Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.52625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 24x^{2} + 19x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.77556\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.49096 | 1.69742 | 0.848711 | − | 0.528856i | \(-0.177379\pi\) | ||||
0.848711 | + | 0.528856i | \(0.177379\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.33343 | 0.647176 | 0.323588 | − | 0.946198i | \(-0.395111\pi\) | ||||
0.323588 | + | 0.946198i | \(0.395111\pi\) | |||||||
\(14\) | 4.49096 | 1.20026 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.15753 | 1.25088 | 0.625442 | − | 0.780270i | \(-0.284918\pi\) | ||||
0.625442 | + | 0.780270i | \(0.284918\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.01163 | 1.37916 | 0.689582 | − | 0.724208i | \(-0.257794\pi\) | ||||
0.689582 | + | 0.724208i | \(0.257794\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 4.49096 | 0.980007 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.88456 | −1.85256 | −0.926279 | − | 0.376838i | \(-0.877011\pi\) | ||||
−0.926279 | + | 0.376838i | \(0.877011\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.33343 | 0.457623 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.49096 | 0.848711 | ||||||||
\(29\) | −7.58113 | −1.40778 | −0.703890 | − | 0.710309i | \(-0.748555\pi\) | ||||
−0.703890 | + | 0.710309i | \(0.748555\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −1.10899 | −0.199181 | −0.0995905 | − | 0.995029i | \(-0.531753\pi\) | ||||
−0.0995905 | + | 0.995029i | \(0.531753\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.15753 | 0.884509 | ||||||||
\(35\) | −4.49096 | −0.759111 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.93310 | 1.30419 | 0.652096 | − | 0.758136i | \(-0.273890\pi\) | ||||
0.652096 | + | 0.758136i | \(0.273890\pi\) | |||||||
\(38\) | 6.01163 | 0.975216 | ||||||||
\(39\) | 2.33343 | 0.373647 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −9.56995 | −1.49458 | −0.747288 | − | 0.664501i | \(-0.768644\pi\) | ||||
−0.747288 | + | 0.664501i | \(0.768644\pi\) | |||||||
\(42\) | 4.49096 | 0.692970 | ||||||||
\(43\) | 0.0785371 | 0.0119768 | 0.00598839 | − | 0.999982i | \(-0.498094\pi\) | ||||
0.00598839 | + | 0.999982i | \(0.498094\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −8.88456 | −1.30996 | ||||||||
\(47\) | 2.90264 | 0.423394 | 0.211697 | − | 0.977335i | \(-0.432101\pi\) | ||||
0.211697 | + | 0.977335i | \(0.432101\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 13.1687 | 1.88124 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 5.15753 | 0.722199 | ||||||||
\(52\) | 2.33343 | 0.323588 | ||||||||
\(53\) | 0.745110 | 0.102349 | 0.0511743 | − | 0.998690i | \(-0.483704\pi\) | ||||
0.0511743 | + | 0.998690i | \(0.483704\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.49096 | 0.600130 | ||||||||
\(57\) | 6.01163 | 0.796260 | ||||||||
\(58\) | −7.58113 | −0.995451 | ||||||||
\(59\) | −5.32624 | −0.693417 | −0.346709 | − | 0.937973i | \(-0.612701\pi\) | ||||
−0.346709 | + | 0.937973i | \(0.612701\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −15.4541 | −1.97869 | −0.989344 | − | 0.145595i | \(-0.953491\pi\) | ||||
−0.989344 | + | 0.145595i | \(0.953491\pi\) | |||||||
\(62\) | −1.10899 | −0.140842 | ||||||||
\(63\) | 4.49096 | 0.565808 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.33343 | −0.289426 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.67821 | −0.205025 | −0.102513 | − | 0.994732i | \(-0.532688\pi\) | ||||
−0.102513 | + | 0.994732i | \(0.532688\pi\) | |||||||
\(68\) | 5.15753 | 0.625442 | ||||||||
\(69\) | −8.88456 | −1.06958 | ||||||||
\(70\) | −4.49096 | −0.536772 | ||||||||
\(71\) | 9.55113 | 1.13351 | 0.566755 | − | 0.823886i | \(-0.308198\pi\) | ||||
0.566755 | + | 0.823886i | \(0.308198\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −10.9443 | −1.28093 | −0.640465 | − | 0.767987i | \(-0.721258\pi\) | ||||
−0.640465 | + | 0.767987i | \(0.721258\pi\) | |||||||
\(74\) | 7.93310 | 0.922204 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 6.01163 | 0.689582 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.33343 | 0.264209 | ||||||||
\(79\) | 5.47259 | 0.615715 | 0.307857 | − | 0.951433i | \(-0.400388\pi\) | ||||
0.307857 | + | 0.951433i | \(0.400388\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.56995 | −1.05682 | ||||||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 4.49096 | 0.490004 | ||||||||
\(85\) | −5.15753 | −0.559413 | ||||||||
\(86\) | 0.0785371 | 0.00846887 | ||||||||
\(87\) | −7.58113 | −0.812782 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.41196 | −0.785667 | −0.392833 | − | 0.919610i | \(-0.628505\pi\) | ||||
−0.392833 | + | 0.919610i | \(0.628505\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 10.4793 | 1.09853 | ||||||||
\(92\) | −8.88456 | −0.926279 | ||||||||
\(93\) | −1.10899 | −0.114997 | ||||||||
\(94\) | 2.90264 | 0.299385 | ||||||||
\(95\) | −6.01163 | −0.616781 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 5.74585 | 0.583403 | 0.291701 | − | 0.956509i | \(-0.405779\pi\) | ||||
0.291701 | + | 0.956509i | \(0.405779\pi\) | |||||||
\(98\) | 13.1687 | 1.33024 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 16.5739 | 1.64917 | 0.824584 | − | 0.565739i | \(-0.191409\pi\) | ||||
0.824584 | + | 0.565739i | \(0.191409\pi\) | |||||||
\(102\) | 5.15753 | 0.510672 | ||||||||
\(103\) | −1.09063 | −0.107463 | −0.0537313 | − | 0.998555i | \(-0.517111\pi\) | ||||
−0.0537313 | + | 0.998555i | \(0.517111\pi\) | |||||||
\(104\) | 2.33343 | 0.228811 | ||||||||
\(105\) | −4.49096 | −0.438273 | ||||||||
\(106\) | 0.745110 | 0.0723714 | ||||||||
\(107\) | −5.68494 | −0.549584 | −0.274792 | − | 0.961504i | \(-0.588609\pi\) | ||||
−0.274792 | + | 0.961504i | \(0.588609\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 8.94427 | 0.856706 | 0.428353 | − | 0.903612i | \(-0.359094\pi\) | ||||
0.428353 | + | 0.903612i | \(0.359094\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.93310 | 0.752976 | ||||||||
\(112\) | 4.49096 | 0.424356 | ||||||||
\(113\) | 3.87292 | 0.364334 | 0.182167 | − | 0.983268i | \(-0.441689\pi\) | ||||
0.182167 | + | 0.983268i | \(0.441689\pi\) | |||||||
\(114\) | 6.01163 | 0.563041 | ||||||||
\(115\) | 8.88456 | 0.828489 | ||||||||
\(116\) | −7.58113 | −0.703890 | ||||||||
\(117\) | 2.33343 | 0.215725 | ||||||||
\(118\) | −5.32624 | −0.490320 | ||||||||
\(119\) | 23.1623 | 2.12328 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −15.4541 | −1.39914 | ||||||||
\(123\) | −9.56995 | −0.862894 | ||||||||
\(124\) | −1.10899 | −0.0995905 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.49096 | 0.400086 | ||||||||
\(127\) | 8.36343 | 0.742134 | 0.371067 | − | 0.928606i | \(-0.378992\pi\) | ||||
0.371067 | + | 0.928606i | \(0.378992\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.0785371 | 0.00691480 | ||||||||
