10.7356 | −0.486975 | ||||||||
\(487\) | 39.0616 | 1.77005 | 0.885025 | − | 0.465544i | \(-0.154141\pi\) | ||||
0.885025 | + | 0.465544i | \(0.154141\pi\) | |||||||
\(488\) | 9.83340 | 0.445137 | ||||||||
\(489\) | −9.20105 | −0.416086 | ||||||||
\(490\) | 8.25667 | 0.372998 | ||||||||
\(491\) | −25.6082 | −1.15568 | −0.577841 | − | 0.816150i | \(-0.696104\pi\) | ||||
−0.577841 | + | 0.816150i | \(0.696104\pi\) | |||||||
\(492\) | 16.6407 | 0.750221 | ||||||||
\(493\) | −9.54181 | −0.429742 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.207751 | −0.00933771 | ||||||||
\(496\) | −26.8334 | −1.20486 | ||||||||
\(497\) | 9.94198 | 0.445959 | ||||||||
\(498\) | −15.3666 | −0.688593 | ||||||||
\(499\) | 1.67563 | 0.0750114 | 0.0375057 | − | 0.999296i | \(-0.488059\pi\) | ||||
0.0375057 | + | 0.999296i | \(0.488059\pi\) | |||||||
\(500\) | −1.24698 | −0.0557666 | ||||||||
\(501\) | 9.33645 | 0.417122 | ||||||||
\(502\) | −18.1371 | −0.809497 | ||||||||
\(503\) | 24.5569 | 1.09494 | 0.547469 | − | 0.836826i | \(-0.315592\pi\) | ||||
0.547469 | + | 0.836826i | \(0.315592\pi\) | |||||||
\(504\) | 1.22819 | 0.0547081 | ||||||||
\(505\) | −1.62565 | −0.0723403 | ||||||||
\(506\) | 5.15106 | 0.228993 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.51573 | −0.333457 | ||||||||
\(509\) | −21.8767 | −0.969667 | −0.484833 | − | 0.874607i | \(-0.661120\pi\) | ||||
−0.484833 | + | 0.874607i | \(0.661120\pi\) | |||||||
\(510\) | −3.74094 | −0.165652 | ||||||||
\(511\) | 24.1414 | 1.06795 | ||||||||
\(512\) | 17.1491 | 0.757892 | ||||||||
\(513\) | −48.1963 | −2.12792 | ||||||||
\(514\) | 19.6582 | 0.867085 | ||||||||
\(515\) | 9.33513 | 0.411355 | ||||||||
\(516\) | 17.9299 | 0.789320 | ||||||||
\(517\) | −1.21983 | −0.0536482 | ||||||||
\(518\) | −12.8998 | −0.566783 | ||||||||
\(519\) | −27.6015 | −1.21157 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.2131 | 1.32366 | 0.661831 | − | 0.749653i | \(-0.269780\pi\) | ||||
0.661831 | + | 0.749653i | \(0.269780\pi\) | |||||||
\(522\) | −7.49635 | −0.328106 | ||||||||
\(523\) | 21.1957 | 0.926822 | 0.463411 | − | 0.886143i | \(-0.346625\pi\) | ||||
0.463411 | + | 0.886143i | \(0.346625\pi\) | |||||||
\(524\) | −12.6039 | −0.550603 | ||||||||
\(525\) | −2.41789 | −0.105526 | ||||||||
\(526\) | −15.1685 | −0.661379 | ||||||||
\(527\) | −7.25368 | −0.315975 | ||||||||
\(528\) | −2.74094 | −0.119284 | ||||||||
\(529\) | 41.1551 | 1.78935 | ||||||||
\(530\) | 4.04892 | 0.175874 | ||||||||
\(531\) | −0.294569 | −0.0127832 | ||||||||
\(532\) | −16.7778 | −0.727409 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −46.4553 | −2.01032 | ||||||||
\(535\) | −16.2228 | −0.701374 | ||||||||
\(536\) | −6.08144 | −0.262678 | ||||||||
\(537\) | 25.7423 | 1.11086 | ||||||||
\(538\) | 34.9560 | 1.50706 | ||||||||
\(539\) | 1.63533 | 0.0704388 | ||||||||
\(540\) | −6.94571 | −0.298896 | ||||||||
\(541\) | −15.4373 | −0.663700 | −0.331850 | − | 0.943332i | \(-0.607673\pi\) | ||||
−0.331850 | + | 0.943332i | \(0.607673\pi\) | |||||||
\(542\) | 5.58642 | 0.239957 | ||||||||
\(543\) | −17.3749 | −0.745630 | ||||||||
\(544\) | 8.25906 | 0.354104 | ||||||||
\(545\) | 5.06638 | 0.217020 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.6722 | −1.65350 | −0.826751 | − | 0.562568i | \(-0.809814\pi\) | ||||
−0.826751 | + | 0.562568i | \(0.809814\pi\) | |||||||
\(548\) | 6.18598 | 0.264252 | ||||||||
\(549\) | 4.21850 | 0.180041 | ||||||||
\(550\) | −0.643104 | −0.0274221 | ||||||||
\(551\) | −61.8394 | −2.63445 | ||||||||
\(552\) | −16.8998 | −0.719302 | ||||||||
\(553\) | −7.23862 | −0.307817 | ||||||||
\(554\) | 12.8073 | 0.544131 | ||||||||
\(555\) | −7.15883 | −0.303876 | ||||||||
