Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8030,2,Mod(1,8030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8030, 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("8030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8030.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: | \(64.1198728231\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 15 x^{12} + 143 x^{11} - 13 x^{10} - 1176 x^{9} + 1018 x^{8} + 4076 x^{7} - 4865 x^{6} - 5483 x^{5} + 7607 x^{4} + 1210 x^{3} - 3153 x^{2} + 878 x - 54 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.856641\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8030.1 |
$q$-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 | ||||||||
\(3\) | −0.856641 | −0.494582 | −0.247291 | − | 0.968941i | \(-0.579540\pi\) | ||||
−0.247291 | + | 0.968941i | \(0.579540\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.856641 | −0.349722 | ||||||||
\(7\) | 1.42002 | 0.536718 | 0.268359 | − | 0.963319i | \(-0.413519\pi\) | ||||
0.268359 | + | 0.963319i | \(0.413519\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.26617 | −0.755389 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.856641 | −0.247291 | ||||||||
\(13\) | 1.92336 | 0.533444 | 0.266722 | − | 0.963774i | \(-0.414060\pi\) | ||||
0.266722 | + | 0.963774i | \(0.414060\pi\) | |||||||
\(14\) | 1.42002 | 0.379517 | ||||||||
\(15\) | 0.856641 | 0.221184 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.77749 | 1.88632 | 0.943159 | − | 0.332342i | \(-0.107839\pi\) | ||||
0.943159 | + | 0.332342i | \(0.107839\pi\) | |||||||
\(18\) | −2.26617 | −0.534141 | ||||||||
\(19\) | −0.319182 | −0.0732253 | −0.0366127 | − | 0.999330i | \(-0.511657\pi\) | ||||
−0.0366127 | + | 0.999330i | \(0.511657\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.21645 | −0.265451 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −0.366337 | −0.0763865 | −0.0381933 | − | 0.999270i | \(-0.512160\pi\) | ||||
−0.0381933 | + | 0.999270i | \(0.512160\pi\) | |||||||
\(24\) | −0.856641 | −0.174861 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.92336 | 0.377202 | ||||||||
\(27\) | 4.51121 | 0.868183 | ||||||||
\(28\) | 1.42002 | 0.268359 | ||||||||
\(29\) | −7.29502 | −1.35465 | −0.677325 | − | 0.735684i | \(-0.736861\pi\) | ||||
−0.677325 | + | 0.735684i | \(0.736861\pi\) | |||||||
\(30\) | 0.856641 | 0.156400 | ||||||||
\(31\) | −5.42821 | −0.974935 | −0.487468 | − | 0.873141i | \(-0.662079\pi\) | ||||
−0.487468 | + | 0.873141i | \(0.662079\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.856641 | −0.149122 | ||||||||
\(34\) | 7.77749 | 1.33383 | ||||||||
\(35\) | −1.42002 | −0.240028 | ||||||||
\(36\) | −2.26617 | −0.377694 | ||||||||
\(37\) | 6.57006 | 1.08011 | 0.540056 | − | 0.841629i | \(-0.318403\pi\) | ||||
0.540056 | + | 0.841629i | \(0.318403\pi\) | |||||||
\(38\) | −0.319182 | −0.0517781 | ||||||||
\(39\) | −1.64763 | −0.263831 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 1.31661 | 0.205620 | 0.102810 | − | 0.994701i | \(-0.467217\pi\) | ||||
0.102810 | + | 0.994701i | \(0.467217\pi\) | |||||||
\(42\) | −1.21645 | −0.187702 | ||||||||
\(43\) | 6.39077 | 0.974584 | 0.487292 | − | 0.873239i | \(-0.337985\pi\) | ||||
0.487292 | + | 0.873239i | \(0.337985\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 2.26617 | 0.337820 | ||||||||
\(46\) | −0.366337 | −0.0540134 | ||||||||
\(47\) | −2.70055 | −0.393915 | −0.196958 | − | 0.980412i | \(-0.563106\pi\) | ||||
−0.196958 | + | 0.980412i | \(0.563106\pi\) | |||||||
\(48\) | −0.856641 | −0.123645 | ||||||||
\(49\) | −4.98354 | −0.711934 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −6.66251 | −0.932938 | ||||||||
\(52\) | 1.92336 | 0.266722 | ||||||||
\(53\) | 1.36622 | 0.187665 | 0.0938326 | − | 0.995588i | \(-0.470088\pi\) | ||||
0.0938326 | + | 0.995588i | \(0.470088\pi\) | |||||||
\(54\) | 4.51121 | 0.613898 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 1.42002 | 0.189758 | ||||||||
\(57\) | 0.273424 | 0.0362159 | ||||||||
\(58\) | −7.29502 | −0.957883 | ||||||||
\(59\) | 10.1268 | 1.31840 | 0.659198 | − | 0.751969i | \(-0.270896\pi\) | ||||
0.659198 | + | 0.751969i | \(0.270896\pi\) | |||||||
\(60\) | 0.856641 | 0.110592 | ||||||||
\(61\) | 0.216728 | 0.0277492 | 0.0138746 | − | 0.999904i | \(-0.495583\pi\) | ||||
0.0138746 | + | 0.999904i | \(0.495583\pi\) | |||||||
\(62\) | −5.42821 | −0.689383 | ||||||||
\(63\) | −3.21801 | −0.405431 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.92336 | −0.238563 | ||||||||
\(66\) | −0.856641 | −0.105445 | ||||||||
\(67\) | 7.17786 | 0.876916 | 0.438458 | − | 0.898752i | \(-0.355525\pi\) | ||||
0.438458 | + | 0.898752i | \(0.355525\pi\) | |||||||
\(68\) | 7.77749 | 0.943159 | ||||||||
\(69\) | 0.313819 | 0.0377794 | ||||||||
\(70\) | −1.42002 | −0.169725 | ||||||||
\(71\) | −15.8861 | −1.88533 | −0.942665 | − | 0.333739i | \(-0.891689\pi\) | ||||
−0.942665 | + | 0.333739i | \(0.891689\pi\) | |||||||
\(72\) | −2.26617 | −0.267070 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | 6.57006 | 0.763754 | ||||||||
\(75\) | −0.856641 | −0.0989163 | ||||||||
\(76\) | −0.319182 | −0.0366127 | ||||||||
\(77\) | 1.42002 | 0.161827 | ||||||||
\(78\) | −1.64763 | −0.186557 | ||||||||
\(79\) | 8.29940 | 0.933756 | 0.466878 | − | 0.884322i | \(-0.345379\pi\) | ||||
0.466878 | + | 0.884322i | \(0.345379\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 2.93401 | 0.326001 | ||||||||
\(82\) | 1.31661 | 0.145396 | ||||||||
\(83\) | −4.11020 | −0.451153 | −0.225576 | − | 0.974226i | \(-0.572426\pi\) | ||||
−0.225576 | + | 0.974226i | \(0.572426\pi\) | |||||||
\(84\) | −1.21645 | −0.132725 | ||||||||
\(85\) | −7.77749 | −0.843587 | ||||||||
\(86\) | 6.39077 | 0.689135 | ||||||||
\(87\) | 6.24921 | 0.669985 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −1.97389 | −0.209232 | −0.104616 | − | 0.994513i | \(-0.533361\pi\) | ||||
−0.104616 | + | 0.994513i | \(0.533361\pi\) | |||||||
\(90\) | 2.26617 | 0.238875 | ||||||||
\(91\) | 2.73121 | 0.286309 | ||||||||
\(92\) | −0.366337 | −0.0381933 | ||||||||
\(93\) | 4.65003 | 0.482185 | ||||||||
\(94\) | −2.70055 | −0.278540 | ||||||||
\(95\) | 0.319182 | 0.0327474 | ||||||||
\(96\) | −0.856641 | −0.0874305 | ||||||||
\(97\) | −0.724943 | −0.0736068 | −0.0368034 | − | 0.999323i | \(-0.511718\pi\) | ||||
−0.0368034 | + | 0.999323i | \(0.511718\pi\) | |||||||
\(98\) | −4.98354 | −0.503413 | ||||||||
\(99\) | −2.26617 | −0.227758 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.90533 | −0.886114 | −0.443057 | − | 0.896494i | \(-0.646106\pi\) | ||||
−0.443057 | + | 0.896494i | \(0.646106\pi\) | |||||||
\(102\) | −6.66251 | −0.659687 | ||||||||
\(103\) | 14.8296 | 1.46120 | 0.730602 | − | 0.682804i | \(-0.239240\pi\) | ||||
0.730602 | + | 0.682804i | \(0.239240\pi\) | |||||||
\(104\) | 1.92336 | 0.188601 | ||||||||
\(105\) | 1.21645 | 0.118713 | ||||||||
\(106\) | 1.36622 | 0.132699 | ||||||||
\(107\) | −3.86024 | −0.373184 | −0.186592 | − | 0.982438i | \(-0.559744\pi\) | ||||
−0.186592 | + | 0.982438i | \(0.559744\pi\) | |||||||
\(108\) | 4.51121 | 0.434092 | ||||||||
\(109\) | −4.81249 | −0.460953 | −0.230476 | − | 0.973078i | \(-0.574028\pi\) | ||||