\(130\) | −2.33343 | −0.204655 | ||||||||
\(131\) | −7.40079 | −0.646610 | −0.323305 | − | 0.946295i | \(-0.604794\pi\) | ||||
−0.323305 | + | 0.946295i | \(0.604794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.9980 | 2.34102 | ||||||||
\(134\) | −1.67821 | −0.144975 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 5.15753 | 0.442255 | ||||||||
\(137\) | −4.44214 | −0.379517 | −0.189759 | − | 0.981831i | \(-0.560771\pi\) | ||||
−0.189759 | + | 0.981831i | \(0.560771\pi\) | |||||||
\(138\) | −8.88456 | −0.756304 | ||||||||
\(139\) | −19.9074 | −1.68852 | −0.844260 | − | 0.535933i | \(-0.819960\pi\) | ||||
−0.844260 | + | 0.535933i | \(0.819960\pi\) | |||||||
\(140\) | −4.49096 | −0.379555 | ||||||||
\(141\) | 2.90264 | 0.244446 | ||||||||
\(142\) | 9.55113 | 0.801513 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.58113 | 0.629578 | ||||||||
\(146\) | −10.9443 | −0.905754 | ||||||||
\(147\) | 13.1687 | 1.08614 | ||||||||
\(148\) | 7.93310 | 0.652096 | ||||||||
\(149\) | 9.31461 | 0.763082 | 0.381541 | − | 0.924352i | \(-0.375393\pi\) | ||||
0.381541 | + | 0.924352i | \(0.375393\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −13.9029 | −1.13140 | −0.565702 | − | 0.824610i | \(-0.691395\pi\) | ||||
−0.565702 | + | 0.824610i | \(0.691395\pi\) | |||||||
\(152\) | 6.01163 | 0.487608 | ||||||||
\(153\) | 5.15753 | 0.416962 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.10899 | 0.0890764 | ||||||||
\(156\) | 2.33343 | 0.186824 | ||||||||
\(157\) | 9.89175 | 0.789447 | 0.394724 | − | 0.918800i | \(-0.370840\pi\) | ||||
0.394724 | + | 0.918800i | \(0.370840\pi\) | |||||||
\(158\) | 5.47259 | 0.435376 | ||||||||
\(159\) | 0.745110 | 0.0590910 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −39.9002 | −3.14457 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 6.43124 | 0.503734 | 0.251867 | − | 0.967762i | \(-0.418955\pi\) | ||||
0.251867 | + | 0.967762i | \(0.418955\pi\) | |||||||
\(164\) | −9.56995 | −0.747288 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.00000 | 0.620920 | ||||||||
\(167\) | 6.04163 | 0.467515 | 0.233758 | − | 0.972295i | \(-0.424898\pi\) | ||||
0.233758 | + | 0.972295i | \(0.424898\pi\) | |||||||
\(168\) | 4.49096 | 0.346485 | ||||||||
\(169\) | −7.55512 | −0.581163 | ||||||||
\(170\) | −5.15753 | −0.395565 | ||||||||
\(171\) | 6.01163 | 0.459721 | ||||||||
\(172\) | 0.0785371 | 0.00598839 | ||||||||
\(173\) | −0.648032 | −0.0492690 | −0.0246345 | − | 0.999697i | \(-0.507842\pi\) | ||||
−0.0246345 | + | 0.999697i | \(0.507842\pi\) | |||||||
\(174\) | −7.58113 | −0.574724 | ||||||||
\(175\) | 4.49096 | 0.339485 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.32624 | −0.400345 | ||||||||
\(178\) | −7.41196 | −0.555550 | ||||||||
\(179\) | 1.56231 | 0.116772 | 0.0583861 | − | 0.998294i | \(-0.481405\pi\) | ||||
0.0583861 | + | 0.998294i | \(0.481405\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 18.4721 | 1.37302 | 0.686512 | − | 0.727119i | \(-0.259141\pi\) | ||||
0.686512 | + | 0.727119i | \(0.259141\pi\) | |||||||
\(182\) | 10.4793 | 0.776779 | ||||||||
\(183\) | −15.4541 | −1.14240 | ||||||||
\(184\) | −8.88456 | −0.654978 | ||||||||
\(185\) | −7.93310 | −0.583253 | ||||||||
\(186\) | −1.10899 | −0.0813153 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.90264 | 0.211697 | ||||||||
\(189\) | 4.49096 | 0.326669 | ||||||||
\(190\) | −6.01163 | −0.436130 | ||||||||
\(191\) | −17.6720 | −1.27870 | −0.639352 | − | 0.768914i | \(-0.720797\pi\) | ||||
−0.639352 | + | 0.768914i | \(0.720797\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 10.4954 | 0.755476 | 0.377738 | − | 0.925913i | \(-0.376702\pi\) | ||||
0.377738 | + | 0.925913i | \(0.376702\pi\) | |||||||
\(194\) | 5.74585 | 0.412528 | ||||||||
\(195\) | −2.33343 | −0.167100 | ||||||||
\(196\) | 13.1687 | 0.940622 | ||||||||
\(197\) | 10.0788 | 0.718086 | 0.359043 | − | 0.933321i | \(-0.383103\pi\) | ||||
0.359043 | + | 0.933321i | \(0.383103\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6906 | −0.970499 | −0.485250 | − | 0.874376i | \(-0.661271\pi\) | ||||
−0.485250 | + | 0.874376i | \(0.661271\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −1.67821 | −0.118371 | ||||||||
\(202\) | 16.5739 | 1.16614 | ||||||||
\(203\) | −34.0465 | −2.38960 | ||||||||
\(204\) | 5.15753 | 0.361099 | ||||||||
\(205\) | 9.56995 | 0.668394 | ||||||||
\(206\) | −1.09063 | −0.0759876 | ||||||||
\(207\) | −8.88456 | −0.617519 | ||||||||
\(208\) | 2.33343 | 0.161794 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.49096 | −0.309906 | ||||||||
\(211\) | −22.8481 | −1.57293 | −0.786464 | − | 0.617636i | \(-0.788091\pi\) | ||||
−0.786464 | + | 0.617636i | \(0.788091\pi\) | |||||||
\(212\) | 0.745110 | 0.0511743 | ||||||||
\(213\) | 9.55113 | 0.654433 | ||||||||
\(214\) | −5.68494 | −0.388614 | ||||||||
\(215\) | −0.0785371 | −0.00535618 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.98044 | −0.338094 | ||||||||
\(218\) | 8.94427 | 0.605783 | ||||||||
\(219\) | −10.9443 | −0.739545 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0347 | 0.809543 | ||||||||
\(222\) | 7.93310 | 0.532435 | ||||||||
\(223\) | −0.490958 | −0.0328770 | −0.0164385 | − | 0.999865i | \(-0.505233\pi\) | ||||
−0.0164385 | + | 0.999865i | \(0.505233\pi\) | |||||||
\(224\) | 4.49096 | 0.300065 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 3.87292 | 0.257623 | ||||||||
\(227\) | −1.49022 | −0.0989093 | −0.0494547 | − | 0.998776i | \(-0.515748\pi\) | ||||
−0.0494547 | + | 0.998776i | \(0.515748\pi\) | |||||||
\(228\) | 6.01163 | 0.398130 | ||||||||
\(229\) | −8.21798 | −0.543060 | −0.271530 | − | 0.962430i | \(-0.587530\pi\) | ||||
−0.271530 | + | 0.962430i | \(0.587530\pi\) | |||||||
\(230\) | 8.88456 | 0.585830 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.58113 | −0.497725 | ||||||||
\(233\) | −6.63686 | −0.434795 | −0.217397 | − | 0.976083i | \(-0.569757\pi\) | ||||
−0.217397 | + | 0.976083i | \(0.569757\pi\) | |||||||
\(234\) | 2.33343 | 0.152541 | ||||||||
\(235\) | −2.90264 | −0.189347 | ||||||||
\(236\) | −5.32624 | −0.346709 | ||||||||
\(237\) | 5.47259 | 0.355483 | ||||||||
\(238\) | 23.1623 | 1.50139 | ||||||||
\(239\) | 6.09764 | 0.394424 | 0.197212 | − | 0.980361i | \(-0.436811\pi\) | ||||
0.197212 | + | 0.980361i | \(0.436811\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −5.70376 | −0.367412 | −0.183706 | − | 0.982981i | \(-0.558809\pi\) | ||||
−0.183706 | + | 0.982981i | \(0.558809\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.4541 | −0.989344 | ||||||||
\(245\) | −13.1687 | −0.841318 | ||||||||
\(246\) | −9.56995 | −0.610158 | ||||||||
\(247\) | 14.0277 | 0.892562 | ||||||||
\(248\) | −1.10899 | −0.0704211 | ||||||||
\(249\) | 8.00000 | 0.506979 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −2.60714 | −0.164561 | −0.0822806 | − | 0.996609i | \(-0.526220\pi\) | ||||