\(556\) | −11.2500 | −0.477105 | ||||||||
\(557\) | 21.9782 | 0.931247 | 0.465624 | − | 0.884983i | \(-0.345830\pi\) | ||||
0.465624 | + | 0.884983i | \(0.345830\pi\) | |||||||
\(558\) | −5.69873 | −0.241246 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 7.67994 | 0.324537 | ||||||||
\(561\) | −0.740939 | −0.0312825 | ||||||||
\(562\) | −15.8659 | −0.669263 | ||||||||
\(563\) | 14.4474 | 0.608887 | 0.304443 | − | 0.952530i | \(-0.401530\pi\) | ||||
0.304443 | + | 0.952530i | \(0.401530\pi\) | |||||||
\(564\) | −6.62730 | −0.279060 | ||||||||
\(565\) | −10.1153 | −0.425554 | ||||||||
\(566\) | −13.6843 | −0.575192 | ||||||||
\(567\) | −10.7523 | −0.451553 | ||||||||
\(568\) | −8.67563 | −0.364021 | ||||||||
\(569\) | −0.305586 | −0.0128108 | −0.00640541 | − | 0.999979i | \(-0.502039\pi\) | ||||
−0.00640541 | + | 0.999979i | \(0.502039\pi\) | |||||||
\(570\) | −24.2446 | −1.01549 | ||||||||
\(571\) | −19.8629 | −0.831238 | −0.415619 | − | 0.909539i | \(-0.636435\pi\) | ||||
−0.415619 | + | 0.909539i | \(0.636435\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.4969 | 0.522067 | ||||||||
\(574\) | −24.0465 | −1.00368 | ||||||||
\(575\) | −8.00969 | −0.334027 | ||||||||
\(576\) | 0.738546 | 0.0307727 | ||||||||
\(577\) | −18.3254 | −0.762898 | −0.381449 | − | 0.924390i | \(-0.624575\pi\) | ||||
−0.381449 | + | 0.924390i | \(0.624575\pi\) | |||||||
\(578\) | −27.4209 | −1.14056 | ||||||||
\(579\) | 24.7131 | 1.02704 | ||||||||
\(580\) | −8.91185 | −0.370045 | ||||||||
\(581\) | 8.52781 | 0.353793 | ||||||||
\(582\) | −29.2325 | −1.21173 | ||||||||
\(583\) | 0.801938 | 0.0332129 | ||||||||
\(584\) | −21.0664 | −0.871733 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.5526 | 0.518542 | ||||||||
\(587\) | 27.0476 | 1.11637 | 0.558187 | − | 0.829715i | \(-0.311497\pi\) | ||||
0.558187 | + | 0.829715i | \(0.311497\pi\) | |||||||
\(588\) | 8.88471 | 0.366399 | ||||||||
\(589\) | −47.0103 | −1.93702 | ||||||||
\(590\) | −0.911854 | −0.0375404 | ||||||||
\(591\) | 31.3658 | 1.29022 | ||||||||
\(592\) | 22.7385 | 0.934548 | ||||||||
\(593\) | 10.6907 | 0.439014 | 0.219507 | − | 0.975611i | \(-0.429555\pi\) | ||||
0.219507 | + | 0.975611i | \(0.429555\pi\) | |||||||
\(594\) | −3.58211 | −0.146976 | ||||||||
\(595\) | 2.07606 | 0.0851103 | ||||||||
\(596\) | −22.6896 | −0.929403 | ||||||||
\(597\) | 18.3666 | 0.751694 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.8702 | 1.34304 | 0.671521 | − | 0.740986i | \(-0.265641\pi\) | ||||
0.671521 | + | 0.740986i | \(0.265641\pi\) | |||||||
\(600\) | 2.10992 | 0.0861370 | ||||||||
\(601\) | −42.1702 | −1.72016 | −0.860079 | − | 0.510161i | \(-0.829586\pi\) | ||||
−0.860079 | + | 0.510161i | \(0.829586\pi\) | |||||||
\(602\) | −25.9095 | −1.05599 | ||||||||
\(603\) | −2.60892 | −0.106244 | ||||||||
\(604\) | −9.00969 | −0.366599 | ||||||||
\(605\) | 10.8726 | 0.442035 | ||||||||
\(606\) | −4.55496 | −0.185033 | ||||||||
\(607\) | 0.687710 | 0.0279133 | 0.0139566 | − | 0.999903i | \(-0.495557\pi\) | ||||
0.0139566 | + | 0.999903i | \(0.495557\pi\) | |||||||
\(608\) | 53.5260 | 2.17077 | ||||||||
\(609\) | −17.2801 | −0.700225 | ||||||||
\(610\) | 13.0586 | 0.528728 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.969132 | 0.0391748 | ||||||||
\(613\) | −34.5080 | −1.39376 | −0.696882 | − | 0.717186i | \(-0.745430\pi\) | ||||
−0.696882 | + | 0.717186i | \(0.745430\pi\) | |||||||
\(614\) | −38.4088 | −1.55005 | ||||||||
\(615\) | −13.3448 | −0.538115 | ||||||||
\(616\) | 0.753020 | 0.0303401 | ||||||||
\(617\) | 10.1612 | 0.409076 | 0.204538 | − | 0.978859i | \(-0.434431\pi\) | ||||
0.204538 | + | 0.978859i | \(0.434431\pi\) | |||||||
\(618\) | 26.1564 | 1.05217 | ||||||||