−0.230476 | + | 0.973078i | \(0.574028\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −5.62818 | −0.534203 | ||||||||
\(112\) | 1.42002 | 0.134179 | ||||||||
\(113\) | 1.53056 | 0.143983 | 0.0719917 | − | 0.997405i | \(-0.477064\pi\) | ||||
0.0719917 | + | 0.997405i | \(0.477064\pi\) | |||||||
\(114\) | 0.273424 | 0.0256085 | ||||||||
\(115\) | 0.366337 | 0.0341611 | ||||||||
\(116\) | −7.29502 | −0.677325 | ||||||||
\(117\) | −4.35865 | −0.402957 | ||||||||
\(118\) | 10.1268 | 0.932247 | ||||||||
\(119\) | 11.0442 | 1.01242 | ||||||||
\(120\) | 0.856641 | 0.0782002 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.216728 | 0.0196217 | ||||||||
\(123\) | −1.12786 | −0.101696 | ||||||||
\(124\) | −5.42821 | −0.487468 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.21801 | −0.286683 | ||||||||
\(127\) | 13.8567 | 1.22959 | 0.614793 | − | 0.788688i | \(-0.289239\pi\) | ||||
0.614793 | + | 0.788688i | \(0.289239\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.47460 | −0.482011 | ||||||||
\(130\) | −1.92336 | −0.168690 | ||||||||
\(131\) | −17.2098 | −1.50363 | −0.751814 | − | 0.659375i | \(-0.770821\pi\) | ||||
−0.751814 | + | 0.659375i | \(0.770821\pi\) | |||||||
\(132\) | −0.856641 | −0.0745610 | ||||||||
\(133\) | −0.453245 | −0.0393013 | ||||||||
\(134\) | 7.17786 | 0.620073 | ||||||||
\(135\) | −4.51121 | −0.388263 | ||||||||
\(136\) | 7.77749 | 0.666914 | ||||||||
\(137\) | 17.0615 | 1.45766 | 0.728829 | − | 0.684696i | \(-0.240065\pi\) | ||||
0.728829 | + | 0.684696i | \(0.240065\pi\) | |||||||
\(138\) | 0.313819 | 0.0267141 | ||||||||
\(139\) | 11.8945 | 1.00887 | 0.504437 | − | 0.863448i | \(-0.331700\pi\) | ||||
0.504437 | + | 0.863448i | \(0.331700\pi\) | |||||||
\(140\) | −1.42002 | −0.120014 | ||||||||
\(141\) | 2.31340 | 0.194823 | ||||||||
\(142\) | −15.8861 | −1.33313 | ||||||||
\(143\) | 1.92336 | 0.160839 | ||||||||
\(144\) | −2.26617 | −0.188847 | ||||||||
\(145\) | 7.29502 | 0.605818 | ||||||||
\(146\) | 1.00000 | 0.0827606 | ||||||||
\(147\) | 4.26910 | 0.352109 | ||||||||
\(148\) | 6.57006 | 0.540056 | ||||||||
\(149\) | 14.9784 | 1.22707 | 0.613537 | − | 0.789666i | \(-0.289746\pi\) | ||||
0.613537 | + | 0.789666i | \(0.289746\pi\) | |||||||
\(150\) | −0.856641 | −0.0699444 | ||||||||
\(151\) | −0.304998 | −0.0248204 | −0.0124102 | − | 0.999923i | \(-0.503950\pi\) | ||||
−0.0124102 | + | 0.999923i | \(0.503950\pi\) | |||||||
\(152\) | −0.319182 | −0.0258891 | ||||||||
\(153\) | −17.6251 | −1.42490 | ||||||||
\(154\) | 1.42002 | 0.114429 | ||||||||
\(155\) | 5.42821 | 0.436004 | ||||||||
\(156\) | −1.64763 | −0.131916 | ||||||||
\(157\) | −18.1757 | −1.45058 | −0.725290 | − | 0.688444i | \(-0.758294\pi\) | ||||
−0.725290 | + | 0.688444i | \(0.758294\pi\) | |||||||
\(158\) | 8.29940 | 0.660265 | ||||||||
\(159\) | −1.17036 | −0.0928158 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −0.520206 | −0.0409980 | ||||||||
\(162\) | 2.93401 | 0.230518 | ||||||||
\(163\) | 7.76954 | 0.608557 | 0.304279 | − | 0.952583i | \(-0.401585\pi\) | ||||
0.304279 | + | 0.952583i | \(0.401585\pi\) | |||||||
\(164\) | 1.31661 | 0.102810 | ||||||||
\(165\) | 0.856641 | 0.0666894 | ||||||||
\(166\) | −4.11020 | −0.319013 | ||||||||
\(167\) | 18.1097 | 1.40137 | 0.700687 | − | 0.713469i | \(-0.252877\pi\) | ||||
0.700687 | + | 0.713469i | \(0.252877\pi\) | |||||||
\(168\) | −1.21645 | −0.0938510 | ||||||||
\(169\) | −9.30069 | −0.715438 | ||||||||
\(170\) | −7.77749 | −0.596506 | ||||||||
\(171\) | 0.723319 | 0.0553136 | ||||||||
\(172\) | 6.39077 | 0.487292 | ||||||||
\(173\) | 15.6310 | 1.18840 | 0.594202 | − | 0.804316i | \(-0.297468\pi\) | ||||
0.594202 | + | 0.804316i | \(0.297468\pi\) | |||||||
\(174\) | 6.24921 | 0.473751 | ||||||||
\(175\) | 1.42002 | 0.107344 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −8.67502 | −0.652054 | ||||||||
\(178\) | −1.97389 | −0.147949 | ||||||||
\(179\) | −12.6009 | −0.941839 | −0.470920 | − | 0.882176i | \(-0.656078\pi\) | ||||
−0.470920 | + | 0.882176i | \(0.656078\pi\) | |||||||
\(180\) | 2.26617 | 0.168910 | ||||||||
\(181\) | 0.664700 | 0.0494068 | 0.0247034 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247034 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(182\) | 2.73121 | 0.202451 | ||||||||
\(183\) | −0.185658 | −0.0137243 | ||||||||
\(184\) | −0.366337 | −0.0270067 | ||||||||
\(185\) | −6.57006 | −0.483040 | ||||||||
\(186\) | 4.65003 | 0.340956 | ||||||||
\(187\) | 7.77749 | 0.568746 | ||||||||
\(188\) | −2.70055 | −0.196958 | ||||||||
\(189\) | 6.40602 | 0.465969 | ||||||||
\(190\) | 0.319182 | 0.0231559 | ||||||||
\(191\) | 12.0626 | 0.872822 | 0.436411 | − | 0.899747i | \(-0.356249\pi\) | ||||
0.436411 | + | 0.899747i | \(0.356249\pi\) | |||||||
\(192\) | −0.856641 | −0.0618227 | ||||||||
\(193\) | 6.55517 | 0.471852 | 0.235926 | − | 0.971771i | \(-0.424188\pi\) | ||||
0.235926 | + | 0.971771i | \(0.424188\pi\) | |||||||
\(194\) | −0.724943 | −0.0520479 | ||||||||
\(195\) | 1.64763 | 0.117989 | ||||||||
\(196\) | −4.98354 | −0.355967 | ||||||||
\(197\) | 25.0254 | 1.78299 | 0.891494 | − | 0.453033i | \(-0.149658\pi\) | ||||
0.891494 | + | 0.453033i | \(0.149658\pi\) | |||||||
\(198\) | −2.26617 | −0.161049 | ||||||||
\(199\) | 5.56402 | 0.394423 | 0.197211 | − | 0.980361i | \(-0.436811\pi\) | ||||
0.197211 | + | 0.980361i | \(0.436811\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −6.14885 | −0.433706 | ||||||||
\(202\) | −8.90533 | −0.626577 | ||||||||
\(203\) | −10.3591 | −0.727065 | ||||||||
\(204\) | −6.66251 | −0.466469 | ||||||||
\(205\) | −1.31661 | −0.0919563 | ||||||||
\(206\) | 14.8296 | 1.03323 | ||||||||
\(207\) | 0.830181 | 0.0577015 | ||||||||
\(208\) | 1.92336 | 0.133361 | ||||||||
\(209\) | −0.319182 | −0.0220783 | ||||||||
\(210\) | 1.21645 | 0.0839429 | ||||||||
\(211\) | −13.8707 | −0.954895 | −0.477448 | − | 0.878660i | \(-0.658438\pi\) | ||||
−0.477448 | + | 0.878660i | \(0.658438\pi\) | |||||||
\(212\) | 1.36622 | 0.0938326 | ||||||||
\(213\) | 13.6087 | 0.932450 | ||||||||
\(214\) | −3.86024 | −0.263881 | ||||||||
\(215\) | −6.39077 | −0.435847 | ||||||||
\(216\) | 4.51121 | 0.306949 | ||||||||
\(217\) | −7.70818 | −0.523265 | ||||||||
\(218\) | −4.81249 | −0.325943 | ||||||||
\(219\) | −0.856641 | −0.0578864 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 14.9589 | 1.00624 | ||||||||
\(222\) | −5.62818 | −0.377739 | ||||||||
\(223\) | −2.04460 | −0.136916 | −0.0684582 | − | 0.997654i | \(-0.521808\pi\) | ||||
−0.0684582 | + | 0.997654i | \(0.521808\pi\) | |||||||
\(224\) | 1.42002 | 0.0948792 | ||||||||
\(225\) | −2.26617 | −0.151078 | ||||||||
\(226\) | 1.53056 | 0.101812 | ||||||||
\(227\) | 9.45412 | 0.627492 | 0.313746 | − | 0.949507i | \(-0.398416\pi\) | ||||
0.313746 | + | 0.949507i | \(0.398416\pi\) | |||||||
\(228\) | 0.273424 | 0.0181080 | ||||||||
\(229\) | 13.6181 | 0.899912 | 0.449956 | − | 0.893051i | \(-0.351440\pi\) | ||||
0.449956 | + | 0.893051i | \(0.351440\pi\) | |||||||
\(230\) | 0.366337 | 0.0241555 | ||||||||
\(231\) | −1.21645 | −0.0800364 | ||||||||
\(232\) | −7.29502 | −0.478941 | ||||||||
\(233\) | 18.4436 | 1.20828 | 0.604140 | − | 0.796878i | \(-0.293517\pi\) | ||||
