Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3174,2,Mod(1,3174)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3174, 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("3174.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3174 = 2 \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3174.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: | \(25.3445176016\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.91899\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3174.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.47889 | −0.661380 | −0.330690 | − | 0.943739i | \(-0.607282\pi\) | ||||
−0.330690 | + | 0.943739i | \(0.607282\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.20362 | −1.21085 | −0.605426 | − | 0.795901i | \(-0.706997\pi\) | ||||
−0.605426 | + | 0.795901i | \(0.706997\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.47889 | −0.467667 | ||||||||
\(11\) | 0.0552927 | 0.0166714 | 0.00833568 | − | 0.999965i | \(-0.497347\pi\) | ||||
0.00833568 | + | 0.999965i | \(0.497347\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.805738 | −0.223472 | −0.111736 | − | 0.993738i | \(-0.535641\pi\) | ||||
−0.111736 | + | 0.993738i | \(0.535641\pi\) | |||||||
\(14\) | −3.20362 | −0.856202 | ||||||||
\(15\) | −1.47889 | −0.381848 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.05954 | 0.499511 | 0.249756 | − | 0.968309i | \(-0.419650\pi\) | ||||
0.249756 | + | 0.968309i | \(0.419650\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.67657 | −0.843464 | −0.421732 | − | 0.906721i | \(-0.638578\pi\) | ||||
−0.421732 | + | 0.906721i | \(0.638578\pi\) | |||||||
\(20\) | −1.47889 | −0.330690 | ||||||||
\(21\) | −3.20362 | −0.699086 | ||||||||
\(22\) | 0.0552927 | 0.0117884 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.81288 | −0.562576 | ||||||||
\(26\) | −0.805738 | −0.158018 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.20362 | −0.605426 | ||||||||
\(29\) | 7.34575 | 1.36407 | 0.682036 | − | 0.731319i | \(-0.261095\pi\) | ||||
0.682036 | + | 0.731319i | \(0.261095\pi\) | |||||||
\(30\) | −1.47889 | −0.270007 | ||||||||
\(31\) | −7.95546 | −1.42884 | −0.714422 | − | 0.699715i | \(-0.753310\pi\) | ||||
−0.714422 | + | 0.699715i | \(0.753310\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.0552927 | 0.00962522 | ||||||||
\(34\) | 2.05954 | 0.353208 | ||||||||
\(35\) | 4.73780 | 0.800834 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.08816 | −0.507690 | −0.253845 | − | 0.967245i | \(-0.581695\pi\) | ||||
−0.253845 | + | 0.967245i | \(0.581695\pi\) | |||||||
\(38\) | −3.67657 | −0.596419 | ||||||||
\(39\) | −0.805738 | −0.129021 | ||||||||
\(40\) | −1.47889 | −0.233833 | ||||||||
\(41\) | −1.45973 | −0.227972 | −0.113986 | − | 0.993482i | \(-0.536362\pi\) | ||||
−0.113986 | + | 0.993482i | \(0.536362\pi\) | |||||||
\(42\) | −3.20362 | −0.494329 | ||||||||
\(43\) | −12.5322 | −1.91115 | −0.955574 | − | 0.294750i | \(-0.904764\pi\) | ||||
−0.955574 | + | 0.294750i | \(0.904764\pi\) | |||||||
\(44\) | 0.0552927 | 0.00833568 | ||||||||
\(45\) | −1.47889 | −0.220460 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.27459 | −0.185918 | −0.0929591 | − | 0.995670i | \(-0.529633\pi\) | ||||
−0.0929591 | + | 0.995670i | \(0.529633\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 3.26315 | 0.466165 | ||||||||
\(50\) | −2.81288 | −0.397801 | ||||||||
\(51\) | 2.05954 | 0.288393 | ||||||||
\(52\) | −0.805738 | −0.111736 | ||||||||
\(53\) | −11.0449 | −1.51713 | −0.758564 | − | 0.651599i | \(-0.774099\pi\) | ||||
−0.758564 | + | 0.651599i | \(0.774099\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.0817718 | −0.0110261 | ||||||||
\(56\) | −3.20362 | −0.428101 | ||||||||
\(57\) | −3.67657 | −0.486974 | ||||||||
\(58\) | 7.34575 | 0.964544 | ||||||||
\(59\) | −5.36077 | −0.697913 | −0.348956 | − | 0.937139i | \(-0.613464\pi\) | ||||
−0.348956 | + | 0.937139i | \(0.613464\pi\) | |||||||
\(60\) | −1.47889 | −0.190924 | ||||||||
\(61\) | 12.2015 | 1.56224 | 0.781120 | − | 0.624380i | \(-0.214648\pi\) | ||||
0.781120 | + | 0.624380i | \(0.214648\pi\) | |||||||
\(62\) | −7.95546 | −1.01034 | ||||||||
\(63\) | −3.20362 | −0.403618 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.19160 | 0.147800 | ||||||||
\(66\) | 0.0552927 | 0.00680606 | ||||||||
\(67\) | 4.52116 | 0.552348 | 0.276174 | − | 0.961108i | \(-0.410933\pi\) | ||||
0.276174 | + | 0.961108i | \(0.410933\pi\) | |||||||
\(68\) | 2.05954 | 0.249756 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.73780 | 0.566275 | ||||||||
\(71\) | −14.6029 | −1.73304 | −0.866522 | − | 0.499138i | \(-0.833650\pi\) | ||||
−0.866522 | + | 0.499138i | \(0.833650\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −9.86160 | −1.15421 | −0.577106 | − | 0.816669i | \(-0.695818\pi\) | ||||
−0.577106 | + | 0.816669i | \(0.695818\pi\) | |||||||
\(74\) | −3.08816 | −0.358991 | ||||||||
\(75\) | −2.81288 | −0.324803 | ||||||||
\(76\) | −3.67657 | −0.421732 | ||||||||
\(77\) | −0.177136 | −0.0201866 | ||||||||
\(78\) | −0.805738 | −0.0912319 | ||||||||
\(79\) | 3.61983 | 0.407262 | 0.203631 | − | 0.979048i | \(-0.434726\pi\) | ||||
0.203631 | + | 0.979048i | \(0.434726\pi\) | |||||||
\(80\) | −1.47889 | −0.165345 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.45973 | −0.161201 | ||||||||
\(83\) | −10.0343 | −1.10140 | −0.550702 | − | 0.834702i | \(-0.685640\pi\) | ||||
−0.550702 | + | 0.834702i | \(0.685640\pi\) | |||||||
\(84\) | −3.20362 | −0.349543 | ||||||||
\(85\) | −3.04583 | −0.330367 | ||||||||
\(86\) | −12.5322 | −1.35139 | ||||||||
\(87\) | 7.34575 | 0.787547 | ||||||||
\(88\) | 0.0552927 | 0.00589422 | ||||||||
\(89\) | −8.25248 | −0.874762 | −0.437381 | − | 0.899276i | \(-0.644094\pi\) | ||||
−0.437381 | + | 0.899276i | \(0.644094\pi\) | |||||||
\(90\) | −1.47889 | −0.155889 | ||||||||
\(91\) | 2.58128 | 0.270591 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.95546 | −0.824943 | ||||||||
\(94\) | −1.27459 | −0.131464 | ||||||||
\(95\) | 5.43725 | 0.557850 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.01618 | 0.712386 | 0.356193 | − | 0.934412i | \(-0.384075\pi\) | ||||
0.356193 | + | 0.934412i | \(0.384075\pi\) | |||||||
\(98\) | 3.26315 | 0.329628 | ||||||||
\(99\) | 0.0552927 | 0.00555712 | ||||||||
\(100\) | −2.81288 | −0.281288 | ||||||||
\(101\) | 15.3507 | 1.52745 | 0.763725 | − | 0.645542i | \(-0.223368\pi\) | ||||
0.763725 | + | 0.645542i | \(0.223368\pi\) | |||||||
\(102\) | 2.05954 | 0.203925 | ||||||||
\(103\) | 15.3219 | 1.50971 | 0.754854 | − | 0.655893i | \(-0.227708\pi\) | ||||
0.754854 | + | 0.655893i | \(0.227708\pi\) | |||||||
\(104\) | −0.805738 | −0.0790091 | ||||||||
\(105\) | 4.73780 | 0.462362 | ||||||||
\(106\) | −11.0449 | −1.07277 | ||||||||
\(107\) | −9.67542 | −0.935358 | −0.467679 | − | 0.883898i | \(-0.654910\pi\) | ||||
−0.467679 | + | 0.883898i | \(0.654910\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −13.4002 | −1.28350 | −0.641752 | − | 0.766912i | \(-0.721792\pi\) | ||||
−0.641752 | + | 0.766912i | \(0.721792\pi\) | |||||||
\(110\) | −0.0817718 | −0.00779664 | ||||||||
\(111\) | −3.08816 | −0.293115 | ||||||||
\(112\) | −3.20362 | −0.302713 | ||||||||
