Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, 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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.04892 | 1.18294 | 0.591471 | − | 0.806326i | \(-0.298547\pi\) | ||||
0.591471 | + | 0.806326i | \(0.298547\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.198062 | 0.0885761 | 0.0442881 | − | 0.999019i | \(-0.485898\pi\) | ||||
0.0442881 | + | 0.999019i | \(0.485898\pi\) | |||||||
\(6\) | 2.04892 | 0.836467 | ||||||||
\(7\) | −0.890084 | −0.336420 | −0.168210 | − | 0.985751i | \(-0.553799\pi\) | ||||
−0.168210 | + | 0.985751i | \(0.553799\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.19806 | 0.399354 | ||||||||
\(10\) | 0.198062 | 0.0626328 | ||||||||
\(11\) | −4.13706 | −1.24737 | −0.623686 | − | 0.781675i | \(-0.714366\pi\) | ||||
−0.623686 | + | 0.781675i | \(0.714366\pi\) | |||||||
\(12\) | 2.04892 | 0.591471 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.890084 | −0.237885 | ||||||||
\(15\) | 0.405813 | 0.104781 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.66487 | −0.646327 | −0.323163 | − | 0.946343i | \(-0.604746\pi\) | ||||
−0.323163 | + | 0.946343i | \(0.604746\pi\) | |||||||
\(18\) | 1.19806 | 0.282386 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.198062 | 0.0442881 | ||||||||
\(21\) | −1.82371 | −0.397966 | ||||||||
\(22\) | −4.13706 | −0.882025 | ||||||||
\(23\) | −8.45473 | −1.76293 | −0.881467 | − | 0.472246i | \(-0.843443\pi\) | ||||
−0.881467 | + | 0.472246i | \(0.843443\pi\) | |||||||
\(24\) | 2.04892 | 0.418234 | ||||||||
\(25\) | −4.96077 | −0.992154 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.69202 | −0.710530 | ||||||||
\(28\) | −0.890084 | −0.168210 | ||||||||
\(29\) | −4.13706 | −0.768233 | −0.384117 | − | 0.923285i | \(-0.625494\pi\) | ||||
−0.384117 | + | 0.923285i | \(0.625494\pi\) | |||||||
\(30\) | 0.405813 | 0.0740910 | ||||||||
\(31\) | 1.08815 | 0.195437 | 0.0977184 | − | 0.995214i | \(-0.468846\pi\) | ||||
0.0977184 | + | 0.995214i | \(0.468846\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −8.47650 | −1.47557 | ||||||||
\(34\) | −2.66487 | −0.457022 | ||||||||
\(35\) | −0.176292 | −0.0297988 | ||||||||
\(36\) | 1.19806 | 0.199677 | ||||||||
\(37\) | 10.7681 | 1.77026 | 0.885131 | − | 0.465342i | \(-0.154068\pi\) | ||||
0.885131 | + | 0.465342i | \(0.154068\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.198062 | 0.0313164 | ||||||||
\(41\) | −6.66487 | −1.04088 | −0.520439 | − | 0.853899i | \(-0.674232\pi\) | ||||
−0.520439 | + | 0.853899i | \(0.674232\pi\) | |||||||
\(42\) | −1.82371 | −0.281404 | ||||||||
\(43\) | 6.19567 | 0.944831 | 0.472415 | − | 0.881376i | \(-0.343382\pi\) | ||||
0.472415 | + | 0.881376i | \(0.343382\pi\) | |||||||
\(44\) | −4.13706 | −0.623686 | ||||||||
\(45\) | 0.237291 | 0.0353732 | ||||||||
\(46\) | −8.45473 | −1.24658 | ||||||||
\(47\) | 7.38404 | 1.07707 | 0.538537 | − | 0.842602i | \(-0.318977\pi\) | ||||
0.538537 | + | 0.842602i | \(0.318977\pi\) | |||||||
\(48\) | 2.04892 | 0.295736 | ||||||||
\(49\) | −6.20775 | −0.886822 | ||||||||
\(50\) | −4.96077 | −0.701559 | ||||||||
\(51\) | −5.46011 | −0.764568 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.40581 | −0.467824 | −0.233912 | − | 0.972258i | \(-0.575153\pi\) | ||||
−0.233912 | + | 0.972258i | \(0.575153\pi\) | |||||||
\(54\) | −3.69202 | −0.502420 | ||||||||
\(55\) | −0.819396 | −0.110487 | ||||||||
\(56\) | −0.890084 | −0.118942 | ||||||||
\(57\) | −2.04892 | −0.271386 | ||||||||
\(58\) | −4.13706 | −0.543223 | ||||||||
\(59\) | 7.20775 | 0.938369 | 0.469185 | − | 0.883100i | \(-0.344548\pi\) | ||||
0.469185 | + | 0.883100i | \(0.344548\pi\) | |||||||
\(60\) | 0.405813 | 0.0523903 | ||||||||
\(61\) | −11.9215 | −1.52640 | −0.763199 | − | 0.646164i | \(-0.776372\pi\) | ||||
−0.763199 | + | 0.646164i | \(0.776372\pi\) | |||||||
\(62\) | 1.08815 | 0.138195 | ||||||||
\(63\) | −1.06638 | −0.134351 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.47650 | −1.04339 | ||||||||
\(67\) | 3.87800 | 0.473773 | 0.236887 | − | 0.971537i | \(-0.423873\pi\) | ||||
0.236887 | + | 0.971537i | \(0.423873\pi\) | |||||||
\(68\) | −2.66487 | −0.323163 | ||||||||
\(69\) | −17.3230 | −2.08545 | ||||||||
\(70\) | −0.176292 | −0.0210709 | ||||||||
\(71\) | 6.07606 | 0.721096 | 0.360548 | − | 0.932741i | \(-0.382590\pi\) | ||||
0.360548 | + | 0.932741i | \(0.382590\pi\) | |||||||
\(72\) | 1.19806 | 0.141193 | ||||||||
\(73\) | −5.16421 | −0.604425 | −0.302213 | − | 0.953241i | \(-0.597725\pi\) | ||||
−0.302213 | + | 0.953241i | \(0.597725\pi\) | |||||||
\(74\) | 10.7681 | 1.25176 | ||||||||
\(75\) | −10.1642 | −1.17366 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 3.68233 | 0.419641 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.6582 | −1.76168 | −0.880841 | − | 0.473412i | \(-0.843022\pi\) | ||||
−0.880841 | + | 0.473412i | \(0.843022\pi\) | |||||||
\(80\) | 0.198062 | 0.0221440 | ||||||||
\(81\) | −11.1588 | −1.23987 | ||||||||
\(82\) | −6.66487 | −0.736012 | ||||||||
\(83\) | −13.1588 | −1.44437 | −0.722185 | − | 0.691700i | \(-0.756862\pi\) | ||||
−0.722185 | + | 0.691700i | \(0.756862\pi\) | |||||||
\(84\) | −1.82371 | −0.198983 | ||||||||
\(85\) | −0.527811 | −0.0572491 | ||||||||
\(86\) | 6.19567 | 0.668096 | ||||||||
\(87\) | −8.47650 | −0.908776 | ||||||||
\(88\) | −4.13706 | −0.441012 | ||||||||
\(89\) | −4.53319 | −0.480517 | −0.240258 | − | 0.970709i | \(-0.577232\pi\) | ||||
−0.240258 | + | 0.970709i | \(0.577232\pi\) | |||||||
\(90\) | 0.237291 | 0.0250127 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.45473 | −0.881467 | ||||||||
\(93\) | 2.22952 | 0.231191 | ||||||||
\(94\) | 7.38404 | 0.761606 | ||||||||
\(95\) | −0.198062 | −0.0203208 | ||||||||
\(96\) | 2.04892 | 0.209117 | ||||||||
\(97\) | 8.18060 | 0.830614 | 0.415307 | − | 0.909681i | \(-0.363674\pi\) | ||||
0.415307 | + | 0.909681i | \(0.363674\pi\) | |||||||
\(98\) | −6.20775 | −0.627078 | ||||||||
\(99\) | −4.95646 | −0.498143 | ||||||||
\(100\) | −4.96077 | −0.496077 | ||||||||
\(101\) | 1.32975 | 0.132315 | 0.0661575 | − | 0.997809i | \(-0.478926\pi\) | ||||
0.0661575 | + | 0.997809i | \(0.478926\pi\) | |||||||
\(102\) | −5.46011 | −0.540631 | ||||||||
\(103\) | −0.670251 | −0.0660418 | −0.0330209 | − | 0.999455i | \(-0.510513\pi\) | ||||
−0.0330209 | + | 0.999455i | \(0.510513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.361208 | −0.0352503 | ||||||||
\(106\) | −3.40581 | −0.330802 | ||||||||
\(107\) | 13.1075 | 1.26715 | 0.633576 | − | 0.773680i | \(-0.281586\pi\) | ||||
0.633576 | + | 0.773680i | \(0.281586\pi\) | |||||||
\(108\) | −3.69202 | −0.355265 | ||||||||
\(109\) | −15.0858 | −1.44495 | −0.722477 | − | 0.691395i | \(-0.756996\pi\) | ||||
−0.722477 | + | 0.691395i | \(0.756996\pi\) | |||||||
\(110\) | −0.819396 | −0.0781264 | ||||||||
\(111\) | 22.0629 | 2.09412 | ||||||||
\(112\) | −0.890084 | −0.0841050 | ||||||||
\(113\) | 19.5254 | 1.83680 | 0.918398 | − | 0.395657i | \(-0.129483\pi\) | ||||
0.918398 | + | 0.395657i | \(0.129483\pi\) | |||||||