\(619\) | −12.8442 | −0.516250 | −0.258125 | − | 0.966112i | \(-0.583105\pi\) | ||||
−0.258125 | + | 0.966112i | \(0.583105\pi\) | |||||||
\(620\) | −6.77479 | −0.272082 | ||||||||
\(621\) | −44.6142 | −1.79030 | ||||||||
\(622\) | −52.9178 | −2.12181 | ||||||||
\(623\) | 25.7808 | 1.03288 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.77048 | 0.150699 | ||||||||
\(627\) | −4.80194 | −0.191771 | ||||||||
\(628\) | −10.9729 | −0.437865 | ||||||||
\(629\) | 6.14675 | 0.245087 | ||||||||
\(630\) | 1.63102 | 0.0649815 | ||||||||
\(631\) | −17.2489 | −0.686668 | −0.343334 | − | 0.939213i | \(-0.611556\pi\) | ||||
−0.343334 | + | 0.939213i | \(0.611556\pi\) | |||||||
\(632\) | 6.31660 | 0.251261 | ||||||||
\(633\) | 37.4711 | 1.48934 | ||||||||
\(634\) | 18.3763 | 0.729815 | ||||||||
\(635\) | 6.02715 | 0.239180 | ||||||||
\(636\) | 4.35690 | 0.172762 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.59611 | −0.181962 | ||||||||
\(639\) | −3.72182 | −0.147233 | ||||||||
\(640\) | −10.0858 | −0.398674 | ||||||||
\(641\) | −11.5526 | −0.456299 | −0.228149 | − | 0.973626i | \(-0.573267\pi\) | ||||
−0.228149 | + | 0.973626i | \(0.573267\pi\) | |||||||
\(642\) | −45.4553 | −1.79398 | ||||||||
\(643\) | −24.9661 | −0.984569 | −0.492284 | − | 0.870434i | \(-0.663838\pi\) | ||||
−0.492284 | + | 0.870434i | \(0.663838\pi\) | |||||||
\(644\) | −15.5308 | −0.611999 | ||||||||
\(645\) | −14.3787 | −0.566159 | ||||||||
\(646\) | 20.8170 | 0.819034 | ||||||||
\(647\) | 17.0852 | 0.671687 | 0.335844 | − | 0.941918i | \(-0.390979\pi\) | ||||
0.335844 | + | 0.941918i | \(0.390979\pi\) | |||||||
\(648\) | 9.38271 | 0.368588 | ||||||||
\(649\) | −0.180604 | −0.00708932 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.1363 | −0.514853 | ||||||||
\(652\) | 7.37867 | 0.288971 | ||||||||
\(653\) | −37.5773 | −1.47051 | −0.735257 | − | 0.677788i | \(-0.762939\pi\) | ||||
−0.735257 | + | 0.677788i | \(0.762939\pi\) | |||||||
\(654\) | 14.1957 | 0.555095 | ||||||||
\(655\) | 10.1075 | 0.394934 | ||||||||
\(656\) | 42.3870 | 1.65494 | ||||||||
\(657\) | −9.03743 | −0.352584 | ||||||||
\(658\) | 9.57673 | 0.373340 | ||||||||
\(659\) | 24.4131 | 0.951000 | 0.475500 | − | 0.879716i | \(-0.342267\pi\) | ||||
0.475500 | + | 0.879716i | \(0.342267\pi\) | |||||||
\(660\) | −0.692021 | −0.0269369 | ||||||||
\(661\) | 9.13467 | 0.355298 | 0.177649 | − | 0.984094i | \(-0.443151\pi\) | ||||
0.177649 | + | 0.984094i | \(0.443151\pi\) | |||||||
\(662\) | −27.4403 | −1.06650 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.44158 | −0.288789 | ||||||||
\(665\) | 13.4547 | 0.521752 | ||||||||
\(666\) | 4.82908 | 0.187123 | ||||||||
\(667\) | −57.2433 | −2.21647 | ||||||||
\(668\) | −7.48725 | −0.289691 | ||||||||
\(669\) | −15.8659 | −0.613412 | ||||||||
\(670\) | −8.07606 | −0.312006 | ||||||||
\(671\) | 2.58642 | 0.0998475 | ||||||||
\(672\) | 14.9571 | 0.576981 | ||||||||
\(673\) | 36.0810 | 1.39082 | 0.695410 | − | 0.718614i | \(-0.255223\pi\) | ||||
0.695410 | + | 0.718614i | \(0.255223\pi\) | |||||||
\(674\) | −1.56704 | −0.0603601 | ||||||||
\(675\) | 5.57002 | 0.214390 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.5905 | 0.791356 | 0.395678 | − | 0.918389i | \(-0.370510\pi\) | ||||
0.395678 | + | 0.918389i | \(0.370510\pi\) | |||||||
\(678\) | −28.3424 | −1.08848 | ||||||||
\(679\) | 16.2228 | 0.622575 | ||||||||
\(680\) | −1.81163 | −0.0694727 | ||||||||
\(681\) | 12.1823 | 0.466825 | ||||||||
\(682\) | −3.49396 | −0.133791 | ||||||||
\(683\) | −6.40821 | −0.245203 | −0.122602 | − | 0.992456i | \(-0.539124\pi\) | ||||
−0.122602 | + | 0.992456i | \(0.539124\pi\) | |||||||
\(684\) | 6.28083 | 0.240154 | ||||||||