−0.0822806 | + | 0.996609i | \(0.526220\pi\) | |||||||
\(252\) | 4.49096 | 0.282904 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.36343 | 0.524768 | ||||||||
\(255\) | −5.15753 | −0.322977 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.4360 | 1.15000 | 0.575002 | − | 0.818152i | \(-0.305001\pi\) | ||||
0.575002 | + | 0.818152i | \(0.305001\pi\) | |||||||
\(258\) | 0.0785371 | 0.00488950 | ||||||||
\(259\) | 35.6272 | 2.21377 | ||||||||
\(260\) | −2.33343 | −0.144713 | ||||||||
\(261\) | −7.58113 | −0.469260 | ||||||||
\(262\) | −7.40079 | −0.457222 | ||||||||
\(263\) | 24.4285 | 1.50633 | 0.753163 | − | 0.657834i | \(-0.228527\pi\) | ||||
0.753163 | + | 0.657834i | \(0.228527\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.745110 | −0.0457717 | ||||||||
\(266\) | 26.9980 | 1.65535 | ||||||||
\(267\) | −7.41196 | −0.453605 | ||||||||
\(268\) | −1.67821 | −0.102513 | ||||||||
\(269\) | −11.0119 | −0.671408 | −0.335704 | − | 0.941967i | \(-0.608974\pi\) | ||||
−0.335704 | + | 0.941967i | \(0.608974\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 0.647750 | 0.0393480 | 0.0196740 | − | 0.999806i | \(-0.493737\pi\) | ||||
0.0196740 | + | 0.999806i | \(0.493737\pi\) | |||||||
\(272\) | 5.15753 | 0.312721 | ||||||||
\(273\) | 10.4793 | 0.634238 | ||||||||
\(274\) | −4.44214 | −0.268359 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.88456 | −0.534788 | ||||||||
\(277\) | −24.6304 | −1.47990 | −0.739949 | − | 0.672663i | \(-0.765150\pi\) | ||||
−0.739949 | + | 0.672663i | \(0.765150\pi\) | |||||||
\(278\) | −19.9074 | −1.19396 | ||||||||
\(279\) | −1.10899 | −0.0663936 | ||||||||
\(280\) | −4.49096 | −0.268386 | ||||||||
\(281\) | 9.49170 | 0.566227 | 0.283114 | − | 0.959086i | \(-0.408633\pi\) | ||||
0.283114 | + | 0.959086i | \(0.408633\pi\) | |||||||
\(282\) | 2.90264 | 0.172850 | ||||||||
\(283\) | −20.2113 | −1.20143 | −0.600717 | − | 0.799462i | \(-0.705118\pi\) | ||||
−0.600717 | + | 0.799462i | \(0.705118\pi\) | |||||||
\(284\) | 9.55113 | 0.566755 | ||||||||
\(285\) | −6.01163 | −0.356098 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −42.9783 | −2.53693 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 9.60013 | 0.564713 | ||||||||
\(290\) | 7.58113 | 0.445179 | ||||||||
\(291\) | 5.74585 | 0.336828 | ||||||||
\(292\) | −10.9443 | −0.640465 | ||||||||
\(293\) | −1.19398 | −0.0697530 | −0.0348765 | − | 0.999392i | \(-0.511104\pi\) | ||||
−0.0348765 | + | 0.999392i | \(0.511104\pi\) | |||||||
\(294\) | 13.1687 | 0.768015 | ||||||||
\(295\) | 5.32624 | 0.310106 | ||||||||
\(296\) | 7.93310 | 0.461102 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.31461 | 0.539581 | ||||||||
\(299\) | −20.7315 | −1.19893 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 0.352707 | 0.0203297 | ||||||||
\(302\) | −13.9029 | −0.800023 | ||||||||
\(303\) | 16.5739 | 0.952148 | ||||||||
\(304\) | 6.01163 | 0.344791 | ||||||||
\(305\) | 15.4541 | 0.884896 | ||||||||
\(306\) | 5.15753 | 0.294836 | ||||||||
\(307\) | −11.3502 | −0.647793 | −0.323896 | − | 0.946093i | \(-0.604993\pi\) | ||||
−0.323896 | + | 0.946093i | \(0.604993\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.09063 | −0.0620436 | ||||||||
\(310\) | 1.10899 | 0.0629865 | ||||||||
\(311\) | −15.1766 | −0.860588 | −0.430294 | − | 0.902689i | \(-0.641590\pi\) | ||||
−0.430294 | + | 0.902689i | \(0.641590\pi\) | |||||||
\(312\) | 2.33343 | 0.132104 | ||||||||
\(313\) | 23.3570 | 1.32021 | 0.660107 | − | 0.751171i | \(-0.270511\pi\) | ||||
0.660107 | + | 0.751171i | \(0.270511\pi\) | |||||||
\(314\) | 9.89175 | 0.558224 | ||||||||
\(315\) | −4.49096 | −0.253037 | ||||||||
\(316\) | 5.47259 | 0.307857 | ||||||||
\(317\) | 10.6641 | 0.598956 | 0.299478 | − | 0.954103i | \(-0.403187\pi\) | ||||
0.299478 | + | 0.954103i | \(0.403187\pi\) | |||||||
\(318\) | 0.745110 | 0.0417837 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −5.68494 | −0.317302 | ||||||||
\(322\) | −39.9002 | −2.22355 | ||||||||
\(323\) | 31.0052 | 1.72517 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.33343 | 0.129435 | ||||||||
\(326\) | 6.43124 | 0.356194 | ||||||||
\(327\) | 8.94427 | 0.494619 | ||||||||
\(328\) | −9.56995 | −0.528412 | ||||||||
\(329\) | 13.0356 | 0.718678 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.42434 | −0.133254 | −0.0666268 | − | 0.997778i | \(-0.521224\pi\) | ||||
−0.0666268 | + | 0.997778i | \(0.521224\pi\) | |||||||
\(332\) | 8.00000 | 0.439057 | ||||||||
\(333\) | 7.93310 | 0.434731 | ||||||||
\(334\) | 6.04163 | 0.330583 | ||||||||
\(335\) | 1.67821 | 0.0916902 | ||||||||
\(336\) | 4.49096 | 0.245002 | ||||||||
\(337\) | −1.17664 | −0.0640954 | −0.0320477 | − | 0.999486i | \(-0.510203\pi\) | ||||
−0.0320477 | + | 0.999486i | \(0.510203\pi\) | |||||||
\(338\) | −7.55512 | −0.410944 | ||||||||
\(339\) | 3.87292 | 0.210348 | ||||||||
\(340\) | −5.15753 | −0.279706 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.01163 | 0.325072 | ||||||||
\(343\) | 27.7034 | 1.49584 | ||||||||
\(344\) | 0.0785371 | 0.00423443 | ||||||||
\(345\) | 8.88456 | 0.478328 | ||||||||
\(346\) | −0.648032 | −0.0348384 | ||||||||
\(347\) | −23.3570 | −1.25387 | −0.626934 | − | 0.779072i | \(-0.715690\pi\) | ||||
−0.626934 | + | 0.779072i | \(0.715690\pi\) | |||||||
\(348\) | −7.58113 | −0.406391 | ||||||||
\(349\) | −0.375059 | −0.0200764 | −0.0100382 | − | 0.999950i | \(-0.503195\pi\) | ||||
−0.0100382 | + | 0.999950i | \(0.503195\pi\) | |||||||
\(350\) | 4.49096 | 0.240052 | ||||||||
\(351\) | 2.33343 | 0.124549 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.07854 | 0.110629 | 0.0553147 | − | 0.998469i | \(-0.482384\pi\) | ||||
0.0553147 | + | 0.998469i | \(0.482384\pi\) | |||||||
\(354\) | −5.32624 | −0.283086 | ||||||||
\(355\) | −9.55113 | −0.506921 | ||||||||
\(356\) | −7.41196 | −0.392833 | ||||||||
\(357\) | 23.1623 | 1.22588 | ||||||||
\(358\) | 1.56231 | 0.0825704 | ||||||||
\(359\) | 0.180340 | 0.00951798 | 0.00475899 | − | 0.999989i | \(-0.498485\pi\) | ||||
0.00475899 | + | 0.999989i | \(0.498485\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 17.1397 | 0.902091 | ||||||||
\(362\) | 18.4721 | 0.970874 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.4793 | 0.549266 | ||||||||
\(365\) | 10.9443 | 0.572849 | ||||||||
\(366\) | −15.4541 | −0.807796 | ||||||||
\(367\) | 11.6706 | 0.609198 | 0.304599 | − | 0.952481i | \(-0.401478\pi\) | ||||
0.304599 | + | 0.952481i | \(0.401478\pi\) | |||||||
\(368\) | −8.88456 | −0.463140 | ||||||||
\(369\) | −9.56995 | −0.498192 | ||||||||
\(370\) | −7.93310 | −0.412422 | ||||||||
\(371\) | 3.34626 | 0.173729 | ||||||||
\(372\) | −1.10899 | −0.0574986 | ||||||||
\(373\) | −10.1687 | −0.526516 | −0.263258 | − | 0.964726i | \(-0.584797\pi\) | ||||
−0.263258 | + | 0.964726i | \(0.584797\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 2.90264 | 0.149692 | ||||||||