\(113\) | 8.22890 | 0.774110 | 0.387055 | − | 0.922057i | \(-0.373492\pi\) | ||||
0.387055 | + | 0.922057i | \(0.373492\pi\) | |||||||
\(114\) | −3.67657 | −0.344343 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.34575 | 0.682036 | ||||||||
\(117\) | −0.805738 | −0.0744905 | ||||||||
\(118\) | −5.36077 | −0.493499 | ||||||||
\(119\) | −6.59797 | −0.604835 | ||||||||
\(120\) | −1.47889 | −0.135004 | ||||||||
\(121\) | −10.9969 | −0.999722 | ||||||||
\(122\) | 12.2015 | 1.10467 | ||||||||
\(123\) | −1.45973 | −0.131620 | ||||||||
\(124\) | −7.95546 | −0.714422 | ||||||||
\(125\) | 11.5544 | 1.03346 | ||||||||
\(126\) | −3.20362 | −0.285401 | ||||||||
\(127\) | 19.3524 | 1.71725 | 0.858624 | − | 0.512606i | \(-0.171320\pi\) | ||||
0.858624 | + | 0.512606i | \(0.171320\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.5322 | −1.10340 | ||||||||
\(130\) | 1.19160 | 0.104510 | ||||||||
\(131\) | −20.9028 | −1.82628 | −0.913141 | − | 0.407643i | \(-0.866351\pi\) | ||||
−0.913141 | + | 0.407643i | \(0.866351\pi\) | |||||||
\(132\) | 0.0552927 | 0.00481261 | ||||||||
\(133\) | 11.7783 | 1.02131 | ||||||||
\(134\) | 4.52116 | 0.390569 | ||||||||
\(135\) | −1.47889 | −0.127283 | ||||||||
\(136\) | 2.05954 | 0.176604 | ||||||||
\(137\) | 5.89909 | 0.503993 | 0.251997 | − | 0.967728i | \(-0.418913\pi\) | ||||
0.251997 | + | 0.967728i | \(0.418913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.04356 | −0.342971 | −0.171485 | − | 0.985187i | \(-0.554857\pi\) | ||||
−0.171485 | + | 0.985187i | \(0.554857\pi\) | |||||||
\(140\) | 4.73780 | 0.400417 | ||||||||
\(141\) | −1.27459 | −0.107340 | ||||||||
\(142\) | −14.6029 | −1.22545 | ||||||||
\(143\) | −0.0445514 | −0.00372558 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −10.8636 | −0.902170 | ||||||||
\(146\) | −9.86160 | −0.816152 | ||||||||
\(147\) | 3.26315 | 0.269140 | ||||||||
\(148\) | −3.08816 | −0.253845 | ||||||||
\(149\) | −8.21355 | −0.672880 | −0.336440 | − | 0.941705i | \(-0.609223\pi\) | ||||
−0.336440 | + | 0.941705i | \(0.609223\pi\) | |||||||
\(150\) | −2.81288 | −0.229671 | ||||||||
\(151\) | −12.8490 | −1.04564 | −0.522820 | − | 0.852443i | \(-0.675120\pi\) | ||||
−0.522820 | + | 0.852443i | \(0.675120\pi\) | |||||||
\(152\) | −3.67657 | −0.298209 | ||||||||
\(153\) | 2.05954 | 0.166504 | ||||||||
\(154\) | −0.177136 | −0.0142741 | ||||||||
\(155\) | 11.7653 | 0.945009 | ||||||||
\(156\) | −0.805738 | −0.0645107 | ||||||||
\(157\) | 3.91879 | 0.312754 | 0.156377 | − | 0.987697i | \(-0.450019\pi\) | ||||
0.156377 | + | 0.987697i | \(0.450019\pi\) | |||||||
\(158\) | 3.61983 | 0.287978 | ||||||||
\(159\) | −11.0449 | −0.875914 | ||||||||
\(160\) | −1.47889 | −0.116917 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 15.7247 | 1.23165 | 0.615825 | − | 0.787883i | \(-0.288823\pi\) | ||||
0.615825 | + | 0.787883i | \(0.288823\pi\) | |||||||
\(164\) | −1.45973 | −0.113986 | ||||||||
\(165\) | −0.0817718 | −0.00636593 | ||||||||
\(166\) | −10.0343 | −0.778810 | ||||||||
\(167\) | −4.01965 | −0.311050 | −0.155525 | − | 0.987832i | \(-0.549707\pi\) | ||||
−0.155525 | + | 0.987832i | \(0.549707\pi\) | |||||||
\(168\) | −3.20362 | −0.247164 | ||||||||
\(169\) | −12.3508 | −0.950060 | ||||||||
\(170\) | −3.04583 | −0.233605 | ||||||||
\(171\) | −3.67657 | −0.281155 | ||||||||
\(172\) | −12.5322 | −0.955574 | ||||||||
\(173\) | 5.25447 | 0.399490 | 0.199745 | − | 0.979848i | \(-0.435989\pi\) | ||||
0.199745 | + | 0.979848i | \(0.435989\pi\) | |||||||
\(174\) | 7.34575 | 0.556880 | ||||||||
\(175\) | 9.01139 | 0.681197 | ||||||||
\(176\) | 0.0552927 | 0.00416784 | ||||||||
\(177\) | −5.36077 | −0.402940 | ||||||||
\(178\) | −8.25248 | −0.618550 | ||||||||
\(179\) | −2.11290 | −0.157926 | −0.0789629 | − | 0.996878i | \(-0.525161\pi\) | ||||
−0.0789629 | + | 0.996878i | \(0.525161\pi\) | |||||||
\(180\) | −1.47889 | −0.110230 | ||||||||
\(181\) | −0.230880 | −0.0171612 | −0.00858058 | − | 0.999963i | \(-0.502731\pi\) | ||||
−0.00858058 | + | 0.999963i | \(0.502731\pi\) | |||||||
\(182\) | 2.58128 | 0.191337 | ||||||||
\(183\) | 12.2015 | 0.901960 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.56705 | 0.335776 | ||||||||
\(186\) | −7.95546 | −0.583323 | ||||||||
\(187\) | 0.113877 | 0.00832753 | ||||||||
\(188\) | −1.27459 | −0.0929591 | ||||||||
\(189\) | −3.20362 | −0.233029 | ||||||||
\(190\) | 5.43725 | 0.394460 | ||||||||
\(191\) | 4.40318 | 0.318603 | 0.159302 | − | 0.987230i | \(-0.449076\pi\) | ||||
0.159302 | + | 0.987230i | \(0.449076\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 21.4973 | 1.54741 | 0.773704 | − | 0.633547i | \(-0.218402\pi\) | ||||
0.773704 | + | 0.633547i | \(0.218402\pi\) | |||||||
\(194\) | 7.01618 | 0.503733 | ||||||||
\(195\) | 1.19160 | 0.0853322 | ||||||||
\(196\) | 3.26315 | 0.233082 | ||||||||
\(197\) | 8.89209 | 0.633535 | 0.316768 | − | 0.948503i | \(-0.397402\pi\) | ||||
0.316768 | + | 0.948503i | \(0.397402\pi\) | |||||||
\(198\) | 0.0552927 | 0.00392948 | ||||||||
\(199\) | 18.1550 | 1.28698 | 0.643488 | − | 0.765456i | \(-0.277487\pi\) | ||||
0.643488 | + | 0.765456i | \(0.277487\pi\) | |||||||
\(200\) | −2.81288 | −0.198901 | ||||||||
\(201\) | 4.52116 | 0.318898 | ||||||||
\(202\) | 15.3507 | 1.08007 | ||||||||
\(203\) | −23.5330 | −1.65169 | ||||||||
\(204\) | 2.05954 | 0.144196 | ||||||||
\(205\) | 2.15879 | 0.150776 | ||||||||
\(206\) | 15.3219 | 1.06752 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.805738 | −0.0558679 | ||||||||
\(209\) | −0.203288 | −0.0140617 | ||||||||
\(210\) | 4.73780 | 0.326939 | ||||||||
\(211\) | 17.2040 | 1.18437 | 0.592187 | − | 0.805801i | \(-0.298265\pi\) | ||||
0.592187 | + | 0.805801i | \(0.298265\pi\) | |||||||
\(212\) | −11.0449 | −0.758564 | ||||||||
\(213\) | −14.6029 | −1.00057 | ||||||||
\(214\) | −9.67542 | −0.661398 | ||||||||
\(215\) | 18.5338 | 1.26400 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 25.4862 | 1.73012 | ||||||||
\(218\) | −13.4002 | −0.907575 | ||||||||
\(219\) | −9.86160 | −0.666385 | ||||||||
\(220\) | −0.0817718 | −0.00551306 | ||||||||
\(221\) | −1.65945 | −0.111627 | ||||||||
\(222\) | −3.08816 | −0.207263 | ||||||||
\(223\) | −9.64578 | −0.645929 | −0.322964 | − | 0.946411i | \(-0.604679\pi\) | ||||
−0.322964 | + | 0.946411i | \(0.604679\pi\) | |||||||
\(224\) | −3.20362 | −0.214051 | ||||||||
\(225\) | −2.81288 | −0.187525 | ||||||||
\(226\) | 8.22890 | 0.547378 | ||||||||
\(227\) | −13.2879 | −0.881951 | −0.440975 | − | 0.897519i | \(-0.645367\pi\) | ||||
−0.440975 | + | 0.897519i | \(0.645367\pi\) | |||||||
\(228\) | −3.67657 | −0.243487 | ||||||||
\(229\) | 10.3343 | 0.682912 | 0.341456 | − | 0.939898i | \(-0.389080\pi\) | ||||
0.341456 | + | 0.939898i | \(0.389080\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.177136 | −0.0116547 | ||||||||
\(232\) | 7.34575 | 0.482272 | ||||||||
\(233\) | −0.221377 | −0.0145029 | −0.00725144 | − | 0.999974i | \(-0.502308\pi\) | ||||
−0.00725144 | + | 0.999974i | \(0.502308\pi\) | |||||||
\(234\) | −0.805738 | −0.0526728 | ||||||||
\(235\) | 1.88498 | 0.122963 | ||||||||
\(236\) | −5.36077 | −0.348956 | ||||||||
\(237\) | 3.61983 | 0.235133 | ||||||||
\(238\) | −6.59797 | −0.427683 | ||||||||