0.604140 | + | 0.796878i | \(0.293517\pi\) | |||||||
\(234\) | −4.35865 | −0.284934 | ||||||||
\(235\) | 2.70055 | 0.176164 | ||||||||
\(236\) | 10.1268 | 0.659198 | ||||||||
\(237\) | −7.10961 | −0.461819 | ||||||||
\(238\) | 11.0442 | 0.715889 | ||||||||
\(239\) | 20.7615 | 1.34295 | 0.671474 | − | 0.741028i | \(-0.265662\pi\) | ||||
0.671474 | + | 0.741028i | \(0.265662\pi\) | |||||||
\(240\) | 0.856641 | 0.0552959 | ||||||||
\(241\) | 14.9961 | 0.965983 | 0.482992 | − | 0.875625i | \(-0.339550\pi\) | ||||
0.482992 | + | 0.875625i | \(0.339550\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −16.0470 | −1.02942 | ||||||||
\(244\) | 0.216728 | 0.0138746 | ||||||||
\(245\) | 4.98354 | 0.318387 | ||||||||
\(246\) | −1.12786 | −0.0719100 | ||||||||
\(247\) | −0.613901 | −0.0390616 | ||||||||
\(248\) | −5.42821 | −0.344692 | ||||||||
\(249\) | 3.52096 | 0.223132 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −13.5759 | −0.856906 | −0.428453 | − | 0.903564i | \(-0.640941\pi\) | ||||
−0.428453 | + | 0.903564i | \(0.640941\pi\) | |||||||
\(252\) | −3.21801 | −0.202715 | ||||||||
\(253\) | −0.366337 | −0.0230314 | ||||||||
\(254\) | 13.8567 | 0.869449 | ||||||||
\(255\) | 6.66251 | 0.417223 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.5016 | −0.655071 | −0.327535 | − | 0.944839i | \(-0.606218\pi\) | ||||
−0.327535 | + | 0.944839i | \(0.606218\pi\) | |||||||
\(258\) | −5.47460 | −0.340834 | ||||||||
\(259\) | 9.32963 | 0.579715 | ||||||||
\(260\) | −1.92336 | −0.119282 | ||||||||
\(261\) | 16.5317 | 1.02329 | ||||||||
\(262\) | −17.2098 | −1.06323 | ||||||||
\(263\) | 4.29740 | 0.264989 | 0.132495 | − | 0.991184i | \(-0.457701\pi\) | ||||
0.132495 | + | 0.991184i | \(0.457701\pi\) | |||||||
\(264\) | −0.856641 | −0.0527226 | ||||||||
\(265\) | −1.36622 | −0.0839264 | ||||||||
\(266\) | −0.453245 | −0.0277902 | ||||||||
\(267\) | 1.69092 | 0.103482 | ||||||||
\(268\) | 7.17786 | 0.438458 | ||||||||
\(269\) | −9.05841 | −0.552301 | −0.276151 | − | 0.961114i | \(-0.589059\pi\) | ||||
−0.276151 | + | 0.961114i | \(0.589059\pi\) | |||||||
\(270\) | −4.51121 | −0.274544 | ||||||||
\(271\) | 12.1871 | 0.740314 | 0.370157 | − | 0.928969i | \(-0.379304\pi\) | ||||
0.370157 | + | 0.928969i | \(0.379304\pi\) | |||||||
\(272\) | 7.77749 | 0.471579 | ||||||||
\(273\) | −2.33967 | −0.141603 | ||||||||
\(274\) | 17.0615 | 1.03072 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0.313819 | 0.0188897 | ||||||||
\(277\) | 17.0729 | 1.02581 | 0.512904 | − | 0.858446i | \(-0.328570\pi\) | ||||
0.512904 | + | 0.858446i | \(0.328570\pi\) | |||||||
\(278\) | 11.8945 | 0.713382 | ||||||||
\(279\) | 12.3012 | 0.736456 | ||||||||
\(280\) | −1.42002 | −0.0848625 | ||||||||
\(281\) | −13.9544 | −0.832451 | −0.416226 | − | 0.909261i | \(-0.636647\pi\) | ||||
−0.416226 | + | 0.909261i | \(0.636647\pi\) | |||||||
\(282\) | 2.31340 | 0.137761 | ||||||||
\(283\) | −16.4666 | −0.978836 | −0.489418 | − | 0.872049i | \(-0.662791\pi\) | ||||
−0.489418 | + | 0.872049i | \(0.662791\pi\) | |||||||
\(284\) | −15.8861 | −0.942665 | ||||||||
\(285\) | −0.273424 | −0.0161962 | ||||||||
\(286\) | 1.92336 | 0.113731 | ||||||||
\(287\) | 1.86962 | 0.110360 | ||||||||
\(288\) | −2.26617 | −0.133535 | ||||||||
\(289\) | 43.4893 | 2.55820 | ||||||||
\(290\) | 7.29502 | 0.428378 | ||||||||
\(291\) | 0.621016 | 0.0364046 | ||||||||
\(292\) | 1.00000 | 0.0585206 | ||||||||
\(293\) | −3.10799 | −0.181571 | −0.0907854 | − | 0.995870i | \(-0.528938\pi\) | ||||
−0.0907854 | + | 0.995870i | \(0.528938\pi\) | |||||||
\(294\) | 4.26910 | 0.248979 | ||||||||
\(295\) | −10.1268 | −0.589605 | ||||||||
\(296\) | 6.57006 | 0.381877 | ||||||||
\(297\) | 4.51121 | 0.261767 | ||||||||
\(298\) | 14.9784 | 0.867673 | ||||||||
\(299\) | −0.704597 | −0.0407479 | ||||||||
\(300\) | −0.856641 | −0.0494582 | ||||||||
\(301\) | 9.07504 | 0.523077 | ||||||||
\(302\) | −0.304998 | −0.0175507 | ||||||||
\(303\) | 7.62867 | 0.438256 | ||||||||
\(304\) | −0.319182 | −0.0183063 | ||||||||
\(305\) | −0.216728 | −0.0124098 | ||||||||
\(306\) | −17.6251 | −1.00756 | ||||||||
\(307\) | 11.7658 | 0.671510 | 0.335755 | − | 0.941949i | \(-0.391009\pi\) | ||||
0.335755 | + | 0.941949i | \(0.391009\pi\) | |||||||
\(308\) | 1.42002 | 0.0809133 | ||||||||
\(309\) | −12.7036 | −0.722684 | ||||||||
\(310\) | 5.42821 | 0.308302 | ||||||||
\(311\) | 26.9845 | 1.53015 | 0.765076 | − | 0.643940i | \(-0.222701\pi\) | ||||
0.765076 | + | 0.643940i | \(0.222701\pi\) | |||||||
\(312\) | −1.64763 | −0.0932785 | ||||||||
\(313\) | 1.88309 | 0.106439 | 0.0532194 | − | 0.998583i | \(-0.483052\pi\) | ||||
0.0532194 | + | 0.998583i | \(0.483052\pi\) | |||||||
\(314\) | −18.1757 | −1.02571 | ||||||||
\(315\) | 3.21801 | 0.181314 | ||||||||
\(316\) | 8.29940 | 0.466878 | ||||||||
\(317\) | 20.8192 | 1.16932 | 0.584661 | − | 0.811278i | \(-0.301228\pi\) | ||||
0.584661 | + | 0.811278i | \(0.301228\pi\) | |||||||
\(318\) | −1.17036 | −0.0656307 | ||||||||
\(319\) | −7.29502 | −0.408443 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 3.30684 | 0.184570 | ||||||||
\(322\) | −0.520206 | −0.0289900 | ||||||||
\(323\) | −2.48243 | −0.138126 | ||||||||
\(324\) | 2.93401 | 0.163001 | ||||||||
\(325\) | 1.92336 | 0.106689 | ||||||||
\(326\) | 7.76954 | 0.430315 | ||||||||
\(327\) | 4.12257 | 0.227979 | ||||||||
\(328\) | 1.31661 | 0.0726978 | ||||||||
\(329\) | −3.83483 | −0.211421 | ||||||||
\(330\) | 0.856641 | 0.0471565 | ||||||||
\(331\) | −4.28694 | −0.235632 | −0.117816 | − | 0.993035i | \(-0.537589\pi\) | ||||
−0.117816 | + | 0.993035i | \(0.537589\pi\) | |||||||
\(332\) | −4.11020 | −0.225576 | ||||||||
\(333\) | −14.8889 | −0.815904 | ||||||||
\(334\) | 18.1097 | 0.990921 | ||||||||
\(335\) | −7.17786 | −0.392169 | ||||||||
\(336\) | −1.21645 | −0.0663627 | ||||||||
\(337\) | −0.552780 | −0.0301119 | −0.0150559 | − | 0.999887i | \(-0.504793\pi\) | ||||
−0.0150559 | + | 0.999887i | \(0.504793\pi\) | |||||||
\(338\) | −9.30069 | −0.505891 | ||||||||
\(339\) | −1.31114 | −0.0712115 | ||||||||
\(340\) | −7.77749 | −0.421794 | ||||||||
\(341\) | −5.42821 | −0.293954 | ||||||||
\(342\) | 0.723319 | 0.0391126 | ||||||||
\(343\) | −17.0169 | −0.918826 | ||||||||
\(344\) | 6.39077 | 0.344567 | ||||||||
\(345\) | −0.313819 | −0.0168954 | ||||||||
\(346\) | 15.6310 | 0.840328 | ||||||||
\(347\) | −25.3958 | −1.36332 | −0.681659 | − | 0.731670i | \(-0.738741\pi\) | ||||
−0.681659 | + | 0.731670i | \(0.738741\pi\) | |||||||
\(348\) | 6.24921 | 0.334993 | ||||||||
\(349\) | −5.69642 | −0.304922 | −0.152461 | − | 0.988309i | \(-0.548720\pi\) | ||||
−0.152461 | + | 0.988309i | \(0.548720\pi\) | |||||||
\(350\) | 1.42002 | 0.0759034 | ||||||||
\(351\) | 8.67668 | 0.463127 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 24.5096 | 1.30451 | 0.652256 | − | 0.757999i | \(-0.273823\pi\) | ||||
0.652256 | + | 0.757999i | \(0.273823\pi\) | |||||||
\(354\) | −8.67502 | −0.461072 | ||||||||
\(355\) | 15.8861 | 0.843146 | ||||||||
\(356\) | −1.97389 | −0.104616 | ||||||||
\(357\) | −9.46091 | −0.500725 | ||||||||
\(358\) | −12.6009 | −0.665981 | ||||||||
\(359\) | 15.1897 | 0.801680 | 0.400840 | − | 0.916148i | \(-0.368718\pi\) | ||||