\(377\) | −17.6900 | −0.911082 | ||||||||
\(378\) | 4.49096 | 0.230990 | ||||||||
\(379\) | 11.0825 | 0.569271 | 0.284636 | − | 0.958636i | \(-0.408127\pi\) | ||||
0.284636 | + | 0.958636i | \(0.408127\pi\) | |||||||
\(380\) | −6.01163 | −0.308390 | ||||||||
\(381\) | 8.36343 | 0.428471 | ||||||||
\(382\) | −17.6720 | −0.904180 | ||||||||
\(383\) | 21.3082 | 1.08880 | 0.544398 | − | 0.838827i | \(-0.316758\pi\) | ||||
0.544398 | + | 0.838827i | \(0.316758\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.4954 | 0.534202 | ||||||||
\(387\) | 0.0785371 | 0.00399226 | ||||||||
\(388\) | 5.74585 | 0.291701 | ||||||||
\(389\) | −37.7362 | −1.91330 | −0.956651 | − | 0.291238i | \(-0.905933\pi\) | ||||
−0.956651 | + | 0.291238i | \(0.905933\pi\) | |||||||
\(390\) | −2.33343 | −0.118158 | ||||||||
\(391\) | −45.8224 | −2.31734 | ||||||||
\(392\) | 13.1687 | 0.665120 | ||||||||
\(393\) | −7.40079 | −0.373320 | ||||||||
\(394\) | 10.0788 | 0.507764 | ||||||||
\(395\) | −5.47259 | −0.275356 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.4348 | −1.12597 | −0.562985 | − | 0.826467i | \(-0.690347\pi\) | ||||
−0.562985 | + | 0.826467i | \(0.690347\pi\) | |||||||
\(398\) | −13.6906 | −0.686247 | ||||||||
\(399\) | 26.9980 | 1.35159 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −25.9002 | −1.29339 | −0.646697 | − | 0.762747i | \(-0.723850\pi\) | ||||
−0.646697 | + | 0.762747i | \(0.723850\pi\) | |||||||
\(402\) | −1.67821 | −0.0837013 | ||||||||
\(403\) | −2.58775 | −0.128905 | ||||||||
\(404\) | 16.5739 | 0.824584 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −34.0465 | −1.68970 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 5.15753 | 0.255336 | ||||||||
\(409\) | −24.7921 | −1.22589 | −0.612945 | − | 0.790125i | \(-0.710015\pi\) | ||||
−0.612945 | + | 0.790125i | \(0.710015\pi\) | |||||||
\(410\) | 9.56995 | 0.472626 | ||||||||
\(411\) | −4.44214 | −0.219114 | ||||||||
\(412\) | −1.09063 | −0.0537313 | ||||||||
\(413\) | −23.9199 | −1.17702 | ||||||||
\(414\) | −8.88456 | −0.436652 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 2.33343 | 0.114406 | ||||||||
\(417\) | −19.9074 | −0.974868 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.8969 | 1.36285 | 0.681427 | − | 0.731886i | \(-0.261360\pi\) | ||||
0.681427 | + | 0.731886i | \(0.261360\pi\) | |||||||
\(420\) | −4.49096 | −0.219136 | ||||||||
\(421\) | 25.0052 | 1.21868 | 0.609339 | − | 0.792910i | \(-0.291435\pi\) | ||||
0.609339 | + | 0.792910i | \(0.291435\pi\) | |||||||
\(422\) | −22.8481 | −1.11223 | ||||||||
\(423\) | 2.90264 | 0.141131 | ||||||||
\(424\) | 0.745110 | 0.0361857 | ||||||||
\(425\) | 5.15753 | 0.250177 | ||||||||
\(426\) | 9.55113 | 0.462754 | ||||||||
\(427\) | −69.4035 | −3.35867 | ||||||||
\(428\) | −5.68494 | −0.274792 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0785371 | −0.00378739 | ||||||||
\(431\) | −17.9624 | −0.865216 | −0.432608 | − | 0.901582i | \(-0.642407\pi\) | ||||
−0.432608 | + | 0.901582i | \(0.642407\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −26.9458 | −1.29493 | −0.647465 | − | 0.762095i | \(-0.724171\pi\) | ||||
−0.647465 | + | 0.762095i | \(0.724171\pi\) | |||||||
\(434\) | −4.98044 | −0.239069 | ||||||||
\(435\) | 7.58113 | 0.363487 | ||||||||
\(436\) | 8.94427 | 0.428353 | ||||||||
\(437\) | −53.4107 | −2.55498 | ||||||||
\(438\) | −10.9443 | −0.522938 | ||||||||
\(439\) | −4.79393 | −0.228802 | −0.114401 | − | 0.993435i | \(-0.536495\pi\) | ||||
−0.114401 | + | 0.993435i | \(0.536495\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.1687 | 0.627081 | ||||||||
\(442\) | 12.0347 | 0.572433 | ||||||||
\(443\) | 10.0600 | 0.477965 | 0.238982 | − | 0.971024i | \(-0.423186\pi\) | ||||
0.238982 | + | 0.971024i | \(0.423186\pi\) | |||||||
\(444\) | 7.93310 | 0.376488 | ||||||||
\(445\) | 7.41196 | 0.351361 | ||||||||
\(446\) | −0.490958 | −0.0232476 | ||||||||
\(447\) | 9.31461 | 0.440566 | ||||||||
\(448\) | 4.49096 | 0.212178 | ||||||||
\(449\) | −0.498148 | −0.0235091 | −0.0117545 | − | 0.999931i | \(-0.503742\pi\) | ||||
−0.0117545 | + | 0.999931i | \(0.503742\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.87292 | 0.182167 | ||||||||
\(453\) | −13.9029 | −0.653216 | ||||||||
\(454\) | −1.49022 | −0.0699395 | ||||||||
\(455\) | −10.4793 | −0.491278 | ||||||||
\(456\) | 6.01163 | 0.281521 | ||||||||
\(457\) | −1.85730 | −0.0868811 | −0.0434405 | − | 0.999056i | \(-0.513832\pi\) | ||||
−0.0434405 | + | 0.999056i | \(0.513832\pi\) | |||||||
\(458\) | −8.21798 | −0.384001 | ||||||||
\(459\) | 5.15753 | 0.240733 | ||||||||
\(460\) | 8.88456 | 0.414245 | ||||||||
\(461\) | −22.1394 | −1.03114 | −0.515568 | − | 0.856848i | \(-0.672419\pi\) | ||||
−0.515568 | + | 0.856848i | \(0.672419\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.1920 | −1.03135 | −0.515674 | − | 0.856785i | \(-0.672459\pi\) | ||||
−0.515674 | + | 0.856785i | \(0.672459\pi\) | |||||||
\(464\) | −7.58113 | −0.351945 | ||||||||
\(465\) | 1.10899 | 0.0514283 | ||||||||
\(466\) | −6.63686 | −0.307446 | ||||||||
\(467\) | 31.6953 | 1.46668 | 0.733342 | − | 0.679860i | \(-0.237959\pi\) | ||||
0.733342 | + | 0.679860i | \(0.237959\pi\) | |||||||
\(468\) | 2.33343 | 0.107863 | ||||||||
\(469\) | −7.53675 | −0.348015 | ||||||||
\(470\) | −2.90264 | −0.133889 | ||||||||
\(471\) | 9.89175 | 0.455788 | ||||||||
\(472\) | −5.32624 | −0.245160 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 5.47259 | 0.251365 | ||||||||
\(475\) | 6.01163 | 0.275833 | ||||||||
\(476\) | 23.1623 | 1.06164 | ||||||||
\(477\) | 0.745110 | 0.0341162 | ||||||||
\(478\) | 6.09764 | 0.278900 | ||||||||
\(479\) | 23.2217 | 1.06103 | 0.530513 | − | 0.847677i | \(-0.321999\pi\) | ||||
0.530513 | + | 0.847677i | \(0.321999\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 18.5113 | 0.844043 | ||||||||
\(482\) | −5.70376 | −0.259799 | ||||||||
\(483\) | −39.9002 | −1.81552 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.74585 | −0.260906 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −38.9081 | −1.76309 | −0.881547 | − | 0.472096i | \(-0.843498\pi\) | ||||
−0.881547 | + | 0.472096i | \(0.843498\pi\) | |||||||
\(488\) | −15.4541 | −0.699572 | ||||||||
\(489\) | 6.43124 | 0.290831 | ||||||||
\(490\) | −13.1687 | −0.594902 | ||||||||
\(491\) | −4.66139 | −0.210366 | −0.105183 | − | 0.994453i | \(-0.533543\pi\) | ||||
−0.105183 | + | 0.994453i | \(0.533543\pi\) | |||||||
\(492\) | −9.56995 | −0.431447 | ||||||||
\(493\) | −39.0999 | −1.76097 | ||||||||
\(494\) | 14.0277 | 0.631136 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.10899 | −0.0497952 | ||||||||
\(497\) | 42.8937 | 1.92405 | ||||||||
\(498\) | 8.00000 | 0.358489 | ||||||||
\(499\) | 16.3933 | 0.733866 | 0.366933 | − | 0.930247i | \(-0.380408\pi\) | ||||
0.366933 | + | 0.930247i | \(0.380408\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 6.04163 | 0.269920 | ||||||||