\(239\) | 10.0933 | 0.652880 | 0.326440 | − | 0.945218i | \(-0.394151\pi\) | ||||
0.326440 | + | 0.945218i | \(0.394151\pi\) | |||||||
\(240\) | −1.47889 | −0.0954620 | ||||||||
\(241\) | −2.49660 | −0.160820 | −0.0804099 | − | 0.996762i | \(-0.525623\pi\) | ||||
−0.0804099 | + | 0.996762i | \(0.525623\pi\) | |||||||
\(242\) | −10.9969 | −0.706910 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.2015 | 0.781120 | ||||||||
\(245\) | −4.82585 | −0.308312 | ||||||||
\(246\) | −1.45973 | −0.0930692 | ||||||||
\(247\) | 2.96236 | 0.188490 | ||||||||
\(248\) | −7.95546 | −0.505172 | ||||||||
\(249\) | −10.0343 | −0.635896 | ||||||||
\(250\) | 11.5544 | 0.730765 | ||||||||
\(251\) | 14.3756 | 0.907379 | 0.453690 | − | 0.891160i | \(-0.350107\pi\) | ||||
0.453690 | + | 0.891160i | \(0.350107\pi\) | |||||||
\(252\) | −3.20362 | −0.201809 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 19.3524 | 1.21428 | ||||||||
\(255\) | −3.04583 | −0.190737 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.1087 | −1.06721 | −0.533606 | − | 0.845733i | \(-0.679164\pi\) | ||||
−0.533606 | + | 0.845733i | \(0.679164\pi\) | |||||||
\(258\) | −12.5322 | −0.780223 | ||||||||
\(259\) | 9.89326 | 0.614738 | ||||||||
\(260\) | 1.19160 | 0.0738999 | ||||||||
\(261\) | 7.34575 | 0.454690 | ||||||||
\(262\) | −20.9028 | −1.29138 | ||||||||
\(263\) | −9.82969 | −0.606125 | −0.303062 | − | 0.952971i | \(-0.598009\pi\) | ||||
−0.303062 | + | 0.952971i | \(0.598009\pi\) | |||||||
\(264\) | 0.0552927 | 0.00340303 | ||||||||
\(265\) | 16.3341 | 1.00340 | ||||||||
\(266\) | 11.7783 | 0.722176 | ||||||||
\(267\) | −8.25248 | −0.505044 | ||||||||
\(268\) | 4.52116 | 0.276174 | ||||||||
\(269\) | 27.0424 | 1.64881 | 0.824404 | − | 0.566002i | \(-0.191511\pi\) | ||||
0.824404 | + | 0.566002i | \(0.191511\pi\) | |||||||
\(270\) | −1.47889 | −0.0900025 | ||||||||
\(271\) | 14.0124 | 0.851195 | 0.425597 | − | 0.904913i | \(-0.360064\pi\) | ||||
0.425597 | + | 0.904913i | \(0.360064\pi\) | |||||||
\(272\) | 2.05954 | 0.124878 | ||||||||
\(273\) | 2.58128 | 0.156226 | ||||||||
\(274\) | 5.89909 | 0.356377 | ||||||||
\(275\) | −0.155532 | −0.00937891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.65528 | −0.399877 | −0.199938 | − | 0.979808i | \(-0.564074\pi\) | ||||
−0.199938 | + | 0.979808i | \(0.564074\pi\) | |||||||
\(278\) | −4.04356 | −0.242517 | ||||||||
\(279\) | −7.95546 | −0.476281 | ||||||||
\(280\) | 4.73780 | 0.283138 | ||||||||
\(281\) | −14.7244 | −0.878384 | −0.439192 | − | 0.898393i | \(-0.644735\pi\) | ||||
−0.439192 | + | 0.898393i | \(0.644735\pi\) | |||||||
\(282\) | −1.27459 | −0.0759008 | ||||||||
\(283\) | −13.6907 | −0.813827 | −0.406914 | − | 0.913467i | \(-0.633395\pi\) | ||||
−0.406914 | + | 0.913467i | \(0.633395\pi\) | |||||||
\(284\) | −14.6029 | −0.866522 | ||||||||
\(285\) | 5.43725 | 0.322075 | ||||||||
\(286\) | −0.0445514 | −0.00263438 | ||||||||
\(287\) | 4.67642 | 0.276041 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −12.7583 | −0.750489 | ||||||||
\(290\) | −10.8636 | −0.637931 | ||||||||
\(291\) | 7.01618 | 0.411296 | ||||||||
\(292\) | −9.86160 | −0.577106 | ||||||||
\(293\) | 29.6195 | 1.73039 | 0.865194 | − | 0.501437i | \(-0.167195\pi\) | ||||
0.865194 | + | 0.501437i | \(0.167195\pi\) | |||||||
\(294\) | 3.26315 | 0.190311 | ||||||||
\(295\) | 7.92800 | 0.461586 | ||||||||
\(296\) | −3.08816 | −0.179495 | ||||||||
\(297\) | 0.0552927 | 0.00320841 | ||||||||
\(298\) | −8.21355 | −0.475798 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.81288 | −0.162402 | ||||||||
\(301\) | 40.1485 | 2.31412 | ||||||||
\(302\) | −12.8490 | −0.739380 | ||||||||
\(303\) | 15.3507 | 0.881873 | ||||||||
\(304\) | −3.67657 | −0.210866 | ||||||||
\(305\) | −18.0447 | −1.03324 | ||||||||
\(306\) | 2.05954 | 0.117736 | ||||||||
\(307\) | 9.12670 | 0.520888 | 0.260444 | − | 0.965489i | \(-0.416131\pi\) | ||||
0.260444 | + | 0.965489i | \(0.416131\pi\) | |||||||
\(308\) | −0.177136 | −0.0100933 | ||||||||
\(309\) | 15.3219 | 0.871630 | ||||||||
\(310\) | 11.7653 | 0.668222 | ||||||||
\(311\) | 22.9754 | 1.30281 | 0.651407 | − | 0.758728i | \(-0.274179\pi\) | ||||
0.651407 | + | 0.758728i | \(0.274179\pi\) | |||||||
\(312\) | −0.805738 | −0.0456159 | ||||||||
\(313\) | 19.7421 | 1.11589 | 0.557946 | − | 0.829877i | \(-0.311590\pi\) | ||||
0.557946 | + | 0.829877i | \(0.311590\pi\) | |||||||
\(314\) | 3.91879 | 0.221150 | ||||||||
\(315\) | 4.73780 | 0.266945 | ||||||||
\(316\) | 3.61983 | 0.203631 | ||||||||
\(317\) | −20.8318 | −1.17003 | −0.585016 | − | 0.811022i | \(-0.698912\pi\) | ||||
−0.585016 | + | 0.811022i | \(0.698912\pi\) | |||||||
\(318\) | −11.0449 | −0.619365 | ||||||||
\(319\) | 0.406166 | 0.0227409 | ||||||||
\(320\) | −1.47889 | −0.0826725 | ||||||||
\(321\) | −9.67542 | −0.540029 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.57204 | −0.421320 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.26645 | 0.125720 | ||||||||
\(326\) | 15.7247 | 0.870909 | ||||||||
\(327\) | −13.4002 | −0.741032 | ||||||||
\(328\) | −1.45973 | −0.0806003 | ||||||||
\(329\) | 4.08330 | 0.225120 | ||||||||
\(330\) | −0.0817718 | −0.00450139 | ||||||||
\(331\) | −15.5468 | −0.854527 | −0.427264 | − | 0.904127i | \(-0.640522\pi\) | ||||
−0.427264 | + | 0.904127i | \(0.640522\pi\) | |||||||
\(332\) | −10.0343 | −0.550702 | ||||||||
\(333\) | −3.08816 | −0.169230 | ||||||||
\(334\) | −4.01965 | −0.219945 | ||||||||
\(335\) | −6.68631 | −0.365312 | ||||||||
\(336\) | −3.20362 | −0.174772 | ||||||||
\(337\) | 7.07769 | 0.385546 | 0.192773 | − | 0.981243i | \(-0.438252\pi\) | ||||
0.192773 | + | 0.981243i | \(0.438252\pi\) | |||||||
\(338\) | −12.3508 | −0.671794 | ||||||||
\(339\) | 8.22890 | 0.446933 | ||||||||
\(340\) | −3.04583 | −0.165183 | ||||||||
\(341\) | −0.439879 | −0.0238208 | ||||||||
\(342\) | −3.67657 | −0.198806 | ||||||||
\(343\) | 11.9714 | 0.646396 | ||||||||
\(344\) | −12.5322 | −0.675693 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.25447 | 0.282482 | ||||||||
\(347\) | −25.4158 | −1.36439 | −0.682195 | − | 0.731170i | \(-0.738975\pi\) | ||||
−0.682195 | + | 0.731170i | \(0.738975\pi\) | |||||||
\(348\) | 7.34575 | 0.393774 | ||||||||
\(349\) | −23.1316 | −1.23821 | −0.619104 | − | 0.785309i | \(-0.712504\pi\) | ||||
−0.619104 | + | 0.785309i | \(0.712504\pi\) | |||||||
\(350\) | 9.01139 | 0.481679 | ||||||||
\(351\) | −0.805738 | −0.0430071 | ||||||||
\(352\) | 0.0552927 | 0.00294711 | ||||||||
\(353\) | 24.0678 | 1.28100 | 0.640500 | − | 0.767958i | \(-0.278727\pi\) | ||||
0.640500 | + | 0.767958i | \(0.278727\pi\) | |||||||
\(354\) | −5.36077 | −0.284922 | ||||||||
\(355\) | 21.5961 | 1.14620 | ||||||||
\(356\) | −8.25248 | −0.437381 | ||||||||
\(357\) | −6.59797 | −0.349201 | ||||||||
\(358\) | −2.11290 | −0.111670 | ||||||||
\(359\) | 19.1724 | 1.01188 | 0.505940 | − | 0.862569i | \(-0.331146\pi\) | ||||
0.505940 | + | 0.862569i | \(0.331146\pi\) | |||||||
\(360\) | −1.47889 | −0.0779444 | ||||||||
\(361\) | −5.48281 | −0.288569 | ||||||||
\(362\) | −0.230880 | −0.0121348 | ||||||||
\(363\) | −10.9969 | −0.577190 | ||||||||
\(364\) | 2.58128 | 0.135296 | ||||||||
\(365\) | 14.5842 | 0.763374 | ||||||||