0.400840 | + | 0.916148i | \(0.368718\pi\) | |||||||
\(360\) | 2.26617 | 0.119437 | ||||||||
\(361\) | −18.8981 | −0.994638 | ||||||||
\(362\) | 0.664700 | 0.0349359 | ||||||||
\(363\) | −0.856641 | −0.0449620 | ||||||||
\(364\) | 2.73121 | 0.143154 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | −0.185658 | −0.00970452 | ||||||||
\(367\) | 30.8165 | 1.60861 | 0.804304 | − | 0.594217i | \(-0.202538\pi\) | ||||
0.804304 | + | 0.594217i | \(0.202538\pi\) | |||||||
\(368\) | −0.366337 | −0.0190966 | ||||||||
\(369\) | −2.98367 | −0.155323 | ||||||||
\(370\) | −6.57006 | −0.341561 | ||||||||
\(371\) | 1.94007 | 0.100723 | ||||||||
\(372\) | 4.65003 | 0.241093 | ||||||||
\(373\) | 21.6159 | 1.11923 | 0.559615 | − | 0.828752i | \(-0.310949\pi\) | ||||
0.559615 | + | 0.828752i | \(0.310949\pi\) | |||||||
\(374\) | 7.77749 | 0.402164 | ||||||||
\(375\) | 0.856641 | 0.0442367 | ||||||||
\(376\) | −2.70055 | −0.139270 | ||||||||
\(377\) | −14.0309 | −0.722630 | ||||||||
\(378\) | 6.40602 | 0.329490 | ||||||||
\(379\) | 21.1598 | 1.08691 | 0.543453 | − | 0.839440i | \(-0.317117\pi\) | ||||
0.543453 | + | 0.839440i | \(0.317117\pi\) | |||||||
\(380\) | 0.319182 | 0.0163737 | ||||||||
\(381\) | −11.8702 | −0.608131 | ||||||||
\(382\) | 12.0626 | 0.617178 | ||||||||
\(383\) | −28.7204 | −1.46755 | −0.733773 | − | 0.679395i | \(-0.762242\pi\) | ||||
−0.733773 | + | 0.679395i | \(0.762242\pi\) | |||||||
\(384\) | −0.856641 | −0.0437153 | ||||||||
\(385\) | −1.42002 | −0.0723710 | ||||||||
\(386\) | 6.55517 | 0.333650 | ||||||||
\(387\) | −14.4826 | −0.736190 | ||||||||
\(388\) | −0.724943 | −0.0368034 | ||||||||
\(389\) | −12.2768 | −0.622461 | −0.311230 | − | 0.950335i | \(-0.600741\pi\) | ||||
−0.311230 | + | 0.950335i | \(0.600741\pi\) | |||||||
\(390\) | 1.64763 | 0.0834308 | ||||||||
\(391\) | −2.84918 | −0.144089 | ||||||||
\(392\) | −4.98354 | −0.251707 | ||||||||
\(393\) | 14.7426 | 0.743667 | ||||||||
\(394\) | 25.0254 | 1.26076 | ||||||||
\(395\) | −8.29940 | −0.417588 | ||||||||
\(396\) | −2.26617 | −0.113879 | ||||||||
\(397\) | 5.06869 | 0.254390 | 0.127195 | − | 0.991878i | \(-0.459403\pi\) | ||||
0.127195 | + | 0.991878i | \(0.459403\pi\) | |||||||
\(398\) | 5.56402 | 0.278899 | ||||||||
\(399\) | 0.388268 | 0.0194377 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 11.7529 | 0.586911 | 0.293455 | − | 0.955973i | \(-0.405195\pi\) | ||||
0.293455 | + | 0.955973i | \(0.405195\pi\) | |||||||
\(402\) | −6.14885 | −0.306677 | ||||||||
\(403\) | −10.4404 | −0.520073 | ||||||||
\(404\) | −8.90533 | −0.443057 | ||||||||
\(405\) | −2.93401 | −0.145792 | ||||||||
\(406\) | −10.3591 | −0.514113 | ||||||||
\(407\) | 6.57006 | 0.325666 | ||||||||
\(408\) | −6.66251 | −0.329843 | ||||||||
\(409\) | −28.3149 | −1.40008 | −0.700041 | − | 0.714103i | \(-0.746835\pi\) | ||||
−0.700041 | + | 0.714103i | \(0.746835\pi\) | |||||||
\(410\) | −1.31661 | −0.0650229 | ||||||||
\(411\) | −14.6155 | −0.720931 | ||||||||
\(412\) | 14.8296 | 0.730602 | ||||||||
\(413\) | 14.3803 | 0.707607 | ||||||||
\(414\) | 0.830181 | 0.0408011 | ||||||||
\(415\) | 4.11020 | 0.201762 | ||||||||
\(416\) | 1.92336 | 0.0943004 | ||||||||
\(417\) | −10.1893 | −0.498971 | ||||||||
\(418\) | −0.319182 | −0.0156117 | ||||||||
\(419\) | 20.7058 | 1.01154 | 0.505771 | − | 0.862668i | \(-0.331208\pi\) | ||||
0.505771 | + | 0.862668i | \(0.331208\pi\) | |||||||
\(420\) | 1.21645 | 0.0593566 | ||||||||
\(421\) | 3.24741 | 0.158269 | 0.0791346 | − | 0.996864i | \(-0.474784\pi\) | ||||
0.0791346 | + | 0.996864i | \(0.474784\pi\) | |||||||
\(422\) | −13.8707 | −0.675213 | ||||||||
\(423\) | 6.11989 | 0.297559 | ||||||||
\(424\) | 1.36622 | 0.0663497 | ||||||||
\(425\) | 7.77749 | 0.377264 | ||||||||
\(426\) | 13.6087 | 0.659342 | ||||||||
\(427\) | 0.307759 | 0.0148935 | ||||||||
\(428\) | −3.86024 | −0.186592 | ||||||||
\(429\) | −1.64763 | −0.0795482 | ||||||||
\(430\) | −6.39077 | −0.308191 | ||||||||
\(431\) | −2.06655 | −0.0995423 | −0.0497711 | − | 0.998761i | \(-0.515849\pi\) | ||||
−0.0497711 | + | 0.998761i | \(0.515849\pi\) | |||||||
\(432\) | 4.51121 | 0.217046 | ||||||||
\(433\) | −33.3595 | −1.60316 | −0.801579 | − | 0.597889i | \(-0.796006\pi\) | ||||
−0.801579 | + | 0.597889i | \(0.796006\pi\) | |||||||
\(434\) | −7.70818 | −0.370004 | ||||||||
\(435\) | −6.24921 | −0.299627 | ||||||||
\(436\) | −4.81249 | −0.230476 | ||||||||
\(437\) | 0.116928 | 0.00559343 | ||||||||
\(438\) | −0.856641 | −0.0409319 | ||||||||
\(439\) | −19.3908 | −0.925473 | −0.462736 | − | 0.886496i | \(-0.653132\pi\) | ||||
−0.462736 | + | 0.886496i | \(0.653132\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 11.2935 | 0.537787 | ||||||||
\(442\) | 14.9589 | 0.711522 | ||||||||
\(443\) | −33.9145 | −1.61132 | −0.805662 | − | 0.592375i | \(-0.798190\pi\) | ||||
−0.805662 | + | 0.592375i | \(0.798190\pi\) | |||||||
\(444\) | −5.62818 | −0.267102 | ||||||||
\(445\) | 1.97389 | 0.0935714 | ||||||||
\(446\) | −2.04460 | −0.0968146 | ||||||||
\(447\) | −12.8311 | −0.606889 | ||||||||
\(448\) | 1.42002 | 0.0670897 | ||||||||
\(449\) | −3.64868 | −0.172192 | −0.0860958 | − | 0.996287i | \(-0.527439\pi\) | ||||
−0.0860958 | + | 0.996287i | \(0.527439\pi\) | |||||||
\(450\) | −2.26617 | −0.106828 | ||||||||
\(451\) | 1.31661 | 0.0619969 | ||||||||
\(452\) | 1.53056 | 0.0719917 | ||||||||
\(453\) | 0.261274 | 0.0122757 | ||||||||
\(454\) | 9.45412 | 0.443704 | ||||||||
\(455\) | −2.73121 | −0.128041 | ||||||||
\(456\) | 0.273424 | 0.0128043 | ||||||||
\(457\) | −2.16910 | −0.101466 | −0.0507330 | − | 0.998712i | \(-0.516156\pi\) | ||||
−0.0507330 | + | 0.998712i | \(0.516156\pi\) | |||||||
\(458\) | 13.6181 | 0.636334 | ||||||||
\(459\) | 35.0859 | 1.63767 | ||||||||
\(460\) | 0.366337 | 0.0170805 | ||||||||
\(461\) | 23.1797 | 1.07958 | 0.539792 | − | 0.841798i | \(-0.318503\pi\) | ||||
0.539792 | + | 0.841798i | \(0.318503\pi\) | |||||||
\(462\) | −1.21645 | −0.0565943 | ||||||||
\(463\) | −32.2635 | −1.49941 | −0.749707 | − | 0.661770i | \(-0.769806\pi\) | ||||
−0.749707 | + | 0.661770i | \(0.769806\pi\) | |||||||
\(464\) | −7.29502 | −0.338663 | ||||||||
\(465\) | −4.65003 | −0.215640 | ||||||||
\(466\) | 18.4436 | 0.854384 | ||||||||
\(467\) | 6.11798 | 0.283106 | 0.141553 | − | 0.989931i | \(-0.454790\pi\) | ||||
0.141553 | + | 0.989931i | \(0.454790\pi\) | |||||||
\(468\) | −4.35865 | −0.201479 | ||||||||
\(469\) | 10.1927 | 0.470656 | ||||||||
\(470\) | 2.70055 | 0.124567 | ||||||||
\(471\) | 15.5700 | 0.717430 | ||||||||
\(472\) | 10.1268 | 0.466123 | ||||||||
\(473\) | 6.39077 | 0.293848 | ||||||||
\(474\) | −7.10961 | −0.326555 | ||||||||
\(475\) | −0.319182 | −0.0146451 | ||||||||
\(476\) | 11.0442 | 0.506210 | ||||||||
\(477\) | −3.09609 | −0.141760 | ||||||||
\(478\) | 20.7615 | 0.949607 | ||||||||
\(479\) | 19.9231 | 0.910311 | 0.455156 | − | 0.890412i | \(-0.349584\pi\) | ||||
0.455156 | + | 0.890412i | \(0.349584\pi\) | |||||||
\(480\) | 0.856641 | 0.0391001 | ||||||||
\(481\) | 12.6366 | 0.576178 | ||||||||
\(482\) | 14.9961 | 0.683053 | ||||||||
\(483\) | 0.445630 | 0.0202769 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0.724943 | 0.0329180 | ||||||||