\(114\) | −2.04892 | −0.191899 | ||||||||
\(115\) | −1.67456 | −0.156154 | ||||||||
\(116\) | −4.13706 | −0.384117 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.20775 | 0.663527 | ||||||||
\(119\) | 2.37196 | 0.217437 | ||||||||
\(120\) | 0.405813 | 0.0370455 | ||||||||
\(121\) | 6.11529 | 0.555936 | ||||||||
\(122\) | −11.9215 | −1.07933 | ||||||||
\(123\) | −13.6558 | −1.23130 | ||||||||
\(124\) | 1.08815 | 0.0977184 | ||||||||
\(125\) | −1.97285 | −0.176457 | ||||||||
\(126\) | −1.06638 | −0.0950003 | ||||||||
\(127\) | −13.2078 | −1.17200 | −0.585999 | − | 0.810312i | \(-0.699298\pi\) | ||||
−0.585999 | + | 0.810312i | \(0.699298\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 12.6944 | 1.11768 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9879 | 1.30950 | 0.654750 | − | 0.755845i | \(-0.272774\pi\) | ||||
0.654750 | + | 0.755845i | \(0.272774\pi\) | |||||||
\(132\) | −8.47650 | −0.737785 | ||||||||
\(133\) | 0.890084 | 0.0771800 | ||||||||
\(134\) | 3.87800 | 0.335008 | ||||||||
\(135\) | −0.731250 | −0.0629360 | ||||||||
\(136\) | −2.66487 | −0.228511 | ||||||||
\(137\) | 17.3056 | 1.47852 | 0.739258 | − | 0.673422i | \(-0.235176\pi\) | ||||
0.739258 | + | 0.673422i | \(0.235176\pi\) | |||||||
\(138\) | −17.3230 | −1.47464 | ||||||||
\(139\) | 14.4155 | 1.22271 | 0.611353 | − | 0.791358i | \(-0.290625\pi\) | ||||
0.611353 | + | 0.791358i | \(0.290625\pi\) | |||||||
\(140\) | −0.176292 | −0.0148994 | ||||||||
\(141\) | 15.1293 | 1.27412 | ||||||||
\(142\) | 6.07606 | 0.509892 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.19806 | 0.0998385 | ||||||||
\(145\) | −0.819396 | −0.0680471 | ||||||||
\(146\) | −5.16421 | −0.427393 | ||||||||
\(147\) | −12.7192 | −1.04906 | ||||||||
\(148\) | 10.7681 | 0.885131 | ||||||||
\(149\) | 5.38942 | 0.441518 | 0.220759 | − | 0.975328i | \(-0.429146\pi\) | ||||
0.220759 | + | 0.975328i | \(0.429146\pi\) | |||||||
\(150\) | −10.1642 | −0.829904 | ||||||||
\(151\) | −15.9366 | −1.29690 | −0.648451 | − | 0.761256i | \(-0.724583\pi\) | ||||
−0.648451 | + | 0.761256i | \(0.724583\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −3.19269 | −0.258113 | ||||||||
\(154\) | 3.68233 | 0.296731 | ||||||||
\(155\) | 0.215521 | 0.0173110 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.5483 | −0.841842 | −0.420921 | − | 0.907097i | \(-0.638293\pi\) | ||||
−0.420921 | + | 0.907097i | \(0.638293\pi\) | |||||||
\(158\) | −15.6582 | −1.24570 | ||||||||
\(159\) | −6.97823 | −0.553410 | ||||||||
\(160\) | 0.198062 | 0.0156582 | ||||||||
\(161\) | 7.52542 | 0.593086 | ||||||||
\(162\) | −11.1588 | −0.876721 | ||||||||
\(163\) | −5.59850 | −0.438508 | −0.219254 | − | 0.975668i | \(-0.570362\pi\) | ||||
−0.219254 | + | 0.975668i | \(0.570362\pi\) | |||||||
\(164\) | −6.66487 | −0.520439 | ||||||||
\(165\) | −1.67887 | −0.130700 | ||||||||
\(166\) | −13.1588 | −1.02132 | ||||||||
\(167\) | 13.8485 | 1.07163 | 0.535813 | − | 0.844337i | \(-0.320005\pi\) | ||||
0.535813 | + | 0.844337i | \(0.320005\pi\) | |||||||
\(168\) | −1.82371 | −0.140702 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.527811 | −0.0404813 | ||||||||
\(171\) | −1.19806 | −0.0916181 | ||||||||
\(172\) | 6.19567 | 0.472415 | ||||||||
\(173\) | 15.4523 | 1.17482 | 0.587410 | − | 0.809290i | \(-0.300148\pi\) | ||||
0.587410 | + | 0.809290i | \(0.300148\pi\) | |||||||
\(174\) | −8.47650 | −0.642602 | ||||||||
\(175\) | 4.41550 | 0.333781 | ||||||||
\(176\) | −4.13706 | −0.311843 | ||||||||
\(177\) | 14.7681 | 1.11004 | ||||||||
\(178\) | −4.53319 | −0.339777 | ||||||||
\(179\) | −12.7114 | −0.950095 | −0.475047 | − | 0.879960i | \(-0.657569\pi\) | ||||
−0.475047 | + | 0.879960i | \(0.657569\pi\) | |||||||
\(180\) | 0.237291 | 0.0176866 | ||||||||
\(181\) | 13.4765 | 1.00170 | 0.500850 | − | 0.865534i | \(-0.333021\pi\) | ||||
0.500850 | + | 0.865534i | \(0.333021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.4263 | −1.80564 | ||||||||
\(184\) | −8.45473 | −0.623291 | ||||||||
\(185\) | 2.13275 | 0.156803 | ||||||||
\(186\) | 2.22952 | 0.163476 | ||||||||
\(187\) | 11.0248 | 0.806210 | ||||||||
\(188\) | 7.38404 | 0.538537 | ||||||||
\(189\) | 3.28621 | 0.239036 | ||||||||
\(190\) | −0.198062 | −0.0143689 | ||||||||
\(191\) | 18.5157 | 1.33975 | 0.669876 | − | 0.742473i | \(-0.266347\pi\) | ||||
0.669876 | + | 0.742473i | \(0.266347\pi\) | |||||||
\(192\) | 2.04892 | 0.147868 | ||||||||
\(193\) | −3.55496 | −0.255891 | −0.127946 | − | 0.991781i | \(-0.540838\pi\) | ||||
−0.127946 | + | 0.991781i | \(0.540838\pi\) | |||||||
\(194\) | 8.18060 | 0.587333 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.20775 | −0.443411 | ||||||||
\(197\) | −2.19567 | −0.156435 | −0.0782175 | − | 0.996936i | \(-0.524923\pi\) | ||||
−0.0782175 | + | 0.996936i | \(0.524923\pi\) | |||||||
\(198\) | −4.95646 | −0.352240 | ||||||||
\(199\) | −15.2228 | −1.07912 | −0.539558 | − | 0.841948i | \(-0.681409\pi\) | ||||
−0.539558 | + | 0.841948i | \(0.681409\pi\) | |||||||
\(200\) | −4.96077 | −0.350780 | ||||||||
\(201\) | 7.94571 | 0.560447 | ||||||||
\(202\) | 1.32975 | 0.0935608 | ||||||||
\(203\) | 3.68233 | 0.258449 | ||||||||
\(204\) | −5.46011 | −0.382284 | ||||||||
\(205\) | −1.32006 | −0.0921970 | ||||||||
\(206\) | −0.670251 | −0.0466986 | ||||||||
\(207\) | −10.1293 | −0.704035 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.13706 | 0.286167 | ||||||||
\(210\) | −0.361208 | −0.0249257 | ||||||||
\(211\) | −17.2905 | −1.19033 | −0.595164 | − | 0.803604i | \(-0.702913\pi\) | ||||
−0.595164 | + | 0.803604i | \(0.702913\pi\) | |||||||
\(212\) | −3.40581 | −0.233912 | ||||||||
\(213\) | 12.4494 | 0.853016 | ||||||||
\(214\) | 13.1075 | 0.896012 | ||||||||
\(215\) | 1.22713 | 0.0836895 | ||||||||
\(216\) | −3.69202 | −0.251210 | ||||||||
\(217\) | −0.968541 | −0.0657489 | ||||||||
\(218\) | −15.0858 | −1.02174 | ||||||||
\(219\) | −10.5810 | −0.715000 | ||||||||
\(220\) | −0.819396 | −0.0552437 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 22.0629 | 1.48077 | ||||||||
\(223\) | 19.8726 | 1.33077 | 0.665385 | − | 0.746501i | \(-0.268268\pi\) | ||||
0.665385 | + | 0.746501i | \(0.268268\pi\) | |||||||
\(224\) | −0.890084 | −0.0594712 | ||||||||
\(225\) | −5.94331 | −0.396221 | ||||||||
\(226\) | 19.5254 | 1.29881 | ||||||||
\(227\) | −4.76809 | −0.316469 | −0.158234 | − | 0.987402i | \(-0.550580\pi\) | ||||
−0.158234 | + | 0.987402i | \(0.550580\pi\) | |||||||
\(228\) | −2.04892 | −0.135693 | ||||||||
\(229\) | −23.8931 | −1.57890 | −0.789449 | − | 0.613816i | \(-0.789634\pi\) | ||||
−0.789449 | + | 0.613816i | \(0.789634\pi\) | |||||||
\(230\) | −1.67456 | −0.110417 | ||||||||
\(231\) | 7.54480 | 0.496411 | ||||||||
\(232\) | −4.13706 | −0.271612 | ||||||||
\(233\) | 11.7778 | 0.771588 | 0.385794 | − | 0.922585i | \(-0.373928\pi\) | ||||
0.385794 | + | 0.922585i | \(0.373928\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.46250 | 0.0954030 | ||||||||
\(236\) | 7.20775 | 0.469185 | ||||||||
\(237\) | −32.0823 | −2.08397 | ||||||||
\(238\) | 2.37196 | 0.153751 | ||||||||