\(502\) | −2.60714 | −0.116362 | ||||||||
\(503\) | 0.684656 | 0.0305273 | 0.0152636 | − | 0.999884i | \(-0.495141\pi\) | ||||
0.0152636 | + | 0.999884i | \(0.495141\pi\) | |||||||
\(504\) | 4.49096 | 0.200043 | ||||||||
\(505\) | −16.5739 | −0.737531 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.55512 | −0.335534 | ||||||||
\(508\) | 8.36343 | 0.371067 | ||||||||
\(509\) | 5.38550 | 0.238708 | 0.119354 | − | 0.992852i | \(-0.461918\pi\) | ||||
0.119354 | + | 0.992852i | \(0.461918\pi\) | |||||||
\(510\) | −5.15753 | −0.228379 | ||||||||
\(511\) | −49.1503 | −2.17428 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.01163 | 0.265420 | ||||||||
\(514\) | 18.4360 | 0.813176 | ||||||||
\(515\) | 1.09063 | 0.0480588 | ||||||||
\(516\) | 0.0785371 | 0.00345740 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 35.6272 | 1.56537 | ||||||||
\(519\) | −0.648032 | −0.0284455 | ||||||||
\(520\) | −2.33343 | −0.102328 | ||||||||
\(521\) | 7.60668 | 0.333255 | 0.166627 | − | 0.986020i | \(-0.446712\pi\) | ||||
0.166627 | + | 0.986020i | \(0.446712\pi\) | |||||||
\(522\) | −7.58113 | −0.331817 | ||||||||
\(523\) | 5.61204 | 0.245397 | 0.122699 | − | 0.992444i | \(-0.460845\pi\) | ||||
0.122699 | + | 0.992444i | \(0.460845\pi\) | |||||||
\(524\) | −7.40079 | −0.323305 | ||||||||
\(525\) | 4.49096 | 0.196001 | ||||||||
\(526\) | 24.4285 | 1.06513 | ||||||||
\(527\) | −5.71966 | −0.249152 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.9354 | 2.43197 | ||||||||
\(530\) | −0.745110 | −0.0323655 | ||||||||
\(531\) | −5.32624 | −0.231139 | ||||||||
\(532\) | 26.9980 | 1.17051 | ||||||||
\(533\) | −22.3308 | −0.967254 | ||||||||
\(534\) | −7.41196 | −0.320747 | ||||||||
\(535\) | 5.68494 | 0.245781 | ||||||||
\(536\) | −1.67821 | −0.0724874 | ||||||||
\(537\) | 1.56231 | 0.0674185 | ||||||||
\(538\) | −11.0119 | −0.474757 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 44.8337 | 1.92755 | 0.963776 | − | 0.266712i | \(-0.0859372\pi\) | ||||
0.963776 | + | 0.266712i | \(0.0859372\pi\) | |||||||
\(542\) | 0.647750 | 0.0278233 | ||||||||
\(543\) | 18.4721 | 0.792715 | ||||||||
\(544\) | 5.15753 | 0.221127 | ||||||||
\(545\) | −8.94427 | −0.383131 | ||||||||
\(546\) | 10.4793 | 0.448474 | ||||||||
\(547\) | −10.7578 | −0.459969 | −0.229984 | − | 0.973194i | \(-0.573868\pi\) | ||||
−0.229984 | + | 0.973194i | \(0.573868\pi\) | |||||||
\(548\) | −4.44214 | −0.189759 | ||||||||
\(549\) | −15.4541 | −0.659563 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45.5750 | −1.94156 | ||||||||
\(552\) | −8.88456 | −0.378152 | ||||||||
\(553\) | 24.5772 | 1.04513 | ||||||||
\(554\) | −24.6304 | −1.04645 | ||||||||
\(555\) | −7.93310 | −0.336741 | ||||||||
\(556\) | −19.9074 | −0.844260 | ||||||||
\(557\) | 21.0762 | 0.893029 | 0.446515 | − | 0.894776i | \(-0.352665\pi\) | ||||
0.446515 | + | 0.894776i | \(0.352665\pi\) | |||||||
\(558\) | −1.10899 | −0.0469474 | ||||||||
\(559\) | 0.183261 | 0.00775109 | ||||||||
\(560\) | −4.49096 | −0.189778 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.49170 | 0.400383 | ||||||||
\(563\) | −26.4216 | −1.11354 | −0.556769 | − | 0.830668i | \(-0.687959\pi\) | ||||
−0.556769 | + | 0.830668i | \(0.687959\pi\) | |||||||
\(564\) | 2.90264 | 0.122223 | ||||||||
\(565\) | −3.87292 | −0.162935 | ||||||||
\(566\) | −20.2113 | −0.849542 | ||||||||
\(567\) | 4.49096 | 0.188603 | ||||||||
\(568\) | 9.55113 | 0.400757 | ||||||||
\(569\) | −32.0892 | −1.34525 | −0.672624 | − | 0.739984i | \(-0.734833\pi\) | ||||
−0.672624 | + | 0.739984i | \(0.734833\pi\) | |||||||
\(570\) | −6.01163 | −0.251800 | ||||||||
\(571\) | −0.842187 | −0.0352444 | −0.0176222 | − | 0.999845i | \(-0.505610\pi\) | ||||
−0.0176222 | + | 0.999845i | \(0.505610\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.6720 | −0.738260 | ||||||||
\(574\) | −42.9783 | −1.79388 | ||||||||
\(575\) | −8.88456 | −0.370512 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −15.5655 | −0.648001 | −0.324000 | − | 0.946057i | \(-0.605028\pi\) | ||||
−0.324000 | + | 0.946057i | \(0.605028\pi\) | |||||||
\(578\) | 9.60013 | 0.399313 | ||||||||
\(579\) | 10.4954 | 0.436174 | ||||||||
\(580\) | 7.58113 | 0.314789 | ||||||||
\(581\) | 35.9277 | 1.49053 | ||||||||
\(582\) | 5.74585 | 0.238173 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.9443 | −0.452877 | ||||||||
\(585\) | −2.33343 | −0.0964754 | ||||||||
\(586\) | −1.19398 | −0.0493229 | ||||||||
\(587\) | 19.2593 | 0.794918 | 0.397459 | − | 0.917620i | \(-0.369892\pi\) | ||||
0.397459 | + | 0.917620i | \(0.369892\pi\) | |||||||
\(588\) | 13.1687 | 0.543068 | ||||||||
\(589\) | −6.66685 | −0.274703 | ||||||||
\(590\) | 5.32624 | 0.219278 | ||||||||
\(591\) | 10.0788 | 0.414587 | ||||||||
\(592\) | 7.93310 | 0.326048 | ||||||||
\(593\) | −21.1332 | −0.867835 | −0.433918 | − | 0.900953i | \(-0.642869\pi\) | ||||
−0.433918 | + | 0.900953i | \(0.642869\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.1623 | −0.949560 | ||||||||
\(596\) | 9.31461 | 0.381541 | ||||||||
\(597\) | −13.6906 | −0.560318 | ||||||||
\(598\) | −20.7315 | −0.847773 | ||||||||
\(599\) | −13.2217 | −0.540224 | −0.270112 | − | 0.962829i | \(-0.587061\pi\) | ||||
−0.270112 | + | 0.962829i | \(0.587061\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −39.2115 | −1.59947 | −0.799736 | − | 0.600352i | \(-0.795027\pi\) | ||||
−0.799736 | + | 0.600352i | \(0.795027\pi\) | |||||||
\(602\) | 0.352707 | 0.0143752 | ||||||||
\(603\) | −1.67821 | −0.0683418 | ||||||||
\(604\) | −13.9029 | −0.565702 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.5739 | 0.673270 | ||||||||
\(607\) | −8.33889 | −0.338465 | −0.169233 | − | 0.985576i | \(-0.554129\pi\) | ||||
−0.169233 | + | 0.985576i | \(0.554129\pi\) | |||||||
\(608\) | 6.01163 | 0.243804 | ||||||||
\(609\) | −34.0465 | −1.37964 | ||||||||
\(610\) | 15.4541 | 0.625716 | ||||||||
\(611\) | 6.77310 | 0.274010 | ||||||||
\(612\) | 5.15753 | 0.208481 | ||||||||
\(613\) | 46.7966 | 1.89010 | 0.945049 | − | 0.326927i | \(-0.106013\pi\) | ||||
0.945049 | + | 0.326927i | \(0.106013\pi\) | |||||||
\(614\) | −11.3502 | −0.458059 | ||||||||
\(615\) | 9.56995 | 0.385898 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.5692 | −0.747568 | −0.373784 | − | 0.927516i | \(-0.621940\pi\) | ||||
−0.373784 | + | 0.927516i | \(0.621940\pi\) | |||||||
\(618\) | −1.09063 | −0.0438714 | ||||||||
\(619\) | −9.05390 | −0.363907 | −0.181953 | − | 0.983307i | \(-0.558242\pi\) | ||||
−0.181953 | + | 0.983307i | \(0.558242\pi\) | |||||||
\(620\) | 1.10899 | 0.0445382 | ||||||||
\(621\) | −8.88456 | −0.356525 | ||||||||
\(622\) | −15.1766 | −0.608528 | ||||||||
\(623\) | −33.2868 | −1.33361 | ||||||||
\(624\) | 2.33343 | 0.0934119 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.3570 | 0.933532 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.89175 | 0.394724 | ||||||||