\(486\) | −16.0470 | −0.727908 | ||||||||
\(487\) | −5.81713 | −0.263599 | −0.131800 | − | 0.991276i | \(-0.542076\pi\) | ||||
−0.131800 | + | 0.991276i | \(0.542076\pi\) | |||||||
\(488\) | 0.216728 | 0.00981084 | ||||||||
\(489\) | −6.65570 | −0.300981 | ||||||||
\(490\) | 4.98354 | 0.225133 | ||||||||
\(491\) | 23.6181 | 1.06587 | 0.532936 | − | 0.846156i | \(-0.321089\pi\) | ||||
0.532936 | + | 0.846156i | \(0.321089\pi\) | |||||||
\(492\) | −1.12786 | −0.0508481 | ||||||||
\(493\) | −56.7369 | −2.55530 | ||||||||
\(494\) | −0.613901 | −0.0276207 | ||||||||
\(495\) | 2.26617 | 0.101857 | ||||||||
\(496\) | −5.42821 | −0.243734 | ||||||||
\(497\) | −22.5586 | −1.01189 | ||||||||
\(498\) | 3.52096 | 0.157778 | ||||||||
\(499\) | −20.6660 | −0.925137 | −0.462568 | − | 0.886584i | \(-0.653072\pi\) | ||||
−0.462568 | + | 0.886584i | \(0.653072\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −15.5135 | −0.693094 | ||||||||
\(502\) | −13.5759 | −0.605924 | ||||||||
\(503\) | 17.0007 | 0.758023 | 0.379011 | − | 0.925392i | \(-0.376264\pi\) | ||||
0.379011 | + | 0.925392i | \(0.376264\pi\) | |||||||
\(504\) | −3.21801 | −0.143341 | ||||||||
\(505\) | 8.90533 | 0.396282 | ||||||||
\(506\) | −0.366337 | −0.0162857 | ||||||||
\(507\) | 7.96735 | 0.353842 | ||||||||
\(508\) | 13.8567 | 0.614793 | ||||||||
\(509\) | 2.52888 | 0.112091 | 0.0560454 | − | 0.998428i | \(-0.482151\pi\) | ||||
0.0560454 | + | 0.998428i | \(0.482151\pi\) | |||||||
\(510\) | 6.66251 | 0.295021 | ||||||||
\(511\) | 1.42002 | 0.0628181 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.43990 | −0.0635730 | ||||||||
\(514\) | −10.5016 | −0.463205 | ||||||||
\(515\) | −14.8296 | −0.653470 | ||||||||
\(516\) | −5.47460 | −0.241006 | ||||||||
\(517\) | −2.70055 | −0.118770 | ||||||||
\(518\) | 9.32963 | 0.409920 | ||||||||
\(519\) | −13.3902 | −0.587763 | ||||||||
\(520\) | −1.92336 | −0.0843449 | ||||||||
\(521\) | −42.7036 | −1.87088 | −0.935440 | − | 0.353487i | \(-0.884996\pi\) | ||||
−0.935440 | + | 0.353487i | \(0.884996\pi\) | |||||||
\(522\) | 16.5317 | 0.723574 | ||||||||
\(523\) | 18.1860 | 0.795217 | 0.397608 | − | 0.917555i | \(-0.369840\pi\) | ||||
0.397608 | + | 0.917555i | \(0.369840\pi\) | |||||||
\(524\) | −17.2098 | −0.751814 | ||||||||
\(525\) | −1.21645 | −0.0530902 | ||||||||
\(526\) | 4.29740 | 0.187376 | ||||||||
\(527\) | −42.2178 | −1.83904 | ||||||||
\(528\) | −0.856641 | −0.0372805 | ||||||||
\(529\) | −22.8658 | −0.994165 | ||||||||
\(530\) | −1.36622 | −0.0593449 | ||||||||
\(531\) | −22.9490 | −0.995902 | ||||||||
\(532\) | −0.453245 | −0.0196507 | ||||||||
\(533\) | 2.53232 | 0.109687 | ||||||||
\(534\) | 1.69092 | 0.0731731 | ||||||||
\(535\) | 3.86024 | 0.166893 | ||||||||
\(536\) | 7.17786 | 0.310037 | ||||||||
\(537\) | 10.7945 | 0.465816 | ||||||||
\(538\) | −9.05841 | −0.390536 | ||||||||
\(539\) | −4.98354 | −0.214656 | ||||||||
\(540\) | −4.51121 | −0.194132 | ||||||||
\(541\) | 7.39842 | 0.318083 | 0.159041 | − | 0.987272i | \(-0.449160\pi\) | ||||
0.159041 | + | 0.987272i | \(0.449160\pi\) | |||||||
\(542\) | 12.1871 | 0.523481 | ||||||||
\(543\) | −0.569409 | −0.0244357 | ||||||||
\(544\) | 7.77749 | 0.333457 | ||||||||
\(545\) | 4.81249 | 0.206144 | ||||||||
\(546\) | −2.33967 | −0.100128 | ||||||||
\(547\) | −15.0443 | −0.643248 | −0.321624 | − | 0.946867i | \(-0.604229\pi\) | ||||
−0.321624 | + | 0.946867i | \(0.604229\pi\) | |||||||
\(548\) | 17.0615 | 0.728829 | ||||||||
\(549\) | −0.491143 | −0.0209615 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 2.32844 | 0.0991947 | ||||||||
\(552\) | 0.313819 | 0.0133570 | ||||||||
\(553\) | 11.7853 | 0.501164 | ||||||||
\(554\) | 17.0729 | 0.725356 | ||||||||
\(555\) | 5.62818 | 0.238903 | ||||||||
\(556\) | 11.8945 | 0.504437 | ||||||||
\(557\) | 31.9988 | 1.35583 | 0.677916 | − | 0.735139i | \(-0.262883\pi\) | ||||
0.677916 | + | 0.735139i | \(0.262883\pi\) | |||||||
\(558\) | 12.3012 | 0.520753 | ||||||||
\(559\) | 12.2918 | 0.519886 | ||||||||
\(560\) | −1.42002 | −0.0600069 | ||||||||
\(561\) | −6.66251 | −0.281291 | ||||||||
\(562\) | −13.9544 | −0.588632 | ||||||||
\(563\) | 18.3938 | 0.775208 | 0.387604 | − | 0.921826i | \(-0.373303\pi\) | ||||
0.387604 | + | 0.921826i | \(0.373303\pi\) | |||||||
\(564\) | 2.31340 | 0.0974116 | ||||||||
\(565\) | −1.53056 | −0.0643913 | ||||||||
\(566\) | −16.4666 | −0.692141 | ||||||||
\(567\) | 4.16636 | 0.174971 | ||||||||
\(568\) | −15.8861 | −0.666565 | ||||||||
\(569\) | −23.0568 | −0.966593 | −0.483296 | − | 0.875457i | \(-0.660561\pi\) | ||||
−0.483296 | + | 0.875457i | \(0.660561\pi\) | |||||||
\(570\) | −0.273424 | −0.0114525 | ||||||||
\(571\) | 26.5044 | 1.10917 | 0.554587 | − | 0.832126i | \(-0.312876\pi\) | ||||
0.554587 | + | 0.832126i | \(0.312876\pi\) | |||||||
\(572\) | 1.92336 | 0.0804197 | ||||||||
\(573\) | −10.3333 | −0.431682 | ||||||||
\(574\) | 1.86962 | 0.0780364 | ||||||||
\(575\) | −0.366337 | −0.0152773 | ||||||||
\(576\) | −2.26617 | −0.0944236 | ||||||||
\(577\) | −5.94907 | −0.247663 | −0.123832 | − | 0.992303i | \(-0.539518\pi\) | ||||
−0.123832 | + | 0.992303i | \(0.539518\pi\) | |||||||
\(578\) | 43.4893 | 1.80892 | ||||||||
\(579\) | −5.61543 | −0.233369 | ||||||||
\(580\) | 7.29502 | 0.302909 | ||||||||
\(581\) | −5.83657 | −0.242142 | ||||||||
\(582\) | 0.621016 | 0.0257419 | ||||||||
\(583\) | 1.36622 | 0.0565832 | ||||||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 4.35865 | 0.180208 | ||||||||
\(586\) | −3.10799 | −0.128390 | ||||||||
\(587\) | −29.6858 | −1.22527 | −0.612633 | − | 0.790368i | \(-0.709890\pi\) | ||||
−0.612633 | + | 0.790368i | \(0.709890\pi\) | |||||||
\(588\) | 4.26910 | 0.176055 | ||||||||
\(589\) | 1.73259 | 0.0713900 | ||||||||
\(590\) | −10.1268 | −0.416913 | ||||||||
\(591\) | −21.4378 | −0.881833 | ||||||||
\(592\) | 6.57006 | 0.270028 | ||||||||
\(593\) | 36.1342 | 1.48385 | 0.741926 | − | 0.670482i | \(-0.233913\pi\) | ||||
0.741926 | + | 0.670482i | \(0.233913\pi\) | |||||||
\(594\) | 4.51121 | 0.185097 | ||||||||
\(595\) | −11.0442 | −0.452768 | ||||||||
\(596\) | 14.9784 | 0.613537 | ||||||||
\(597\) | −4.76636 | −0.195074 | ||||||||
\(598\) | −0.704597 | −0.0288131 | ||||||||
\(599\) | 6.73300 | 0.275103 | 0.137552 | − | 0.990495i | \(-0.456077\pi\) | ||||
0.137552 | + | 0.990495i | \(0.456077\pi\) | |||||||
\(600\) | −0.856641 | −0.0349722 | ||||||||
\(601\) | −23.3603 | −0.952886 | −0.476443 | − | 0.879205i | \(-0.658074\pi\) | ||||
−0.476443 | + | 0.879205i | \(0.658074\pi\) | |||||||
\(602\) | 9.07504 | 0.369871 | ||||||||
\(603\) | −16.2662 | −0.662412 | ||||||||
\(604\) | −0.304998 | −0.0124102 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 7.62867 | 0.309893 | ||||||||
\(607\) | 12.3739 | 0.502241 | 0.251120 | − | 0.967956i | \(-0.419201\pi\) | ||||
0.251120 | + | 0.967956i | \(0.419201\pi\) | |||||||
\(608\) | −0.319182 | −0.0129445 | ||||||||
\(609\) | 8.87401 | 0.359593 | ||||||||
\(610\) | −0.216728 | −0.00877508 | ||||||||
\(611\) | −5.19412 | −0.210132 | ||||||||
\(612\) | −17.6251 | −0.712452 | ||||||||
\(613\) | −5.74470 | −0.232026 | −0.116013 | − | 0.993248i | \(-0.537011\pi\) | ||||