\(239\) | −12.2983 | −0.795510 | −0.397755 | − | 0.917492i | \(-0.630211\pi\) | ||||
−0.397755 | + | 0.917492i | \(0.630211\pi\) | |||||||
\(240\) | 0.405813 | 0.0261951 | ||||||||
\(241\) | 0.613564 | 0.0395231 | 0.0197616 | − | 0.999805i | \(-0.493709\pi\) | ||||
0.0197616 | + | 0.999805i | \(0.493709\pi\) | |||||||
\(242\) | 6.11529 | 0.393106 | ||||||||
\(243\) | −11.7875 | −0.756166 | ||||||||
\(244\) | −11.9215 | −0.763199 | ||||||||
\(245\) | −1.22952 | −0.0785512 | ||||||||
\(246\) | −13.6558 | −0.870661 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.08815 | 0.0690973 | ||||||||
\(249\) | −26.9614 | −1.70861 | ||||||||
\(250\) | −1.97285 | −0.124774 | ||||||||
\(251\) | −21.1836 | −1.33710 | −0.668548 | − | 0.743669i | \(-0.733084\pi\) | ||||
−0.668548 | + | 0.743669i | \(0.733084\pi\) | |||||||
\(252\) | −1.06638 | −0.0671754 | ||||||||
\(253\) | 34.9778 | 2.19903 | ||||||||
\(254\) | −13.2078 | −0.828728 | ||||||||
\(255\) | −1.08144 | −0.0677225 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.1535 | 0.945247 | 0.472623 | − | 0.881265i | \(-0.343307\pi\) | ||||
0.472623 | + | 0.881265i | \(0.343307\pi\) | |||||||
\(258\) | 12.6944 | 0.790320 | ||||||||
\(259\) | −9.58450 | −0.595552 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.95646 | −0.306797 | ||||||||
\(262\) | 14.9879 | 0.925957 | ||||||||
\(263\) | −9.45712 | −0.583151 | −0.291576 | − | 0.956548i | \(-0.594179\pi\) | ||||
−0.291576 | + | 0.956548i | \(0.594179\pi\) | |||||||
\(264\) | −8.47650 | −0.521693 | ||||||||
\(265\) | −0.674563 | −0.0414381 | ||||||||
\(266\) | 0.890084 | 0.0545745 | ||||||||
\(267\) | −9.28813 | −0.568424 | ||||||||
\(268\) | 3.87800 | 0.236887 | ||||||||
\(269\) | −13.4034 | −0.817221 | −0.408610 | − | 0.912709i | \(-0.633987\pi\) | ||||
−0.408610 | + | 0.912709i | \(0.633987\pi\) | |||||||
\(270\) | −0.731250 | −0.0445025 | ||||||||
\(271\) | −24.7138 | −1.50126 | −0.750628 | − | 0.660725i | \(-0.770249\pi\) | ||||
−0.750628 | + | 0.660725i | \(0.770249\pi\) | |||||||
\(272\) | −2.66487 | −0.161582 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.3056 | 1.04547 | ||||||||
\(275\) | 20.5230 | 1.23758 | ||||||||
\(276\) | −17.3230 | −1.04272 | ||||||||
\(277\) | 8.78746 | 0.527987 | 0.263994 | − | 0.964524i | \(-0.414960\pi\) | ||||
0.263994 | + | 0.964524i | \(0.414960\pi\) | |||||||
\(278\) | 14.4155 | 0.864584 | ||||||||
\(279\) | 1.30367 | 0.0780485 | ||||||||
\(280\) | −0.176292 | −0.0105355 | ||||||||
\(281\) | −17.7168 | −1.05689 | −0.528447 | − | 0.848966i | \(-0.677226\pi\) | ||||
−0.528447 | + | 0.848966i | \(0.677226\pi\) | |||||||
\(282\) | 15.1293 | 0.900936 | ||||||||
\(283\) | −9.96508 | −0.592363 | −0.296181 | − | 0.955132i | \(-0.595713\pi\) | ||||
−0.296181 | + | 0.955132i | \(0.595713\pi\) | |||||||
\(284\) | 6.07606 | 0.360548 | ||||||||
\(285\) | −0.405813 | −0.0240383 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.93230 | 0.350172 | ||||||||
\(288\) | 1.19806 | 0.0705965 | ||||||||
\(289\) | −9.89844 | −0.582261 | ||||||||
\(290\) | −0.819396 | −0.0481166 | ||||||||
\(291\) | 16.7614 | 0.982570 | ||||||||
\(292\) | −5.16421 | −0.302213 | ||||||||
\(293\) | 11.1099 | 0.649048 | 0.324524 | − | 0.945877i | \(-0.394796\pi\) | ||||
0.324524 | + | 0.945877i | \(0.394796\pi\) | |||||||
\(294\) | −12.7192 | −0.741797 | ||||||||
\(295\) | 1.42758 | 0.0831171 | ||||||||
\(296\) | 10.7681 | 0.625882 | ||||||||
\(297\) | 15.2741 | 0.886295 | ||||||||
\(298\) | 5.38942 | 0.312201 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10.1642 | −0.586831 | ||||||||
\(301\) | −5.51466 | −0.317860 | ||||||||
\(302\) | −15.9366 | −0.917049 | ||||||||
\(303\) | 2.72455 | 0.156521 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −2.36121 | −0.135202 | ||||||||
\(306\) | −3.19269 | −0.182514 | ||||||||
\(307\) | 9.83446 | 0.561282 | 0.280641 | − | 0.959813i | \(-0.409453\pi\) | ||||
0.280641 | + | 0.959813i | \(0.409453\pi\) | |||||||
\(308\) | 3.68233 | 0.209820 | ||||||||
\(309\) | −1.37329 | −0.0781237 | ||||||||
\(310\) | 0.215521 | 0.0122408 | ||||||||
\(311\) | 11.8726 | 0.673235 | 0.336617 | − | 0.941642i | \(-0.390717\pi\) | ||||
0.336617 | + | 0.941642i | \(0.390717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.81402 | −0.498198 | −0.249099 | − | 0.968478i | \(-0.580134\pi\) | ||||
−0.249099 | + | 0.968478i | \(0.580134\pi\) | |||||||
\(314\) | −10.5483 | −0.595272 | ||||||||
\(315\) | −0.211209 | −0.0119003 | ||||||||
\(316\) | −15.6582 | −0.880841 | ||||||||
\(317\) | −12.7138 | −0.714078 | −0.357039 | − | 0.934090i | \(-0.616214\pi\) | ||||
−0.357039 | + | 0.934090i | \(0.616214\pi\) | |||||||
\(318\) | −6.97823 | −0.391320 | ||||||||
\(319\) | 17.1153 | 0.958272 | ||||||||
\(320\) | 0.198062 | 0.0110720 | ||||||||
\(321\) | 26.8562 | 1.49897 | ||||||||
\(322\) | 7.52542 | 0.419375 | ||||||||
\(323\) | 2.66487 | 0.148278 | ||||||||
\(324\) | −11.1588 | −0.619935 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.59850 | −0.310072 | ||||||||
\(327\) | −30.9095 | −1.70930 | ||||||||
\(328\) | −6.66487 | −0.368006 | ||||||||
\(329\) | −6.57242 | −0.362349 | ||||||||
\(330\) | −1.67887 | −0.0924190 | ||||||||
\(331\) | −18.1715 | −0.998796 | −0.499398 | − | 0.866373i | \(-0.666446\pi\) | ||||
−0.499398 | + | 0.866373i | \(0.666446\pi\) | |||||||
\(332\) | −13.1588 | −0.722185 | ||||||||
\(333\) | 12.9008 | 0.706962 | ||||||||
\(334\) | 13.8485 | 0.757754 | ||||||||
\(335\) | 0.768086 | 0.0419650 | ||||||||
\(336\) | −1.82371 | −0.0994914 | ||||||||
\(337\) | 13.9323 | 0.758941 | 0.379470 | − | 0.925204i | \(-0.376106\pi\) | ||||
0.379470 | + | 0.925204i | \(0.376106\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 40.0060 | 2.17283 | ||||||||
\(340\) | −0.527811 | −0.0286246 | ||||||||
\(341\) | −4.50173 | −0.243782 | ||||||||
\(342\) | −1.19806 | −0.0647838 | ||||||||
\(343\) | 11.7560 | 0.634765 | ||||||||
\(344\) | 6.19567 | 0.334048 | ||||||||
\(345\) | −3.43104 | −0.184721 | ||||||||
\(346\) | 15.4523 | 0.830723 | ||||||||
\(347\) | −8.02416 | −0.430760 | −0.215380 | − | 0.976530i | \(-0.569099\pi\) | ||||
−0.215380 | + | 0.976530i | \(0.569099\pi\) | |||||||
\(348\) | −8.47650 | −0.454388 | ||||||||
\(349\) | 10.7192 | 0.573784 | 0.286892 | − | 0.957963i | \(-0.407378\pi\) | ||||
0.286892 | + | 0.957963i | \(0.407378\pi\) | |||||||
\(350\) | 4.41550 | 0.236019 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.13706 | −0.220506 | ||||||||
\(353\) | 36.1172 | 1.92233 | 0.961163 | − | 0.275983i | \(-0.0890032\pi\) | ||||
0.961163 | + | 0.275983i | \(0.0890032\pi\) | |||||||
\(354\) | 14.7681 | 0.784915 | ||||||||
\(355\) | 1.20344 | 0.0638719 | ||||||||
\(356\) | −4.53319 | −0.240258 | ||||||||
\(357\) | 4.85995 | 0.257216 | ||||||||
\(358\) | −12.7114 | −0.671818 | ||||||||
\(359\) | 32.3129 | 1.70541 | 0.852704 | − | 0.522394i | \(-0.174961\pi\) | ||||
0.852704 | + | 0.522394i | \(0.174961\pi\) | |||||||
\(360\) | 0.237291 | 0.0125063 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 13.4765 | 0.708309 | ||||||||
