Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, 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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
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 | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.381966 | −0.270091 | −0.135045 | − | 0.990839i | \(-0.543118\pi\) | ||||
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(3\) | −2.23607 | −1.29099 | −0.645497 | − | 0.763763i | \(-0.723350\pi\) | ||||
−0.645497 | + | 0.763763i | \(0.723350\pi\) | |||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.854102 | 0.348686 | ||||||||
\(7\) | −0.236068 | −0.0892253 | −0.0446127 | − | 0.999004i | \(-0.514205\pi\) | ||||
−0.0446127 | + | 0.999004i | \(0.514205\pi\) | |||||||
\(8\) | 1.47214 | 0.520479 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.47214 | −1.04689 | −0.523444 | − | 0.852060i | \(-0.675353\pi\) | ||||
−0.523444 | + | 0.852060i | \(0.675353\pi\) | |||||||
\(12\) | 4.14590 | 1.19682 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0.0901699 | 0.0240989 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | −1.85410 | −0.449686 | −0.224843 | − | 0.974395i | \(-0.572187\pi\) | ||||
−0.224843 | + | 0.974395i | \(0.572187\pi\) | |||||||
\(18\) | −0.763932 | −0.180061 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.527864 | 0.115189 | ||||||||
\(22\) | 1.32624 | 0.282755 | ||||||||
\(23\) | −3.23607 | −0.674767 | −0.337383 | − | 0.941367i | \(-0.609542\pi\) | ||||
−0.337383 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(24\) | −3.29180 | −0.671935 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.763932 | −0.149819 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 0.437694 | 0.0827164 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.85410 | 0.871822 | 0.435911 | − | 0.899990i | \(-0.356426\pi\) | ||||
0.435911 | + | 0.899990i | \(0.356426\pi\) | |||||||
\(32\) | −4.14590 | −0.732898 | ||||||||
\(33\) | 7.76393 | 1.35153 | ||||||||
\(34\) | 0.708204 | 0.121456 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.70820 | −0.618034 | ||||||||
\(37\) | −10.8541 | −1.78440 | −0.892202 | − | 0.451637i | \(-0.850840\pi\) | ||||
−0.892202 | + | 0.451637i | \(0.850840\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.47214 | −0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.61803 | −1.34591 | −0.672955 | − | 0.739683i | \(-0.734975\pi\) | ||||
−0.672955 | + | 0.739683i | \(0.734975\pi\) | |||||||
\(42\) | −0.201626 | −0.0311116 | ||||||||
\(43\) | 9.56231 | 1.45824 | 0.729119 | − | 0.684387i | \(-0.239930\pi\) | ||||
0.729119 | + | 0.684387i | \(0.239930\pi\) | |||||||
\(44\) | 6.43769 | 0.970519 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.23607 | 0.182248 | ||||||||
\(47\) | 5.38197 | 0.785040 | 0.392520 | − | 0.919743i | \(-0.371603\pi\) | ||||
0.392520 | + | 0.919743i | \(0.371603\pi\) | |||||||
\(48\) | −7.03444 | −1.01533 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.14590 | 0.580542 | ||||||||
\(52\) | −3.70820 | −0.514235 | ||||||||
\(53\) | 8.61803 | 1.18378 | 0.591889 | − | 0.806019i | \(-0.298382\pi\) | ||||
0.591889 | + | 0.806019i | \(0.298382\pi\) | |||||||
\(54\) | −0.854102 | −0.116229 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.347524 | −0.0464399 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.29180 | −0.300928 | ||||||||
\(59\) | −7.23607 | −0.942056 | −0.471028 | − | 0.882118i | \(-0.656117\pi\) | ||||
−0.471028 | + | 0.882118i | \(0.656117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.5623 | 1.86451 | 0.932256 | − | 0.361799i | \(-0.117837\pi\) | ||||
0.932256 | + | 0.361799i | \(0.117837\pi\) | |||||||
\(62\) | −1.85410 | −0.235471 | ||||||||
\(63\) | −0.472136 | −0.0594835 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.96556 | −0.365035 | ||||||||
\(67\) | −4.70820 | −0.575199 | −0.287599 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287599 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(68\) | 3.43769 | 0.416882 | ||||||||
\(69\) | 7.23607 | 0.871120 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.4721 | −1.59885 | −0.799424 | − | 0.600767i | \(-0.794862\pi\) | ||||
−0.799424 | + | 0.600767i | \(0.794862\pi\) | |||||||
\(72\) | 2.94427 | 0.346986 | ||||||||
\(73\) | −2.70820 | −0.316971 | −0.158486 | − | 0.987361i | \(-0.550661\pi\) | ||||
−0.158486 | + | 0.987361i | \(0.550661\pi\) | |||||||
\(74\) | 4.14590 | 0.481951 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.819660 | 0.0934089 | ||||||||
\(78\) | 1.70820 | 0.193416 | ||||||||
\(79\) | 1.00000 | 0.112509 | 0.0562544 | − | 0.998416i | \(-0.482084\pi\) | ||||
0.0562544 | + | 0.998416i | \(0.482084\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 3.29180 | 0.363518 | ||||||||
\(83\) | 10.0902 | 1.10754 | 0.553770 | − | 0.832670i | \(-0.313189\pi\) | ||||
0.553770 | + | 0.832670i | \(0.313189\pi\) | |||||||
\(84\) | −0.978714 | −0.106786 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.65248 | −0.393857 | ||||||||
\(87\) | −13.4164 | −1.43839 | ||||||||
\(88\) | −5.11146 | −0.544883 | ||||||||
\(89\) | −9.70820 | −1.02907 | −0.514534 | − | 0.857470i | \(-0.672035\pi\) | ||||
−0.514534 | + | 0.857470i | \(0.672035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.472136 | −0.0494933 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | −10.8541 | −1.12552 | ||||||||
\(94\) | −2.05573 | −0.212032 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.27051 | 0.946167 | ||||||||
\(97\) | −9.61803 | −0.976563 | −0.488282 | − | 0.872686i | \(-0.662376\pi\) | ||||
−0.488282 | + | 0.872686i | \(0.662376\pi\) | |||||||
\(98\) | 2.65248 | 0.267941 | ||||||||
\(99\) | −6.94427 | −0.697926 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.0344 | 1.59549 | 0.797743 | − | 0.602997i | \(-0.206027\pi\) | ||||
0.797743 | + | 0.602997i | \(0.206027\pi\) | |||||||
\(102\) | −1.58359 | −0.156799 | ||||||||
\(103\) | −3.23607 | −0.318859 | −0.159430 | − | 0.987209i | \(-0.550966\pi\) | ||||
−0.159430 | + | 0.987209i | \(0.550966\pi\) | |||||||
\(104\) | 2.94427 | 0.288710 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.29180 | −0.319727 | ||||||||
\(107\) | 13.1459 | 1.27086 | 0.635431 | − | 0.772158i | \(-0.280822\pi\) | ||||
0.635431 | + | 0.772158i | \(0.280822\pi\) | |||||||
\(108\) | −4.14590 | −0.398939 | ||||||||
\(109\) | −9.94427 | −0.952489 | −0.476244 | − | 0.879313i | \(-0.658002\pi\) | ||||
−0.476244 | + | 0.879313i | \(0.658002\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.2705 | 2.30365 | ||||||||
\(112\) | −0.742646 | −0.0701734 | ||||||||
\(113\) | −6.32624 | −0.595122 | −0.297561 | − | 0.954703i | \(-0.596173\pi\) | ||||