−0.116013 | + | 0.993248i | \(0.537011\pi\) | |||||||
\(614\) | 11.7658 | 0.474829 | ||||||||
\(615\) | 1.12786 | 0.0454799 | ||||||||
\(616\) | 1.42002 | 0.0572143 | ||||||||
\(617\) | −0.237263 | −0.00955185 | −0.00477593 | − | 0.999989i | \(-0.501520\pi\) | ||||
−0.00477593 | + | 0.999989i | \(0.501520\pi\) | |||||||
\(618\) | −12.7036 | −0.511015 | ||||||||
\(619\) | −26.1137 | −1.04960 | −0.524799 | − | 0.851226i | \(-0.675860\pi\) | ||||
−0.524799 | + | 0.851226i | \(0.675860\pi\) | |||||||
\(620\) | 5.42821 | 0.218002 | ||||||||
\(621\) | −1.65262 | −0.0663175 | ||||||||
\(622\) | 26.9845 | 1.08198 | ||||||||
\(623\) | −2.80297 | −0.112299 | ||||||||
\(624\) | −1.64763 | −0.0659579 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.88309 | 0.0752636 | ||||||||
\(627\) | 0.273424 | 0.0109195 | ||||||||
\(628\) | −18.1757 | −0.725290 | ||||||||
\(629\) | 51.0986 | 2.03743 | ||||||||
\(630\) | 3.21801 | 0.128208 | ||||||||
\(631\) | −36.3962 | −1.44891 | −0.724455 | − | 0.689322i | \(-0.757908\pi\) | ||||
−0.724455 | + | 0.689322i | \(0.757908\pi\) | |||||||
\(632\) | 8.29940 | 0.330133 | ||||||||
\(633\) | 11.8822 | 0.472274 | ||||||||
\(634\) | 20.8192 | 0.826835 | ||||||||
\(635\) | −13.8567 | −0.549888 | ||||||||
\(636\) | −1.17036 | −0.0464079 | ||||||||
\(637\) | −9.58513 | −0.379777 | ||||||||
\(638\) | −7.29502 | −0.288812 | ||||||||
\(639\) | 36.0005 | 1.42416 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −4.27457 | −0.168835 | −0.0844176 | − | 0.996430i | \(-0.526903\pi\) | ||||
−0.0844176 | + | 0.996430i | \(0.526903\pi\) | |||||||
\(642\) | 3.30684 | 0.130511 | ||||||||
\(643\) | 45.3473 | 1.78832 | 0.894161 | − | 0.447745i | \(-0.147773\pi\) | ||||
0.894161 | + | 0.447745i | \(0.147773\pi\) | |||||||
\(644\) | −0.520206 | −0.0204990 | ||||||||
\(645\) | 5.47460 | 0.215562 | ||||||||
\(646\) | −2.48243 | −0.0976700 | ||||||||
\(647\) | −38.8178 | −1.52608 | −0.763042 | − | 0.646349i | \(-0.776295\pi\) | ||||
−0.763042 | + | 0.646349i | \(0.776295\pi\) | |||||||
\(648\) | 2.93401 | 0.115259 | ||||||||
\(649\) | 10.1268 | 0.397511 | ||||||||
\(650\) | 1.92336 | 0.0754403 | ||||||||
\(651\) | 6.60314 | 0.258797 | ||||||||
\(652\) | 7.76954 | 0.304279 | ||||||||
\(653\) | −29.6602 | −1.16069 | −0.580347 | − | 0.814369i | \(-0.697083\pi\) | ||||
−0.580347 | + | 0.814369i | \(0.697083\pi\) | |||||||
\(654\) | 4.12257 | 0.161205 | ||||||||
\(655\) | 17.2098 | 0.672443 | ||||||||
\(656\) | 1.31661 | 0.0514051 | ||||||||
\(657\) | −2.26617 | −0.0884116 | ||||||||
\(658\) | −3.83483 | −0.149497 | ||||||||
\(659\) | 19.1253 | 0.745018 | 0.372509 | − | 0.928029i | \(-0.378498\pi\) | ||||
0.372509 | + | 0.928029i | \(0.378498\pi\) | |||||||
\(660\) | 0.856641 | 0.0333447 | ||||||||
\(661\) | 26.9202 | 1.04707 | 0.523536 | − | 0.852003i | \(-0.324612\pi\) | ||||
0.523536 | + | 0.852003i | \(0.324612\pi\) | |||||||
\(662\) | −4.28694 | −0.166617 | ||||||||
\(663\) | −12.8144 | −0.497670 | ||||||||
\(664\) | −4.11020 | −0.159507 | ||||||||
\(665\) | 0.453245 | 0.0175761 | ||||||||
\(666\) | −14.8889 | −0.576931 | ||||||||
\(667\) | 2.67243 | 0.103477 | ||||||||
\(668\) | 18.1097 | 0.700687 | ||||||||
\(669\) | 1.75149 | 0.0677164 | ||||||||
\(670\) | −7.17786 | −0.277305 | ||||||||
\(671\) | 0.216728 | 0.00836671 | ||||||||
\(672\) | −1.21645 | −0.0469255 | ||||||||
\(673\) | 29.7766 | 1.14780 | 0.573902 | − | 0.818924i | \(-0.305429\pi\) | ||||
0.573902 | + | 0.818924i | \(0.305429\pi\) | |||||||
\(674\) | −0.552780 | −0.0212923 | ||||||||
\(675\) | 4.51121 | 0.173637 | ||||||||
\(676\) | −9.30069 | −0.357719 | ||||||||
\(677\) | 13.1342 | 0.504789 | 0.252395 | − | 0.967624i | \(-0.418782\pi\) | ||||
0.252395 | + | 0.967624i | \(0.418782\pi\) | |||||||
\(678\) | −1.31114 | −0.0503542 | ||||||||
\(679\) | −1.02944 | −0.0395061 | ||||||||
\(680\) | −7.77749 | −0.298253 | ||||||||
\(681\) | −8.09878 | −0.310346 | ||||||||
\(682\) | −5.42821 | −0.207857 | ||||||||
\(683\) | 5.19913 | 0.198939 | 0.0994697 | − | 0.995041i | \(-0.468285\pi\) | ||||
0.0994697 | + | 0.995041i | \(0.468285\pi\) | |||||||
\(684\) | 0.723319 | 0.0276568 | ||||||||
\(685\) | −17.0615 | −0.651885 | ||||||||
\(686\) | −17.0169 | −0.649708 | ||||||||
\(687\) | −11.6659 | −0.445080 | ||||||||
\(688\) | 6.39077 | 0.243646 | ||||||||
\(689\) | 2.62774 | 0.100109 | ||||||||
\(690\) | −0.313819 | −0.0119469 | ||||||||
\(691\) | −24.2108 | −0.921021 | −0.460511 | − | 0.887654i | \(-0.652334\pi\) | ||||
−0.460511 | + | 0.887654i | \(0.652334\pi\) | |||||||
\(692\) | 15.6310 | 0.594202 | ||||||||
\(693\) | −3.21801 | −0.122242 | ||||||||
\(694\) | −25.3958 | −0.964012 | ||||||||
\(695\) | −11.8945 | −0.451183 | ||||||||
\(696\) | 6.24921 | 0.236876 | ||||||||
\(697\) | 10.2399 | 0.387866 | ||||||||
\(698\) | −5.69642 | −0.215613 | ||||||||
\(699\) | −15.7995 | −0.597594 | ||||||||
\(700\) | 1.42002 | 0.0536718 | ||||||||
\(701\) | −38.1565 | −1.44115 | −0.720575 | − | 0.693377i | \(-0.756122\pi\) | ||||
−0.720575 | + | 0.693377i | \(0.756122\pi\) | |||||||
\(702\) | 8.67668 | 0.327480 | ||||||||
\(703\) | −2.09704 | −0.0790915 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −2.31340 | −0.0871276 | ||||||||
\(706\) | 24.5096 | 0.922429 | ||||||||
\(707\) | −12.6458 | −0.475593 | ||||||||
\(708\) | −8.67502 | −0.326027 | ||||||||
\(709\) | 9.03220 | 0.339211 | 0.169606 | − | 0.985512i | \(-0.445751\pi\) | ||||
0.169606 | + | 0.985512i | \(0.445751\pi\) | |||||||
\(710\) | 15.8861 | 0.596194 | ||||||||
\(711\) | −18.8078 | −0.705349 | ||||||||
\(712\) | −1.97389 | −0.0739747 | ||||||||
\(713\) | 1.98855 | 0.0744719 | ||||||||
\(714\) | −9.46091 | −0.354066 | ||||||||
\(715\) | −1.92336 | −0.0719295 | ||||||||
\(716\) | −12.6009 | −0.470920 | ||||||||
\(717\) | −17.7851 | −0.664197 | ||||||||
\(718\) | 15.1897 | 0.566873 | ||||||||
\(719\) | 21.4938 | 0.801584 | 0.400792 | − | 0.916169i | \(-0.368735\pi\) | ||||
0.400792 | + | 0.916169i | \(0.368735\pi\) | |||||||
\(720\) | 2.26617 | 0.0844551 | ||||||||
\(721\) | 21.0583 | 0.784254 | ||||||||
\(722\) | −18.8981 | −0.703315 | ||||||||
\(723\) | −12.8463 | −0.477758 | ||||||||
\(724\) | 0.664700 | 0.0247034 | ||||||||
\(725\) | −7.29502 | −0.270930 | ||||||||
\(726\) | −0.856641 | −0.0317929 | ||||||||
\(727\) | 45.9739 | 1.70508 | 0.852538 | − | 0.522665i | \(-0.175062\pi\) | ||||
0.852538 | + | 0.522665i | \(0.175062\pi\) | |||||||
\(728\) | 2.73121 | 0.101225 | ||||||||
\(729\) | 4.94450 | 0.183130 | ||||||||
\(730\) | −1.00000 | −0.0370117 | ||||||||
\(731\) | 49.7042 | 1.83838 | ||||||||
\(732\) | −0.185658 | −0.00686213 | ||||||||
\(733\) | −37.1150 | −1.37087 | −0.685437 | − | 0.728132i | \(-0.740389\pi\) | ||||
−0.685437 | + | 0.728132i | \(0.740389\pi\) | |||||||
\(734\) | 30.8165 | 1.13746 | ||||||||
\(735\) | −4.26910 | −0.157468 | ||||||||
\(736\) | −0.366337 | −0.0135034 | ||||||||
\(737\) | 7.17786 | 0.264400 | ||||||||
\(738\) | −2.98367 | −0.109830 | ||||||||
\(739\) | 35.3924 | 1.30193 | 0.650965 | − | 0.759107i | \(-0.274364\pi\) | ||||
0.650965 | + | 0.759107i | \(0.274364\pi\) | |||||||
\(740\) | −6.57006 | −0.241520 | ||||||||
\(741\) | 0.525893 | 0.0193191 | ||||||||
\(742\) | 1.94007 | 0.0712221 | ||||||||