\(629\) | 40.9152 | 1.63140 | ||||||||
\(630\) | −4.49096 | −0.178924 | ||||||||
\(631\) | 37.0223 | 1.47383 | 0.736917 | − | 0.675983i | \(-0.236281\pi\) | ||||
0.736917 | + | 0.675983i | \(0.236281\pi\) | |||||||
\(632\) | 5.47259 | 0.217688 | ||||||||
\(633\) | −22.8481 | −0.908131 | ||||||||
\(634\) | 10.6641 | 0.423526 | ||||||||
\(635\) | −8.36343 | −0.331892 | ||||||||
\(636\) | 0.745110 | 0.0295455 | ||||||||
\(637\) | 30.7282 | 1.21750 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.55113 | 0.377837 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −10.8499 | −0.428547 | −0.214273 | − | 0.976774i | \(-0.568738\pi\) | ||||
−0.214273 | + | 0.976774i | \(0.568738\pi\) | |||||||
\(642\) | −5.68494 | −0.224367 | ||||||||
\(643\) | 29.4482 | 1.16132 | 0.580662 | − | 0.814144i | \(-0.302794\pi\) | ||||
0.580662 | + | 0.814144i | \(0.302794\pi\) | |||||||
\(644\) | −39.9002 | −1.57229 | ||||||||
\(645\) | −0.0785371 | −0.00309239 | ||||||||
\(646\) | 31.0052 | 1.21988 | ||||||||
\(647\) | −33.9447 | −1.33450 | −0.667252 | − | 0.744832i | \(-0.732530\pi\) | ||||
−0.667252 | + | 0.744832i | \(0.732530\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.33343 | 0.0915246 | ||||||||
\(651\) | −4.98044 | −0.195199 | ||||||||
\(652\) | 6.43124 | 0.251867 | ||||||||
\(653\) | −19.0906 | −0.747074 | −0.373537 | − | 0.927615i | \(-0.621855\pi\) | ||||
−0.373537 | + | 0.927615i | \(0.621855\pi\) | |||||||
\(654\) | 8.94427 | 0.349749 | ||||||||
\(655\) | 7.40079 | 0.289173 | ||||||||
\(656\) | −9.56995 | −0.373644 | ||||||||
\(657\) | −10.9443 | −0.426977 | ||||||||
\(658\) | 13.0356 | 0.508182 | ||||||||
\(659\) | 9.56904 | 0.372757 | 0.186378 | − | 0.982478i | \(-0.440325\pi\) | ||||
0.186378 | + | 0.982478i | \(0.440325\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.7878 | 0.652968 | 0.326484 | − | 0.945203i | \(-0.394136\pi\) | ||||
0.326484 | + | 0.945203i | \(0.394136\pi\) | |||||||
\(662\) | −2.42434 | −0.0942245 | ||||||||
\(663\) | 12.0347 | 0.467390 | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | −26.9980 | −1.04694 | ||||||||
\(666\) | 7.93310 | 0.307401 | ||||||||
\(667\) | 67.3550 | 2.60799 | ||||||||
\(668\) | 6.04163 | 0.233758 | ||||||||
\(669\) | −0.490958 | −0.0189815 | ||||||||
\(670\) | 1.67821 | 0.0648347 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.49096 | 0.173242 | ||||||||
\(673\) | −46.2878 | −1.78426 | −0.892131 | − | 0.451776i | \(-0.850791\pi\) | ||||
−0.892131 | + | 0.451776i | \(0.850791\pi\) | |||||||
\(674\) | −1.17664 | −0.0453223 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −7.55512 | −0.290581 | ||||||||
\(677\) | −27.2450 | −1.04711 | −0.523554 | − | 0.851992i | \(-0.675394\pi\) | ||||
−0.523554 | + | 0.851992i | \(0.675394\pi\) | |||||||
\(678\) | 3.87292 | 0.148739 | ||||||||
\(679\) | 25.8044 | 0.990281 | ||||||||
\(680\) | −5.15753 | −0.197782 | ||||||||
\(681\) | −1.49022 | −0.0571053 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.62551 | 0.138726 | 0.0693631 | − | 0.997591i | \(-0.477903\pi\) | ||||
0.0693631 | + | 0.997591i | \(0.477903\pi\) | |||||||
\(684\) | 6.01163 | 0.229861 | ||||||||
\(685\) | 4.44214 | 0.169725 | ||||||||
\(686\) | 27.7034 | 1.05772 | ||||||||
\(687\) | −8.21798 | −0.313536 | ||||||||
\(688\) | 0.0785371 | 0.00299420 | ||||||||
\(689\) | 1.73866 | 0.0662376 | ||||||||
\(690\) | 8.88456 | 0.338229 | ||||||||
\(691\) | −50.3666 | −1.91604 | −0.958018 | − | 0.286708i | \(-0.907439\pi\) | ||||
−0.958018 | + | 0.286708i | \(0.907439\pi\) | |||||||
\(692\) | −0.648032 | −0.0246345 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.3570 | −0.886619 | ||||||||
\(695\) | 19.9074 | 0.755129 | ||||||||
\(696\) | −7.58113 | −0.287362 | ||||||||
\(697\) | −49.3573 | −1.86954 | ||||||||
\(698\) | −0.375059 | −0.0141962 | ||||||||
\(699\) | −6.63686 | −0.251029 | ||||||||
\(700\) | 4.49096 | 0.169742 | ||||||||
\(701\) | 17.1399 | 0.647365 | 0.323683 | − | 0.946166i | \(-0.395079\pi\) | ||||
0.323683 | + | 0.946166i | \(0.395079\pi\) | |||||||
\(702\) | 2.33343 | 0.0880695 | ||||||||
\(703\) | 47.6909 | 1.79869 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.90264 | −0.109320 | ||||||||
\(706\) | 2.07854 | 0.0782268 | ||||||||
\(707\) | 74.4329 | 2.79934 | ||||||||
\(708\) | −5.32624 | −0.200172 | ||||||||
\(709\) | 29.1399 | 1.09437 | 0.547186 | − | 0.837011i | \(-0.315699\pi\) | ||||
0.547186 | + | 0.837011i | \(0.315699\pi\) | |||||||
\(710\) | −9.55113 | −0.358448 | ||||||||
\(711\) | 5.47259 | 0.205238 | ||||||||
\(712\) | −7.41196 | −0.277775 | ||||||||
\(713\) | 9.85291 | 0.368994 | ||||||||
\(714\) | 23.1623 | 0.866826 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.56231 | 0.0583861 | ||||||||
\(717\) | 6.09764 | 0.227721 | ||||||||
\(718\) | 0.180340 | 0.00673022 | ||||||||
\(719\) | 30.8625 | 1.15098 | 0.575488 | − | 0.817810i | \(-0.304812\pi\) | ||||
0.575488 | + | 0.817810i | \(0.304812\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −4.89796 | −0.182410 | ||||||||
\(722\) | 17.1397 | 0.637875 | ||||||||
\(723\) | −5.70376 | −0.212125 | ||||||||
\(724\) | 18.4721 | 0.686512 | ||||||||
\(725\) | −7.58113 | −0.281556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.64376 | −0.135140 | −0.0675699 | − | 0.997715i | \(-0.521525\pi\) | ||||
−0.0675699 | + | 0.997715i | \(0.521525\pi\) | |||||||
\(728\) | 10.4793 | 0.388390 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.9443 | 0.405066 | ||||||||
\(731\) | 0.405057 | 0.0149816 | ||||||||
\(732\) | −15.4541 | −0.571198 | ||||||||
\(733\) | 7.78765 | 0.287644 | 0.143822 | − | 0.989604i | \(-0.454061\pi\) | ||||
0.143822 | + | 0.989604i | \(0.454061\pi\) | |||||||
\(734\) | 11.6706 | 0.430768 | ||||||||
\(735\) | −13.1687 | −0.485735 | ||||||||
\(736\) | −8.88456 | −0.327489 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −9.56995 | −0.352275 | ||||||||
\(739\) | 9.07455 | 0.333813 | 0.166906 | − | 0.985973i | \(-0.446622\pi\) | ||||
0.166906 | + | 0.985973i | \(0.446622\pi\) | |||||||
\(740\) | −7.93310 | −0.291626 | ||||||||
\(741\) | 14.0277 | 0.515321 | ||||||||
\(742\) | 3.34626 | 0.122845 | ||||||||
\(743\) | −9.48702 | −0.348045 | −0.174022 | − | 0.984742i | \(-0.555677\pi\) | ||||
−0.174022 | + | 0.984742i | \(0.555677\pi\) | |||||||
\(744\) | −1.10899 | −0.0406576 | ||||||||
\(745\) | −9.31461 | −0.341261 | ||||||||
\(746\) | −10.1687 | −0.372303 | ||||||||
\(747\) | 8.00000 | 0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.5308 | −0.932876 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 49.4211 | 1.80340 | 0.901701 | − | 0.432359i | \(-0.142319\pi\) | ||||
0.901701 | + | 0.432359i | \(0.142319\pi\) | |||||||
\(752\) | 2.90264 | 0.105848 | ||||||||
\(753\) | −2.60714 | −0.0950095 | ||||||||
\(754\) | −17.6900 | −0.644232 | ||||||||
\(755\) | 13.9029 | 0.505979 | ||||||||