\(366\) | 12.2015 | 0.637782 | ||||||||
\(367\) | −26.2686 | −1.37121 | −0.685606 | − | 0.727973i | \(-0.740463\pi\) | ||||
−0.685606 | + | 0.727973i | \(0.740463\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.45973 | −0.0759907 | ||||||||
\(370\) | 4.56705 | 0.237429 | ||||||||
\(371\) | 35.3835 | 1.83702 | ||||||||
\(372\) | −7.95546 | −0.412472 | ||||||||
\(373\) | 20.4049 | 1.05653 | 0.528263 | − | 0.849081i | \(-0.322844\pi\) | ||||
0.528263 | + | 0.849081i | \(0.322844\pi\) | |||||||
\(374\) | 0.113877 | 0.00588846 | ||||||||
\(375\) | 11.5544 | 0.596667 | ||||||||
\(376\) | −1.27459 | −0.0657320 | ||||||||
\(377\) | −5.91875 | −0.304831 | ||||||||
\(378\) | −3.20362 | −0.164776 | ||||||||
\(379\) | 3.99029 | 0.204968 | 0.102484 | − | 0.994735i | \(-0.467321\pi\) | ||||
0.102484 | + | 0.994735i | \(0.467321\pi\) | |||||||
\(380\) | 5.43725 | 0.278925 | ||||||||
\(381\) | 19.3524 | 0.991454 | ||||||||
\(382\) | 4.40318 | 0.225286 | ||||||||
\(383\) | 6.32220 | 0.323049 | 0.161525 | − | 0.986869i | \(-0.448359\pi\) | ||||
0.161525 | + | 0.986869i | \(0.448359\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0.261966 | 0.0133510 | ||||||||
\(386\) | 21.4973 | 1.09418 | ||||||||
\(387\) | −12.5322 | −0.637050 | ||||||||
\(388\) | 7.01618 | 0.356193 | ||||||||
\(389\) | −25.4165 | −1.28867 | −0.644335 | − | 0.764743i | \(-0.722866\pi\) | ||||
−0.644335 | + | 0.764743i | \(0.722866\pi\) | |||||||
\(390\) | 1.19160 | 0.0603390 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.26315 | 0.164814 | ||||||||
\(393\) | −20.9028 | −1.05440 | ||||||||
\(394\) | 8.89209 | 0.447977 | ||||||||
\(395\) | −5.35333 | −0.269355 | ||||||||
\(396\) | 0.0552927 | 0.00277856 | ||||||||
\(397\) | −3.43509 | −0.172402 | −0.0862011 | − | 0.996278i | \(-0.527473\pi\) | ||||
−0.0862011 | + | 0.996278i | \(0.527473\pi\) | |||||||
\(398\) | 18.1550 | 0.910029 | ||||||||
\(399\) | 11.7783 | 0.589654 | ||||||||
\(400\) | −2.81288 | −0.140644 | ||||||||
\(401\) | −8.35498 | −0.417228 | −0.208614 | − | 0.977998i | \(-0.566895\pi\) | ||||
−0.208614 | + | 0.977998i | \(0.566895\pi\) | |||||||
\(402\) | 4.52116 | 0.225495 | ||||||||
\(403\) | 6.41002 | 0.319306 | ||||||||
\(404\) | 15.3507 | 0.763725 | ||||||||
\(405\) | −1.47889 | −0.0734867 | ||||||||
\(406\) | −23.5330 | −1.16792 | ||||||||
\(407\) | −0.170752 | −0.00846388 | ||||||||
\(408\) | 2.05954 | 0.101962 | ||||||||
\(409\) | −4.18657 | −0.207013 | −0.103506 | − | 0.994629i | \(-0.533006\pi\) | ||||
−0.103506 | + | 0.994629i | \(0.533006\pi\) | |||||||
\(410\) | 2.15879 | 0.106615 | ||||||||
\(411\) | 5.89909 | 0.290981 | ||||||||
\(412\) | 15.3219 | 0.754854 | ||||||||
\(413\) | 17.1738 | 0.845070 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.8396 | 0.728447 | ||||||||
\(416\) | −0.805738 | −0.0395046 | ||||||||
\(417\) | −4.04356 | −0.198014 | ||||||||
\(418\) | −0.203288 | −0.00994312 | ||||||||
\(419\) | 8.98508 | 0.438950 | 0.219475 | − | 0.975618i | \(-0.429566\pi\) | ||||
0.219475 | + | 0.975618i | \(0.429566\pi\) | |||||||
\(420\) | 4.73780 | 0.231181 | ||||||||
\(421\) | −6.75886 | −0.329407 | −0.164703 | − | 0.986343i | \(-0.552667\pi\) | ||||
−0.164703 | + | 0.986343i | \(0.552667\pi\) | |||||||
\(422\) | 17.2040 | 0.837478 | ||||||||
\(423\) | −1.27459 | −0.0619727 | ||||||||
\(424\) | −11.0449 | −0.536386 | ||||||||
\(425\) | −5.79323 | −0.281013 | ||||||||
\(426\) | −14.6029 | −0.707513 | ||||||||
\(427\) | −39.0889 | −1.89164 | ||||||||
\(428\) | −9.67542 | −0.467679 | ||||||||
\(429\) | −0.0445514 | −0.00215096 | ||||||||
\(430\) | 18.5338 | 0.893780 | ||||||||
\(431\) | −22.6737 | −1.09216 | −0.546078 | − | 0.837734i | \(-0.683880\pi\) | ||||
−0.546078 | + | 0.837734i | \(0.683880\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 29.9541 | 1.43950 | 0.719752 | − | 0.694231i | \(-0.244256\pi\) | ||||
0.719752 | + | 0.694231i | \(0.244256\pi\) | |||||||
\(434\) | 25.4862 | 1.22338 | ||||||||
\(435\) | −10.8636 | −0.520868 | ||||||||
\(436\) | −13.4002 | −0.641752 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −9.86160 | −0.471205 | ||||||||
\(439\) | −1.50141 | −0.0716585 | −0.0358292 | − | 0.999358i | \(-0.511407\pi\) | ||||
−0.0358292 | + | 0.999358i | \(0.511407\pi\) | |||||||
\(440\) | −0.0817718 | −0.00389832 | ||||||||
\(441\) | 3.26315 | 0.155388 | ||||||||
\(442\) | −1.65945 | −0.0789319 | ||||||||
\(443\) | −5.89537 | −0.280097 | −0.140049 | − | 0.990145i | \(-0.544726\pi\) | ||||
−0.140049 | + | 0.990145i | \(0.544726\pi\) | |||||||
\(444\) | −3.08816 | −0.146557 | ||||||||
\(445\) | 12.2045 | 0.578550 | ||||||||
\(446\) | −9.64578 | −0.456741 | ||||||||
\(447\) | −8.21355 | −0.388487 | ||||||||
\(448\) | −3.20362 | −0.151357 | ||||||||
\(449\) | −36.8587 | −1.73947 | −0.869734 | − | 0.493520i | \(-0.835710\pi\) | ||||
−0.869734 | + | 0.493520i | \(0.835710\pi\) | |||||||
\(450\) | −2.81288 | −0.132600 | ||||||||
\(451\) | −0.0807125 | −0.00380061 | ||||||||
\(452\) | 8.22890 | 0.387055 | ||||||||
\(453\) | −12.8490 | −0.603701 | ||||||||
\(454\) | −13.2879 | −0.623633 | ||||||||
\(455\) | −3.81743 | −0.178964 | ||||||||
\(456\) | −3.67657 | −0.172171 | ||||||||
\(457\) | −5.79767 | −0.271203 | −0.135602 | − | 0.990763i | \(-0.543297\pi\) | ||||
−0.135602 | + | 0.990763i | \(0.543297\pi\) | |||||||
\(458\) | 10.3343 | 0.482892 | ||||||||
\(459\) | 2.05954 | 0.0961310 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.1277 | −0.890864 | −0.445432 | − | 0.895316i | \(-0.646950\pi\) | ||||
−0.445432 | + | 0.895316i | \(0.646950\pi\) | |||||||
\(462\) | −0.177136 | −0.00824113 | ||||||||
\(463\) | −20.3367 | −0.945126 | −0.472563 | − | 0.881297i | \(-0.656671\pi\) | ||||
−0.472563 | + | 0.881297i | \(0.656671\pi\) | |||||||
\(464\) | 7.34575 | 0.341018 | ||||||||
\(465\) | 11.7653 | 0.545601 | ||||||||
\(466\) | −0.221377 | −0.0102551 | ||||||||
\(467\) | 27.1467 | 1.25620 | 0.628101 | − | 0.778132i | \(-0.283833\pi\) | ||||
0.628101 | + | 0.778132i | \(0.283833\pi\) | |||||||
\(468\) | −0.805738 | −0.0372453 | ||||||||
\(469\) | −14.4841 | −0.668812 | ||||||||
\(470\) | 1.88498 | 0.0869477 | ||||||||
\(471\) | 3.91879 | 0.180568 | ||||||||
\(472\) | −5.36077 | −0.246749 | ||||||||
\(473\) | −0.692941 | −0.0318615 | ||||||||
\(474\) | 3.61983 | 0.166264 | ||||||||
\(475\) | 10.3418 | 0.474512 | ||||||||
\(476\) | −6.59797 | −0.302417 | ||||||||
\(477\) | −11.0449 | −0.505709 | ||||||||
\(478\) | 10.0933 | 0.461656 | ||||||||
\(479\) | −3.73359 | −0.170592 | −0.0852961 | − | 0.996356i | \(-0.527184\pi\) | ||||
−0.0852961 | + | 0.996356i | \(0.527184\pi\) | |||||||
\(480\) | −1.47889 | −0.0675019 | ||||||||
\(481\) | 2.48825 | 0.113454 | ||||||||
\(482\) | −2.49660 | −0.113717 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9969 | −0.499861 | ||||||||
\(485\) | −10.3762 | −0.471158 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 23.0573 | 1.04483 | 0.522413 | − | 0.852693i | \(-0.325032\pi\) | ||||
0.522413 | + | 0.852693i | \(0.325032\pi\) | |||||||
\(488\) | 12.2015 | 0.552336 | ||||||||
\(489\) | 15.7247 | 0.711094 | ||||||||
\(490\) | −4.82585 | −0.218010 | ||||||||
\(491\) | −1.12229 | −0.0506483 | −0.0253241 | − | 0.999679i | \(-0.508062\pi\) | ||||