\(685\) | −4.96077 | −0.189541 | ||||||||
\(686\) | −32.4523 | −1.23904 | ||||||||
\(687\) | −10.2875 | −0.392494 | ||||||||
\(688\) | 45.6708 | 1.74118 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −22.4426 | −0.854377 | ||||||||
\(691\) | −1.76032 | −0.0669656 | −0.0334828 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334828 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(692\) | 22.1347 | 0.841434 | ||||||||
\(693\) | 0.323044 | 0.0122714 | ||||||||
\(694\) | −30.2030 | −1.14649 | ||||||||
\(695\) | 9.02177 | 0.342215 | ||||||||
\(696\) | 15.0790 | 0.571570 | ||||||||
\(697\) | 11.4582 | 0.434010 | ||||||||
\(698\) | −42.0538 | −1.59176 | ||||||||
\(699\) | −2.13334 | −0.0806904 | ||||||||
\(700\) | 1.93900 | 0.0732874 | ||||||||
\(701\) | 24.3532 | 0.919807 | 0.459903 | − | 0.887969i | \(-0.347884\pi\) | ||||
0.459903 | + | 0.887969i | \(0.347884\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.8364 | 1.50246 | ||||||||
\(704\) | 0.452812 | 0.0170660 | ||||||||
\(705\) | 5.31468 | 0.200163 | ||||||||
\(706\) | 55.1159 | 2.07431 | ||||||||
\(707\) | 2.52781 | 0.0950681 | ||||||||
\(708\) | −0.981214 | −0.0368763 | ||||||||
\(709\) | 31.4916 | 1.18269 | 0.591345 | − | 0.806418i | \(-0.298597\pi\) | ||||
0.591345 | + | 0.806418i | \(0.298597\pi\) | |||||||
\(710\) | −11.5211 | −0.432379 | ||||||||
\(711\) | 2.70981 | 0.101626 | ||||||||
\(712\) | −22.4969 | −0.843109 | ||||||||
\(713\) | −43.5163 | −1.62970 | ||||||||
\(714\) | 5.81700 | 0.217696 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.6437 | −0.771491 | ||||||||
\(717\) | 3.27247 | 0.122213 | ||||||||
\(718\) | −22.2392 | −0.829960 | ||||||||
\(719\) | 20.1304 | 0.750736 | 0.375368 | − | 0.926876i | \(-0.377516\pi\) | ||||
0.375368 | + | 0.926876i | \(0.377516\pi\) | |||||||
\(720\) | −2.87502 | −0.107146 | ||||||||
\(721\) | −14.5157 | −0.540594 | ||||||||
\(722\) | 100.676 | 3.74676 | ||||||||
\(723\) | −29.8380 | −1.10969 | ||||||||
\(724\) | 13.9336 | 0.517839 | ||||||||
\(725\) | 7.14675 | 0.265424 | ||||||||
\(726\) | 30.4644 | 1.13064 | ||||||||
\(727\) | 13.8183 | 0.512494 | 0.256247 | − | 0.966611i | \(-0.417514\pi\) | ||||
0.256247 | + | 0.966611i | \(0.417514\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0086 | 1.11143 | ||||||||
\(730\) | −27.9758 | −1.03543 | ||||||||
\(731\) | 12.3459 | 0.456629 | ||||||||
\(732\) | 14.0519 | 0.519373 | ||||||||
\(733\) | −3.47086 | −0.128199 | −0.0640996 | − | 0.997944i | \(-0.520418\pi\) | ||||
−0.0640996 | + | 0.997944i | \(0.520418\pi\) | |||||||
\(734\) | 33.4383 | 1.23423 | ||||||||
\(735\) | −7.12498 | −0.262809 | ||||||||
\(736\) | 49.5478 | 1.82636 | ||||||||
\(737\) | −1.59956 | −0.0589207 | ||||||||
\(738\) | 9.00192 | 0.331365 | ||||||||
\(739\) | 33.0495 | 1.21575 | 0.607873 | − | 0.794034i | \(-0.292023\pi\) | ||||
0.607873 | + | 0.794034i | \(0.292023\pi\) | |||||||
\(740\) | 5.74094 | 0.211041 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.29590 | −0.231130 | ||||||||
\(743\) | −18.3840 | −0.674445 | −0.337223 | − | 0.941425i | \(-0.609487\pi\) | ||||
−0.337223 | + | 0.941425i | \(0.609487\pi\) | |||||||
\(744\) | 11.4631 | 0.420257 | ||||||||
\(745\) | 18.1957 | 0.666638 | ||||||||
\(746\) | −43.1105 | −1.57839 | ||||||||
\(747\) | −3.19242 | −0.116805 | ||||||||
\(748\) | 0.594187 | 0.0217256 | ||||||||
\(749\) | 25.2258 | 0.921731 | ||||||||
\(750\) | 2.80194 | 0.102312 | ||||||||
\(751\) | 28.8127 | 1.05139 | 0.525695 | − | 0.850673i | \(-0.323805\pi\) | ||||
0.525695 | + | 0.850673i | \(0.323805\pi\) | |||||||
\(752\) | −16.8810 | −0.615586 | ||||||||
\(753\) | 15.6511 | 0.570359 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.22521 | 0.262952 | ||||||||