\(363\) | 12.5297 | 0.657640 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.02284 | −0.0535376 | ||||||||
\(366\) | −24.4263 | −1.27678 | ||||||||
\(367\) | 5.24027 | 0.273540 | 0.136770 | − | 0.990603i | \(-0.456328\pi\) | ||||
0.136770 | + | 0.990603i | \(0.456328\pi\) | |||||||
\(368\) | −8.45473 | −0.440733 | ||||||||
\(369\) | −7.98493 | −0.415679 | ||||||||
\(370\) | 2.13275 | 0.110876 | ||||||||
\(371\) | 3.03146 | 0.157386 | ||||||||
\(372\) | 2.22952 | 0.115595 | ||||||||
\(373\) | −14.6213 | −0.757064 | −0.378532 | − | 0.925588i | \(-0.623571\pi\) | ||||
−0.378532 | + | 0.925588i | \(0.623571\pi\) | |||||||
\(374\) | 11.0248 | 0.570076 | ||||||||
\(375\) | −4.04221 | −0.208739 | ||||||||
\(376\) | 7.38404 | 0.380803 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.28621 | 0.169024 | ||||||||
\(379\) | −14.8116 | −0.760822 | −0.380411 | − | 0.924818i | \(-0.624217\pi\) | ||||
−0.380411 | + | 0.924818i | \(0.624217\pi\) | |||||||
\(380\) | −0.198062 | −0.0101604 | ||||||||
\(381\) | −27.0616 | −1.38641 | ||||||||
\(382\) | 18.5157 | 0.947347 | ||||||||
\(383\) | 12.2524 | 0.626066 | 0.313033 | − | 0.949742i | \(-0.398655\pi\) | ||||
0.313033 | + | 0.949742i | \(0.398655\pi\) | |||||||
\(384\) | 2.04892 | 0.104558 | ||||||||
\(385\) | 0.729331 | 0.0371702 | ||||||||
\(386\) | −3.55496 | −0.180943 | ||||||||
\(387\) | 7.42280 | 0.377322 | ||||||||
\(388\) | 8.18060 | 0.415307 | ||||||||
\(389\) | 33.6969 | 1.70850 | 0.854251 | − | 0.519861i | \(-0.174016\pi\) | ||||
0.854251 | + | 0.519861i | \(0.174016\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.5308 | 1.13943 | ||||||||
\(392\) | −6.20775 | −0.313539 | ||||||||
\(393\) | 30.7090 | 1.54906 | ||||||||
\(394\) | −2.19567 | −0.110616 | ||||||||
\(395\) | −3.10129 | −0.156043 | ||||||||
\(396\) | −4.95646 | −0.249071 | ||||||||
\(397\) | −0.198062 | −0.00994046 | −0.00497023 | − | 0.999988i | \(-0.501582\pi\) | ||||
−0.00497023 | + | 0.999988i | \(0.501582\pi\) | |||||||
\(398\) | −15.2228 | −0.763051 | ||||||||
\(399\) | 1.82371 | 0.0912996 | ||||||||
\(400\) | −4.96077 | −0.248039 | ||||||||
\(401\) | 7.22952 | 0.361025 | 0.180513 | − | 0.983573i | \(-0.442224\pi\) | ||||
0.180513 | + | 0.983573i | \(0.442224\pi\) | |||||||
\(402\) | 7.94571 | 0.396296 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.32975 | 0.0661575 | ||||||||
\(405\) | −2.21014 | −0.109823 | ||||||||
\(406\) | 3.68233 | 0.182751 | ||||||||
\(407\) | −44.5483 | −2.20817 | ||||||||
\(408\) | −5.46011 | −0.270316 | ||||||||
\(409\) | 10.5483 | 0.521578 | 0.260789 | − | 0.965396i | \(-0.416017\pi\) | ||||
0.260789 | + | 0.965396i | \(0.416017\pi\) | |||||||
\(410\) | −1.32006 | −0.0651931 | ||||||||
\(411\) | 35.4577 | 1.74900 | ||||||||
\(412\) | −0.670251 | −0.0330209 | ||||||||
\(413\) | −6.41550 | −0.315686 | ||||||||
\(414\) | −10.1293 | −0.497828 | ||||||||
\(415\) | −2.60627 | −0.127937 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.5362 | 1.44639 | ||||||||
\(418\) | 4.13706 | 0.202350 | ||||||||
\(419\) | −9.92154 | −0.484699 | −0.242350 | − | 0.970189i | \(-0.577918\pi\) | ||||
−0.242350 | + | 0.970189i | \(0.577918\pi\) | |||||||
\(420\) | −0.361208 | −0.0176251 | ||||||||
\(421\) | −25.4577 | −1.24073 | −0.620367 | − | 0.784312i | \(-0.713016\pi\) | ||||
−0.620367 | + | 0.784312i | \(0.713016\pi\) | |||||||
\(422\) | −17.2905 | −0.841689 | ||||||||
\(423\) | 8.84654 | 0.430134 | ||||||||
\(424\) | −3.40581 | −0.165401 | ||||||||
\(425\) | 13.2198 | 0.641256 | ||||||||
\(426\) | 12.4494 | 0.603173 | ||||||||
\(427\) | 10.6112 | 0.513511 | ||||||||
\(428\) | 13.1075 | 0.633576 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.22713 | 0.0591774 | ||||||||
\(431\) | −1.26145 | −0.0607621 | −0.0303811 | − | 0.999538i | \(-0.509672\pi\) | ||||
−0.0303811 | + | 0.999538i | \(0.509672\pi\) | |||||||
\(432\) | −3.69202 | −0.177632 | ||||||||
\(433\) | −5.78017 | −0.277777 | −0.138889 | − | 0.990308i | \(-0.544353\pi\) | ||||
−0.138889 | + | 0.990308i | \(0.544353\pi\) | |||||||
\(434\) | −0.968541 | −0.0464915 | ||||||||
\(435\) | −1.67887 | −0.0804959 | ||||||||
\(436\) | −15.0858 | −0.722477 | ||||||||
\(437\) | 8.45473 | 0.404445 | ||||||||
\(438\) | −10.5810 | −0.505582 | ||||||||
\(439\) | 15.6668 | 0.747735 | 0.373868 | − | 0.927482i | \(-0.378031\pi\) | ||||
0.373868 | + | 0.927482i | \(0.378031\pi\) | |||||||
\(440\) | −0.819396 | −0.0390632 | ||||||||
\(441\) | −7.43727 | −0.354156 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.89008 | 0.232335 | 0.116167 | − | 0.993230i | \(-0.462939\pi\) | ||||
0.116167 | + | 0.993230i | \(0.462939\pi\) | |||||||
\(444\) | 22.0629 | 1.04706 | ||||||||
\(445\) | −0.897853 | −0.0425623 | ||||||||
\(446\) | 19.8726 | 0.940996 | ||||||||
\(447\) | 11.0425 | 0.522291 | ||||||||
\(448\) | −0.890084 | −0.0420525 | ||||||||
\(449\) | 0.347207 | 0.0163857 | 0.00819286 | − | 0.999966i | \(-0.497392\pi\) | ||||
0.00819286 | + | 0.999966i | \(0.497392\pi\) | |||||||
\(450\) | −5.94331 | −0.280170 | ||||||||
\(451\) | 27.5730 | 1.29836 | ||||||||
\(452\) | 19.5254 | 0.918398 | ||||||||
\(453\) | −32.6528 | −1.53416 | ||||||||
\(454\) | −4.76809 | −0.223777 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.04892 | −0.0959493 | ||||||||
\(457\) | 31.7754 | 1.48639 | 0.743195 | − | 0.669075i | \(-0.233310\pi\) | ||||
0.743195 | + | 0.669075i | \(0.233310\pi\) | |||||||
\(458\) | −23.8931 | −1.11645 | ||||||||
\(459\) | 9.83877 | 0.459235 | ||||||||
\(460\) | −1.67456 | −0.0780769 | ||||||||
\(461\) | −28.2543 | −1.31593 | −0.657966 | − | 0.753047i | \(-0.728583\pi\) | ||||
−0.657966 | + | 0.753047i | \(0.728583\pi\) | |||||||
\(462\) | 7.54480 | 0.351016 | ||||||||
\(463\) | −2.42029 | −0.112480 | −0.0562402 | − | 0.998417i | \(-0.517911\pi\) | ||||
−0.0562402 | + | 0.998417i | \(0.517911\pi\) | |||||||
\(464\) | −4.13706 | −0.192058 | ||||||||
\(465\) | 0.441584 | 0.0204780 | ||||||||
\(466\) | 11.7778 | 0.545595 | ||||||||
\(467\) | −10.5724 | −0.489233 | −0.244617 | − | 0.969620i | \(-0.578662\pi\) | ||||
−0.244617 | + | 0.969620i | \(0.578662\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.45175 | −0.159387 | ||||||||
\(470\) | 1.46250 | 0.0674601 | ||||||||
\(471\) | −21.6125 | −0.995851 | ||||||||
\(472\) | 7.20775 | 0.331764 | ||||||||
\(473\) | −25.6319 | −1.17855 | ||||||||
\(474\) | −32.0823 | −1.47359 | ||||||||
\(475\) | 4.96077 | 0.227616 | ||||||||
\(476\) | 2.37196 | 0.108719 | ||||||||
\(477\) | −4.08038 | −0.186828 | ||||||||
\(478\) | −12.2983 | −0.562511 | ||||||||
\(479\) | −29.0616 | −1.32786 | −0.663929 | − | 0.747796i | \(-0.731112\pi\) | ||||
−0.663929 | + | 0.747796i | \(0.731112\pi\) | |||||||
\(480\) | 0.405813 | 0.0185228 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.613564 | 0.0279471 | ||||||||
\(483\) | 15.4190 | 0.701587 | ||||||||
\(484\) | 6.11529 | 0.277968 | ||||||||
\(485\) | 1.62027 | 0.0735726 | ||||||||
\(486\) | −11.7875 | −0.534690 | ||||||||
\(487\) | 11.9366 | 0.540899 | 0.270450 | − | 0.962734i | \(-0.412828\pi\) | ||||
0.270450 | + | 0.962734i | \(0.412828\pi\) | |||||||