−0.0253241 | + | 0.999679i | \(0.508062\pi\) | |||||||
\(492\) | −1.45973 | −0.0658099 | ||||||||
\(493\) | 15.1288 | 0.681369 | ||||||||
\(494\) | 2.96236 | 0.133283 | ||||||||
\(495\) | −0.0817718 | −0.00367537 | ||||||||
\(496\) | −7.95546 | −0.357211 | ||||||||
\(497\) | 46.7821 | 2.09846 | ||||||||
\(498\) | −10.0343 | −0.449646 | ||||||||
\(499\) | 39.6576 | 1.77532 | 0.887659 | − | 0.460502i | \(-0.152331\pi\) | ||||
0.887659 | + | 0.460502i | \(0.152331\pi\) | |||||||
\(500\) | 11.5544 | 0.516729 | ||||||||
\(501\) | −4.01965 | −0.179585 | ||||||||
\(502\) | 14.3756 | 0.641614 | ||||||||
\(503\) | −34.0385 | −1.51770 | −0.758850 | − | 0.651266i | \(-0.774238\pi\) | ||||
−0.758850 | + | 0.651266i | \(0.774238\pi\) | |||||||
\(504\) | −3.20362 | −0.142700 | ||||||||
\(505\) | −22.7020 | −1.01023 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.3508 | −0.548518 | ||||||||
\(508\) | 19.3524 | 0.858624 | ||||||||
\(509\) | 0.940632 | 0.0416928 | 0.0208464 | − | 0.999783i | \(-0.493364\pi\) | ||||
0.0208464 | + | 0.999783i | \(0.493364\pi\) | |||||||
\(510\) | −3.04583 | −0.134872 | ||||||||
\(511\) | 31.5928 | 1.39758 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.67657 | −0.162325 | ||||||||
\(514\) | −17.1087 | −0.754633 | ||||||||
\(515\) | −22.6594 | −0.998491 | ||||||||
\(516\) | −12.5322 | −0.551701 | ||||||||
\(517\) | −0.0704755 | −0.00309951 | ||||||||
\(518\) | 9.89326 | 0.434685 | ||||||||
\(519\) | 5.25447 | 0.230646 | ||||||||
\(520\) | 1.19160 | 0.0522551 | ||||||||
\(521\) | −40.4064 | −1.77024 | −0.885119 | − | 0.465366i | \(-0.845923\pi\) | ||||
−0.885119 | + | 0.465366i | \(0.845923\pi\) | |||||||
\(522\) | 7.34575 | 0.321515 | ||||||||
\(523\) | −14.0908 | −0.616146 | −0.308073 | − | 0.951363i | \(-0.599684\pi\) | ||||
−0.308073 | + | 0.951363i | \(0.599684\pi\) | |||||||
\(524\) | −20.9028 | −0.913141 | ||||||||
\(525\) | 9.01139 | 0.393289 | ||||||||
\(526\) | −9.82969 | −0.428595 | ||||||||
\(527\) | −16.3846 | −0.713723 | ||||||||
\(528\) | 0.0552927 | 0.00240630 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 16.3341 | 0.709510 | ||||||||
\(531\) | −5.36077 | −0.232638 | ||||||||
\(532\) | 11.7783 | 0.510655 | ||||||||
\(533\) | 1.17616 | 0.0509453 | ||||||||
\(534\) | −8.25248 | −0.357120 | ||||||||
\(535\) | 14.3089 | 0.618628 | ||||||||
\(536\) | 4.52116 | 0.195285 | ||||||||
\(537\) | −2.11290 | −0.0911785 | ||||||||
\(538\) | 27.0424 | 1.16588 | ||||||||
\(539\) | 0.180428 | 0.00777160 | ||||||||
\(540\) | −1.47889 | −0.0636414 | ||||||||
\(541\) | −32.0267 | −1.37694 | −0.688468 | − | 0.725267i | \(-0.741716\pi\) | ||||
−0.688468 | + | 0.725267i | \(0.741716\pi\) | |||||||
\(542\) | 14.0124 | 0.601885 | ||||||||
\(543\) | −0.230880 | −0.00990800 | ||||||||
\(544\) | 2.05954 | 0.0883019 | ||||||||
\(545\) | 19.8174 | 0.848885 | ||||||||
\(546\) | 2.58128 | 0.110468 | ||||||||
\(547\) | −34.2269 | −1.46344 | −0.731718 | − | 0.681607i | \(-0.761281\pi\) | ||||
−0.731718 | + | 0.681607i | \(0.761281\pi\) | |||||||
\(548\) | 5.89909 | 0.251997 | ||||||||
\(549\) | 12.2015 | 0.520747 | ||||||||
\(550\) | −0.155532 | −0.00663189 | ||||||||
\(551\) | −27.0072 | −1.15054 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.5965 | −0.493135 | ||||||||
\(554\) | −6.65528 | −0.282756 | ||||||||
\(555\) | 4.56705 | 0.193860 | ||||||||
\(556\) | −4.04356 | −0.171485 | ||||||||
\(557\) | −11.3076 | −0.479117 | −0.239559 | − | 0.970882i | \(-0.577003\pi\) | ||||
−0.239559 | + | 0.970882i | \(0.577003\pi\) | |||||||
\(558\) | −7.95546 | −0.336782 | ||||||||
\(559\) | 10.0977 | 0.427087 | ||||||||
\(560\) | 4.73780 | 0.200209 | ||||||||
\(561\) | 0.113877 | 0.00480790 | ||||||||
\(562\) | −14.7244 | −0.621111 | ||||||||
\(563\) | 17.2976 | 0.729006 | 0.364503 | − | 0.931202i | \(-0.381239\pi\) | ||||
0.364503 | + | 0.931202i | \(0.381239\pi\) | |||||||
\(564\) | −1.27459 | −0.0536700 | ||||||||
\(565\) | −12.1697 | −0.511981 | ||||||||
\(566\) | −13.6907 | −0.575463 | ||||||||
\(567\) | −3.20362 | −0.134539 | ||||||||
\(568\) | −14.6029 | −0.612724 | ||||||||
\(569\) | 29.0600 | 1.21826 | 0.609129 | − | 0.793071i | \(-0.291519\pi\) | ||||
0.609129 | + | 0.793071i | \(0.291519\pi\) | |||||||
\(570\) | 5.43725 | 0.227741 | ||||||||
\(571\) | 3.14635 | 0.131671 | 0.0658354 | − | 0.997830i | \(-0.479029\pi\) | ||||
0.0658354 | + | 0.997830i | \(0.479029\pi\) | |||||||
\(572\) | −0.0445514 | −0.00186279 | ||||||||
\(573\) | 4.40318 | 0.183946 | ||||||||
\(574\) | 4.67642 | 0.195190 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 10.8526 | 0.451799 | 0.225900 | − | 0.974151i | \(-0.427468\pi\) | ||||
0.225900 | + | 0.974151i | \(0.427468\pi\) | |||||||
\(578\) | −12.7583 | −0.530676 | ||||||||
\(579\) | 21.4973 | 0.893397 | ||||||||
\(580\) | −10.8636 | −0.451085 | ||||||||
\(581\) | 32.1459 | 1.33364 | ||||||||
\(582\) | 7.01618 | 0.290830 | ||||||||
\(583\) | −0.610700 | −0.0252926 | ||||||||
\(584\) | −9.86160 | −0.408076 | ||||||||
\(585\) | 1.19160 | 0.0492666 | ||||||||
\(586\) | 29.6195 | 1.22357 | ||||||||
\(587\) | −32.2820 | −1.33242 | −0.666210 | − | 0.745764i | \(-0.732085\pi\) | ||||
−0.666210 | + | 0.745764i | \(0.732085\pi\) | |||||||
\(588\) | 3.26315 | 0.134570 | ||||||||
\(589\) | 29.2488 | 1.20518 | ||||||||
\(590\) | 7.92800 | 0.326390 | ||||||||
\(591\) | 8.89209 | 0.365772 | ||||||||
\(592\) | −3.08816 | −0.126922 | ||||||||
\(593\) | 35.1225 | 1.44231 | 0.721154 | − | 0.692774i | \(-0.243612\pi\) | ||||
0.721154 | + | 0.692774i | \(0.243612\pi\) | |||||||
\(594\) | 0.0552927 | 0.00226869 | ||||||||
\(595\) | 9.75768 | 0.400026 | ||||||||
\(596\) | −8.21355 | −0.336440 | ||||||||
\(597\) | 18.1550 | 0.743036 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.0831 | −1.35174 | −0.675870 | − | 0.737021i | \(-0.736232\pi\) | ||||
−0.675870 | + | 0.737021i | \(0.736232\pi\) | |||||||
\(600\) | −2.81288 | −0.114835 | ||||||||
\(601\) | −40.9247 | −1.66935 | −0.834677 | − | 0.550740i | \(-0.814345\pi\) | ||||
−0.834677 | + | 0.550740i | \(0.814345\pi\) | |||||||
\(602\) | 40.1485 | 1.63633 | ||||||||
\(603\) | 4.52116 | 0.184116 | ||||||||
\(604\) | −12.8490 | −0.522820 | ||||||||
\(605\) | 16.2633 | 0.661197 | ||||||||
\(606\) | 15.3507 | 0.623579 | ||||||||
\(607\) | 0.867250 | 0.0352006 | 0.0176003 | − | 0.999845i | \(-0.494397\pi\) | ||||
0.0176003 | + | 0.999845i | \(0.494397\pi\) | |||||||
\(608\) | −3.67657 | −0.149105 | ||||||||
\(609\) | −23.5330 | −0.953604 | ||||||||
\(610\) | −18.0447 | −0.730608 | ||||||||
\(611\) | 1.02699 | 0.0415474 | ||||||||
\(612\) | 2.05954 | 0.0832519 | ||||||||
\(613\) | 13.5982 | 0.549227 | 0.274614 | − | 0.961555i | \(-0.411450\pi\) | ||||
0.274614 | + | 0.961555i | \(0.411450\pi\) | |||||||
\(614\) | 9.12670 | 0.368324 | ||||||||
\(615\) | 2.15879 | 0.0870507 | ||||||||
\(616\) | −0.177136 | −0.00713703 | ||||||||
\(617\) | −42.6638 | −1.71758 | −0.858790 | − | 0.512328i | \(-0.828783\pi\) | ||||
−0.858790 | + | 0.512328i | \(0.828783\pi\) | |||||||
\(618\) | 15.3219 | 0.616335 | ||||||||
\(619\) | −31.5251 | −1.26710 | −0.633551 | − | 0.773701i | \(-0.718403\pi\) | ||||
−0.633551 | + | 0.773701i | \(0.718403\pi\) | |||||||