\(743\) | 15.9911 | 0.586658 | 0.293329 | − | 0.956012i | \(-0.405237\pi\) | ||||
0.293329 | + | 0.956012i | \(0.405237\pi\) | |||||||
\(744\) | 4.65003 | 0.170478 | ||||||||
\(745\) | −14.9784 | −0.548765 | ||||||||
\(746\) | 21.6159 | 0.791416 | ||||||||
\(747\) | 9.31439 | 0.340796 | ||||||||
\(748\) | 7.77749 | 0.284373 | ||||||||
\(749\) | −5.48163 | −0.200294 | ||||||||
\(750\) | 0.856641 | 0.0312801 | ||||||||
\(751\) | 12.6936 | 0.463195 | 0.231597 | − | 0.972812i | \(-0.425605\pi\) | ||||
0.231597 | + | 0.972812i | \(0.425605\pi\) | |||||||
\(752\) | −2.70055 | −0.0984788 | ||||||||
\(753\) | 11.6297 | 0.423810 | ||||||||
\(754\) | −14.0309 | −0.510976 | ||||||||
\(755\) | 0.304998 | 0.0111000 | ||||||||
\(756\) | 6.40602 | 0.232985 | ||||||||
\(757\) | 5.74200 | 0.208696 | 0.104348 | − | 0.994541i | \(-0.466724\pi\) | ||||
0.104348 | + | 0.994541i | \(0.466724\pi\) | |||||||
\(758\) | 21.1598 | 0.768558 | ||||||||
\(759\) | 0.313819 | 0.0113909 | ||||||||
\(760\) | 0.319182 | 0.0115779 | ||||||||
\(761\) | −45.3644 | −1.64446 | −0.822229 | − | 0.569157i | \(-0.807270\pi\) | ||||
−0.822229 | + | 0.569157i | \(0.807270\pi\) | |||||||
\(762\) | −11.8702 | −0.430013 | ||||||||
\(763\) | −6.83384 | −0.247401 | ||||||||
\(764\) | 12.0626 | 0.436411 | ||||||||
\(765\) | 17.6251 | 0.637236 | ||||||||
\(766\) | −28.7204 | −1.03771 | ||||||||
\(767\) | 19.4774 | 0.703290 | ||||||||
\(768\) | −0.856641 | −0.0309114 | ||||||||
\(769\) | 37.8677 | 1.36554 | 0.682772 | − | 0.730632i | \(-0.260774\pi\) | ||||
0.682772 | + | 0.730632i | \(0.260774\pi\) | |||||||
\(770\) | −1.42002 | −0.0511740 | ||||||||
\(771\) | 8.99608 | 0.323986 | ||||||||
\(772\) | 6.55517 | 0.235926 | ||||||||
\(773\) | −46.7882 | −1.68286 | −0.841428 | − | 0.540369i | \(-0.818285\pi\) | ||||
−0.841428 | + | 0.540369i | \(0.818285\pi\) | |||||||
\(774\) | −14.4826 | −0.520565 | ||||||||
\(775\) | −5.42821 | −0.194987 | ||||||||
\(776\) | −0.724943 | −0.0260239 | ||||||||
\(777\) | −7.99214 | −0.286716 | ||||||||
\(778\) | −12.2768 | −0.440146 | ||||||||
\(779\) | −0.420239 | −0.0150566 | ||||||||
\(780\) | 1.64763 | 0.0589945 | ||||||||
\(781\) | −15.8861 | −0.568449 | ||||||||
\(782\) | −2.84918 | −0.101887 | ||||||||
\(783\) | −32.9094 | −1.17608 | ||||||||
\(784\) | −4.98354 | −0.177983 | ||||||||
\(785\) | 18.1757 | 0.648719 | ||||||||
\(786\) | 14.7426 | 0.525852 | ||||||||
\(787\) | 36.1280 | 1.28783 | 0.643913 | − | 0.765099i | \(-0.277310\pi\) | ||||
0.643913 | + | 0.765099i | \(0.277310\pi\) | |||||||
\(788\) | 25.0254 | 0.891494 | ||||||||
\(789\) | −3.68133 | −0.131059 | ||||||||
\(790\) | −8.29940 | −0.295280 | ||||||||
\(791\) | 2.17344 | 0.0772785 | ||||||||
\(792\) | −2.26617 | −0.0805247 | ||||||||
\(793\) | 0.416847 | 0.0148027 | ||||||||
\(794\) | 5.06869 | 0.179881 | ||||||||
\(795\) | 1.17036 | 0.0415085 | ||||||||
\(796\) | 5.56402 | 0.197211 | ||||||||
\(797\) | −25.5167 | −0.903847 | −0.451924 | − | 0.892057i | \(-0.649262\pi\) | ||||
−0.451924 | + | 0.892057i | \(0.649262\pi\) | |||||||
\(798\) | 0.388268 | 0.0137445 | ||||||||
\(799\) | −21.0035 | −0.743049 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 4.47317 | 0.158052 | ||||||||
\(802\) | 11.7529 | 0.415009 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −6.14885 | −0.216853 | ||||||||
\(805\) | 0.520206 | 0.0183349 | ||||||||
\(806\) | −10.4404 | −0.367747 | ||||||||
\(807\) | 7.75980 | 0.273158 | ||||||||
\(808\) | −8.90533 | −0.313288 | ||||||||
\(809\) | −24.4471 | −0.859513 | −0.429757 | − | 0.902945i | \(-0.641401\pi\) | ||||
−0.429757 | + | 0.902945i | \(0.641401\pi\) | |||||||
\(810\) | −2.93401 | −0.103091 | ||||||||
\(811\) | 43.4252 | 1.52486 | 0.762432 | − | 0.647069i | \(-0.224005\pi\) | ||||
0.762432 | + | 0.647069i | \(0.224005\pi\) | |||||||
\(812\) | −10.3591 | −0.363533 | ||||||||
\(813\) | −10.4400 | −0.366146 | ||||||||
\(814\) | 6.57006 | 0.230280 | ||||||||
\(815\) | −7.76954 | −0.272155 | ||||||||
\(816\) | −6.66251 | −0.233235 | ||||||||
\(817\) | −2.03982 | −0.0713642 | ||||||||
\(818\) | −28.3149 | −0.990007 | ||||||||
\(819\) | −6.18938 | −0.216274 | ||||||||
\(820\) | −1.31661 | −0.0459781 | ||||||||
\(821\) | −7.50953 | −0.262084 | −0.131042 | − | 0.991377i | \(-0.541832\pi\) | ||||
−0.131042 | + | 0.991377i | \(0.541832\pi\) | |||||||
\(822\) | −14.6155 | −0.509775 | ||||||||
\(823\) | −39.8884 | −1.39042 | −0.695211 | − | 0.718806i | \(-0.744689\pi\) | ||||
−0.695211 | + | 0.718806i | \(0.744689\pi\) | |||||||
\(824\) | 14.8296 | 0.516613 | ||||||||
\(825\) | −0.856641 | −0.0298244 | ||||||||
\(826\) | 14.3803 | 0.500353 | ||||||||
\(827\) | 12.1798 | 0.423534 | 0.211767 | − | 0.977320i | \(-0.432078\pi\) | ||||
0.211767 | + | 0.977320i | \(0.432078\pi\) | |||||||
\(828\) | 0.830181 | 0.0288508 | ||||||||
\(829\) | 5.50080 | 0.191051 | 0.0955254 | − | 0.995427i | \(-0.469547\pi\) | ||||
0.0955254 | + | 0.995427i | \(0.469547\pi\) | |||||||
\(830\) | 4.11020 | 0.142667 | ||||||||
\(831\) | −14.6253 | −0.507346 | ||||||||
\(832\) | 1.92336 | 0.0666805 | ||||||||
\(833\) | −38.7594 | −1.34293 | ||||||||
\(834\) | −10.1893 | −0.352826 | ||||||||
\(835\) | −18.1097 | −0.626714 | ||||||||
\(836\) | −0.319182 | −0.0110391 | ||||||||
\(837\) | −24.4878 | −0.846423 | ||||||||
\(838\) | 20.7058 | 0.715269 | ||||||||
\(839\) | 34.0175 | 1.17441 | 0.587207 | − | 0.809437i | \(-0.300228\pi\) | ||||
0.587207 | + | 0.809437i | \(0.300228\pi\) | |||||||
\(840\) | 1.21645 | 0.0419715 | ||||||||
\(841\) | 24.2173 | 0.835078 | ||||||||
\(842\) | 3.24741 | 0.111913 | ||||||||
\(843\) | 11.9539 | 0.411715 | ||||||||
\(844\) | −13.8707 | −0.477448 | ||||||||
\(845\) | 9.30069 | 0.319954 | ||||||||
\(846\) | 6.11989 | 0.210406 | ||||||||
\(847\) | 1.42002 | 0.0487925 | ||||||||
\(848\) | 1.36622 | 0.0469163 | ||||||||
\(849\) | 14.1059 | 0.484114 | ||||||||
\(850\) | 7.77749 | 0.266766 | ||||||||
\(851\) | −2.40686 | −0.0825059 | ||||||||
\(852\) | 13.6087 | 0.466225 | ||||||||
\(853\) | 55.0578 | 1.88514 | 0.942571 | − | 0.334007i | \(-0.108401\pi\) | ||||
0.942571 | + | 0.334007i | \(0.108401\pi\) | |||||||
\(854\) | 0.307759 | 0.0105313 | ||||||||
\(855\) | −0.723319 | −0.0247370 | ||||||||
\(856\) | −3.86024 | −0.131940 | ||||||||
\(857\) | −39.5466 | −1.35089 | −0.675444 | − | 0.737412i | \(-0.736048\pi\) | ||||
−0.675444 | + | 0.737412i | \(0.736048\pi\) | |||||||
\(858\) | −1.64763 | −0.0562491 | ||||||||
\(859\) | −6.67313 | −0.227684 | −0.113842 | − | 0.993499i | \(-0.536316\pi\) | ||||
−0.113842 | + | 0.993499i | \(0.536316\pi\) | |||||||
\(860\) | −6.39077 | −0.217924 | ||||||||
\(861\) | −1.60159 | −0.0545821 | ||||||||
\(862\) | −2.06655 | −0.0703870 | ||||||||
\(863\) | −27.1979 | −0.925826 | −0.462913 | − | 0.886404i | \(-0.653196\pi\) | ||||
−0.462913 | + | 0.886404i | \(0.653196\pi\) | |||||||
\(864\) | 4.51121 | 0.153475 | ||||||||
\(865\) | −15.6310 | −0.531470 | ||||||||
\(866\) | −33.3595 | −1.13360 | ||||||||
\(867\) | −37.2547 | −1.26524 | ||||||||
\(868\) | −7.70818 | −0.261633 | ||||||||
\(869\) | 8.29940 | 0.281538 | ||||||||
\(870\) | −6.24921 | −0.211868 | ||||||||
\(871\) | 13.8056 | 0.467785 | ||||||||