−0.297561 | + | 0.954703i | \(0.596173\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.1246 | −1.03289 | ||||||||
\(117\) | 4.00000 | 0.369800 | ||||||||
\(118\) | 2.76393 | 0.254441 | ||||||||
\(119\) | 0.437694 | 0.0401234 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.05573 | 0.0959753 | ||||||||
\(122\) | −5.56231 | −0.503588 | ||||||||
\(123\) | 19.2705 | 1.73756 | ||||||||
\(124\) | −9.00000 | −0.808224 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.180340 | 0.0160660 | ||||||||
\(127\) | 5.85410 | 0.519468 | 0.259734 | − | 0.965680i | \(-0.416365\pi\) | ||||
0.259734 | + | 0.965680i | \(0.416365\pi\) | |||||||
\(128\) | 10.0902 | 0.891853 | ||||||||
\(129\) | −21.3820 | −1.88258 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | −14.3951 | −1.25293 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.79837 | 0.155356 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.72949 | −0.234052 | ||||||||
\(137\) | 4.76393 | 0.407010 | 0.203505 | − | 0.979074i | \(-0.434767\pi\) | ||||
0.203505 | + | 0.979074i | \(0.434767\pi\) | |||||||
\(138\) | −2.76393 | −0.235282 | ||||||||
\(139\) | −14.0000 | −1.18746 | −0.593732 | − | 0.804663i | \(-0.702346\pi\) | ||||
−0.593732 | + | 0.804663i | \(0.702346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.0344 | −1.01348 | ||||||||
\(142\) | 5.14590 | 0.431834 | ||||||||
\(143\) | −6.94427 | −0.580709 | ||||||||
\(144\) | 6.29180 | 0.524316 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.03444 | 0.0856110 | ||||||||
\(147\) | 15.5279 | 1.28072 | ||||||||
\(148\) | 20.1246 | 1.65423 | ||||||||
\(149\) | −0.527864 | −0.0432443 | −0.0216222 | − | 0.999766i | \(-0.506883\pi\) | ||||
−0.0216222 | + | 0.999766i | \(0.506883\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.7984 | −1.52979 | −0.764895 | − | 0.644155i | \(-0.777209\pi\) | ||||
−0.764895 | + | 0.644155i | \(0.777209\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.70820 | −0.299791 | ||||||||
\(154\) | −0.313082 | −0.0252289 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.29180 | 0.663875 | ||||||||
\(157\) | −24.1803 | −1.92980 | −0.964901 | − | 0.262615i | \(-0.915415\pi\) | ||||
−0.964901 | + | 0.262615i | \(0.915415\pi\) | |||||||
\(158\) | −0.381966 | −0.0303876 | ||||||||
\(159\) | −19.2705 | −1.52825 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.763932 | 0.0602063 | ||||||||
\(162\) | 4.20163 | 0.330111 | ||||||||
\(163\) | 7.23607 | 0.566773 | 0.283386 | − | 0.959006i | \(-0.408542\pi\) | ||||
0.283386 | + | 0.959006i | \(0.408542\pi\) | |||||||
\(164\) | 15.9787 | 1.24773 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.85410 | −0.299136 | ||||||||
\(167\) | 0.763932 | 0.0591148 | 0.0295574 | − | 0.999563i | \(-0.490590\pi\) | ||||
0.0295574 | + | 0.999563i | \(0.490590\pi\) | |||||||
\(168\) | 0.777088 | 0.0599536 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −17.7295 | −1.35186 | ||||||||
\(173\) | 11.6525 | 0.885921 | 0.442961 | − | 0.896541i | \(-0.353928\pi\) | ||||
0.442961 | + | 0.896541i | \(0.353928\pi\) | |||||||
\(174\) | 5.12461 | 0.388496 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.9230 | −0.823351 | ||||||||
\(177\) | 16.1803 | 1.21619 | ||||||||
\(178\) | 3.70820 | 0.277942 | ||||||||
\(179\) | −11.1803 | −0.835658 | −0.417829 | − | 0.908526i | \(-0.637209\pi\) | ||||
−0.417829 | + | 0.908526i | \(0.637209\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.29180 | −0.393336 | −0.196668 | − | 0.980470i | \(-0.563012\pi\) | ||||
−0.196668 | + | 0.980470i | \(0.563012\pi\) | |||||||
\(182\) | 0.180340 | 0.0133677 | ||||||||
\(183\) | −32.5623 | −2.40707 | ||||||||
\(184\) | −4.76393 | −0.351202 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.14590 | 0.303992 | ||||||||
\(187\) | 6.43769 | 0.470771 | ||||||||
\(188\) | −9.97871 | −0.727772 | ||||||||
\(189\) | −0.527864 | −0.0383965 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0557281 | −0.00403234 | −0.00201617 | − | 0.999998i | \(-0.500642\pi\) | ||||
−0.00201617 | + | 0.999998i | \(0.500642\pi\) | |||||||
\(192\) | 10.5279 | 0.759783 | ||||||||
\(193\) | 10.2705 | 0.739287 | 0.369644 | − | 0.929174i | \(-0.379480\pi\) | ||||
0.369644 | + | 0.929174i | \(0.379480\pi\) | |||||||
\(194\) | 3.67376 | 0.263761 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.8754 | 0.919671 | ||||||||
\(197\) | −1.47214 | −0.104885 | −0.0524427 | − | 0.998624i | \(-0.516701\pi\) | ||||
−0.0524427 | + | 0.998624i | \(0.516701\pi\) | |||||||
\(198\) | 2.65248 | 0.188503 | ||||||||
\(199\) | −7.41641 | −0.525735 | −0.262868 | − | 0.964832i | \(-0.584668\pi\) | ||||
−0.262868 | + | 0.964832i | \(0.584668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5279 | 0.742578 | ||||||||
\(202\) | −6.12461 | −0.430926 | ||||||||
\(203\) | −1.41641 | −0.0994123 | ||||||||
\(204\) | −7.68692 | −0.538192 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.23607 | 0.0861209 | ||||||||
\(207\) | −6.47214 | −0.449845 | ||||||||
\(208\) | 6.29180 | 0.436258 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.76393 | −0.534491 | −0.267246 | − | 0.963628i | \(-0.586113\pi\) | ||||
−0.267246 | + | 0.963628i | \(0.586113\pi\) | |||||||
\(212\) | −15.9787 | −1.09742 | ||||||||
\(213\) | 30.1246 | 2.06410 | ||||||||
\(214\) | −5.02129 | −0.343248 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.29180 | 0.223978 | ||||||||
\(217\) | −1.14590 | −0.0777886 | ||||||||
\(218\) | 3.79837 | 0.257258 | ||||||||
\(219\) | 6.05573 | 0.409208 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.70820 | −0.249441 | ||||||||
\(222\) | −9.27051 | −0.622196 | ||||||||
\(223\) | 16.8885 | 1.13094 | 0.565470 | − | 0.824769i | \(-0.308695\pi\) | ||||
0.565470 | + | 0.824769i | \(0.308695\pi\) | |||||||
\(224\) | 0.978714 | 0.0653931 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.41641 | 0.160737 | ||||||||
\(227\) | −5.52786 | −0.366897 | −0.183449 | − | 0.983029i | \(-0.558726\pi\) | ||||
−0.183449 | + | 0.983029i | \(0.558726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.6525 | −0.703935 | −0.351968 | − | 0.936012i | \(-0.614487\pi\) | ||||
−0.351968 | + | 0.936012i | \(0.614487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.83282 | −0.120590 | ||||||||
\(232\) | 8.83282 | 0.579903 | ||||||||
\(233\) | 25.4721 | 1.66874 | 0.834368 | − | 0.551208i | \(-0.185833\pi\) | ||||
0.834368 | + | 0.551208i | \(0.185833\pi\) | |||||||
\(234\) | −1.52786 | −0.0998796 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.4164 | 0.873334 | ||||||||
\(237\) | −2.23607 | −0.145248 | ||||||||
\(238\) | −0.167184 | −0.0108369 | ||||||||
\(239\) | −12.7082 | −0.822025 | −0.411013 | − | 0.911630i | \(-0.634825\pi\) | ||||