\(756\) | 4.49096 | 0.163335 | ||||||||
\(757\) | −25.2771 | −0.918713 | −0.459357 | − | 0.888252i | \(-0.651920\pi\) | ||||
−0.459357 | + | 0.888252i | \(0.651920\pi\) | |||||||
\(758\) | 11.0825 | 0.402535 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.01163 | −0.218065 | ||||||||
\(761\) | −22.6301 | −0.820341 | −0.410171 | − | 0.912009i | \(-0.634531\pi\) | ||||
−0.410171 | + | 0.912009i | \(0.634531\pi\) | |||||||
\(762\) | 8.36343 | 0.302975 | ||||||||
\(763\) | 40.1684 | 1.45419 | ||||||||
\(764\) | −17.6720 | −0.639352 | ||||||||
\(765\) | −5.15753 | −0.186471 | ||||||||
\(766\) | 21.3082 | 0.769895 | ||||||||
\(767\) | −12.4284 | −0.448763 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −11.4015 | −0.411150 | −0.205575 | − | 0.978641i | \(-0.565906\pi\) | ||||
−0.205575 | + | 0.978641i | \(0.565906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.4360 | 0.663955 | ||||||||
\(772\) | 10.4954 | 0.377738 | ||||||||
\(773\) | 18.8896 | 0.679413 | 0.339706 | − | 0.940532i | \(-0.389672\pi\) | ||||
0.339706 | + | 0.940532i | \(0.389672\pi\) | |||||||
\(774\) | 0.0785371 | 0.00282296 | ||||||||
\(775\) | −1.10899 | −0.0398362 | ||||||||
\(776\) | 5.74585 | 0.206264 | ||||||||
\(777\) | 35.6272 | 1.27812 | ||||||||
\(778\) | −37.7362 | −1.35291 | ||||||||
\(779\) | −57.5310 | −2.06126 | ||||||||
\(780\) | −2.33343 | −0.0835501 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −45.8224 | −1.63860 | ||||||||
\(783\) | −7.58113 | −0.270927 | ||||||||
\(784\) | 13.1687 | 0.470311 | ||||||||
\(785\) | −9.89175 | −0.353052 | ||||||||
\(786\) | −7.40079 | −0.263977 | ||||||||
\(787\) | 30.9628 | 1.10371 | 0.551853 | − | 0.833942i | \(-0.313921\pi\) | ||||
0.551853 | + | 0.833942i | \(0.313921\pi\) | |||||||
\(788\) | 10.0788 | 0.359043 | ||||||||
\(789\) | 24.4285 | 0.869678 | ||||||||
\(790\) | −5.47259 | −0.194706 | ||||||||
\(791\) | 17.3931 | 0.618429 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0609 | −1.28056 | ||||||||
\(794\) | −22.4348 | −0.796180 | ||||||||
\(795\) | −0.745110 | −0.0264263 | ||||||||
\(796\) | −13.6906 | −0.485250 | ||||||||
\(797\) | −7.93634 | −0.281120 | −0.140560 | − | 0.990072i | \(-0.544890\pi\) | ||||
−0.140560 | + | 0.990072i | \(0.544890\pi\) | |||||||
\(798\) | 26.9980 | 0.955719 | ||||||||
\(799\) | 14.9705 | 0.529617 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −7.41196 | −0.261889 | ||||||||
\(802\) | −25.9002 | −0.914567 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.67821 | −0.0591857 | ||||||||
\(805\) | 39.9002 | 1.40630 | ||||||||
\(806\) | −2.58775 | −0.0911497 | ||||||||
\(807\) | −11.0119 | −0.387638 | ||||||||
\(808\) | 16.5739 | 0.583069 | ||||||||
\(809\) | 5.56276 | 0.195576 | 0.0977882 | − | 0.995207i | \(-0.468823\pi\) | ||||
0.0977882 | + | 0.995207i | \(0.468823\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 32.1021 | 1.12726 | 0.563628 | − | 0.826029i | \(-0.309405\pi\) | ||||
0.563628 | + | 0.826029i | \(0.309405\pi\) | |||||||
\(812\) | −34.0465 | −1.19480 | ||||||||
\(813\) | 0.647750 | 0.0227176 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.43124 | −0.225277 | ||||||||
\(816\) | 5.15753 | 0.180550 | ||||||||
\(817\) | 0.472136 | 0.0165179 | ||||||||
\(818\) | −24.7921 | −0.866835 | ||||||||
\(819\) | 10.4793 | 0.366177 | ||||||||
\(820\) | 9.56995 | 0.334197 | ||||||||
\(821\) | −21.1255 | −0.737286 | −0.368643 | − | 0.929571i | \(-0.620177\pi\) | ||||
−0.368643 | + | 0.929571i | \(0.620177\pi\) | |||||||
\(822\) | −4.44214 | −0.154937 | ||||||||
\(823\) | 4.94702 | 0.172442 | 0.0862211 | − | 0.996276i | \(-0.472521\pi\) | ||||
0.0862211 | + | 0.996276i | \(0.472521\pi\) | |||||||
\(824\) | −1.09063 | −0.0379938 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.9199 | −0.832280 | ||||||||
\(827\) | 44.5554 | 1.54934 | 0.774672 | − | 0.632364i | \(-0.217915\pi\) | ||||
0.774672 | + | 0.632364i | \(0.217915\pi\) | |||||||
\(828\) | −8.88456 | −0.308760 | ||||||||
\(829\) | −21.6706 | −0.752650 | −0.376325 | − | 0.926488i | \(-0.622812\pi\) | ||||
−0.376325 | + | 0.926488i | \(0.622812\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | −24.6304 | −0.854419 | ||||||||
\(832\) | 2.33343 | 0.0808970 | ||||||||
\(833\) | 67.9180 | 2.35322 | ||||||||
\(834\) | −19.9074 | −0.689336 | ||||||||
\(835\) | −6.04163 | −0.209079 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.10899 | −0.0383324 | ||||||||
\(838\) | 27.8969 | 0.963683 | ||||||||
\(839\) | 45.7186 | 1.57838 | 0.789190 | − | 0.614149i | \(-0.210501\pi\) | ||||
0.789190 | + | 0.614149i | \(0.210501\pi\) | |||||||
\(840\) | −4.49096 | −0.154953 | ||||||||
\(841\) | 28.4735 | 0.981845 | ||||||||
\(842\) | 25.0052 | 0.861735 | ||||||||
\(843\) | 9.49170 | 0.326911 | ||||||||
\(844\) | −22.8481 | −0.786464 | ||||||||
\(845\) | 7.55512 | 0.259904 | ||||||||
\(846\) | 2.90264 | 0.0997948 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.745110 | 0.0255872 | ||||||||
\(849\) | −20.2113 | −0.693648 | ||||||||
\(850\) | 5.15753 | 0.176902 | ||||||||
\(851\) | −70.4820 | −2.41609 | ||||||||
\(852\) | 9.55113 | 0.327216 | ||||||||
\(853\) | 3.27816 | 0.112242 | 0.0561210 | − | 0.998424i | \(-0.482127\pi\) | ||||
0.0561210 | + | 0.998424i | \(0.482127\pi\) | |||||||
\(854\) | −69.4035 | −2.37494 | ||||||||
\(855\) | −6.01163 | −0.205594 | ||||||||
\(856\) | −5.68494 | −0.194307 | ||||||||
\(857\) | 0.297435 | 0.0101602 | 0.00508010 | − | 0.999987i | \(-0.498383\pi\) | ||||
0.00508010 | + | 0.999987i | \(0.498383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.7745 | 1.35709 | 0.678544 | − | 0.734560i | \(-0.262611\pi\) | ||||
0.678544 | + | 0.734560i | \(0.262611\pi\) | |||||||
\(860\) | −0.0785371 | −0.00267809 | ||||||||
\(861\) | −42.9783 | −1.46470 | ||||||||
\(862\) | −17.9624 | −0.611800 | ||||||||
\(863\) | −15.0483 | −0.512249 | −0.256124 | − | 0.966644i | \(-0.582446\pi\) | ||||
−0.256124 | + | 0.966644i | \(0.582446\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0.648032 | 0.0220338 | ||||||||
\(866\) | −26.9458 | −0.915654 | ||||||||
\(867\) | 9.60013 | 0.326037 | ||||||||
\(868\) | −4.98044 | −0.169047 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 7.58113 | 0.257024 | ||||||||
\(871\) | −3.91597 | −0.132688 | ||||||||
\(872\) | 8.94427 | 0.302891 | ||||||||
\(873\) | 5.74585 | 0.194468 | ||||||||
\(874\) | −53.4107 | −1.80664 | ||||||||
\(875\) | −4.49096 | −0.151822 | ||||||||
\(876\) | −10.9443 | −0.369773 | ||||||||
\(877\) | −38.5856 | −1.30294 | −0.651471 | − | 0.758673i | \(-0.725848\pi\) | ||||
−0.651471 | + | 0.758673i | \(0.725848\pi\) | |||||||
\(878\) | −4.79393 | −0.161787 | ||||||||
\(879\) | −1.19398 | −0.0402719 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.2135 | −0.478866 | −0.239433 | − | 0.970913i | \(-0.576962\pi\) | ||||
−0.239433 | + | 0.970913i | \(0.576962\pi\) | |||||||