\(488\) | −11.9215 | −0.539663 | ||||||||
\(489\) | −11.4709 | −0.518730 | ||||||||
\(490\) | −1.22952 | −0.0555441 | ||||||||
\(491\) | −29.3163 | −1.32303 | −0.661514 | − | 0.749933i | \(-0.730086\pi\) | ||||
−0.661514 | + | 0.749933i | \(0.730086\pi\) | |||||||
\(492\) | −13.6558 | −0.615650 | ||||||||
\(493\) | 11.0248 | 0.496530 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.981688 | −0.0441236 | ||||||||
\(496\) | 1.08815 | 0.0488592 | ||||||||
\(497\) | −5.40821 | −0.242591 | ||||||||
\(498\) | −26.9614 | −1.20817 | ||||||||
\(499\) | 1.30499 | 0.0584196 | 0.0292098 | − | 0.999573i | \(-0.490701\pi\) | ||||
0.0292098 | + | 0.999573i | \(0.490701\pi\) | |||||||
\(500\) | −1.97285 | −0.0882287 | ||||||||
\(501\) | 28.3744 | 1.26767 | ||||||||
\(502\) | −21.1836 | −0.945470 | ||||||||
\(503\) | −6.13275 | −0.273446 | −0.136723 | − | 0.990609i | \(-0.543657\pi\) | ||||
−0.136723 | + | 0.990609i | \(0.543657\pi\) | |||||||
\(504\) | −1.06638 | −0.0475002 | ||||||||
\(505\) | 0.263373 | 0.0117199 | ||||||||
\(506\) | 34.9778 | 1.55495 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.2078 | −0.585999 | ||||||||
\(509\) | −22.6219 | −1.00270 | −0.501350 | − | 0.865245i | \(-0.667163\pi\) | ||||
−0.501350 | + | 0.865245i | \(0.667163\pi\) | |||||||
\(510\) | −1.08144 | −0.0478870 | ||||||||
\(511\) | 4.59658 | 0.203341 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.69202 | 0.163007 | ||||||||
\(514\) | 15.1535 | 0.668390 | ||||||||
\(515\) | −0.132751 | −0.00584973 | ||||||||
\(516\) | 12.6944 | 0.558840 | ||||||||
\(517\) | −30.5483 | −1.34351 | ||||||||
\(518\) | −9.58450 | −0.421119 | ||||||||
\(519\) | 31.6606 | 1.38974 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0858 | −0.485676 | −0.242838 | − | 0.970067i | \(-0.578078\pi\) | ||||
−0.242838 | + | 0.970067i | \(0.578078\pi\) | |||||||
\(522\) | −4.95646 | −0.216938 | ||||||||
\(523\) | −35.0834 | −1.53409 | −0.767044 | − | 0.641594i | \(-0.778273\pi\) | ||||
−0.767044 | + | 0.641594i | \(0.778273\pi\) | |||||||
\(524\) | 14.9879 | 0.654750 | ||||||||
\(525\) | 9.04700 | 0.394843 | ||||||||
\(526\) | −9.45712 | −0.412350 | ||||||||
\(527\) | −2.89977 | −0.126316 | ||||||||
\(528\) | −8.47650 | −0.368892 | ||||||||
\(529\) | 48.4825 | 2.10793 | ||||||||
\(530\) | −0.674563 | −0.0293011 | ||||||||
\(531\) | 8.63533 | 0.374742 | ||||||||
\(532\) | 0.890084 | 0.0385900 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.28813 | −0.401937 | ||||||||
\(535\) | 2.59611 | 0.112239 | ||||||||
\(536\) | 3.87800 | 0.167504 | ||||||||
\(537\) | −26.0446 | −1.12391 | ||||||||
\(538\) | −13.4034 | −0.577862 | ||||||||
\(539\) | 25.6819 | 1.10620 | ||||||||
\(540\) | −0.731250 | −0.0314680 | ||||||||
\(541\) | 17.8261 | 0.766404 | 0.383202 | − | 0.923665i | \(-0.374821\pi\) | ||||
0.383202 | + | 0.923665i | \(0.374821\pi\) | |||||||
\(542\) | −24.7138 | −1.06155 | ||||||||
\(543\) | 27.6122 | 1.18495 | ||||||||
\(544\) | −2.66487 | −0.114256 | ||||||||
\(545\) | −2.98792 | −0.127988 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.1075 | −0.560437 | −0.280219 | − | 0.959936i | \(-0.590407\pi\) | ||||
−0.280219 | + | 0.959936i | \(0.590407\pi\) | |||||||
\(548\) | 17.3056 | 0.739258 | ||||||||
\(549\) | −14.2828 | −0.609573 | ||||||||
\(550\) | 20.5230 | 0.875105 | ||||||||
\(551\) | 4.13706 | 0.176245 | ||||||||
\(552\) | −17.3230 | −0.737318 | ||||||||
\(553\) | 13.9371 | 0.592665 | ||||||||
\(554\) | 8.78746 | 0.373344 | ||||||||
\(555\) | 4.36983 | 0.185489 | ||||||||
\(556\) | 14.4155 | 0.611353 | ||||||||
\(557\) | −35.4534 | −1.50221 | −0.751104 | − | 0.660183i | \(-0.770479\pi\) | ||||
−0.751104 | + | 0.660183i | \(0.770479\pi\) | |||||||
\(558\) | 1.30367 | 0.0551886 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.176292 | −0.00744970 | ||||||||
\(561\) | 22.5888 | 0.953700 | ||||||||
\(562\) | −17.7168 | −0.747337 | ||||||||
\(563\) | 3.14914 | 0.132721 | 0.0663603 | − | 0.997796i | \(-0.478861\pi\) | ||||
0.0663603 | + | 0.997796i | \(0.478861\pi\) | |||||||
\(564\) | 15.1293 | 0.637058 | ||||||||
\(565\) | 3.86725 | 0.162696 | ||||||||
\(566\) | −9.96508 | −0.418864 | ||||||||
\(567\) | 9.93230 | 0.417117 | ||||||||
\(568\) | 6.07606 | 0.254946 | ||||||||
\(569\) | 20.3827 | 0.854488 | 0.427244 | − | 0.904136i | \(-0.359485\pi\) | ||||
0.427244 | + | 0.904136i | \(0.359485\pi\) | |||||||
\(570\) | −0.405813 | −0.0169976 | ||||||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.9372 | 1.58485 | ||||||||
\(574\) | 5.93230 | 0.247609 | ||||||||
\(575\) | 41.9420 | 1.74910 | ||||||||
\(576\) | 1.19806 | 0.0499193 | ||||||||
\(577\) | −30.6219 | −1.27481 | −0.637404 | − | 0.770530i | \(-0.719992\pi\) | ||||
−0.637404 | + | 0.770530i | \(0.719992\pi\) | |||||||
\(578\) | −9.89844 | −0.411721 | ||||||||
\(579\) | −7.28382 | −0.302705 | ||||||||
\(580\) | −0.819396 | −0.0340236 | ||||||||
\(581\) | 11.7125 | 0.485915 | ||||||||
\(582\) | 16.7614 | 0.694782 | ||||||||
\(583\) | 14.0901 | 0.583551 | ||||||||
\(584\) | −5.16421 | −0.213697 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.1099 | 0.458946 | ||||||||
\(587\) | 3.40342 | 0.140474 | 0.0702371 | − | 0.997530i | \(-0.477624\pi\) | ||||
0.0702371 | + | 0.997530i | \(0.477624\pi\) | |||||||
\(588\) | −12.7192 | −0.524530 | ||||||||
\(589\) | −1.08815 | −0.0448363 | ||||||||
\(590\) | 1.42758 | 0.0587727 | ||||||||
\(591\) | −4.49875 | −0.185054 | ||||||||
\(592\) | 10.7681 | 0.442566 | ||||||||
\(593\) | −4.31767 | −0.177305 | −0.0886527 | − | 0.996063i | \(-0.528256\pi\) | ||||
−0.0886527 | + | 0.996063i | \(0.528256\pi\) | |||||||
\(594\) | 15.2741 | 0.626705 | ||||||||
\(595\) | 0.469796 | 0.0192598 | ||||||||
\(596\) | 5.38942 | 0.220759 | ||||||||
\(597\) | −31.1903 | −1.27653 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0616 | −0.533682 | −0.266841 | − | 0.963741i | \(-0.585980\pi\) | ||||
−0.266841 | + | 0.963741i | \(0.585980\pi\) | |||||||
\(600\) | −10.1642 | −0.414952 | ||||||||
\(601\) | −42.7284 | −1.74293 | −0.871464 | − | 0.490460i | \(-0.836829\pi\) | ||||
−0.871464 | + | 0.490460i | \(0.836829\pi\) | |||||||
\(602\) | −5.51466 | −0.224761 | ||||||||
\(603\) | 4.64609 | 0.189203 | ||||||||
\(604\) | −15.9366 | −0.648451 | ||||||||
\(605\) | 1.21121 | 0.0492426 | ||||||||
\(606\) | 2.72455 | 0.110677 | ||||||||
\(607\) | −43.9168 | −1.78253 | −0.891263 | − | 0.453487i | \(-0.850180\pi\) | ||||
−0.891263 | + | 0.453487i | \(0.850180\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 7.54480 | 0.305731 | ||||||||
\(610\) | −2.36121 | −0.0956025 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.19269 | −0.129057 | ||||||||
\(613\) | −1.42519 | −0.0575629 | −0.0287815 | − | 0.999586i | \(-0.509163\pi\) | ||||
−0.0287815 | + | 0.999586i | \(0.509163\pi\) | |||||||
\(614\) | 9.83446 | 0.396887 | ||||||||
\(615\) | −2.70469 | −0.109064 | ||||||||
\(616\) | 3.68233 | 0.148365 | ||||||||
\(617\) | 12.4832 | 0.502555 | 0.251277 | − | 0.967915i | \(-0.419149\pi\) | ||||
0.251277 | + | 0.967915i | \(0.419149\pi\) | |||||||