−0.411013 | + | 0.911630i | \(0.634825\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | −0.837404 | −0.418702 | − | 0.908124i | \(-0.637515\pi\) | ||||
−0.418702 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(242\) | −0.403252 | −0.0259220 | ||||||||
\(243\) | 17.8885 | 1.14755 | ||||||||
\(244\) | −27.0000 | −1.72850 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.36068 | −0.469300 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.14590 | 0.453765 | ||||||||
\(249\) | −22.5623 | −1.42983 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.0902 | 1.07872 | 0.539361 | − | 0.842075i | \(-0.318666\pi\) | ||||
0.539361 | + | 0.842075i | \(0.318666\pi\) | |||||||
\(252\) | 0.875388 | 0.0551443 | ||||||||
\(253\) | 11.2361 | 0.706406 | ||||||||
\(254\) | −2.23607 | −0.140303 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | −28.7984 | −1.79639 | −0.898197 | − | 0.439594i | \(-0.855122\pi\) | ||||
−0.898197 | + | 0.439594i | \(0.855122\pi\) | |||||||
\(258\) | 8.16718 | 0.508467 | ||||||||
\(259\) | 2.56231 | 0.159214 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0000 | 0.742781 | ||||||||
\(262\) | 4.58359 | 0.283175 | ||||||||
\(263\) | 20.3820 | 1.25681 | 0.628403 | − | 0.777888i | \(-0.283709\pi\) | ||||
0.628403 | + | 0.777888i | \(0.283709\pi\) | |||||||
\(264\) | 11.4296 | 0.703441 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.7082 | 1.32852 | ||||||||
\(268\) | 8.72949 | 0.533238 | ||||||||
\(269\) | −13.1803 | −0.803620 | −0.401810 | − | 0.915723i | \(-0.631619\pi\) | ||||
−0.401810 | + | 0.915723i | \(0.631619\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.32624 | 0.262800 | 0.131400 | − | 0.991329i | \(-0.458053\pi\) | ||||
0.131400 | + | 0.991329i | \(0.458053\pi\) | |||||||
\(272\) | −5.83282 | −0.353666 | ||||||||
\(273\) | 1.05573 | 0.0638956 | ||||||||
\(274\) | −1.81966 | −0.109930 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.4164 | −0.807573 | ||||||||
\(277\) | −12.0000 | −0.721010 | −0.360505 | − | 0.932757i | \(-0.617396\pi\) | ||||
−0.360505 | + | 0.932757i | \(0.617396\pi\) | |||||||
\(278\) | 5.34752 | 0.320723 | ||||||||
\(279\) | 9.70820 | 0.581215 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.38197 | 0.142096 | 0.0710481 | − | 0.997473i | \(-0.477366\pi\) | ||||
0.0710481 | + | 0.997473i | \(0.477366\pi\) | |||||||
\(282\) | 4.59675 | 0.273732 | ||||||||
\(283\) | −28.2361 | −1.67846 | −0.839230 | − | 0.543777i | \(-0.816994\pi\) | ||||
−0.839230 | + | 0.543777i | \(0.816994\pi\) | |||||||
\(284\) | 24.9787 | 1.48221 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.65248 | 0.156844 | ||||||||
\(287\) | 2.03444 | 0.120089 | ||||||||
\(288\) | −8.29180 | −0.488599 | ||||||||
\(289\) | −13.5623 | −0.797783 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.5066 | 1.26074 | ||||||||
\(292\) | 5.02129 | 0.293849 | ||||||||
\(293\) | 4.52786 | 0.264521 | 0.132260 | − | 0.991215i | \(-0.457777\pi\) | ||||
0.132260 | + | 0.991215i | \(0.457777\pi\) | |||||||
\(294\) | −5.93112 | −0.345910 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −15.9787 | −0.928744 | ||||||||
\(297\) | −7.76393 | −0.450509 | ||||||||
\(298\) | 0.201626 | 0.0116799 | ||||||||
\(299\) | −6.47214 | −0.374293 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.25735 | −0.130112 | ||||||||
\(302\) | 7.18034 | 0.413182 | ||||||||
\(303\) | −35.8541 | −2.05976 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.41641 | 0.0809706 | ||||||||
\(307\) | 12.4377 | 0.709857 | 0.354928 | − | 0.934894i | \(-0.384505\pi\) | ||||
0.354928 | + | 0.934894i | \(0.384505\pi\) | |||||||
\(308\) | −1.51973 | −0.0865948 | ||||||||
\(309\) | 7.23607 | 0.411646 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.7639 | 0.667071 | 0.333536 | − | 0.942737i | \(-0.391758\pi\) | ||||
0.333536 | + | 0.942737i | \(0.391758\pi\) | |||||||
\(312\) | −6.58359 | −0.372723 | ||||||||
\(313\) | 2.05573 | 0.116197 | 0.0580983 | − | 0.998311i | \(-0.481496\pi\) | ||||
0.0580983 | + | 0.998311i | \(0.481496\pi\) | |||||||
\(314\) | 9.23607 | 0.521221 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.85410 | −0.104301 | ||||||||
\(317\) | 6.94427 | 0.390029 | 0.195015 | − | 0.980800i | \(-0.437525\pi\) | ||||
0.195015 | + | 0.980800i | \(0.437525\pi\) | |||||||
\(318\) | 7.36068 | 0.412766 | ||||||||
\(319\) | −20.8328 | −1.16641 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.3951 | −1.64068 | ||||||||
\(322\) | −0.291796 | −0.0162612 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 20.3951 | 1.13306 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.76393 | −0.153080 | ||||||||
\(327\) | 22.2361 | 1.22966 | ||||||||
\(328\) | −12.6869 | −0.700518 | ||||||||
\(329\) | −1.27051 | −0.0700455 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.56231 | 0.360697 | 0.180348 | − | 0.983603i | \(-0.442277\pi\) | ||||
0.180348 | + | 0.983603i | \(0.442277\pi\) | |||||||
\(332\) | −18.7082 | −1.02675 | ||||||||
\(333\) | −21.7082 | −1.18960 | ||||||||
\(334\) | −0.291796 | −0.0159664 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.66061 | 0.0905935 | ||||||||
\(337\) | −8.70820 | −0.474366 | −0.237183 | − | 0.971465i | \(-0.576224\pi\) | ||||
−0.237183 | + | 0.971465i | \(0.576224\pi\) | |||||||
\(338\) | 3.43769 | 0.186986 | ||||||||
\(339\) | 14.1459 | 0.768300 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.8541 | −0.912701 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | 14.0770 | 0.758982 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.45085 | −0.239279 | ||||||||
\(347\) | 24.5279 | 1.31672 | 0.658362 | − | 0.752701i | \(-0.271249\pi\) | ||||
0.658362 | + | 0.752701i | \(0.271249\pi\) | |||||||
\(348\) | 24.8754 | 1.33346 | ||||||||
\(349\) | 31.0689 | 1.66308 | 0.831540 | − | 0.555465i | \(-0.187460\pi\) | ||||
0.831540 | + | 0.555465i | \(0.187460\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 14.3951 | 0.767263 | ||||||||
\(353\) | −25.4721 | −1.35574 | −0.677872 | − | 0.735179i | \(-0.737098\pi\) | ||||
−0.677872 | + | 0.735179i | \(0.737098\pi\) | |||||||
\(354\) | −6.18034 | −0.328481 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.0000 | 0.953998 | ||||||||
\(357\) | −0.978714 | −0.0517990 | ||||||||
\(358\) | 4.27051 | 0.225703 | ||||||||
\(359\) | 26.5967 | 1.40372 | 0.701861 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701861 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 2.02129 | 0.106236 | ||||||||
\(363\) | −2.36068 | −0.123904 | ||||||||
\(364\) | 0.875388 | 0.0458828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.4377 | 0.650129 | ||||||||
\(367\) | 3.52786 | 0.184153 | 0.0920765 | − | 0.995752i | \(-0.470650\pi\) | ||||