\(756\) | 10.8003 | 0.392802 | ||||||||
\(757\) | 31.3435 | 1.13920 | 0.569599 | − | 0.821923i | \(-0.307098\pi\) | ||||
0.569599 | + | 0.821923i | \(0.307098\pi\) | |||||||
\(758\) | −14.1564 | −0.514185 | ||||||||
\(759\) | −4.44504 | −0.161345 | ||||||||
\(760\) | −11.7409 | −0.425889 | ||||||||
\(761\) | −18.0489 | −0.654273 | −0.327136 | − | 0.944977i | \(-0.606084\pi\) | ||||
−0.327136 | + | 0.944977i | \(0.606084\pi\) | |||||||
\(762\) | 16.8877 | 0.611776 | ||||||||
\(763\) | −7.87800 | −0.285203 | ||||||||
\(764\) | −10.0218 | −0.362575 | ||||||||
\(765\) | −0.777184 | −0.0280991 | ||||||||
\(766\) | −9.82908 | −0.355139 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −32.2054 | −1.16211 | ||||||||
\(769\) | 9.42626 | 0.339919 | 0.169960 | − | 0.985451i | \(-0.445636\pi\) | ||||
0.169960 | + | 0.985451i | \(0.445636\pi\) | |||||||
\(770\) | 1.00000 | 0.0360375 | ||||||||
\(771\) | −16.9638 | −0.610935 | ||||||||
\(772\) | −19.8183 | −0.713277 | ||||||||
\(773\) | 23.6305 | 0.849932 | 0.424966 | − | 0.905209i | \(-0.360286\pi\) | ||||
0.424966 | + | 0.905209i | \(0.360286\pi\) | |||||||
\(774\) | 9.69932 | 0.348635 | ||||||||
\(775\) | 5.43296 | 0.195158 | ||||||||
\(776\) | −14.1564 | −0.508187 | ||||||||
\(777\) | 11.1317 | 0.399347 | ||||||||
\(778\) | −32.4499 | −1.16339 | ||||||||
\(779\) | 74.2592 | 2.66061 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.28190 | −0.0816527 | ||||||||
\(782\) | 19.2698 | 0.689087 | ||||||||
\(783\) | 39.8076 | 1.42261 | ||||||||
\(784\) | 22.6310 | 0.808251 | ||||||||
\(785\) | 8.79954 | 0.314069 | ||||||||
\(786\) | 28.3207 | 1.01016 | ||||||||
\(787\) | −17.5948 | −0.627186 | −0.313593 | − | 0.949557i | \(-0.601533\pi\) | ||||
−0.313593 | + | 0.949557i | \(0.601533\pi\) | |||||||
\(788\) | −25.1535 | −0.896055 | ||||||||
\(789\) | 13.0895 | 0.465998 | ||||||||
\(790\) | 8.38835 | 0.298444 | ||||||||
\(791\) | 15.7289 | 0.559254 | ||||||||
\(792\) | −0.281896 | −0.0100168 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −32.9898 | −1.17077 | ||||||||
\(795\) | −3.49396 | −0.123918 | ||||||||
\(796\) | −14.7289 | −0.522051 | ||||||||
\(797\) | 15.6813 | 0.555459 | 0.277730 | − | 0.960659i | \(-0.410418\pi\) | ||||
0.277730 | + | 0.960659i | \(0.410418\pi\) | |||||||
\(798\) | 37.6993 | 1.33454 | ||||||||
\(799\) | −4.56332 | −0.161439 | ||||||||
\(800\) | −6.18598 | −0.218707 | ||||||||
\(801\) | −9.65114 | −0.341006 | ||||||||
\(802\) | 34.5483 | 1.21994 | ||||||||
\(803\) | −5.54096 | −0.195536 | ||||||||
\(804\) | −8.69037 | −0.306486 | ||||||||
\(805\) | 12.4547 | 0.438972 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.1648 | −1.06185 | ||||||||
\(808\) | −2.20583 | −0.0776009 | ||||||||
\(809\) | −19.2301 | −0.676095 | −0.338047 | − | 0.941129i | \(-0.609766\pi\) | ||||
−0.338047 | + | 0.941129i | \(0.609766\pi\) | |||||||
\(810\) | 12.4601 | 0.437804 | ||||||||
\(811\) | −31.4432 | −1.10412 | −0.552061 | − | 0.833804i | \(-0.686158\pi\) | ||||
−0.552061 | + | 0.833804i | \(0.686158\pi\) | |||||||
\(812\) | 13.8576 | 0.486305 | ||||||||
\(813\) | −4.82072 | −0.169070 | ||||||||
\(814\) | 2.96077 | 0.103775 | ||||||||
\(815\) | −5.91723 | −0.207272 | ||||||||
\(816\) | −10.2537 | −0.358951 | ||||||||
\(817\) | 80.0122 | 2.79927 | ||||||||
\(818\) | 13.0140 | 0.455024 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.7017 | 0.373720 | ||||||||
\(821\) | −10.6286 | −0.370942 | −0.185471 | − | 0.982650i | \(-0.559381\pi\) | ||||
−0.185471 | + | 0.982650i | \(0.559381\pi\) | |||||||
\(822\) | −13.8998 | −0.484810 | ||||||||
\(823\) | −36.8963 | −1.28612 | −0.643062 | − | 0.765814i | \(-0.722336\pi\) | ||||