\(620\) | 11.7653 | 0.472505 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.9754 | 0.921229 | ||||||||
\(623\) | 26.4378 | 1.05921 | ||||||||
\(624\) | −0.805738 | −0.0322553 | ||||||||
\(625\) | −3.02331 | −0.120932 | ||||||||
\(626\) | 19.7421 | 0.789054 | ||||||||
\(627\) | −0.203288 | −0.00811852 | ||||||||
\(628\) | 3.91879 | 0.156377 | ||||||||
\(629\) | −6.36017 | −0.253597 | ||||||||
\(630\) | 4.73780 | 0.188758 | ||||||||
\(631\) | −48.7324 | −1.94001 | −0.970003 | − | 0.243093i | \(-0.921838\pi\) | ||||
−0.970003 | + | 0.243093i | \(0.921838\pi\) | |||||||
\(632\) | 3.61983 | 0.143989 | ||||||||
\(633\) | 17.2040 | 0.683798 | ||||||||
\(634\) | −20.8318 | −0.827337 | ||||||||
\(635\) | −28.6201 | −1.13575 | ||||||||
\(636\) | −11.0449 | −0.437957 | ||||||||
\(637\) | −2.62925 | −0.104175 | ||||||||
\(638\) | 0.406166 | 0.0160803 | ||||||||
\(639\) | −14.6029 | −0.577682 | ||||||||
\(640\) | −1.47889 | −0.0584583 | ||||||||
\(641\) | 30.1834 | 1.19217 | 0.596086 | − | 0.802920i | \(-0.296722\pi\) | ||||
0.596086 | + | 0.802920i | \(0.296722\pi\) | |||||||
\(642\) | −9.67542 | −0.381858 | ||||||||
\(643\) | 34.4723 | 1.35946 | 0.679728 | − | 0.733464i | \(-0.262098\pi\) | ||||
0.679728 | + | 0.733464i | \(0.262098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.5338 | 0.729769 | ||||||||
\(646\) | −7.57204 | −0.297918 | ||||||||
\(647\) | 13.9668 | 0.549092 | 0.274546 | − | 0.961574i | \(-0.411472\pi\) | ||||
0.274546 | + | 0.961574i | \(0.411472\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −0.296411 | −0.0116352 | ||||||||
\(650\) | 2.26645 | 0.0888973 | ||||||||
\(651\) | 25.4862 | 0.998885 | ||||||||
\(652\) | 15.7247 | 0.615825 | ||||||||
\(653\) | 36.9272 | 1.44507 | 0.722537 | − | 0.691332i | \(-0.242976\pi\) | ||||
0.722537 | + | 0.691332i | \(0.242976\pi\) | |||||||
\(654\) | −13.4002 | −0.523988 | ||||||||
\(655\) | 30.9129 | 1.20787 | ||||||||
\(656\) | −1.45973 | −0.0569930 | ||||||||
\(657\) | −9.86160 | −0.384738 | ||||||||
\(658\) | 4.08330 | 0.159184 | ||||||||
\(659\) | −11.0352 | −0.429872 | −0.214936 | − | 0.976628i | \(-0.568954\pi\) | ||||
−0.214936 | + | 0.976628i | \(0.568954\pi\) | |||||||
\(660\) | −0.0817718 | −0.00318296 | ||||||||
\(661\) | 33.9751 | 1.32148 | 0.660738 | − | 0.750616i | \(-0.270243\pi\) | ||||
0.660738 | + | 0.750616i | \(0.270243\pi\) | |||||||
\(662\) | −15.5468 | −0.604242 | ||||||||
\(663\) | −1.65945 | −0.0644476 | ||||||||
\(664\) | −10.0343 | −0.389405 | ||||||||
\(665\) | −17.4189 | −0.675475 | ||||||||
\(666\) | −3.08816 | −0.119664 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −4.01965 | −0.155525 | ||||||||
\(669\) | −9.64578 | −0.372927 | ||||||||
\(670\) | −6.68631 | −0.258315 | ||||||||
\(671\) | 0.674653 | 0.0260447 | ||||||||
\(672\) | −3.20362 | −0.123582 | ||||||||
\(673\) | −31.3928 | −1.21010 | −0.605052 | − | 0.796186i | \(-0.706848\pi\) | ||||
−0.605052 | + | 0.796186i | \(0.706848\pi\) | |||||||
\(674\) | 7.07769 | 0.272622 | ||||||||
\(675\) | −2.81288 | −0.108268 | ||||||||
\(676\) | −12.3508 | −0.475030 | ||||||||
\(677\) | −39.3382 | −1.51189 | −0.755944 | − | 0.654636i | \(-0.772822\pi\) | ||||
−0.755944 | + | 0.654636i | \(0.772822\pi\) | |||||||
\(678\) | 8.22890 | 0.316029 | ||||||||
\(679\) | −22.4772 | −0.862594 | ||||||||
\(680\) | −3.04583 | −0.116802 | ||||||||
\(681\) | −13.2879 | −0.509194 | ||||||||
\(682\) | −0.439879 | −0.0168438 | ||||||||
\(683\) | 31.6224 | 1.21000 | 0.604998 | − | 0.796227i | \(-0.293174\pi\) | ||||
0.604998 | + | 0.796227i | \(0.293174\pi\) | |||||||
\(684\) | −3.67657 | −0.140577 | ||||||||
\(685\) | −8.72412 | −0.333331 | ||||||||
\(686\) | 11.9714 | 0.457071 | ||||||||
\(687\) | 10.3343 | 0.394279 | ||||||||
\(688\) | −12.5322 | −0.477787 | ||||||||
\(689\) | 8.89927 | 0.339035 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.2620 | 0.846886 | 0.423443 | − | 0.905923i | \(-0.360821\pi\) | ||||
0.423443 | + | 0.905923i | \(0.360821\pi\) | |||||||
\(692\) | 5.25447 | 0.199745 | ||||||||
\(693\) | −0.177136 | −0.00672886 | ||||||||
\(694\) | −25.4158 | −0.964770 | ||||||||
\(695\) | 5.97999 | 0.226834 | ||||||||
\(696\) | 7.34575 | 0.278440 | ||||||||
\(697\) | −3.00638 | −0.113875 | ||||||||
\(698\) | −23.1316 | −0.875545 | ||||||||
\(699\) | −0.221377 | −0.00837325 | ||||||||
\(700\) | 9.01139 | 0.340598 | ||||||||
\(701\) | 13.8462 | 0.522964 | 0.261482 | − | 0.965208i | \(-0.415789\pi\) | ||||
0.261482 | + | 0.965208i | \(0.415789\pi\) | |||||||
\(702\) | −0.805738 | −0.0304106 | ||||||||
\(703\) | 11.3538 | 0.428218 | ||||||||
\(704\) | 0.0552927 | 0.00208392 | ||||||||
\(705\) | 1.88498 | 0.0709925 | ||||||||
\(706\) | 24.0678 | 0.905804 | ||||||||
\(707\) | −49.1777 | −1.84952 | ||||||||
\(708\) | −5.36077 | −0.201470 | ||||||||
\(709\) | 49.1026 | 1.84409 | 0.922043 | − | 0.387087i | \(-0.126519\pi\) | ||||
0.922043 | + | 0.387087i | \(0.126519\pi\) | |||||||
\(710\) | 21.5961 | 0.810487 | ||||||||
\(711\) | 3.61983 | 0.135754 | ||||||||
\(712\) | −8.25248 | −0.309275 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −6.59797 | −0.246923 | ||||||||
\(715\) | 0.0658867 | 0.00246402 | ||||||||
\(716\) | −2.11290 | −0.0789629 | ||||||||
\(717\) | 10.0933 | 0.376940 | ||||||||
\(718\) | 19.1724 | 0.715507 | ||||||||
\(719\) | 36.5928 | 1.36468 | 0.682341 | − | 0.731034i | \(-0.260962\pi\) | ||||
0.682341 | + | 0.731034i | \(0.260962\pi\) | |||||||
\(720\) | −1.47889 | −0.0551150 | ||||||||
\(721\) | −49.0853 | −1.82803 | ||||||||
\(722\) | −5.48281 | −0.204049 | ||||||||
\(723\) | −2.49660 | −0.0928494 | ||||||||
\(724\) | −0.230880 | −0.00858058 | ||||||||
\(725\) | −20.6627 | −0.767394 | ||||||||
\(726\) | −10.9969 | −0.408135 | ||||||||
\(727\) | 18.6107 | 0.690232 | 0.345116 | − | 0.938560i | \(-0.387840\pi\) | ||||
0.345116 | + | 0.938560i | \(0.387840\pi\) | |||||||
\(728\) | 2.58128 | 0.0956684 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.5842 | 0.539787 | ||||||||
\(731\) | −25.8106 | −0.954640 | ||||||||
\(732\) | 12.2015 | 0.450980 | ||||||||
\(733\) | −22.6156 | −0.835327 | −0.417664 | − | 0.908602i | \(-0.637151\pi\) | ||||
−0.417664 | + | 0.908602i | \(0.637151\pi\) | |||||||
\(734\) | −26.2686 | −0.969593 | ||||||||
\(735\) | −4.82585 | −0.178004 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.249987 | 0.00920840 | ||||||||
\(738\) | −1.45973 | −0.0537335 | ||||||||
\(739\) | −17.8869 | −0.657982 | −0.328991 | − | 0.944333i | \(-0.606709\pi\) | ||||
−0.328991 | + | 0.944333i | \(0.606709\pi\) | |||||||
\(740\) | 4.56705 | 0.167888 | ||||||||
\(741\) | 2.96236 | 0.108825 | ||||||||
\(742\) | 35.3835 | 1.29897 | ||||||||
\(743\) | −22.4379 | −0.823168 | −0.411584 | − | 0.911372i | \(-0.635024\pi\) | ||||
−0.411584 | + | 0.911372i | \(0.635024\pi\) | |||||||
\(744\) | −7.95546 | −0.291661 | ||||||||
\(745\) | 12.1469 | 0.445030 | ||||||||
\(746\) | 20.4049 | 0.747076 | ||||||||
\(747\) | −10.0343 | −0.367135 | ||||||||
\(748\) | 0.113877 | 0.00416377 | ||||||||
\(749\) | 30.9963 | 1.13258 | ||||||||
\(750\) | 11.5544 | 0.421907 | ||||||||
\(751\) | 46.9846 | 1.71449 | 0.857246 | − | 0.514907i | \(-0.172174\pi\) | ||||