0.0920765 | + | 0.995752i | \(0.470650\pi\) | |||||||
\(368\) | −10.1803 | −0.530687 | ||||||||
\(369\) | −17.2361 | −0.897274 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.03444 | −0.105623 | ||||||||
\(372\) | 20.1246 | 1.04341 | ||||||||
\(373\) | −19.8541 | −1.02801 | −0.514003 | − | 0.857788i | \(-0.671838\pi\) | ||||
−0.514003 | + | 0.857788i | \(0.671838\pi\) | |||||||
\(374\) | −2.45898 | −0.127151 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.92299 | 0.408597 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0.201626 | 0.0103705 | ||||||||
\(379\) | 30.5410 | 1.56879 | 0.784393 | − | 0.620264i | \(-0.212974\pi\) | ||||
0.784393 | + | 0.620264i | \(0.212974\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.0902 | −0.670630 | ||||||||
\(382\) | 0.0212862 | 0.00108910 | ||||||||
\(383\) | −36.0689 | −1.84303 | −0.921517 | − | 0.388338i | \(-0.873049\pi\) | ||||
−0.921517 | + | 0.388338i | \(0.873049\pi\) | |||||||
\(384\) | −22.5623 | −1.15138 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.92299 | −0.199675 | ||||||||
\(387\) | 19.1246 | 0.972159 | ||||||||
\(388\) | 17.8328 | 0.905324 | ||||||||
\(389\) | 4.47214 | 0.226746 | 0.113373 | − | 0.993552i | \(-0.463834\pi\) | ||||
0.113373 | + | 0.993552i | \(0.463834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.00000 | 0.303433 | ||||||||
\(392\) | −10.2229 | −0.516335 | ||||||||
\(393\) | 26.8328 | 1.35354 | ||||||||
\(394\) | 0.562306 | 0.0283286 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.8754 | 0.647013 | ||||||||
\(397\) | −20.0344 | −1.00550 | −0.502750 | − | 0.864432i | \(-0.667678\pi\) | ||||
−0.502750 | + | 0.864432i | \(0.667678\pi\) | |||||||
\(398\) | 2.83282 | 0.141996 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8885 | 1.49256 | 0.746281 | − | 0.665631i | \(-0.231837\pi\) | ||||
0.746281 | + | 0.665631i | \(0.231837\pi\) | |||||||
\(402\) | −4.02129 | −0.200564 | ||||||||
\(403\) | 9.70820 | 0.483600 | ||||||||
\(404\) | −29.7295 | −1.47910 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.541020 | 0.0268504 | ||||||||
\(407\) | 37.6869 | 1.86807 | ||||||||
\(408\) | 6.10333 | 0.302160 | ||||||||
\(409\) | 36.5623 | 1.80789 | 0.903945 | − | 0.427649i | \(-0.140658\pi\) | ||||
0.903945 | + | 0.427649i | \(0.140658\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.6525 | −0.525448 | ||||||||
\(412\) | 6.00000 | 0.295599 | ||||||||
\(413\) | 1.70820 | 0.0840552 | ||||||||
\(414\) | 2.47214 | 0.121499 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8.29180 | −0.406539 | ||||||||
\(417\) | 31.3050 | 1.53301 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.4721 | −0.902423 | −0.451211 | − | 0.892417i | \(-0.649008\pi\) | ||||
−0.451211 | + | 0.892417i | \(0.649008\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.0000 | −0.731055 | −0.365528 | − | 0.930800i | \(-0.619111\pi\) | ||||
−0.365528 | + | 0.930800i | \(0.619111\pi\) | |||||||
\(422\) | 2.96556 | 0.144361 | ||||||||
\(423\) | 10.7639 | 0.523360 | ||||||||
\(424\) | 12.6869 | 0.616131 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −11.5066 | −0.557496 | ||||||||
\(427\) | −3.43769 | −0.166362 | ||||||||
\(428\) | −24.3738 | −1.17815 | ||||||||
\(429\) | 15.5279 | 0.749692 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.6525 | 0.994795 | 0.497397 | − | 0.867523i | \(-0.334289\pi\) | ||||
0.497397 | + | 0.867523i | \(0.334289\pi\) | |||||||
\(432\) | 7.03444 | 0.338445 | ||||||||
\(433\) | 11.3607 | 0.545959 | 0.272980 | − | 0.962020i | \(-0.411991\pi\) | ||||
0.272980 | + | 0.962020i | \(0.411991\pi\) | |||||||
\(434\) | 0.437694 | 0.0210100 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.4377 | 0.883005 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −2.31308 | −0.110523 | ||||||||
\(439\) | −1.50658 | −0.0719050 | −0.0359525 | − | 0.999353i | \(-0.511447\pi\) | ||||
−0.0359525 | + | 0.999353i | \(0.511447\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.8885 | −0.661359 | ||||||||
\(442\) | 1.41641 | 0.0673717 | ||||||||
\(443\) | 28.3262 | 1.34582 | 0.672910 | − | 0.739724i | \(-0.265044\pi\) | ||||
0.672910 | + | 0.739724i | \(0.265044\pi\) | |||||||
\(444\) | −45.0000 | −2.13561 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.45085 | −0.305457 | ||||||||
\(447\) | 1.18034 | 0.0558282 | ||||||||
\(448\) | 1.11146 | 0.0525114 | ||||||||
\(449\) | 0.201626 | 0.00951533 | 0.00475766 | − | 0.999989i | \(-0.498486\pi\) | ||||
0.00475766 | + | 0.999989i | \(0.498486\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.9230 | 1.40902 | ||||||||
\(452\) | 11.7295 | 0.551709 | ||||||||
\(453\) | 42.0344 | 1.97495 | ||||||||
\(454\) | 2.11146 | 0.0990955 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5623 | 0.681196 | 0.340598 | − | 0.940209i | \(-0.389371\pi\) | ||||
0.340598 | + | 0.940209i | \(0.389371\pi\) | |||||||
\(458\) | 4.06888 | 0.190126 | ||||||||
\(459\) | −4.14590 | −0.193514 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.0344 | 0.979672 | 0.489836 | − | 0.871815i | \(-0.337057\pi\) | ||||
0.489836 | + | 0.871815i | \(0.337057\pi\) | |||||||
\(462\) | 0.700073 | 0.0325704 | ||||||||
\(463\) | 40.8673 | 1.89926 | 0.949631 | − | 0.313370i | \(-0.101458\pi\) | ||||
0.949631 | + | 0.313370i | \(0.101458\pi\) | |||||||
\(464\) | 18.8754 | 0.876268 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.72949 | −0.450710 | ||||||||
\(467\) | 36.2705 | 1.67840 | 0.839200 | − | 0.543824i | \(-0.183024\pi\) | ||||
0.839200 | + | 0.543824i | \(0.183024\pi\) | |||||||
\(468\) | −7.41641 | −0.342824 | ||||||||
\(469\) | 1.11146 | 0.0513223 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 54.0689 | 2.49136 | ||||||||
\(472\) | −10.6525 | −0.490320 | ||||||||
\(473\) | −33.2016 | −1.52661 | ||||||||
\(474\) | 0.854102 | 0.0392302 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.811529 | −0.0371964 | ||||||||
\(477\) | 17.2361 | 0.789185 | ||||||||
\(478\) | 4.85410 | 0.222021 | ||||||||
\(479\) | 14.7426 | 0.673609 | 0.336804 | − | 0.941575i | \(-0.390654\pi\) | ||||
0.336804 | + | 0.941575i | \(0.390654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.7082 | −0.989809 | ||||||||
\(482\) | 4.96556 | 0.226175 | ||||||||
\(483\) | −1.70820 | −0.0777260 | ||||||||
\(484\) | −1.95743 | −0.0889740 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.83282 | −0.309943 | ||||||||
\(487\) | −30.1246 | −1.36508 | −0.682538 | − | 0.730850i | \(-0.739124\pi\) | ||||
−0.682538 | + | 0.730850i | \(0.739124\pi\) | |||||||
\(488\) | 21.4377 | 0.970439 | ||||||||
\(489\) | −16.1803 | −0.731700 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.2361 | −1.45479 | −0.727397 | − | 0.686217i | \(-0.759270\pi\) | ||||