−0.643062 | + | 0.765814i | \(0.722336\pi\) | |||||||
\(824\) | 12.6668 | 0.441269 | ||||||||
\(825\) | 0.554958 | 0.0193212 | ||||||||
\(826\) | 1.41789 | 0.0493349 | ||||||||
\(827\) | 18.7006 | 0.650285 | 0.325143 | − | 0.945665i | \(-0.394588\pi\) | ||||
0.325143 | + | 0.945665i | \(0.394588\pi\) | |||||||
\(828\) | 5.81402 | 0.202051 | ||||||||
\(829\) | −13.4437 | −0.466919 | −0.233460 | − | 0.972366i | \(-0.575005\pi\) | ||||
−0.233460 | + | 0.972366i | \(0.575005\pi\) | |||||||
\(830\) | −9.88231 | −0.343020 | ||||||||
\(831\) | −11.0519 | −0.383386 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.11769 | 0.211965 | ||||||||
\(834\) | 25.2784 | 0.875321 | ||||||||
\(835\) | 6.00431 | 0.207788 | ||||||||
\(836\) | 3.85086 | 0.133185 | ||||||||
\(837\) | 30.2617 | 1.04600 | ||||||||
\(838\) | 0.488582 | 0.0168778 | ||||||||
\(839\) | 26.4547 | 0.913319 | 0.456659 | − | 0.889642i | \(-0.349046\pi\) | ||||
0.456659 | + | 0.889642i | \(0.349046\pi\) | |||||||
\(840\) | −3.28083 | −0.113199 | ||||||||
\(841\) | 22.0761 | 0.761244 | ||||||||
\(842\) | 64.2006 | 2.21250 | ||||||||
\(843\) | 13.6913 | 0.471553 | ||||||||
\(844\) | −30.0495 | −1.03435 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.58509 | −0.123258 | ||||||||
\(847\) | −16.9065 | −0.580913 | ||||||||
\(848\) | 11.0978 | 0.381101 | ||||||||
\(849\) | 11.8086 | 0.405272 | ||||||||
\(850\) | −2.40581 | −0.0825187 | ||||||||
\(851\) | 36.8756 | 1.26408 | ||||||||
\(852\) | −12.3975 | −0.424730 | ||||||||
\(853\) | −44.7222 | −1.53126 | −0.765629 | − | 0.643283i | \(-0.777572\pi\) | ||||
−0.765629 | + | 0.643283i | \(0.777572\pi\) | |||||||
\(854\) | −20.3056 | −0.694843 | ||||||||
\(855\) | −5.03684 | −0.172256 | ||||||||
\(856\) | −22.0127 | −0.752378 | ||||||||
\(857\) | −23.6969 | −0.809472 | −0.404736 | − | 0.914434i | \(-0.632636\pi\) | ||||
−0.404736 | + | 0.914434i | \(0.632636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0814 | −1.19696 | −0.598482 | − | 0.801137i | \(-0.704229\pi\) | ||||
−0.598482 | + | 0.801137i | \(0.704229\pi\) | |||||||
\(860\) | 11.5308 | 0.393197 | ||||||||
\(861\) | 20.7506 | 0.707179 | ||||||||
\(862\) | 63.9614 | 2.17853 | ||||||||
\(863\) | 22.7439 | 0.774212 | 0.387106 | − | 0.922035i | \(-0.373475\pi\) | ||||
0.387106 | + | 0.922035i | \(0.373475\pi\) | |||||||
\(864\) | −34.4561 | −1.17222 | ||||||||
\(865\) | −17.7506 | −0.603539 | ||||||||
\(866\) | 28.5797 | 0.971178 | ||||||||
\(867\) | 23.6625 | 0.803620 | ||||||||
\(868\) | 10.5345 | 0.357565 | ||||||||
\(869\) | 1.66142 | 0.0563597 | ||||||||
\(870\) | 20.0248 | 0.678903 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.87454 | 0.232801 | ||||||||
\(873\) | −6.07308 | −0.205543 | ||||||||
\(874\) | 124.885 | 4.22431 | ||||||||
\(875\) | −1.55496 | −0.0525672 | ||||||||
\(876\) | −30.1038 | −1.01711 | ||||||||
\(877\) | 6.14483 | 0.207496 | 0.103748 | − | 0.994604i | \(-0.466916\pi\) | ||||
0.103748 | + | 0.994604i | \(0.466916\pi\) | |||||||
\(878\) | −46.7265 | −1.57694 | ||||||||
\(879\) | −10.8321 | −0.365357 | ||||||||
\(880\) | −1.76271 | −0.0594209 | ||||||||
\(881\) | −11.6517 | −0.392557 | −0.196278 | − | 0.980548i | \(-0.562886\pi\) | ||||
−0.196278 | + | 0.980548i | \(0.562886\pi\) | |||||||
\(882\) | 4.80625 | 0.161835 | ||||||||
\(883\) | 12.7694 | 0.429725 | 0.214862 | − | 0.976644i | \(-0.431070\pi\) | ||||
0.214862 | + | 0.976644i | \(0.431070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.786872 | 0.0264504 | ||||||||
\(886\) | −20.2368 | −0.679869 | ||||||||
\(887\) | 27.4993 | 0.923337 | 0.461669 | − | 0.887052i | \(-0.347251\pi\) | ||||
0.461669 | + | 0.887052i | \(0.347251\pi\) | |||||||