\(882\) | 13.1687 | 0.443413 | ||||||||
\(883\) | −2.27417 | −0.0765319 | −0.0382660 | − | 0.999268i | \(-0.512183\pi\) | ||||
−0.0382660 | + | 0.999268i | \(0.512183\pi\) | |||||||
\(884\) | 12.0347 | 0.404772 | ||||||||
\(885\) | 5.32624 | 0.179040 | ||||||||
\(886\) | 10.0600 | 0.337972 | ||||||||
\(887\) | −52.2657 | −1.75491 | −0.877455 | − | 0.479658i | \(-0.840761\pi\) | ||||
−0.877455 | + | 0.479658i | \(0.840761\pi\) | |||||||
\(888\) | 7.93310 | 0.266217 | ||||||||
\(889\) | 37.5598 | 1.25972 | ||||||||
\(890\) | 7.41196 | 0.248450 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.490958 | −0.0164385 | ||||||||
\(893\) | 17.4496 | 0.583929 | ||||||||
\(894\) | 9.31461 | 0.311527 | ||||||||
\(895\) | −1.56231 | −0.0522221 | ||||||||
\(896\) | 4.49096 | 0.150032 | ||||||||
\(897\) | −20.7315 | −0.692204 | ||||||||
\(898\) | −0.498148 | −0.0166234 | ||||||||
\(899\) | 8.40741 | 0.280403 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 3.84293 | 0.128026 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.352707 | 0.0117373 | ||||||||
\(904\) | 3.87292 | 0.128812 | ||||||||
\(905\) | −18.4721 | −0.614035 | ||||||||
\(906\) | −13.9029 | −0.461894 | ||||||||
\(907\) | −53.0605 | −1.76184 | −0.880922 | − | 0.473262i | \(-0.843076\pi\) | ||||
−0.880922 | + | 0.473262i | \(0.843076\pi\) | |||||||
\(908\) | −1.49022 | −0.0494547 | ||||||||
\(909\) | 16.5739 | 0.549723 | ||||||||
\(910\) | −10.4793 | −0.347386 | ||||||||
\(911\) | −39.3570 | −1.30395 | −0.651977 | − | 0.758238i | \(-0.726060\pi\) | ||||
−0.651977 | + | 0.758238i | \(0.726060\pi\) | |||||||
\(912\) | 6.01163 | 0.199065 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.85730 | −0.0614342 | ||||||||
\(915\) | 15.4541 | 0.510895 | ||||||||
\(916\) | −8.21798 | −0.271530 | ||||||||
\(917\) | −33.2366 | −1.09757 | ||||||||
\(918\) | 5.15753 | 0.170224 | ||||||||
\(919\) | 7.44841 | 0.245700 | 0.122850 | − | 0.992425i | \(-0.460797\pi\) | ||||
0.122850 | + | 0.992425i | \(0.460797\pi\) | |||||||
\(920\) | 8.88456 | 0.292915 | ||||||||
\(921\) | −11.3502 | −0.374003 | ||||||||
\(922\) | −22.1394 | −0.729124 | ||||||||
\(923\) | 22.2869 | 0.733581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.93310 | 0.260839 | ||||||||
\(926\) | −22.1920 | −0.729273 | ||||||||
\(927\) | −1.09063 | −0.0358209 | ||||||||
\(928\) | −7.58113 | −0.248863 | ||||||||
\(929\) | 7.70376 | 0.252752 | 0.126376 | − | 0.991982i | \(-0.459665\pi\) | ||||
0.126376 | + | 0.991982i | \(0.459665\pi\) | |||||||
\(930\) | 1.10899 | 0.0363653 | ||||||||
\(931\) | 79.1654 | 2.59454 | ||||||||
\(932\) | −6.63686 | −0.217397 | ||||||||
\(933\) | −15.1766 | −0.496861 | ||||||||
\(934\) | 31.6953 | 1.03710 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.33343 | 0.0762705 | ||||||||
\(937\) | −23.8429 | −0.778914 | −0.389457 | − | 0.921045i | \(-0.627337\pi\) | ||||
−0.389457 | + | 0.921045i | \(0.627337\pi\) | |||||||
\(938\) | −7.53675 | −0.246084 | ||||||||
\(939\) | 23.3570 | 0.762226 | ||||||||
\(940\) | −2.90264 | −0.0946737 | ||||||||
\(941\) | 20.4887 | 0.667912 | 0.333956 | − | 0.942589i | \(-0.391616\pi\) | ||||
0.333956 | + | 0.942589i | \(0.391616\pi\) | |||||||
\(942\) | 9.89175 | 0.322291 | ||||||||
\(943\) | 85.0248 | 2.76879 | ||||||||
\(944\) | −5.32624 | −0.173354 | ||||||||
\(945\) | −4.49096 | −0.146091 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.3389 | 0.595934 | 0.297967 | − | 0.954576i | \(-0.403691\pi\) | ||||
0.297967 | + | 0.954576i | \(0.403691\pi\) | |||||||
\(948\) | 5.47259 | 0.177742 | ||||||||
\(949\) | −25.5377 | −0.828988 | ||||||||
\(950\) | 6.01163 | 0.195043 | ||||||||
\(951\) | 10.6641 | 0.345807 | ||||||||
\(952\) | 23.1623 | 0.750693 | ||||||||
\(953\) | 43.6768 | 1.41483 | 0.707415 | − | 0.706799i | \(-0.249861\pi\) | ||||
0.707415 | + | 0.706799i | \(0.249861\pi\) | |||||||
\(954\) | 0.745110 | 0.0241238 | ||||||||
\(955\) | 17.6720 | 0.571854 | ||||||||
\(956\) | 6.09764 | 0.197212 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.2217 | 0.750259 | ||||||||
\(959\) | −19.9495 | −0.644201 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −29.7701 | −0.960327 | ||||||||
\(962\) | 18.5113 | 0.596828 | ||||||||
\(963\) | −5.68494 | −0.183195 | ||||||||
\(964\) | −5.70376 | −0.183706 | ||||||||
\(965\) | −10.4954 | −0.337859 | ||||||||
\(966\) | −39.9002 | −1.28377 | ||||||||
\(967\) | 44.2296 | 1.42233 | 0.711164 | − | 0.703026i | \(-0.248168\pi\) | ||||
0.711164 | + | 0.703026i | \(0.248168\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.0052 | 0.996030 | ||||||||
\(970\) | −5.74585 | −0.184488 | ||||||||
\(971\) | 19.8847 | 0.638129 | 0.319065 | − | 0.947733i | \(-0.396631\pi\) | ||||
0.319065 | + | 0.947733i | \(0.396631\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −89.4032 | −2.86613 | ||||||||
\(974\) | −38.9081 | −1.24670 | ||||||||
\(975\) | 2.33343 | 0.0747295 | ||||||||
\(976\) | −15.4541 | −0.494672 | ||||||||
\(977\) | −33.8058 | −1.08154 | −0.540772 | − | 0.841169i | \(-0.681868\pi\) | ||||
−0.540772 | + | 0.841169i | \(0.681868\pi\) | |||||||
\(978\) | 6.43124 | 0.205648 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −13.1687 | −0.420659 | ||||||||
\(981\) | 8.94427 | 0.285569 | ||||||||
\(982\) | −4.66139 | −0.148751 | ||||||||
\(983\) | −10.0792 | −0.321476 | −0.160738 | − | 0.986997i | \(-0.551387\pi\) | ||||
−0.160738 | + | 0.986997i | \(0.551387\pi\) | |||||||
\(984\) | −9.56995 | −0.305079 | ||||||||
\(985\) | −10.0788 | −0.321138 | ||||||||
\(986\) | −39.0999 | −1.24519 | ||||||||
\(987\) | 13.0356 | 0.414929 | ||||||||
\(988\) | 14.0277 | 0.446281 | ||||||||
\(989\) | −0.697767 | −0.0221877 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.6906 | 0.816088 | 0.408044 | − | 0.912962i | \(-0.366211\pi\) | ||||
0.408044 | + | 0.912962i | \(0.366211\pi\) | |||||||
\(992\) | −1.10899 | −0.0352105 | ||||||||
\(993\) | −2.42434 | −0.0769340 | ||||||||
\(994\) | 42.8937 | 1.36051 | ||||||||
\(995\) | 13.6906 | 0.434020 | ||||||||
\(996\) | 8.00000 | 0.253490 | ||||||||
\(997\) | −42.8994 | −1.35864 | −0.679318 | − | 0.733844i | \(-0.737724\pi\) | ||||
−0.679318 | + | 0.733844i | \(0.737724\pi\) | |||||||
\(998\) | 16.3933 | 0.518921 | ||||||||
\(999\) | 7.93310 | 0.250992 |
(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 | 3630.2.a.bs.1.4 | 4 | ||
11.2 | odd | 10 | 330.2.m.f.301.1 | yes | 8 | ||
11.6 | odd | 10 | 330.2.m.f.91.1 | ✓ | 8 | ||
11.10 | odd | 2 | 3630.2.a.bq.1.1 | 4 | |||
33.2 | even | 10 | 990.2.n.i.631.1 | 8 | |||
33.17 | even | 10 | 990.2.n.i.91.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.f.91.1 | ✓ | 8 | 11.6 | odd | 10 | ||
330.2.m.f.301.1 | yes | 8 | 11.2 | odd | 10 | ||
990.2.n.i.91.1 | 8 | 33.17 | even | 10 | |||
990.2.n.i.631.1 | 8 | 33.2 | even | 10 | |||
3630.2.a.bq.1.1 | 4 | 11.10 | odd | 2 | |||
3630.2.a.bs.1.4 | 4 | 1.1 | even | 1 | trivial |