0.857246 | + | 0.514907i | \(0.172174\pi\) | |||||||
\(752\) | −1.27459 | −0.0464795 | ||||||||
\(753\) | 14.3756 | 0.523876 | ||||||||
\(754\) | −5.91875 | −0.215548 | ||||||||
\(755\) | 19.0023 | 0.691566 | ||||||||
\(756\) | −3.20362 | −0.116514 | ||||||||
\(757\) | 28.7306 | 1.04423 | 0.522115 | − | 0.852875i | \(-0.325143\pi\) | ||||
0.522115 | + | 0.852875i | \(0.325143\pi\) | |||||||
\(758\) | 3.99029 | 0.144934 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.43725 | 0.197230 | ||||||||
\(761\) | 15.6869 | 0.568651 | 0.284326 | − | 0.958728i | \(-0.408230\pi\) | ||||
0.284326 | + | 0.958728i | \(0.408230\pi\) | |||||||
\(762\) | 19.3524 | 0.701064 | ||||||||
\(763\) | 42.9290 | 1.55413 | ||||||||
\(764\) | 4.40318 | 0.159302 | ||||||||
\(765\) | −3.04583 | −0.110122 | ||||||||
\(766\) | 6.32220 | 0.228430 | ||||||||
\(767\) | 4.31938 | 0.155964 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −19.8140 | −0.714509 | −0.357255 | − | 0.934007i | \(-0.616287\pi\) | ||||
−0.357255 | + | 0.934007i | \(0.616287\pi\) | |||||||
\(770\) | 0.261966 | 0.00944058 | ||||||||
\(771\) | −17.1087 | −0.616155 | ||||||||
\(772\) | 21.4973 | 0.773704 | ||||||||
\(773\) | 19.5152 | 0.701915 | 0.350957 | − | 0.936391i | \(-0.385856\pi\) | ||||
0.350957 | + | 0.936391i | \(0.385856\pi\) | |||||||
\(774\) | −12.5322 | −0.450462 | ||||||||
\(775\) | 22.3778 | 0.803833 | ||||||||
\(776\) | 7.01618 | 0.251866 | ||||||||
\(777\) | 9.89326 | 0.354919 | ||||||||
\(778\) | −25.4165 | −0.911227 | ||||||||
\(779\) | 5.36682 | 0.192286 | ||||||||
\(780\) | 1.19160 | 0.0426661 | ||||||||
\(781\) | −0.807433 | −0.0288922 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.34575 | 0.262516 | ||||||||
\(784\) | 3.26315 | 0.116541 | ||||||||
\(785\) | −5.79547 | −0.206849 | ||||||||
\(786\) | −20.9028 | −0.745577 | ||||||||
\(787\) | 20.0112 | 0.713321 | 0.356661 | − | 0.934234i | \(-0.383915\pi\) | ||||
0.356661 | + | 0.934234i | \(0.383915\pi\) | |||||||
\(788\) | 8.89209 | 0.316768 | ||||||||
\(789\) | −9.82969 | −0.349946 | ||||||||
\(790\) | −5.35333 | −0.190463 | ||||||||
\(791\) | −26.3622 | −0.937333 | ||||||||
\(792\) | 0.0552927 | 0.00196474 | ||||||||
\(793\) | −9.83121 | −0.349116 | ||||||||
\(794\) | −3.43509 | −0.121907 | ||||||||
\(795\) | 16.3341 | 0.579313 | ||||||||
\(796\) | 18.1550 | 0.643488 | ||||||||
\(797\) | −19.7315 | −0.698927 | −0.349464 | − | 0.936950i | \(-0.613636\pi\) | ||||
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(798\) | 11.7783 | 0.416948 | ||||||||
\(799\) | −2.62507 | −0.0928682 | ||||||||
\(800\) | −2.81288 | −0.0994503 | ||||||||
\(801\) | −8.25248 | −0.291587 | ||||||||
\(802\) | −8.35498 | −0.295024 | ||||||||
\(803\) | −0.545274 | −0.0192423 | ||||||||
\(804\) | 4.52116 | 0.159449 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.41002 | 0.225783 | ||||||||
\(807\) | 27.0424 | 0.951939 | ||||||||
\(808\) | 15.3507 | 0.540035 | ||||||||
\(809\) | 27.7606 | 0.976009 | 0.488005 | − | 0.872841i | \(-0.337725\pi\) | ||||
0.488005 | + | 0.872841i | \(0.337725\pi\) | |||||||
\(810\) | −1.47889 | −0.0519629 | ||||||||
\(811\) | 18.4982 | 0.649560 | 0.324780 | − | 0.945790i | \(-0.394710\pi\) | ||||
0.324780 | + | 0.945790i | \(0.394710\pi\) | |||||||
\(812\) | −23.5330 | −0.825845 | ||||||||
\(813\) | 14.0124 | 0.491437 | ||||||||
\(814\) | −0.170752 | −0.00598487 | ||||||||
\(815\) | −23.2551 | −0.814590 | ||||||||
\(816\) | 2.05954 | 0.0720982 | ||||||||
\(817\) | 46.0757 | 1.61198 | ||||||||
\(818\) | −4.18657 | −0.146380 | ||||||||
\(819\) | 2.58128 | 0.0901971 | ||||||||
\(820\) | 2.15879 | 0.0753881 | ||||||||
\(821\) | −3.89872 | −0.136066 | −0.0680332 | − | 0.997683i | \(-0.521672\pi\) | ||||
−0.0680332 | + | 0.997683i | \(0.521672\pi\) | |||||||
\(822\) | 5.89909 | 0.205754 | ||||||||
\(823\) | −13.6654 | −0.476345 | −0.238173 | − | 0.971223i | \(-0.576548\pi\) | ||||
−0.238173 | + | 0.971223i | \(0.576548\pi\) | |||||||
\(824\) | 15.3219 | 0.533762 | ||||||||
\(825\) | −0.155532 | −0.00541492 | ||||||||
\(826\) | 17.1738 | 0.597554 | ||||||||
\(827\) | 1.97288 | 0.0686037 | 0.0343019 | − | 0.999412i | \(-0.489079\pi\) | ||||
0.0343019 | + | 0.999412i | \(0.489079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.37133 | 0.221285 | 0.110643 | − | 0.993860i | \(-0.464709\pi\) | ||||
0.110643 | + | 0.993860i | \(0.464709\pi\) | |||||||
\(830\) | 14.8396 | 0.515090 | ||||||||
\(831\) | −6.65528 | −0.230869 | ||||||||
\(832\) | −0.805738 | −0.0279339 | ||||||||
\(833\) | 6.72059 | 0.232855 | ||||||||
\(834\) | −4.04356 | −0.140017 | ||||||||
\(835\) | 5.94462 | 0.205722 | ||||||||
\(836\) | −0.203288 | −0.00703085 | ||||||||
\(837\) | −7.95546 | −0.274981 | ||||||||
\(838\) | 8.98508 | 0.310384 | ||||||||
\(839\) | −0.347463 | −0.0119957 | −0.00599787 | − | 0.999982i | \(-0.501909\pi\) | ||||
−0.00599787 | + | 0.999982i | \(0.501909\pi\) | |||||||
\(840\) | 4.73780 | 0.163470 | ||||||||
\(841\) | 24.9600 | 0.860691 | ||||||||
\(842\) | −6.75886 | −0.232926 | ||||||||
\(843\) | −14.7244 | −0.507135 | ||||||||
\(844\) | 17.2040 | 0.592187 | ||||||||
\(845\) | 18.2655 | 0.628351 | ||||||||
\(846\) | −1.27459 | −0.0438213 | ||||||||
\(847\) | 35.2300 | 1.21052 | ||||||||
\(848\) | −11.0449 | −0.379282 | ||||||||
\(849\) | −13.6907 | −0.469863 | ||||||||
\(850\) | −5.79323 | −0.198706 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −14.6029 | −0.500287 | ||||||||
\(853\) | −22.0786 | −0.755958 | −0.377979 | − | 0.925814i | \(-0.623381\pi\) | ||||
−0.377979 | + | 0.925814i | \(0.623381\pi\) | |||||||
\(854\) | −39.0889 | −1.33759 | ||||||||
\(855\) | 5.43725 | 0.185950 | ||||||||
\(856\) | −9.67542 | −0.330699 | ||||||||
\(857\) | −19.3638 | −0.661454 | −0.330727 | − | 0.943726i | \(-0.607294\pi\) | ||||
−0.330727 | + | 0.943726i | \(0.607294\pi\) | |||||||
\(858\) | −0.0445514 | −0.00152096 | ||||||||
\(859\) | −10.1662 | −0.346866 | −0.173433 | − | 0.984846i | \(-0.555486\pi\) | ||||
−0.173433 | + | 0.984846i | \(0.555486\pi\) | |||||||
\(860\) | 18.5338 | 0.631998 | ||||||||
\(861\) | 4.67642 | 0.159372 | ||||||||
\(862\) | −22.6737 | −0.772271 | ||||||||
\(863\) | −11.7222 | −0.399027 | −0.199514 | − | 0.979895i | \(-0.563936\pi\) | ||||
−0.199514 | + | 0.979895i | \(0.563936\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −7.77079 | −0.264215 | ||||||||
\(866\) | 29.9541 | 1.01788 | ||||||||
\(867\) | −12.7583 | −0.433295 | ||||||||
\(868\) | 25.4862 | 0.865060 | ||||||||
\(869\) | 0.200150 | 0.00678962 | ||||||||
\(870\) | −10.8636 | −0.368309 | ||||||||
\(871\) | −3.64287 | −0.123434 | ||||||||
\(872\) | −13.4002 | −0.453787 | ||||||||
\(873\) | 7.01618 | 0.237462 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −37.0159 | −1.25136 | ||||||||
\(876\) | −9.86160 | −0.333193 | ||||||||
\(877\) | −30.3909 | −1.02623 | −0.513114 | − | 0.858321i | \(-0.671508\pi\) | ||||
−0.513114 | + | 0.858321i | \(0.671508\pi\) | |||||||
\(878\) | −1.50141 | −0.0506702 | ||||||||
\(879\) | 29.6195 | 0.999040 | ||||||||
\(880\) | −0.0817718 | −0.00275653 | ||||||||
\(881\) | −33.3403 | −1.12326 | −0.561632 | − | 0.827387i | \(-0.689826\pi\) | ||||
−0.561632 | + | 0.827387i | \(0.689826\pi\) | |||||||
\(882\) | 3.26315 | 0.109876 | ||||||||