−0.727397 | + | 0.686217i | \(0.759270\pi\) | |||||||
\(492\) | −35.7295 | −1.61081 | ||||||||
\(493\) | −11.1246 | −0.501027 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.2705 | 0.685666 | ||||||||
\(497\) | 3.18034 | 0.142658 | ||||||||
\(498\) | 8.61803 | 0.386183 | ||||||||
\(499\) | 38.5967 | 1.72783 | 0.863914 | − | 0.503640i | \(-0.168006\pi\) | ||||
0.863914 | + | 0.503640i | \(0.168006\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.70820 | −0.0763169 | ||||||||
\(502\) | −6.52786 | −0.291353 | ||||||||
\(503\) | −23.7426 | −1.05863 | −0.529316 | − | 0.848425i | \(-0.677551\pi\) | ||||
−0.529316 | + | 0.848425i | \(0.677551\pi\) | |||||||
\(504\) | −0.695048 | −0.0309599 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.29180 | −0.190794 | ||||||||
\(507\) | 20.1246 | 0.893765 | ||||||||
\(508\) | −10.8541 | −0.481573 | ||||||||
\(509\) | −16.0344 | −0.710714 | −0.355357 | − | 0.934731i | \(-0.615641\pi\) | ||||
−0.355357 | + | 0.934731i | \(0.615641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.639320 | 0.0282819 | ||||||||
\(512\) | −22.3050 | −0.985749 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.0000 | 0.485189 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 39.6443 | 1.74524 | ||||||||
\(517\) | −18.6869 | −0.821850 | ||||||||
\(518\) | −0.978714 | −0.0430022 | ||||||||
\(519\) | −26.0557 | −1.14372 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.7639 | 0.690630 | 0.345315 | − | 0.938487i | \(-0.387772\pi\) | ||||
0.345315 | + | 0.938487i | \(0.387772\pi\) | |||||||
\(522\) | −4.58359 | −0.200618 | ||||||||
\(523\) | −4.61803 | −0.201933 | −0.100966 | − | 0.994890i | \(-0.532193\pi\) | ||||
−0.100966 | + | 0.994890i | \(0.532193\pi\) | |||||||
\(524\) | 22.2492 | 0.971962 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.78522 | −0.339452 | ||||||||
\(527\) | −9.00000 | −0.392046 | ||||||||
\(528\) | 24.4245 | 1.06294 | ||||||||
\(529\) | −12.5279 | −0.544690 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.4721 | −0.628037 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.2361 | −0.746577 | ||||||||
\(534\) | −8.29180 | −0.358821 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.93112 | −0.299379 | ||||||||
\(537\) | 25.0000 | 1.07883 | ||||||||
\(538\) | 5.03444 | 0.217050 | ||||||||
\(539\) | 24.1115 | 1.03855 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.6525 | 1.66180 | 0.830900 | − | 0.556422i | \(-0.187826\pi\) | ||||
0.830900 | + | 0.556422i | \(0.187826\pi\) | |||||||
\(542\) | −1.65248 | −0.0709799 | ||||||||
\(543\) | 11.8328 | 0.507795 | ||||||||
\(544\) | 7.68692 | 0.329574 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.403252 | −0.0172576 | ||||||||
\(547\) | 20.4164 | 0.872943 | 0.436471 | − | 0.899718i | \(-0.356228\pi\) | ||||
0.436471 | + | 0.899718i | \(0.356228\pi\) | |||||||
\(548\) | −8.83282 | −0.377319 | ||||||||
\(549\) | 29.1246 | 1.24301 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 10.6525 | 0.453399 | ||||||||
\(553\) | −0.236068 | −0.0100386 | ||||||||
\(554\) | 4.58359 | 0.194738 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 25.9574 | 1.10084 | ||||||||
\(557\) | −4.49342 | −0.190392 | −0.0951962 | − | 0.995459i | \(-0.530348\pi\) | ||||
−0.0951962 | + | 0.995459i | \(0.530348\pi\) | |||||||
\(558\) | −3.70820 | −0.156981 | ||||||||
\(559\) | 19.1246 | 0.808885 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.3951 | −0.607763 | ||||||||
\(562\) | −0.909830 | −0.0383789 | ||||||||
\(563\) | 32.5967 | 1.37379 | 0.686895 | − | 0.726757i | \(-0.258973\pi\) | ||||
0.686895 | + | 0.726757i | \(0.258973\pi\) | |||||||
\(564\) | 22.3131 | 0.939550 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.7852 | 0.453337 | ||||||||
\(567\) | 2.59675 | 0.109053 | ||||||||
\(568\) | −19.8328 | −0.832166 | ||||||||
\(569\) | 11.2918 | 0.473377 | 0.236688 | − | 0.971586i | \(-0.423938\pi\) | ||||
0.236688 | + | 0.971586i | \(0.423938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.2492 | −1.51698 | −0.758491 | − | 0.651683i | \(-0.774063\pi\) | ||||
−0.758491 | + | 0.651683i | \(0.774063\pi\) | |||||||
\(572\) | 12.8754 | 0.538347 | ||||||||
\(573\) | 0.124612 | 0.00520573 | ||||||||
\(574\) | −0.777088 | −0.0324350 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.41641 | −0.392350 | ||||||||
\(577\) | 15.3050 | 0.637153 | 0.318577 | − | 0.947897i | \(-0.396795\pi\) | ||||
0.318577 | + | 0.947897i | \(0.396795\pi\) | |||||||
\(578\) | 5.18034 | 0.215474 | ||||||||
\(579\) | −22.9656 | −0.954416 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.38197 | −0.0988206 | ||||||||
\(582\) | −8.21478 | −0.340514 | ||||||||
\(583\) | −29.9230 | −1.23928 | ||||||||
\(584\) | −3.98684 | −0.164977 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.72949 | −0.0714446 | ||||||||
\(587\) | 43.3262 | 1.78827 | 0.894133 | − | 0.447802i | \(-0.147793\pi\) | ||||
0.894133 | + | 0.447802i | \(0.147793\pi\) | |||||||
\(588\) | −28.7902 | −1.18729 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.29180 | 0.135406 | ||||||||
\(592\) | −34.1459 | −1.40339 | ||||||||
\(593\) | 36.5967 | 1.50285 | 0.751424 | − | 0.659819i | \(-0.229367\pi\) | ||||
0.751424 | + | 0.659819i | \(0.229367\pi\) | |||||||
\(594\) | 2.96556 | 0.121678 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.978714 | 0.0400897 | ||||||||
\(597\) | 16.5836 | 0.678721 | ||||||||
\(598\) | 2.47214 | 0.101093 | ||||||||
\(599\) | 17.0689 | 0.697416 | 0.348708 | − | 0.937231i | \(-0.386621\pi\) | ||||
0.348708 | + | 0.937231i | \(0.386621\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.6869 | −1.70044 | −0.850222 | − | 0.526424i | \(-0.823533\pi\) | ||||
−0.850222 | + | 0.526424i | \(0.823533\pi\) | |||||||
\(602\) | 0.862233 | 0.0351420 | ||||||||
\(603\) | −9.41641 | −0.383466 | ||||||||
\(604\) | 34.8541 | 1.41819 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.6950 | 0.556323 | ||||||||
\(607\) | 19.9787 | 0.810911 | 0.405455 | − | 0.914115i | \(-0.367113\pi\) | ||||
0.405455 | + | 0.914115i | \(0.367113\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.16718 | 0.128341 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.7639 | 0.435462 | ||||||||
\(612\) | 6.87539 | 0.277921 | ||||||||
\(613\) | −30.5066 | −1.23215 | −0.616075 | − | 0.787688i | \(-0.711278\pi\) | ||||
−0.616075 | + | 0.787688i | \(0.711278\pi\) | |||||||
\(614\) | −4.75078 | −0.191726 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.20665 | 0.0486174 | ||||||||
\(617\) | 28.5066 | 1.14763 | 0.573816 | − | 0.818984i | \(-0.305463\pi\) | ||||
0.573816 | + | 0.818984i | \(0.305463\pi\) | |||||||
\(618\) | −2.76393 | −0.111182 | ||||||||