\(872\) | −4.81249 | −0.162971 | ||||||||
\(873\) | 1.64284 | 0.0556018 | ||||||||
\(874\) | 0.116928 | 0.00395515 | ||||||||
\(875\) | −1.42002 | −0.0480055 | ||||||||
\(876\) | −0.856641 | −0.0289432 | ||||||||
\(877\) | 51.7917 | 1.74888 | 0.874440 | − | 0.485134i | \(-0.161229\pi\) | ||||
0.874440 | + | 0.485134i | \(0.161229\pi\) | |||||||
\(878\) | −19.3908 | −0.654408 | ||||||||
\(879\) | 2.66243 | 0.0898016 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 6.86060 | 0.231140 | 0.115570 | − | 0.993299i | \(-0.463131\pi\) | ||||
0.115570 | + | 0.993299i | \(0.463131\pi\) | |||||||
\(882\) | 11.2935 | 0.380273 | ||||||||
\(883\) | −30.4470 | −1.02462 | −0.512312 | − | 0.858799i | \(-0.671211\pi\) | ||||
−0.512312 | + | 0.858799i | \(0.671211\pi\) | |||||||
\(884\) | 14.9589 | 0.503122 | ||||||||
\(885\) | 8.67502 | 0.291608 | ||||||||
\(886\) | −33.9145 | −1.13938 | ||||||||
\(887\) | −12.3277 | −0.413924 | −0.206962 | − | 0.978349i | \(-0.566358\pi\) | ||||
−0.206962 | + | 0.978349i | \(0.566358\pi\) | |||||||
\(888\) | −5.62818 | −0.188869 | ||||||||
\(889\) | 19.6769 | 0.659941 | ||||||||
\(890\) | 1.97389 | 0.0661650 | ||||||||
\(891\) | 2.93401 | 0.0982931 | ||||||||
\(892\) | −2.04460 | −0.0684582 | ||||||||
\(893\) | 0.861965 | 0.0288446 | ||||||||
\(894\) | −12.8311 | −0.429135 | ||||||||
\(895\) | 12.6009 | 0.421203 | ||||||||
\(896\) | 1.42002 | 0.0474396 | ||||||||
\(897\) | 0.603587 | 0.0201532 | ||||||||
\(898\) | −3.64868 | −0.121758 | ||||||||
\(899\) | 39.5989 | 1.32070 | ||||||||
\(900\) | −2.26617 | −0.0755389 | ||||||||
\(901\) | 10.6258 | 0.353996 | ||||||||
\(902\) | 1.31661 | 0.0438384 | ||||||||
\(903\) | −7.77405 | −0.258704 | ||||||||
\(904\) | 1.53056 | 0.0509058 | ||||||||
\(905\) | −0.664700 | −0.0220954 | ||||||||
\(906\) | 0.261274 | 0.00868023 | ||||||||
\(907\) | −28.9561 | −0.961472 | −0.480736 | − | 0.876865i | \(-0.659630\pi\) | ||||
−0.480736 | + | 0.876865i | \(0.659630\pi\) | |||||||
\(908\) | 9.45412 | 0.313746 | ||||||||
\(909\) | 20.1810 | 0.669361 | ||||||||
\(910\) | −2.73121 | −0.0905388 | ||||||||
\(911\) | −20.1064 | −0.666153 | −0.333077 | − | 0.942900i | \(-0.608087\pi\) | ||||
−0.333077 | + | 0.942900i | \(0.608087\pi\) | |||||||
\(912\) | 0.273424 | 0.00905398 | ||||||||
\(913\) | −4.11020 | −0.136028 | ||||||||
\(914\) | −2.16910 | −0.0717473 | ||||||||
\(915\) | 0.185658 | 0.00613768 | ||||||||
\(916\) | 13.6181 | 0.449956 | ||||||||
\(917\) | −24.4383 | −0.807024 | ||||||||
\(918\) | 35.0859 | 1.15801 | ||||||||
\(919\) | 6.73924 | 0.222307 | 0.111154 | − | 0.993803i | \(-0.464545\pi\) | ||||
0.111154 | + | 0.993803i | \(0.464545\pi\) | |||||||
\(920\) | 0.366337 | 0.0120778 | ||||||||
\(921\) | −10.0791 | −0.332117 | ||||||||
\(922\) | 23.1797 | 0.763381 | ||||||||
\(923\) | −30.5546 | −1.00572 | ||||||||
\(924\) | −1.21645 | −0.0400182 | ||||||||
\(925\) | 6.57006 | 0.216022 | ||||||||
\(926\) | −32.2635 | −1.06025 | ||||||||
\(927\) | −33.6063 | −1.10378 | ||||||||
\(928\) | −7.29502 | −0.239471 | ||||||||
\(929\) | 59.6218 | 1.95613 | 0.978065 | − | 0.208302i | \(-0.0667936\pi\) | ||||
0.978065 | + | 0.208302i | \(0.0667936\pi\) | |||||||
\(930\) | −4.65003 | −0.152480 | ||||||||
\(931\) | 1.59065 | 0.0521316 | ||||||||
\(932\) | 18.4436 | 0.604140 | ||||||||
\(933\) | −23.1160 | −0.756785 | ||||||||
\(934\) | 6.11798 | 0.200186 | ||||||||
\(935\) | −7.77749 | −0.254351 | ||||||||
\(936\) | −4.35865 | −0.142467 | ||||||||
\(937\) | −9.94544 | −0.324903 | −0.162452 | − | 0.986717i | \(-0.551940\pi\) | ||||
−0.162452 | + | 0.986717i | \(0.551940\pi\) | |||||||
\(938\) | 10.1927 | 0.332804 | ||||||||
\(939\) | −1.61313 | −0.0526427 | ||||||||
\(940\) | 2.70055 | 0.0880821 | ||||||||
\(941\) | −27.2194 | −0.887328 | −0.443664 | − | 0.896193i | \(-0.646322\pi\) | ||||
−0.443664 | + | 0.896193i | \(0.646322\pi\) | |||||||
\(942\) | 15.5700 | 0.507300 | ||||||||
\(943\) | −0.482324 | −0.0157066 | ||||||||
\(944\) | 10.1268 | 0.329599 | ||||||||
\(945\) | −6.40602 | −0.208388 | ||||||||
\(946\) | 6.39077 | 0.207782 | ||||||||
\(947\) | 41.5656 | 1.35070 | 0.675350 | − | 0.737497i | \(-0.263993\pi\) | ||||
0.675350 | + | 0.737497i | \(0.263993\pi\) | |||||||
\(948\) | −7.10961 | −0.230909 | ||||||||
\(949\) | 1.92336 | 0.0624349 | ||||||||
\(950\) | −0.319182 | −0.0103556 | ||||||||
\(951\) | −17.8346 | −0.578325 | ||||||||
\(952\) | 11.0442 | 0.357945 | ||||||||
\(953\) | −48.4306 | −1.56882 | −0.784410 | − | 0.620243i | \(-0.787034\pi\) | ||||
−0.784410 | + | 0.620243i | \(0.787034\pi\) | |||||||
\(954\) | −3.09609 | −0.100240 | ||||||||
\(955\) | −12.0626 | −0.390338 | ||||||||
\(956\) | 20.7615 | 0.671474 | ||||||||
\(957\) | 6.24921 | 0.202008 | ||||||||
\(958\) | 19.9231 | 0.643687 | ||||||||
\(959\) | 24.2276 | 0.782351 | ||||||||
\(960\) | 0.856641 | 0.0276480 | ||||||||
\(961\) | −1.53453 | −0.0495008 | ||||||||
\(962\) | 12.6366 | 0.407420 | ||||||||
\(963\) | 8.74795 | 0.281899 | ||||||||
\(964\) | 14.9961 | 0.482992 | ||||||||
\(965\) | −6.55517 | −0.211019 | ||||||||
\(966\) | 0.445630 | 0.0143379 | ||||||||
\(967\) | −10.8619 | −0.349295 | −0.174648 | − | 0.984631i | \(-0.555879\pi\) | ||||
−0.174648 | + | 0.984631i | \(0.555879\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 2.12655 | 0.0683147 | ||||||||
\(970\) | 0.724943 | 0.0232765 | ||||||||
\(971\) | 9.71748 | 0.311849 | 0.155924 | − | 0.987769i | \(-0.450164\pi\) | ||||
0.155924 | + | 0.987769i | \(0.450164\pi\) | |||||||
\(972\) | −16.0470 | −0.514709 | ||||||||
\(973\) | 16.8904 | 0.541481 | ||||||||
\(974\) | −5.81713 | −0.186393 | ||||||||
\(975\) | −1.64763 | −0.0527663 | ||||||||
\(976\) | 0.216728 | 0.00693731 | ||||||||
\(977\) | −31.9230 | −1.02131 | −0.510654 | − | 0.859786i | \(-0.670597\pi\) | ||||
−0.510654 | + | 0.859786i | \(0.670597\pi\) | |||||||
\(978\) | −6.65570 | −0.212826 | ||||||||
\(979\) | −1.97389 | −0.0630858 | ||||||||
\(980\) | 4.98354 | 0.159193 | ||||||||
\(981\) | 10.9059 | 0.348199 | ||||||||
\(982\) | 23.6181 | 0.753685 | ||||||||
\(983\) | 29.0080 | 0.925213 | 0.462606 | − | 0.886564i | \(-0.346914\pi\) | ||||
0.462606 | + | 0.886564i | \(0.346914\pi\) | |||||||
\(984\) | −1.12786 | −0.0359550 | ||||||||
\(985\) | −25.0254 | −0.797376 | ||||||||
\(986\) | −56.7369 | −1.80687 | ||||||||
\(987\) | 3.28508 | 0.104565 | ||||||||
\(988\) | −0.613901 | −0.0195308 | ||||||||
\(989\) | −2.34118 | −0.0744451 | ||||||||
\(990\) | 2.26617 | 0.0720235 | ||||||||
\(991\) | −15.5813 | −0.494955 | −0.247478 | − | 0.968894i | \(-0.579602\pi\) | ||||
−0.247478 | + | 0.968894i | \(0.579602\pi\) | |||||||
\(992\) | −5.42821 | −0.172346 | ||||||||
\(993\) | 3.67237 | 0.116539 | ||||||||
\(994\) | −22.5586 | −0.715515 | ||||||||
\(995\) | −5.56402 | −0.176391 | ||||||||
\(996\) | 3.52096 | 0.111566 | ||||||||
\(997\) | 62.8524 | 1.99055 | 0.995277 | − | 0.0970708i | \(-0.0309473\pi\) | ||||
0.995277 | + | 0.0970708i | \(0.0309473\pi\) | |||||||
\(998\) | −20.6660 | −0.654170 | ||||||||
\(999\) | 29.6389 | 0.937734 |
(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 | 8030.2.a.bd.1.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8030.2.a.bd.1.5 | ✓ | 14 | 1.1 | even | 1 | trivial |