\(883\) | −5.16297 | −0.173748 | −0.0868740 | − | 0.996219i | \(-0.527688\pi\) | ||||
−0.0868740 | + | 0.996219i | \(0.527688\pi\) | |||||||
\(884\) | −1.65945 | −0.0558133 | ||||||||
\(885\) | 7.92800 | 0.266497 | ||||||||
\(886\) | −5.89537 | −0.198059 | ||||||||
\(887\) | −13.6271 | −0.457555 | −0.228777 | − | 0.973479i | \(-0.573473\pi\) | ||||
−0.228777 | + | 0.973479i | \(0.573473\pi\) | |||||||
\(888\) | −3.08816 | −0.103632 | ||||||||
\(889\) | −61.9977 | −2.07933 | ||||||||
\(890\) | 12.2045 | 0.409097 | ||||||||
\(891\) | 0.0552927 | 0.00185237 | ||||||||
\(892\) | −9.64578 | −0.322964 | ||||||||
\(893\) | 4.68613 | 0.156815 | ||||||||
\(894\) | −8.21355 | −0.274702 | ||||||||
\(895\) | 3.12476 | 0.104449 | ||||||||
\(896\) | −3.20362 | −0.107025 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.8587 | −1.22999 | ||||||||
\(899\) | −58.4388 | −1.94904 | ||||||||
\(900\) | −2.81288 | −0.0937627 | ||||||||
\(901\) | −22.7473 | −0.757822 | ||||||||
\(902\) | −0.0807125 | −0.00268743 | ||||||||
\(903\) | 40.1485 | 1.33606 | ||||||||
\(904\) | 8.22890 | 0.273689 | ||||||||
\(905\) | 0.341446 | 0.0113500 | ||||||||
\(906\) | −12.8490 | −0.426881 | ||||||||
\(907\) | −22.2146 | −0.737623 | −0.368811 | − | 0.929504i | \(-0.620235\pi\) | ||||
−0.368811 | + | 0.929504i | \(0.620235\pi\) | |||||||
\(908\) | −13.2879 | −0.440975 | ||||||||
\(909\) | 15.3507 | 0.509150 | ||||||||
\(910\) | −3.81743 | −0.126546 | ||||||||
\(911\) | −18.1822 | −0.602402 | −0.301201 | − | 0.953561i | \(-0.597388\pi\) | ||||
−0.301201 | + | 0.953561i | \(0.597388\pi\) | |||||||
\(912\) | −3.67657 | −0.121744 | ||||||||
\(913\) | −0.554821 | −0.0183619 | ||||||||
\(914\) | −5.79767 | −0.191770 | ||||||||
\(915\) | −18.0447 | −0.596539 | ||||||||
\(916\) | 10.3343 | 0.341456 | ||||||||
\(917\) | 66.9644 | 2.21136 | ||||||||
\(918\) | 2.05954 | 0.0679749 | ||||||||
\(919\) | −30.2025 | −0.996289 | −0.498145 | − | 0.867094i | \(-0.665985\pi\) | ||||
−0.498145 | + | 0.867094i | \(0.665985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.12670 | 0.300735 | ||||||||
\(922\) | −19.1277 | −0.629936 | ||||||||
\(923\) | 11.7661 | 0.387286 | ||||||||
\(924\) | −0.177136 | −0.00582736 | ||||||||
\(925\) | 8.68661 | 0.285614 | ||||||||
\(926\) | −20.3367 | −0.668305 | ||||||||
\(927\) | 15.3219 | 0.503236 | ||||||||
\(928\) | 7.34575 | 0.241136 | ||||||||
\(929\) | −25.8080 | −0.846733 | −0.423366 | − | 0.905959i | \(-0.639152\pi\) | ||||
−0.423366 | + | 0.905959i | \(0.639152\pi\) | |||||||
\(930\) | 11.7653 | 0.385798 | ||||||||
\(931\) | −11.9972 | −0.393193 | ||||||||
\(932\) | −0.221377 | −0.00725144 | ||||||||
\(933\) | 22.9754 | 0.752180 | ||||||||
\(934\) | 27.1467 | 0.888268 | ||||||||
\(935\) | −0.168412 | −0.00550767 | ||||||||
\(936\) | −0.805738 | −0.0263364 | ||||||||
\(937\) | −15.1514 | −0.494976 | −0.247488 | − | 0.968891i | \(-0.579605\pi\) | ||||
−0.247488 | + | 0.968891i | \(0.579605\pi\) | |||||||
\(938\) | −14.4841 | −0.472922 | ||||||||
\(939\) | 19.7421 | 0.644260 | ||||||||
\(940\) | 1.88498 | 0.0614813 | ||||||||
\(941\) | 25.1968 | 0.821391 | 0.410695 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410695 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(942\) | 3.91879 | 0.127681 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −5.36077 | −0.174478 | ||||||||
\(945\) | 4.73780 | 0.154121 | ||||||||
\(946\) | −0.692941 | −0.0225295 | ||||||||
\(947\) | −0.612556 | −0.0199054 | −0.00995271 | − | 0.999950i | \(-0.503168\pi\) | ||||
−0.00995271 | + | 0.999950i | \(0.503168\pi\) | |||||||
\(948\) | 3.61983 | 0.117567 | ||||||||
\(949\) | 7.94587 | 0.257934 | ||||||||
\(950\) | 10.3418 | 0.335531 | ||||||||
\(951\) | −20.8318 | −0.675518 | ||||||||
\(952\) | −6.59797 | −0.213841 | ||||||||
\(953\) | 34.2779 | 1.11037 | 0.555185 | − | 0.831727i | \(-0.312647\pi\) | ||||
0.555185 | + | 0.831727i | \(0.312647\pi\) | |||||||
\(954\) | −11.0449 | −0.357591 | ||||||||
\(955\) | −6.51183 | −0.210718 | ||||||||
\(956\) | 10.0933 | 0.326440 | ||||||||
\(957\) | 0.406166 | 0.0131295 | ||||||||
\(958\) | −3.73359 | −0.120627 | ||||||||
\(959\) | −18.8984 | −0.610262 | ||||||||
\(960\) | −1.47889 | −0.0477310 | ||||||||
\(961\) | 32.2894 | 1.04159 | ||||||||
\(962\) | 2.48825 | 0.0802242 | ||||||||
\(963\) | −9.67542 | −0.311786 | ||||||||
\(964\) | −2.49660 | −0.0804099 | ||||||||
\(965\) | −31.7921 | −1.02343 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.9004 | 1.05801 | 0.529003 | − | 0.848620i | \(-0.322566\pi\) | ||||
0.529003 | + | 0.848620i | \(0.322566\pi\) | |||||||
\(968\) | −10.9969 | −0.353455 | ||||||||
\(969\) | −7.57204 | −0.243249 | ||||||||
\(970\) | −10.3762 | −0.333159 | ||||||||
\(971\) | −15.3464 | −0.492488 | −0.246244 | − | 0.969208i | \(-0.579197\pi\) | ||||
−0.246244 | + | 0.969208i | \(0.579197\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 12.9540 | 0.415287 | ||||||||
\(974\) | 23.0573 | 0.738804 | ||||||||
\(975\) | 2.26645 | 0.0725843 | ||||||||
\(976\) | 12.2015 | 0.390560 | ||||||||
\(977\) | −7.59382 | −0.242948 | −0.121474 | − | 0.992595i | \(-0.538762\pi\) | ||||
−0.121474 | + | 0.992595i | \(0.538762\pi\) | |||||||
\(978\) | 15.7247 | 0.502819 | ||||||||
\(979\) | −0.456302 | −0.0145835 | ||||||||
\(980\) | −4.82585 | −0.154156 | ||||||||
\(981\) | −13.4002 | −0.427835 | ||||||||
\(982\) | −1.12229 | −0.0358137 | ||||||||
\(983\) | 2.79957 | 0.0892924 | 0.0446462 | − | 0.999003i | \(-0.485784\pi\) | ||||
0.0446462 | + | 0.999003i | \(0.485784\pi\) | |||||||
\(984\) | −1.45973 | −0.0465346 | ||||||||
\(985\) | −13.1504 | −0.419008 | ||||||||
\(986\) | 15.1288 | 0.481801 | ||||||||
\(987\) | 4.08330 | 0.129973 | ||||||||
\(988\) | 2.96236 | 0.0942451 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −0.0817718 | −0.00259888 | ||||||||
\(991\) | 0.506808 | 0.0160993 | 0.00804964 | − | 0.999968i | \(-0.497438\pi\) | ||||
0.00804964 | + | 0.999968i | \(0.497438\pi\) | |||||||
\(992\) | −7.95546 | −0.252586 | ||||||||
\(993\) | −15.5468 | −0.493361 | ||||||||
\(994\) | 46.7821 | 1.48384 | ||||||||
\(995\) | −26.8493 | −0.851181 | ||||||||
\(996\) | −10.0343 | −0.317948 | ||||||||
\(997\) | 12.1136 | 0.383640 | 0.191820 | − | 0.981430i | \(-0.438561\pi\) | ||||
0.191820 | + | 0.981430i | \(0.438561\pi\) | |||||||
\(998\) | 39.6576 | 1.25534 | ||||||||
\(999\) | −3.08816 | −0.0977049 |
(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 | 3174.2.a.bc.1.3 | 5 | ||
3.2 | odd | 2 | 9522.2.a.bt.1.3 | 5 | |||
23.4 | even | 11 | 138.2.e.a.85.1 | yes | 10 | ||
23.6 | even | 11 | 138.2.e.a.13.1 | ✓ | 10 | ||
23.22 | odd | 2 | 3174.2.a.bd.1.3 | 5 | |||
69.29 | odd | 22 | 414.2.i.d.289.1 | 10 | |||
69.50 | odd | 22 | 414.2.i.d.361.1 | 10 | |||
69.68 | even | 2 | 9522.2.a.bq.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.e.a.13.1 | ✓ | 10 | 23.6 | even | 11 | ||
138.2.e.a.85.1 | yes | 10 | 23.4 | even | 11 | ||
414.2.i.d.289.1 | 10 | 69.29 | odd | 22 | |||
414.2.i.d.361.1 | 10 | 69.50 | odd | 22 | |||
3174.2.a.bc.1.3 | 5 | 1.1 | even | 1 | trivial | ||
3174.2.a.bd.1.3 | 5 | 23.22 | odd | 2 | |||
9522.2.a.bq.1.3 | 5 | 69.68 | even | 2 | |||
9522.2.a.bt.1.3 | 5 | 3.2 | odd | 2 |