\(619\) | −1.50658 | −0.0605545 | −0.0302772 | − | 0.999542i | \(-0.509639\pi\) | ||||
−0.0302772 | + | 0.999542i | \(0.509639\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.23607 | −0.290373 | ||||||||
\(622\) | −4.49342 | −0.180170 | ||||||||
\(623\) | 2.29180 | 0.0918189 | ||||||||
\(624\) | −14.0689 | −0.563206 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.785218 | −0.0313836 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 44.8328 | 1.78902 | ||||||||
\(629\) | 20.1246 | 0.802421 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9787 | 0.516674 | 0.258337 | − | 0.966055i | \(-0.416825\pi\) | ||||
0.258337 | + | 0.966055i | \(0.416825\pi\) | |||||||
\(632\) | 1.47214 | 0.0585584 | ||||||||
\(633\) | 17.3607 | 0.690025 | ||||||||
\(634\) | −2.65248 | −0.105343 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 35.7295 | 1.41677 | ||||||||
\(637\) | −13.8885 | −0.550284 | ||||||||
\(638\) | 7.95743 | 0.315038 | ||||||||
\(639\) | −26.9443 | −1.06590 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.7082 | 1.21290 | 0.606451 | − | 0.795121i | \(-0.292593\pi\) | ||||
0.606451 | + | 0.795121i | \(0.292593\pi\) | |||||||
\(642\) | 11.2279 | 0.443131 | ||||||||
\(643\) | 24.3050 | 0.958494 | 0.479247 | − | 0.877680i | \(-0.340910\pi\) | ||||
0.479247 | + | 0.877680i | \(0.340910\pi\) | |||||||
\(644\) | −1.41641 | −0.0558143 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.5066 | −0.648941 | −0.324470 | − | 0.945896i | \(-0.605186\pi\) | ||||
−0.324470 | + | 0.945896i | \(0.605186\pi\) | |||||||
\(648\) | −16.1935 | −0.636141 | ||||||||
\(649\) | 25.1246 | 0.986227 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.56231 | 0.100425 | ||||||||
\(652\) | −13.4164 | −0.525427 | ||||||||
\(653\) | 26.1246 | 1.02234 | 0.511168 | − | 0.859481i | \(-0.329213\pi\) | ||||
0.511168 | + | 0.859481i | \(0.329213\pi\) | |||||||
\(654\) | −8.49342 | −0.332119 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27.1115 | −1.05852 | ||||||||
\(657\) | −5.41641 | −0.211314 | ||||||||
\(658\) | 0.485292 | 0.0189186 | ||||||||
\(659\) | −43.0689 | −1.67773 | −0.838863 | − | 0.544343i | \(-0.816779\pi\) | ||||
−0.838863 | + | 0.544343i | \(0.816779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.58359 | −0.0615946 | −0.0307973 | − | 0.999526i | \(-0.509805\pi\) | ||||
−0.0307973 | + | 0.999526i | \(0.509805\pi\) | |||||||
\(662\) | −2.50658 | −0.0974209 | ||||||||
\(663\) | 8.29180 | 0.322027 | ||||||||
\(664\) | 14.8541 | 0.576451 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.29180 | 0.321301 | ||||||||
\(667\) | −19.4164 | −0.751806 | ||||||||
\(668\) | −1.41641 | −0.0548025 | ||||||||
\(669\) | −37.7639 | −1.46004 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.5623 | −1.95194 | ||||||||
\(672\) | −2.18847 | −0.0844221 | ||||||||
\(673\) | −25.1803 | −0.970631 | −0.485315 | − | 0.874339i | \(-0.661295\pi\) | ||||
−0.485315 | + | 0.874339i | \(0.661295\pi\) | |||||||
\(674\) | 3.32624 | 0.128122 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.6869 | 0.641805 | ||||||||
\(677\) | −24.9098 | −0.957363 | −0.478681 | − | 0.877989i | \(-0.658885\pi\) | ||||
−0.478681 | + | 0.877989i | \(0.658885\pi\) | |||||||
\(678\) | −5.40325 | −0.207511 | ||||||||
\(679\) | 2.27051 | 0.0871342 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.3607 | 0.473662 | ||||||||
\(682\) | 6.43769 | 0.246512 | ||||||||
\(683\) | −12.2016 | −0.466882 | −0.233441 | − | 0.972371i | \(-0.574999\pi\) | ||||
−0.233441 | + | 0.972371i | \(0.574999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.25735 | −0.0480060 | ||||||||
\(687\) | 23.8197 | 0.908777 | ||||||||
\(688\) | 30.0820 | 1.14687 | ||||||||
\(689\) | 17.2361 | 0.656642 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.6525 | 0.899783 | 0.449891 | − | 0.893083i | \(-0.351463\pi\) | ||||
0.449891 | + | 0.893083i | \(0.351463\pi\) | |||||||
\(692\) | −21.6049 | −0.821294 | ||||||||
\(693\) | 1.63932 | 0.0622726 | ||||||||
\(694\) | −9.36881 | −0.355635 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −19.7508 | −0.748651 | ||||||||
\(697\) | 15.9787 | 0.605237 | ||||||||
\(698\) | −11.8673 | −0.449182 | ||||||||
\(699\) | −56.9574 | −2.15433 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.0557 | −1.17296 | −0.586479 | − | 0.809964i | \(-0.699486\pi\) | ||||
−0.586479 | + | 0.809964i | \(0.699486\pi\) | |||||||
\(702\) | −1.70820 | −0.0644720 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 16.3475 | 0.616120 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.72949 | 0.366174 | ||||||||
\(707\) | −3.78522 | −0.142358 | ||||||||
\(708\) | −30.0000 | −1.12747 | ||||||||
\(709\) | −44.8328 | −1.68373 | −0.841866 | − | 0.539687i | \(-0.818543\pi\) | ||||
−0.841866 | + | 0.539687i | \(0.818543\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.00000 | 0.0750059 | ||||||||
\(712\) | −14.2918 | −0.535608 | ||||||||
\(713\) | −15.7082 | −0.588277 | ||||||||
\(714\) | 0.373835 | 0.0139904 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20.7295 | 0.774697 | ||||||||
\(717\) | 28.4164 | 1.06123 | ||||||||
\(718\) | −10.1591 | −0.379133 | ||||||||
\(719\) | −7.76393 | −0.289546 | −0.144773 | − | 0.989465i | \(-0.546245\pi\) | ||||
−0.144773 | + | 0.989465i | \(0.546245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.763932 | 0.0284503 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.0689 | 1.08108 | ||||||||
\(724\) | 9.81153 | 0.364643 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.901699 | 0.0334652 | ||||||||
\(727\) | 19.6869 | 0.730147 | 0.365074 | − | 0.930979i | \(-0.381044\pi\) | ||||
0.365074 | + | 0.930979i | \(0.381044\pi\) | |||||||
\(728\) | −0.695048 | −0.0257602 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.7295 | −0.655749 | ||||||||
\(732\) | 60.3738 | 2.23148 | ||||||||
\(733\) | −19.1591 | −0.707656 | −0.353828 | − | 0.935311i | \(-0.615120\pi\) | ||||
−0.353828 | + | 0.935311i | \(0.615120\pi\) | |||||||
\(734\) | −1.34752 | −0.0497380 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.4164 | 0.494535 | ||||||||
\(737\) | 16.3475 | 0.602169 | ||||||||
\(738\) | 6.58359 | 0.242345 | ||||||||
\(739\) | −18.5623 | −0.682825 | −0.341413 | − | 0.939913i | \(-0.610905\pi\) | ||||
−0.341413 | + | 0.939913i | \(0.610905\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.777088 | 0.0285278 | ||||||||
\(743\) | −13.2361 | −0.485584 | −0.242792 | − | 0.970078i | \(-0.578063\pi\) | ||||
−0.242792 | + | 0.970078i | \(0.578063\pi\) | |||||||
\(744\) | −15.9787 | −0.585808 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.58359 | 0.277655 | ||||||||
\(747\) | 20.1803 | 0.738360 | ||||||||
\(748\) | −11.9361 | −0.436429 | ||||||||