\(888\) | −9.71379 | −0.325974 | ||||||||
\(889\) | −9.37196 | −0.314325 | ||||||||
\(890\) | −29.8756 | −1.00143 | ||||||||
\(891\) | 2.46788 | 0.0826770 | ||||||||
\(892\) | 12.7235 | 0.426014 | ||||||||
\(893\) | −29.5743 | −0.989667 | ||||||||
\(894\) | 50.9831 | 1.70513 | ||||||||
\(895\) | 16.5550 | 0.553371 | ||||||||
\(896\) | 15.6829 | 0.523930 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −66.3962 | −2.21567 | ||||||||
\(899\) | 38.8280 | 1.29499 | ||||||||
\(900\) | −0.725873 | −0.0241958 | ||||||||
\(901\) | 3.00000 | 0.0999445 | ||||||||
\(902\) | 5.51919 | 0.183769 | ||||||||
\(903\) | 22.3582 | 0.744035 | ||||||||
\(904\) | −13.7254 | −0.456500 | ||||||||
\(905\) | −11.1739 | −0.371433 | ||||||||
\(906\) | 20.2446 | 0.672581 | ||||||||
\(907\) | −11.4668 | −0.380749 | −0.190375 | − | 0.981712i | \(-0.560970\pi\) | ||||
−0.190375 | + | 0.981712i | \(0.560970\pi\) | |||||||
\(908\) | −9.76941 | −0.324209 | ||||||||
\(909\) | −0.946297 | −0.0313867 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.1943 | −0.768463 | −0.384231 | − | 0.923237i | \(-0.625534\pi\) | ||||
−0.384231 | + | 0.923237i | \(0.625534\pi\) | |||||||
\(912\) | −66.4529 | −2.20048 | ||||||||
\(913\) | −1.95731 | −0.0647776 | ||||||||
\(914\) | 39.6209 | 1.31054 | ||||||||
\(915\) | −11.2687 | −0.372533 | ||||||||
\(916\) | 8.24996 | 0.272586 | ||||||||
\(917\) | −15.7168 | −0.519014 | ||||||||
\(918\) | −13.4004 | −0.442280 | ||||||||
\(919\) | −59.0702 | −1.94855 | −0.974273 | − | 0.225370i | \(-0.927641\pi\) | ||||
−0.974273 | + | 0.225370i | \(0.927641\pi\) | |||||||
\(920\) | −10.8683 | −0.358318 | ||||||||
\(921\) | 33.1444 | 1.09214 | ||||||||
\(922\) | −15.3840 | −0.506646 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.07606 | 0.0353999 | ||||||||
\(925\) | −4.60388 | −0.151374 | ||||||||
\(926\) | −37.8267 | −1.24306 | ||||||||
\(927\) | 5.43403 | 0.178477 | ||||||||
\(928\) | −44.2097 | −1.45125 | ||||||||
\(929\) | 23.9124 | 0.784542 | 0.392271 | − | 0.919850i | \(-0.371690\pi\) | ||||
0.392271 | + | 0.919850i | \(0.371690\pi\) | |||||||
\(930\) | 15.2228 | 0.499176 | ||||||||
\(931\) | 39.6480 | 1.29941 | ||||||||
\(932\) | 1.71081 | 0.0560394 | ||||||||
\(933\) | 45.6647 | 1.49500 | ||||||||
\(934\) | 25.2228 | 0.825316 | ||||||||
\(935\) | −0.476501 | −0.0155832 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.9667 | −0.423605 | −0.211802 | − | 0.977312i | \(-0.567933\pi\) | ||||
−0.211802 | + | 0.977312i | \(0.567933\pi\) | |||||||
\(938\) | 12.5579 | 0.410031 | ||||||||
\(939\) | −3.25368 | −0.106180 | ||||||||
\(940\) | −4.26205 | −0.139013 | ||||||||
\(941\) | 45.5585 | 1.48517 | 0.742583 | − | 0.669754i | \(-0.233601\pi\) | ||||
0.742583 | + | 0.669754i | \(0.233601\pi\) | |||||||
\(942\) | 24.6558 | 0.803329 | ||||||||
\(943\) | 68.7400 | 2.23848 | ||||||||
\(944\) | −2.49934 | −0.0813465 | ||||||||
\(945\) | −8.66115 | −0.281747 | ||||||||
\(946\) | 5.94677 | 0.193346 | ||||||||
\(947\) | 5.78017 | 0.187830 | 0.0939151 | − | 0.995580i | \(-0.470062\pi\) | ||||
0.0939151 | + | 0.995580i | \(0.470062\pi\) | |||||||
\(948\) | 9.02641 | 0.293164 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −15.5918 | −0.505865 | ||||||||
\(951\) | −15.8576 | −0.514217 | ||||||||
\(952\) | 2.81700 | 0.0912996 | ||||||||
\(953\) | −47.4058 | −1.53562 | −0.767812 | − | 0.640675i | \(-0.778655\pi\) | ||||
−0.767812 | + | 0.640675i | \(0.778655\pi\) | |||||||
\(954\) | 2.35690 | 0.0763073 | ||||||||
\(955\) | 8.03684 | 0.260066 | ||||||||
\(956\) | −2.62432 | −0.0848765 | ||||||||
\(957\) | 3.96615 | 0.128207 | ||||||||
\(958\) | −26.3327 | −0.850772 | ||||||||
\(959\) | 7.71379 | 0.249091 | ||||||||