\(618\) | −1.37329 | −0.0552418 | ||||||||
\(619\) | 36.1148 | 1.45158 | 0.725789 | − | 0.687918i | \(-0.241475\pi\) | ||||
0.725789 | + | 0.687918i | \(0.241475\pi\) | |||||||
\(620\) | 0.215521 | 0.00865552 | ||||||||
\(621\) | 31.2150 | 1.25262 | ||||||||
\(622\) | 11.8726 | 0.476049 | ||||||||
\(623\) | 4.03492 | 0.161656 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4131 | 0.976524 | ||||||||
\(626\) | −8.81402 | −0.352279 | ||||||||
\(627\) | 8.47650 | 0.338519 | ||||||||
\(628\) | −10.5483 | −0.420921 | ||||||||
\(629\) | −28.6956 | −1.14417 | ||||||||
\(630\) | −0.211209 | −0.00841476 | ||||||||
\(631\) | −2.85517 | −0.113662 | −0.0568312 | − | 0.998384i | \(-0.518100\pi\) | ||||
−0.0568312 | + | 0.998384i | \(0.518100\pi\) | |||||||
\(632\) | −15.6582 | −0.622849 | ||||||||
\(633\) | −35.4268 | −1.40809 | ||||||||
\(634\) | −12.7138 | −0.504929 | ||||||||
\(635\) | −2.61596 | −0.103811 | ||||||||
\(636\) | −6.97823 | −0.276705 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 17.1153 | 0.677601 | ||||||||
\(639\) | 7.27950 | 0.287973 | ||||||||
\(640\) | 0.198062 | 0.00782910 | ||||||||
\(641\) | −19.0508 | −0.752463 | −0.376231 | − | 0.926526i | \(-0.622780\pi\) | ||||
−0.376231 | + | 0.926526i | \(0.622780\pi\) | |||||||
\(642\) | 26.8562 | 1.05993 | ||||||||
\(643\) | −50.0877 | −1.97526 | −0.987632 | − | 0.156787i | \(-0.949886\pi\) | ||||
−0.987632 | + | 0.156787i | \(0.949886\pi\) | |||||||
\(644\) | 7.52542 | 0.296543 | ||||||||
\(645\) | 2.51428 | 0.0989999 | ||||||||
\(646\) | 2.66487 | 0.104848 | ||||||||
\(647\) | 4.00836 | 0.157585 | 0.0787925 | − | 0.996891i | \(-0.474894\pi\) | ||||
0.0787925 | + | 0.996891i | \(0.474894\pi\) | |||||||
\(648\) | −11.1588 | −0.438360 | ||||||||
\(649\) | −29.8189 | −1.17050 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.98446 | −0.0777771 | ||||||||
\(652\) | −5.59850 | −0.219254 | ||||||||
\(653\) | 14.8116 | 0.579624 | 0.289812 | − | 0.957084i | \(-0.406407\pi\) | ||||
0.289812 | + | 0.957084i | \(0.406407\pi\) | |||||||
\(654\) | −30.9095 | −1.20866 | ||||||||
\(655\) | 2.96854 | 0.115990 | ||||||||
\(656\) | −6.66487 | −0.260220 | ||||||||
\(657\) | −6.18705 | −0.241380 | ||||||||
\(658\) | −6.57242 | −0.256219 | ||||||||
\(659\) | 13.0019 | 0.506483 | 0.253241 | − | 0.967403i | \(-0.418503\pi\) | ||||
0.253241 | + | 0.967403i | \(0.418503\pi\) | |||||||
\(660\) | −1.67887 | −0.0653501 | ||||||||
\(661\) | 2.18705 | 0.0850662 | 0.0425331 | − | 0.999095i | \(-0.486457\pi\) | ||||
0.0425331 | + | 0.999095i | \(0.486457\pi\) | |||||||
\(662\) | −18.1715 | −0.706256 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.1588 | −0.510662 | ||||||||
\(665\) | 0.176292 | 0.00683631 | ||||||||
\(666\) | 12.9008 | 0.499897 | ||||||||
\(667\) | 34.9778 | 1.35434 | ||||||||
\(668\) | 13.8485 | 0.535813 | ||||||||
\(669\) | 40.7174 | 1.57422 | ||||||||
\(670\) | 0.768086 | 0.0296737 | ||||||||
\(671\) | 49.3202 | 1.90398 | ||||||||
\(672\) | −1.82371 | −0.0703511 | ||||||||
\(673\) | −40.6762 | −1.56795 | −0.783977 | − | 0.620790i | \(-0.786812\pi\) | ||||
−0.783977 | + | 0.620790i | \(0.786812\pi\) | |||||||
\(674\) | 13.9323 | 0.536652 | ||||||||
\(675\) | 18.3153 | 0.704955 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.47757 | −0.0567875 | −0.0283937 | − | 0.999597i | \(-0.509039\pi\) | ||||
−0.0283937 | + | 0.999597i | \(0.509039\pi\) | |||||||
\(678\) | 40.0060 | 1.53642 | ||||||||
\(679\) | −7.28142 | −0.279435 | ||||||||
\(680\) | −0.527811 | −0.0202406 | ||||||||
\(681\) | −9.76941 | −0.374365 | ||||||||
\(682\) | −4.50173 | −0.172380 | ||||||||
\(683\) | −48.2210 | −1.84513 | −0.922563 | − | 0.385847i | \(-0.873909\pi\) | ||||
−0.922563 | + | 0.385847i | \(0.873909\pi\) | |||||||
\(684\) | −1.19806 | −0.0458091 | ||||||||
\(685\) | 3.42758 | 0.130961 | ||||||||
\(686\) | 11.7560 | 0.448846 | ||||||||
\(687\) | −48.9549 | −1.86775 | ||||||||
\(688\) | 6.19567 | 0.236208 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.43104 | −0.130618 | ||||||||
\(691\) | 9.73019 | 0.370154 | 0.185077 | − | 0.982724i | \(-0.440747\pi\) | ||||
0.185077 | + | 0.982724i | \(0.440747\pi\) | |||||||
\(692\) | 15.4523 | 0.587410 | ||||||||
\(693\) | 4.41166 | 0.167585 | ||||||||
\(694\) | −8.02416 | −0.304593 | ||||||||
\(695\) | 2.85517 | 0.108303 | ||||||||
\(696\) | −8.47650 | −0.321301 | ||||||||
\(697\) | 17.7611 | 0.672748 | ||||||||
\(698\) | 10.7192 | 0.405727 | ||||||||
\(699\) | 24.1317 | 0.912744 | ||||||||
\(700\) | 4.41550 | 0.166890 | ||||||||
\(701\) | 33.2030 | 1.25406 | 0.627029 | − | 0.778996i | \(-0.284271\pi\) | ||||
0.627029 | + | 0.778996i | \(0.284271\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.7681 | −0.406126 | ||||||||
\(704\) | −4.13706 | −0.155921 | ||||||||
\(705\) | 2.99654 | 0.112856 | ||||||||
\(706\) | 36.1172 | 1.35929 | ||||||||
\(707\) | −1.18359 | −0.0445134 | ||||||||
\(708\) | 14.7681 | 0.555019 | ||||||||
\(709\) | 12.1715 | 0.457111 | 0.228555 | − | 0.973531i | \(-0.426600\pi\) | ||||
0.228555 | + | 0.973531i | \(0.426600\pi\) | |||||||
\(710\) | 1.20344 | 0.0451643 | ||||||||
\(711\) | −18.7595 | −0.703535 | ||||||||
\(712\) | −4.53319 | −0.169888 | ||||||||
\(713\) | −9.19998 | −0.344542 | ||||||||
\(714\) | 4.85995 | 0.181879 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.7114 | −0.475047 | ||||||||
\(717\) | −25.1982 | −0.941043 | ||||||||
\(718\) | 32.3129 | 1.20591 | ||||||||
\(719\) | −8.43967 | −0.314746 | −0.157373 | − | 0.987539i | \(-0.550303\pi\) | ||||
−0.157373 | + | 0.987539i | \(0.550303\pi\) | |||||||
\(720\) | 0.237291 | 0.00884331 | ||||||||
\(721\) | 0.596580 | 0.0222178 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 1.25714 | 0.0467536 | ||||||||
\(724\) | 13.4765 | 0.500850 | ||||||||
\(725\) | 20.5230 | 0.762206 | ||||||||
\(726\) | 12.5297 | 0.465022 | ||||||||
\(727\) | 16.8498 | 0.624924 | 0.312462 | − | 0.949930i | \(-0.398846\pi\) | ||||
0.312462 | + | 0.949930i | \(0.398846\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.32496 | 0.345369 | ||||||||
\(730\) | −1.02284 | −0.0378568 | ||||||||
\(731\) | −16.5107 | −0.610670 | ||||||||
\(732\) | −24.4263 | −0.902820 | ||||||||
\(733\) | 50.3086 | 1.85819 | 0.929095 | − | 0.369842i | \(-0.120588\pi\) | ||||
0.929095 | + | 0.369842i | \(0.120588\pi\) | |||||||
\(734\) | 5.24027 | 0.193422 | ||||||||
\(735\) | −2.51919 | −0.0929216 | ||||||||
\(736\) | −8.45473 | −0.311646 | ||||||||
\(737\) | −16.0435 | −0.590971 | ||||||||
\(738\) | −7.98493 | −0.293930 | ||||||||
\(739\) | −9.67324 | −0.355836 | −0.177918 | − | 0.984045i | \(-0.556936\pi\) | ||||
−0.177918 | + | 0.984045i | \(0.556936\pi\) | |||||||
\(740\) | 2.13275 | 0.0784015 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.03146 | 0.111288 | ||||||||
\(743\) | 41.6364 | 1.52749 | 0.763746 | − | 0.645517i | \(-0.223358\pi\) | ||||
0.763746 | + | 0.645517i | \(0.223358\pi\) | |||||||
\(744\) | 2.22952 | 0.0817382 | ||||||||
\(745\) | 1.06744 | 0.0391080 | ||||||||
\(746\) | −14.6213 | −0.535325 | ||||||||
\(747\) | −15.7651 | −0.576815 | ||||||||