\(749\) | −3.10333 | −0.113393 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.5623 | 1.73557 | 0.867787 | − | 0.496937i | \(-0.165542\pi\) | ||||
0.867787 | + | 0.496937i | \(0.165542\pi\) | |||||||
\(752\) | 16.9311 | 0.617414 | ||||||||
\(753\) | −38.2148 | −1.39262 | ||||||||
\(754\) | −4.58359 | −0.166925 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.978714 | 0.0355955 | ||||||||
\(757\) | 28.8885 | 1.04997 | 0.524986 | − | 0.851111i | \(-0.324071\pi\) | ||||
0.524986 | + | 0.851111i | \(0.324071\pi\) | |||||||
\(758\) | −11.6656 | −0.423715 | ||||||||
\(759\) | −25.1246 | −0.911966 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.6180 | 1.07365 | 0.536826 | − | 0.843693i | \(-0.319623\pi\) | ||||
0.536826 | + | 0.843693i | \(0.319623\pi\) | |||||||
\(762\) | 5.00000 | 0.181131 | ||||||||
\(763\) | 2.34752 | 0.0849861 | ||||||||
\(764\) | 0.103326 | 0.00373819 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.7771 | 0.497786 | ||||||||
\(767\) | −14.4721 | −0.522559 | ||||||||
\(768\) | −12.4377 | −0.448807 | ||||||||
\(769\) | −18.2705 | −0.658851 | −0.329426 | − | 0.944181i | \(-0.606855\pi\) | ||||
−0.329426 | + | 0.944181i | \(0.606855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 64.3951 | 2.31913 | ||||||||
\(772\) | −19.0426 | −0.685357 | ||||||||
\(773\) | −18.9656 | −0.682144 | −0.341072 | − | 0.940037i | \(-0.610790\pi\) | ||||
−0.341072 | + | 0.940037i | \(0.610790\pi\) | |||||||
\(774\) | −7.30495 | −0.262571 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.1591 | −0.508280 | ||||||||
\(777\) | −5.72949 | −0.205544 | ||||||||
\(778\) | −1.70820 | −0.0612421 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.7771 | 1.67382 | ||||||||
\(782\) | −2.29180 | −0.0819545 | ||||||||
\(783\) | 13.4164 | 0.479463 | ||||||||
\(784\) | −21.8460 | −0.780213 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.2492 | −0.365578 | ||||||||
\(787\) | −5.59675 | −0.199503 | −0.0997513 | − | 0.995012i | \(-0.531805\pi\) | ||||
−0.0997513 | + | 0.995012i | \(0.531805\pi\) | |||||||
\(788\) | 2.72949 | 0.0972341 | ||||||||
\(789\) | −45.5755 | −1.62253 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.49342 | 0.0531000 | ||||||||
\(792\) | −10.2229 | −0.363255 | ||||||||
\(793\) | 29.1246 | 1.03425 | ||||||||
\(794\) | 7.65248 | 0.271576 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.7508 | 0.487383 | ||||||||
\(797\) | 54.8673 | 1.94350 | 0.971749 | − | 0.236017i | \(-0.0758420\pi\) | ||||
0.971749 | + | 0.236017i | \(0.0758420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.97871 | −0.353022 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.4164 | −0.686045 | ||||||||
\(802\) | −11.4164 | −0.403127 | ||||||||
\(803\) | 9.40325 | 0.331834 | ||||||||
\(804\) | −19.5197 | −0.688408 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.70820 | −0.130616 | ||||||||
\(807\) | 29.4721 | 1.03747 | ||||||||
\(808\) | 23.6049 | 0.830417 | ||||||||
\(809\) | 2.23607 | 0.0786160 | 0.0393080 | − | 0.999227i | \(-0.487485\pi\) | ||||
0.0393080 | + | 0.999227i | \(0.487485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.38197 | −0.259216 | −0.129608 | − | 0.991565i | \(-0.541372\pi\) | ||||
−0.129608 | + | 0.991565i | \(0.541372\pi\) | |||||||
\(812\) | 2.62616 | 0.0921603 | ||||||||
\(813\) | −9.67376 | −0.339274 | ||||||||
\(814\) | −14.3951 | −0.504549 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.0426 | 0.456581 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −13.9656 | −0.488294 | ||||||||
\(819\) | −0.944272 | −0.0329955 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.9230 | −1.28862 | −0.644311 | − | 0.764764i | \(-0.722856\pi\) | ||||
−0.644311 | + | 0.764764i | \(0.722856\pi\) | |||||||
\(822\) | 4.06888 | 0.141919 | ||||||||
\(823\) | −5.74265 | −0.200176 | −0.100088 | − | 0.994979i | \(-0.531912\pi\) | ||||
−0.100088 | + | 0.994979i | \(0.531912\pi\) | |||||||
\(824\) | −4.76393 | −0.165959 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.652476 | −0.0227025 | ||||||||
\(827\) | −49.2492 | −1.71256 | −0.856282 | − | 0.516509i | \(-0.827231\pi\) | ||||
−0.856282 | + | 0.516509i | \(0.827231\pi\) | |||||||
\(828\) | 12.0000 | 0.417029 | ||||||||
\(829\) | 1.00000 | 0.0347314 | 0.0173657 | − | 0.999849i | \(-0.494472\pi\) | ||||
0.0173657 | + | 0.999849i | \(0.494472\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.8328 | 0.930820 | ||||||||
\(832\) | −9.41641 | −0.326455 | ||||||||
\(833\) | 12.8754 | 0.446106 | ||||||||
\(834\) | −11.9574 | −0.414052 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.8541 | 0.375173 | ||||||||
\(838\) | 7.05573 | 0.243736 | ||||||||
\(839\) | 49.7639 | 1.71804 | 0.859021 | − | 0.511941i | \(-0.171073\pi\) | ||||
0.859021 | + | 0.511941i | \(0.171073\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 5.72949 | 0.197451 | ||||||||
\(843\) | −5.32624 | −0.183445 | ||||||||
\(844\) | 14.3951 | 0.495501 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.11146 | −0.141355 | ||||||||
\(847\) | −0.249224 | −0.00856342 | ||||||||
\(848\) | 27.1115 | 0.931011 | ||||||||
\(849\) | 63.1378 | 2.16688 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.1246 | 1.20406 | ||||||||
\(852\) | −55.8541 | −1.91353 | ||||||||
\(853\) | 40.1459 | 1.37457 | 0.687285 | − | 0.726388i | \(-0.258802\pi\) | ||||
0.687285 | + | 0.726388i | \(0.258802\pi\) | |||||||
\(854\) | 1.31308 | 0.0449328 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.3525 | 0.661457 | ||||||||
\(857\) | 47.1803 | 1.61165 | 0.805825 | − | 0.592154i | \(-0.201722\pi\) | ||||
0.805825 | + | 0.592154i | \(0.201722\pi\) | |||||||
\(858\) | −5.93112 | −0.202485 | ||||||||
\(859\) | 23.0902 | 0.787826 | 0.393913 | − | 0.919148i | \(-0.371121\pi\) | ||||
0.393913 | + | 0.919148i | \(0.371121\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.54915 | −0.155035 | ||||||||
\(862\) | −7.88854 | −0.268685 | ||||||||
\(863\) | 32.9230 | 1.12071 | 0.560356 | − | 0.828252i | \(-0.310664\pi\) | ||||
0.560356 | + | 0.828252i | \(0.310664\pi\) | |||||||
\(864\) | −9.27051 | −0.315389 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.33939 | −0.147459 | ||||||||
\(867\) | 30.3262 | 1.02993 | ||||||||
\(868\) | 2.12461 | 0.0721140 | ||||||||
\(869\) | −3.47214 | −0.117784 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.41641 | −0.319063 | ||||||||
\(872\) | −14.6393 | −0.495750 | ||||||||
\(873\) | −19.2361 | −0.651042 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.2279 | −0.379357 | ||||||||
\(877\) | 15.9656 | 0.539119 | 0.269559 | − | 0.962984i | \(-0.413122\pi\) | ||||
0.269559 | + | 0.962984i | \(0.413122\pi\) | |||||||
\(878\) | 0.575462 | 0.0194209 | ||||||||