\(960\) | −1.97285 | −0.0636736 | ||||||||
\(961\) | −1.48294 | −0.0478369 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.44339 | −0.304309 | ||||||||
\(964\) | 23.9282 | 0.770677 | ||||||||
\(965\) | 15.8931 | 0.511616 | ||||||||
\(966\) | 34.8974 | 1.12280 | ||||||||
\(967\) | −7.63102 | −0.245397 | −0.122699 | − | 0.992444i | \(-0.539155\pi\) | ||||
−0.122699 | + | 0.992444i | \(0.539155\pi\) | |||||||
\(968\) | 14.7530 | 0.474180 | ||||||||
\(969\) | −17.9638 | −0.577079 | ||||||||
\(970\) | −18.7995 | −0.603617 | ||||||||
\(971\) | 45.8273 | 1.47067 | 0.735334 | − | 0.677705i | \(-0.237025\pi\) | ||||
0.735334 | + | 0.677705i | \(0.237025\pi\) | |||||||
\(972\) | −7.42924 | −0.238293 | ||||||||
\(973\) | −14.0285 | −0.449732 | ||||||||
\(974\) | 70.3866 | 2.25533 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35.7928 | 1.14570 | ||||||||
\(977\) | −4.59983 | −0.147161 | −0.0735807 | − | 0.997289i | \(-0.523443\pi\) | ||||
−0.0735807 | + | 0.997289i | \(0.523443\pi\) | |||||||
\(978\) | −16.5797 | −0.530161 | ||||||||
\(979\) | −5.91723 | −0.189116 | ||||||||
\(980\) | 5.71379 | 0.182520 | ||||||||
\(981\) | 2.94916 | 0.0941596 | ||||||||
\(982\) | −46.1444 | −1.47253 | ||||||||
\(983\) | −16.2728 | −0.519022 | −0.259511 | − | 0.965740i | \(-0.583561\pi\) | ||||
−0.259511 | + | 0.965740i | \(0.583561\pi\) | |||||||
\(984\) | −18.1075 | −0.577247 | ||||||||
\(985\) | 20.1715 | 0.642718 | ||||||||
\(986\) | −17.1938 | −0.547561 | ||||||||
\(987\) | −8.26411 | −0.263050 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 74.0654 | 2.35514 | ||||||||
\(990\) | −0.374354 | −0.0118978 | ||||||||
\(991\) | −34.9898 | −1.11149 | −0.555744 | − | 0.831353i | \(-0.687567\pi\) | ||||
−0.555744 | + | 0.831353i | \(0.687567\pi\) | |||||||
\(992\) | −33.6082 | −1.06706 | ||||||||
\(993\) | 23.6792 | 0.751437 | ||||||||
\(994\) | 17.9148 | 0.568224 | ||||||||
\(995\) | 11.8116 | 0.374454 | ||||||||
\(996\) | −10.6340 | −0.336951 | ||||||||
\(997\) | −37.8353 | −1.19826 | −0.599128 | − | 0.800653i | \(-0.704486\pi\) | ||||
−0.599128 | + | 0.800653i | \(0.704486\pi\) | |||||||
\(998\) | 3.01938 | 0.0955767 | ||||||||
\(999\) | −25.6437 | −0.811331 |
(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 | 845.2.a.j.1.3 | yes | 3 | |
3.2 | odd | 2 | 7605.2.a.br.1.1 | 3 | |||
5.4 | even | 2 | 4225.2.a.bd.1.1 | 3 | |||
13.2 | odd | 12 | 845.2.m.i.316.6 | 12 | |||
13.3 | even | 3 | 845.2.e.j.191.1 | 6 | |||
13.4 | even | 6 | 845.2.e.l.146.3 | 6 | |||
13.5 | odd | 4 | 845.2.c.f.506.1 | 6 | |||
13.6 | odd | 12 | 845.2.m.i.361.1 | 12 | |||
13.7 | odd | 12 | 845.2.m.i.361.6 | 12 | |||
13.8 | odd | 4 | 845.2.c.f.506.6 | 6 | |||
13.9 | even | 3 | 845.2.e.j.146.1 | 6 | |||
13.10 | even | 6 | 845.2.e.l.191.3 | 6 | |||
13.11 | odd | 12 | 845.2.m.i.316.1 | 12 | |||
13.12 | even | 2 | 845.2.a.h.1.1 | ✓ | 3 | ||
39.38 | odd | 2 | 7605.2.a.by.1.3 | 3 | |||
65.64 | even | 2 | 4225.2.a.bf.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.a.h.1.1 | ✓ | 3 | 13.12 | even | 2 | ||
845.2.a.j.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
845.2.c.f.506.1 | 6 | 13.5 | odd | 4 | |||
845.2.c.f.506.6 | 6 | 13.8 | odd | 4 | |||
845.2.e.j.146.1 | 6 | 13.9 | even | 3 | |||
845.2.e.j.191.1 | 6 | 13.3 | even | 3 | |||
845.2.e.l.146.3 | 6 | 13.4 | even | 6 | |||
845.2.e.l.191.3 | 6 | 13.10 | even | 6 | |||
845.2.m.i.316.1 | 12 | 13.11 | odd | 12 | |||
845.2.m.i.316.6 | 12 | 13.2 | odd | 12 | |||
845.2.m.i.361.1 | 12 | 13.6 | odd | 12 | |||
845.2.m.i.361.6 | 12 | 13.7 | odd | 12 | |||
4225.2.a.bd.1.1 | 3 | 5.4 | even | 2 | |||
4225.2.a.bf.1.3 | 3 | 65.64 | even | 2 | |||
7605.2.a.br.1.1 | 3 | 3.2 | odd | 2 | |||
7605.2.a.by.1.3 | 3 | 39.38 | odd | 2 |