\(748\) | 11.0248 | 0.403105 | ||||||||
\(749\) | −11.6668 | −0.426295 | ||||||||
\(750\) | −4.04221 | −0.147601 | ||||||||
\(751\) | −43.1680 | −1.57522 | −0.787612 | − | 0.616171i | \(-0.788683\pi\) | ||||
−0.787612 | + | 0.616171i | \(0.788683\pi\) | |||||||
\(752\) | 7.38404 | 0.269268 | ||||||||
\(753\) | −43.4034 | −1.58171 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.15644 | −0.114875 | ||||||||
\(756\) | 3.28621 | 0.119518 | ||||||||
\(757\) | 23.1535 | 0.841527 | 0.420763 | − | 0.907170i | \(-0.361762\pi\) | ||||
0.420763 | + | 0.907170i | \(0.361762\pi\) | |||||||
\(758\) | −14.8116 | −0.537982 | ||||||||
\(759\) | 71.6665 | 2.60133 | ||||||||
\(760\) | −0.198062 | −0.00718447 | ||||||||
\(761\) | −22.2258 | −0.805685 | −0.402842 | − | 0.915269i | \(-0.631978\pi\) | ||||
−0.402842 | + | 0.915269i | \(0.631978\pi\) | |||||||
\(762\) | −27.0616 | −0.980338 | ||||||||
\(763\) | 13.4276 | 0.486111 | ||||||||
\(764\) | 18.5157 | 0.669876 | ||||||||
\(765\) | −0.632351 | −0.0228627 | ||||||||
\(766\) | 12.2524 | 0.442696 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.04892 | 0.0739339 | ||||||||
\(769\) | −14.8552 | −0.535691 | −0.267846 | − | 0.963462i | \(-0.586312\pi\) | ||||
−0.267846 | + | 0.963462i | \(0.586312\pi\) | |||||||
\(770\) | 0.729331 | 0.0262833 | ||||||||
\(771\) | 31.0482 | 1.11817 | ||||||||
\(772\) | −3.55496 | −0.127946 | ||||||||
\(773\) | 0.537500 | 0.0193325 | 0.00966626 | − | 0.999953i | \(-0.496923\pi\) | ||||
0.00966626 | + | 0.999953i | \(0.496923\pi\) | |||||||
\(774\) | 7.42280 | 0.266807 | ||||||||
\(775\) | −5.39804 | −0.193903 | ||||||||
\(776\) | 8.18060 | 0.293667 | ||||||||
\(777\) | −19.6378 | −0.704504 | ||||||||
\(778\) | 33.6969 | 1.20809 | ||||||||
\(779\) | 6.66487 | 0.238794 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.1371 | −0.899475 | ||||||||
\(782\) | 22.5308 | 0.805700 | ||||||||
\(783\) | 15.2741 | 0.545853 | ||||||||
\(784\) | −6.20775 | −0.221705 | ||||||||
\(785\) | −2.08921 | −0.0745671 | ||||||||
\(786\) | 30.7090 | 1.09535 | ||||||||
\(787\) | −36.1124 | −1.28727 | −0.643634 | − | 0.765333i | \(-0.722574\pi\) | ||||
−0.643634 | + | 0.765333i | \(0.722574\pi\) | |||||||
\(788\) | −2.19567 | −0.0782175 | ||||||||
\(789\) | −19.3769 | −0.689835 | ||||||||
\(790\) | −3.10129 | −0.110339 | ||||||||
\(791\) | −17.3793 | −0.617935 | ||||||||
\(792\) | −4.95646 | −0.176120 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.198062 | −0.00702897 | ||||||||
\(795\) | −1.38212 | −0.0490189 | ||||||||
\(796\) | −15.2228 | −0.539558 | ||||||||
\(797\) | 20.4413 | 0.724069 | 0.362034 | − | 0.932165i | \(-0.382082\pi\) | ||||
0.362034 | + | 0.932165i | \(0.382082\pi\) | |||||||
\(798\) | 1.82371 | 0.0645586 | ||||||||
\(799\) | −19.6775 | −0.696142 | ||||||||
\(800\) | −4.96077 | −0.175390 | ||||||||
\(801\) | −5.43104 | −0.191896 | ||||||||
\(802\) | 7.22952 | 0.255283 | ||||||||
\(803\) | 21.3647 | 0.753943 | ||||||||
\(804\) | 7.94571 | 0.280223 | ||||||||
\(805\) | 1.49050 | 0.0525333 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.4625 | −0.966726 | ||||||||
\(808\) | 1.32975 | 0.0467804 | ||||||||
\(809\) | 35.5271 | 1.24907 | 0.624533 | − | 0.780999i | \(-0.285289\pi\) | ||||
0.624533 | + | 0.780999i | \(0.285289\pi\) | |||||||
\(810\) | −2.21014 | −0.0776565 | ||||||||
\(811\) | 12.9250 | 0.453858 | 0.226929 | − | 0.973911i | \(-0.427131\pi\) | ||||
0.226929 | + | 0.973911i | \(0.427131\pi\) | |||||||
\(812\) | 3.68233 | 0.129225 | ||||||||
\(813\) | −50.6365 | −1.77590 | ||||||||
\(814\) | −44.5483 | −1.56142 | ||||||||
\(815\) | −1.10885 | −0.0388414 | ||||||||
\(816\) | −5.46011 | −0.191142 | ||||||||
\(817\) | −6.19567 | −0.216759 | ||||||||
\(818\) | 10.5483 | 0.368811 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.32006 | −0.0460985 | ||||||||
\(821\) | 41.4905 | 1.44803 | 0.724014 | − | 0.689785i | \(-0.242295\pi\) | ||||
0.724014 | + | 0.689785i | \(0.242295\pi\) | |||||||
\(822\) | 35.4577 | 1.23673 | ||||||||
\(823\) | 2.29185 | 0.0798888 | 0.0399444 | − | 0.999202i | \(-0.487282\pi\) | ||||
0.0399444 | + | 0.999202i | \(0.487282\pi\) | |||||||
\(824\) | −0.670251 | −0.0233493 | ||||||||
\(825\) | 42.0500 | 1.46399 | ||||||||
\(826\) | −6.41550 | −0.223224 | ||||||||
\(827\) | −28.0194 | −0.974329 | −0.487165 | − | 0.873310i | \(-0.661969\pi\) | ||||
−0.487165 | + | 0.873310i | \(0.661969\pi\) | |||||||
\(828\) | −10.1293 | −0.352017 | ||||||||
\(829\) | −20.1497 | −0.699829 | −0.349915 | − | 0.936782i | \(-0.613789\pi\) | ||||
−0.349915 | + | 0.936782i | \(0.613789\pi\) | |||||||
\(830\) | −2.60627 | −0.0904649 | ||||||||
\(831\) | 18.0048 | 0.624579 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.5429 | 0.573177 | ||||||||
\(834\) | 29.5362 | 1.02275 | ||||||||
\(835\) | 2.74286 | 0.0949205 | ||||||||
\(836\) | 4.13706 | 0.143083 | ||||||||
\(837\) | −4.01746 | −0.138864 | ||||||||
\(838\) | −9.92154 | −0.342734 | ||||||||
\(839\) | 46.7348 | 1.61347 | 0.806733 | − | 0.590917i | \(-0.201234\pi\) | ||||
0.806733 | + | 0.590917i | \(0.201234\pi\) | |||||||
\(840\) | −0.361208 | −0.0124629 | ||||||||
\(841\) | −11.8847 | −0.409817 | ||||||||
\(842\) | −25.4577 | −0.877331 | ||||||||
\(843\) | −36.3002 | −1.25025 | ||||||||
\(844\) | −17.2905 | −0.595164 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.84654 | 0.304150 | ||||||||
\(847\) | −5.44312 | −0.187028 | ||||||||
\(848\) | −3.40581 | −0.116956 | ||||||||
\(849\) | −20.4176 | −0.700731 | ||||||||
\(850\) | 13.2198 | 0.453437 | ||||||||
\(851\) | −91.0413 | −3.12085 | ||||||||
\(852\) | 12.4494 | 0.426508 | ||||||||
\(853\) | 9.02608 | 0.309047 | 0.154524 | − | 0.987989i | \(-0.450616\pi\) | ||||
0.154524 | + | 0.987989i | \(0.450616\pi\) | |||||||
\(854\) | 10.6112 | 0.363107 | ||||||||
\(855\) | −0.237291 | −0.00811518 | ||||||||
\(856\) | 13.1075 | 0.448006 | ||||||||
\(857\) | −14.0194 | −0.478893 | −0.239446 | − | 0.970910i | \(-0.576966\pi\) | ||||
−0.239446 | + | 0.970910i | \(0.576966\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.1500 | −1.09694 | −0.548472 | − | 0.836169i | \(-0.684790\pi\) | ||||
−0.548472 | + | 0.836169i | \(0.684790\pi\) | |||||||
\(860\) | 1.22713 | 0.0418447 | ||||||||
\(861\) | 12.1548 | 0.414234 | ||||||||
\(862\) | −1.26145 | −0.0429653 | ||||||||
\(863\) | 31.5357 | 1.07349 | 0.536744 | − | 0.843745i | \(-0.319654\pi\) | ||||
0.536744 | + | 0.843745i | \(0.319654\pi\) | |||||||
\(864\) | −3.69202 | −0.125605 | ||||||||
\(865\) | 3.06052 | 0.104061 | ||||||||
\(866\) | −5.78017 | −0.196418 | ||||||||
\(867\) | −20.2811 | −0.688782 | ||||||||
\(868\) | −0.968541 | −0.0328744 | ||||||||
\(869\) | 64.7788 | 2.19747 | ||||||||
\(870\) | −1.67887 | −0.0569192 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15.0858 | −0.510868 | ||||||||
\(873\) | 9.80087 | 0.331709 | ||||||||
\(874\) | 8.45473 | 0.285986 | ||||||||
\(875\) | 1.75600 | 0.0593638 | ||||||||
\(876\) | −10.5810 | −0.357500 | ||||||||
\(877\) | 39.3551 | 1.32893 | 0.664464 | − | 0.747321i | \(-0.268660\pi\) | ||||