\(879\) | −10.1246 | −0.341495 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.47214 | −0.0495975 | −0.0247988 | − | 0.999692i | \(-0.507894\pi\) | ||||
−0.0247988 | + | 0.999692i | \(0.507894\pi\) | |||||||
\(882\) | 5.30495 | 0.178627 | ||||||||
\(883\) | 49.7771 | 1.67513 | 0.837566 | − | 0.546336i | \(-0.183978\pi\) | ||||
0.837566 | + | 0.546336i | \(0.183978\pi\) | |||||||
\(884\) | 6.87539 | 0.231244 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.8197 | −0.363494 | ||||||||
\(887\) | −19.0557 | −0.639829 | −0.319914 | − | 0.947446i | \(-0.603654\pi\) | ||||
−0.319914 | + | 0.947446i | \(0.603654\pi\) | |||||||
\(888\) | 35.7295 | 1.19900 | ||||||||
\(889\) | −1.38197 | −0.0463497 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 38.1935 | 1.27953 | ||||||||
\(892\) | −31.3131 | −1.04844 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.450850 | −0.0150787 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.38197 | −0.0795759 | ||||||||
\(897\) | 14.4721 | 0.483211 | ||||||||
\(898\) | −0.0770143 | −0.00257000 | ||||||||
\(899\) | 29.1246 | 0.971360 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.9787 | −0.532328 | ||||||||
\(902\) | −11.4296 | −0.380563 | ||||||||
\(903\) | 5.04760 | 0.167974 | ||||||||
\(904\) | −9.31308 | −0.309749 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −16.0557 | −0.533416 | ||||||||
\(907\) | 54.9574 | 1.82483 | 0.912416 | − | 0.409265i | \(-0.134215\pi\) | ||||
0.912416 | + | 0.409265i | \(0.134215\pi\) | |||||||
\(908\) | 10.2492 | 0.340132 | ||||||||
\(909\) | 32.0689 | 1.06366 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.1459 | 0.534937 | 0.267469 | − | 0.963567i | \(-0.413813\pi\) | ||||
0.267469 | + | 0.963567i | \(0.413813\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.0344 | −1.15947 | ||||||||
\(914\) | −5.56231 | −0.183985 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.7508 | 0.652584 | ||||||||
\(917\) | 2.83282 | 0.0935478 | ||||||||
\(918\) | 1.58359 | 0.0522663 | ||||||||
\(919\) | 7.50658 | 0.247619 | 0.123810 | − | 0.992306i | \(-0.460489\pi\) | ||||
0.123810 | + | 0.992306i | \(0.460489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.8115 | −0.916421 | ||||||||
\(922\) | −8.03444 | −0.264600 | ||||||||
\(923\) | −26.9443 | −0.886882 | ||||||||
\(924\) | 3.39823 | 0.111793 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.6099 | −0.512973 | ||||||||
\(927\) | −6.47214 | −0.212573 | ||||||||
\(928\) | −24.8754 | −0.816575 | ||||||||
\(929\) | 16.5279 | 0.542262 | 0.271131 | − | 0.962543i | \(-0.412602\pi\) | ||||
0.271131 | + | 0.962543i | \(0.412602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −47.2279 | −1.54700 | ||||||||
\(933\) | −26.3050 | −0.861185 | ||||||||
\(934\) | −13.8541 | −0.453320 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.88854 | 0.192473 | ||||||||
\(937\) | −26.8328 | −0.876590 | −0.438295 | − | 0.898831i | \(-0.644417\pi\) | ||||
−0.438295 | + | 0.898831i | \(0.644417\pi\) | |||||||
\(938\) | −0.424538 | −0.0138617 | ||||||||
\(939\) | −4.59675 | −0.150009 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.2574 | 0.562574 | 0.281287 | − | 0.959624i | \(-0.409239\pi\) | ||||
0.281287 | + | 0.959624i | \(0.409239\pi\) | |||||||
\(942\) | −20.6525 | −0.672894 | ||||||||
\(943\) | 27.8885 | 0.908176 | ||||||||
\(944\) | −22.7639 | −0.740903 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.6819 | 0.412324 | ||||||||
\(947\) | 22.6869 | 0.737226 | 0.368613 | − | 0.929583i | \(-0.379833\pi\) | ||||
0.368613 | + | 0.929583i | \(0.379833\pi\) | |||||||
\(948\) | 4.14590 | 0.134653 | ||||||||
\(949\) | −5.41641 | −0.175824 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.5279 | −0.503525 | ||||||||
\(952\) | 0.644345 | 0.0208833 | ||||||||
\(953\) | 13.4164 | 0.434600 | 0.217300 | − | 0.976105i | \(-0.430275\pi\) | ||||
0.217300 | + | 0.976105i | \(0.430275\pi\) | |||||||
\(954\) | −6.58359 | −0.213152 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 23.5623 | 0.762059 | ||||||||
\(957\) | 46.5836 | 1.50583 | ||||||||
\(958\) | −5.63119 | −0.181935 | ||||||||
\(959\) | −1.12461 | −0.0363156 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.43769 | −0.239926 | ||||||||
\(962\) | 8.29180 | 0.267338 | ||||||||
\(963\) | 26.2918 | 0.847241 | ||||||||
\(964\) | 24.1033 | 0.776316 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.652476 | 0.0209931 | ||||||||
\(967\) | −5.09017 | −0.163689 | −0.0818444 | − | 0.996645i | \(-0.526081\pi\) | ||||
−0.0818444 | + | 0.996645i | \(0.526081\pi\) | |||||||
\(968\) | 1.55418 | 0.0499531 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.7984 | −1.40556 | −0.702778 | − | 0.711409i | \(-0.748057\pi\) | ||||
−0.702778 | + | 0.711409i | \(0.748057\pi\) | |||||||
\(972\) | −33.1672 | −1.06384 | ||||||||
\(973\) | 3.30495 | 0.105952 | ||||||||
\(974\) | 11.5066 | 0.368695 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 45.8115 | 1.46639 | ||||||||
\(977\) | −19.2148 | −0.614735 | −0.307368 | − | 0.951591i | \(-0.599448\pi\) | ||||
−0.307368 | + | 0.951591i | \(0.599448\pi\) | |||||||
\(978\) | 6.18034 | 0.197625 | ||||||||
\(979\) | 33.7082 | 1.07732 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.8885 | −0.634992 | ||||||||
\(982\) | 12.3131 | 0.392926 | ||||||||
\(983\) | −33.9787 | −1.08375 | −0.541876 | − | 0.840458i | \(-0.682286\pi\) | ||||
−0.541876 | + | 0.840458i | \(0.682286\pi\) | |||||||
\(984\) | 28.3688 | 0.904365 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.24922 | 0.135323 | ||||||||
\(987\) | 2.84095 | 0.0904283 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.9443 | −0.983971 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.4164 | 0.362654 | 0.181327 | − | 0.983423i | \(-0.441961\pi\) | ||||
0.181327 | + | 0.983423i | \(0.441961\pi\) | |||||||
\(992\) | −20.1246 | −0.638957 | ||||||||
\(993\) | −14.6738 | −0.465658 | ||||||||
\(994\) | −1.21478 | −0.0385305 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 41.8328 | 1.32552 | ||||||||
\(997\) | 35.7426 | 1.13198 | 0.565990 | − | 0.824412i | \(-0.308494\pi\) | ||||
0.565990 | + | 0.824412i | \(0.308494\pi\) | |||||||
\(998\) | −14.7426 | −0.466670 | ||||||||
\(999\) | −24.2705 | −0.767885 |
(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 | 9025.2.a.m.1.2 | yes | 2 | |
5.4 | even | 2 | 9025.2.a.t.1.1 | yes | 2 | ||
19.18 | odd | 2 | 9025.2.a.u.1.1 | yes | 2 | ||
95.94 | odd | 2 | 9025.2.a.l.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9025.2.a.l.1.2 | ✓ | 2 | 95.94 | odd | 2 | ||
9025.2.a.m.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
9025.2.a.t.1.1 | yes | 2 | 5.4 | even | 2 | ||
9025.2.a.u.1.1 | yes | 2 | 19.18 | odd | 2 |