0.664464 | + | 0.747321i | \(0.268660\pi\) | |||||||
\(878\) | 15.6668 | 0.528729 | ||||||||
\(879\) | 22.7633 | 0.767787 | ||||||||
\(880\) | −0.819396 | −0.0276218 | ||||||||
\(881\) | −39.9734 | −1.34674 | −0.673370 | − | 0.739306i | \(-0.735154\pi\) | ||||
−0.673370 | + | 0.739306i | \(0.735154\pi\) | |||||||
\(882\) | −7.43727 | −0.250426 | ||||||||
\(883\) | 30.1366 | 1.01418 | 0.507088 | − | 0.861894i | \(-0.330722\pi\) | ||||
0.507088 | + | 0.861894i | \(0.330722\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.92500 | 0.0983228 | ||||||||
\(886\) | 4.89008 | 0.164286 | ||||||||
\(887\) | −34.0823 | −1.14437 | −0.572186 | − | 0.820124i | \(-0.693904\pi\) | ||||
−0.572186 | + | 0.820124i | \(0.693904\pi\) | |||||||
\(888\) | 22.0629 | 0.740383 | ||||||||
\(889\) | 11.7560 | 0.394284 | ||||||||
\(890\) | −0.897853 | −0.0300961 | ||||||||
\(891\) | 46.1648 | 1.54658 | ||||||||
\(892\) | 19.8726 | 0.665385 | ||||||||
\(893\) | −7.38404 | −0.247098 | ||||||||
\(894\) | 11.0425 | 0.369316 | ||||||||
\(895\) | −2.51765 | −0.0841557 | ||||||||
\(896\) | −0.890084 | −0.0297356 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.347207 | 0.0115865 | ||||||||
\(899\) | −4.50173 | −0.150141 | ||||||||
\(900\) | −5.94331 | −0.198110 | ||||||||
\(901\) | 9.07606 | 0.302368 | ||||||||
\(902\) | 27.5730 | 0.918081 | ||||||||
\(903\) | −11.2991 | −0.376010 | ||||||||
\(904\) | 19.5254 | 0.649406 | ||||||||
\(905\) | 2.66919 | 0.0887268 | ||||||||
\(906\) | −32.6528 | −1.08482 | ||||||||
\(907\) | 35.2403 | 1.17013 | 0.585067 | − | 0.810985i | \(-0.301068\pi\) | ||||
0.585067 | + | 0.810985i | \(0.301068\pi\) | |||||||
\(908\) | −4.76809 | −0.158234 | ||||||||
\(909\) | 1.59312 | 0.0528405 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.8237 | 0.789315 | 0.394657 | − | 0.918828i | \(-0.370863\pi\) | ||||
0.394657 | + | 0.918828i | \(0.370863\pi\) | |||||||
\(912\) | −2.04892 | −0.0678464 | ||||||||
\(913\) | 54.4389 | 1.80167 | ||||||||
\(914\) | 31.7754 | 1.05104 | ||||||||
\(915\) | −4.83792 | −0.159937 | ||||||||
\(916\) | −23.8931 | −0.789449 | ||||||||
\(917\) | −13.3405 | −0.440542 | ||||||||
\(918\) | 9.83877 | 0.324728 | ||||||||
\(919\) | −19.1675 | −0.632276 | −0.316138 | − | 0.948713i | \(-0.602386\pi\) | ||||
−0.316138 | + | 0.948713i | \(0.602386\pi\) | |||||||
\(920\) | −1.67456 | −0.0552087 | ||||||||
\(921\) | 20.1500 | 0.663965 | ||||||||
\(922\) | −28.2543 | −0.930505 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 7.54480 | 0.248206 | ||||||||
\(925\) | −53.4180 | −1.75637 | ||||||||
\(926\) | −2.42029 | −0.0795356 | ||||||||
\(927\) | −0.803003 | −0.0263741 | ||||||||
\(928\) | −4.13706 | −0.135806 | ||||||||
\(929\) | 59.9120 | 1.96565 | 0.982824 | − | 0.184545i | \(-0.0590812\pi\) | ||||
0.982824 | + | 0.184545i | \(0.0590812\pi\) | |||||||
\(930\) | 0.441584 | 0.0144801 | ||||||||
\(931\) | 6.20775 | 0.203451 | ||||||||
\(932\) | 11.7778 | 0.385794 | ||||||||
\(933\) | 24.3260 | 0.796398 | ||||||||
\(934\) | −10.5724 | −0.345940 | ||||||||
\(935\) | 2.18359 | 0.0714110 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.9057 | −1.49968 | −0.749838 | − | 0.661622i | \(-0.769868\pi\) | ||||
−0.749838 | + | 0.661622i | \(0.769868\pi\) | |||||||
\(938\) | −3.45175 | −0.112704 | ||||||||
\(939\) | −18.0592 | −0.589340 | ||||||||
\(940\) | 1.46250 | 0.0477015 | ||||||||
\(941\) | −16.8009 | −0.547693 | −0.273846 | − | 0.961773i | \(-0.588296\pi\) | ||||
−0.273846 | + | 0.961773i | \(0.588296\pi\) | |||||||
\(942\) | −21.6125 | −0.704173 | ||||||||
\(943\) | 56.3497 | 1.83500 | ||||||||
\(944\) | 7.20775 | 0.234592 | ||||||||
\(945\) | 0.650874 | 0.0211729 | ||||||||
\(946\) | −25.6319 | −0.833364 | ||||||||
\(947\) | 8.02774 | 0.260866 | 0.130433 | − | 0.991457i | \(-0.458363\pi\) | ||||
0.130433 | + | 0.991457i | \(0.458363\pi\) | |||||||
\(948\) | −32.0823 | −1.04198 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.96077 | 0.160949 | ||||||||
\(951\) | −26.0495 | −0.844713 | ||||||||
\(952\) | 2.37196 | 0.0768757 | ||||||||
\(953\) | 23.1353 | 0.749425 | 0.374712 | − | 0.927141i | \(-0.377741\pi\) | ||||
0.374712 | + | 0.927141i | \(0.377741\pi\) | |||||||
\(954\) | −4.08038 | −0.132107 | ||||||||
\(955\) | 3.66727 | 0.118670 | ||||||||
\(956\) | −12.2983 | −0.397755 | ||||||||
\(957\) | 35.0678 | 1.13358 | ||||||||
\(958\) | −29.0616 | −0.938937 | ||||||||
\(959\) | −15.4034 | −0.497402 | ||||||||
\(960\) | 0.405813 | 0.0130976 | ||||||||
\(961\) | −29.8159 | −0.961804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.7036 | 0.506042 | ||||||||
\(964\) | 0.613564 | 0.0197616 | ||||||||
\(965\) | −0.704103 | −0.0226659 | ||||||||
\(966\) | 15.4190 | 0.496097 | ||||||||
\(967\) | 3.93495 | 0.126540 | 0.0632698 | − | 0.997996i | \(-0.479847\pi\) | ||||
0.0632698 | + | 0.997996i | \(0.479847\pi\) | |||||||
\(968\) | 6.11529 | 0.196553 | ||||||||
\(969\) | 5.46011 | 0.175404 | ||||||||
\(970\) | 1.62027 | 0.0520237 | ||||||||
\(971\) | −9.46011 | −0.303589 | −0.151795 | − | 0.988412i | \(-0.548505\pi\) | ||||
−0.151795 | + | 0.988412i | \(0.548505\pi\) | |||||||
\(972\) | −11.7875 | −0.378083 | ||||||||
\(973\) | −12.8310 | −0.411343 | ||||||||
\(974\) | 11.9366 | 0.382474 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.9215 | −0.381599 | ||||||||
\(977\) | −33.8340 | −1.08245 | −0.541223 | − | 0.840879i | \(-0.682038\pi\) | ||||
−0.541223 | + | 0.840879i | \(0.682038\pi\) | |||||||
\(978\) | −11.4709 | −0.366798 | ||||||||
\(979\) | 18.7541 | 0.599383 | ||||||||
\(980\) | −1.22952 | −0.0392756 | ||||||||
\(981\) | −18.0737 | −0.577048 | ||||||||
\(982\) | −29.3163 | −0.935522 | ||||||||
\(983\) | 13.7614 | 0.438920 | 0.219460 | − | 0.975622i | \(-0.429570\pi\) | ||||
0.219460 | + | 0.975622i | \(0.429570\pi\) | |||||||
\(984\) | −13.6558 | −0.435330 | ||||||||
\(985\) | −0.434879 | −0.0138564 | ||||||||
\(986\) | 11.0248 | 0.351100 | ||||||||
\(987\) | −13.4663 | −0.428638 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −52.3827 | −1.66567 | ||||||||
\(990\) | −0.981688 | −0.0312001 | ||||||||
\(991\) | 24.7525 | 0.786291 | 0.393145 | − | 0.919476i | \(-0.371387\pi\) | ||||
0.393145 | + | 0.919476i | \(0.371387\pi\) | |||||||
\(992\) | 1.08815 | 0.0345487 | ||||||||
\(993\) | −37.2319 | −1.18152 | ||||||||
\(994\) | −5.40821 | −0.171538 | ||||||||
\(995\) | −3.01507 | −0.0955840 | ||||||||
\(996\) | −26.9614 | −0.854303 | ||||||||
\(997\) | 58.4951 | 1.85256 | 0.926280 | − | 0.376836i | \(-0.122988\pi\) | ||||
0.926280 | + | 0.376836i | \(0.122988\pi\) | |||||||
\(998\) | 1.30499 | 0.0413089 | ||||||||
\(999\) | −39.7560 | −1.25782 |
(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 | 6422.2.a.t.1.3 | 3 | ||
13.5 | odd | 4 | 494.2.d.b.77.3 | ✓ | 6 | ||
13.8 | odd | 4 | 494.2.d.b.77.6 | yes | 6 | ||
13.12 | even | 2 | 6422.2.a.k.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.d.b.77.3 | ✓ | 6 | 13.5 | odd | 4 | ||
494.2.d.b.77.6 | yes | 6 | 13.8 | odd | 4 | ||
6422.2.a.k.1.3 | 3 | 13.12 | even | 2 | |||
6422.2.a.t.1.3 | 3 | 1.1 | even | 1 | trivial |