Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3720,2,Mod(1,3720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3720.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3720 = 2^{3} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3720.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: | \(29.7043495519\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2294036.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 8x^{3} + 8x^{2} + 6x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.36670\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3720.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.13213 | 0.805869 | 0.402934 | − | 0.915229i | \(-0.367990\pi\) | ||||
0.402934 | + | 0.915229i | \(0.367990\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.64738 | −1.09973 | −0.549864 | − | 0.835254i | \(-0.685320\pi\) | ||||
−0.549864 | + | 0.835254i | \(0.685320\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.85276 | 1.34591 | 0.672956 | − | 0.739682i | \(-0.265024\pi\) | ||||
0.672956 | + | 0.739682i | \(0.265024\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.80665 | 0.438176 | 0.219088 | − | 0.975705i | \(-0.429692\pi\) | ||||
0.219088 | + | 0.975705i | \(0.429692\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.72063 | 1.08299 | 0.541493 | − | 0.840705i | \(-0.317859\pi\) | ||||
0.541493 | + | 0.840705i | \(0.317859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.13213 | 0.465268 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.38079 | 1.33049 | 0.665243 | − | 0.746627i | \(-0.268328\pi\) | ||||
0.665243 | + | 0.746627i | \(0.268328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.65940 | −0.865230 | −0.432615 | − | 0.901579i | \(-0.642409\pi\) | ||||
−0.432615 | + | 0.901579i | \(0.642409\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.64738 | −0.634928 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.13213 | −0.360395 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.588501 | −0.0967490 | −0.0483745 | − | 0.998829i | \(-0.515404\pi\) | ||||
−0.0483745 | + | 0.998829i | \(0.515404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.85276 | 0.777063 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.90806 | −1.39121 | −0.695603 | − | 0.718427i | \(-0.744863\pi\) | ||||
−0.695603 | + | 0.718427i | \(0.744863\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.18743 | −0.943575 | −0.471787 | − | 0.881712i | \(-0.656391\pi\) | ||||
−0.471787 | + | 0.881712i | \(0.656391\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.73340 | −0.398708 | −0.199354 | − | 0.979928i | \(-0.563884\pi\) | ||||
−0.199354 | + | 0.979928i | \(0.563884\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.45403 | −0.350576 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.80665 | 0.252981 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.9208 | 1.50009 | 0.750046 | − | 0.661386i | \(-0.230031\pi\) | ||||
0.750046 | + | 0.661386i | \(0.230031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.64738 | 0.491813 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.72063 | 0.625263 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.58616 | −0.727256 | −0.363628 | − | 0.931544i | \(-0.618462\pi\) | ||||
−0.363628 | + | 0.931544i | \(0.618462\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92676 | 0.630806 | 0.315403 | − | 0.948958i | \(-0.397860\pi\) | ||||
0.315403 | + | 0.948958i | \(0.397860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.13213 | 0.268623 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.85276 | −0.601910 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.9088 | 1.69923 | 0.849616 | − | 0.527401i | \(-0.176834\pi\) | ||||
0.849616 | + | 0.527401i | \(0.176834\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.38079 | 0.768156 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.5710 | −1.72926 | −0.864632 | − | 0.502405i | \(-0.832449\pi\) | ||||
−0.864632 | + | 0.502405i | \(0.832449\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.67218 | −0.312755 | −0.156377 | − | 0.987697i | \(-0.549982\pi\) | ||||
−0.156377 | + | 0.987697i | \(0.549982\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.77669 | −0.886236 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4845 | 1.62964 | 0.814819 | − | 0.579715i | \(-0.196836\pi\) | ||||
0.814819 | + | 0.579715i | \(0.196836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0282 | 1.10073 | 0.550367 | − | 0.834923i | \(-0.314488\pi\) | ||||
0.550367 | + | 0.834923i | \(0.314488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.80665 | −0.195958 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.65940 | −0.499541 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.747764 | 0.0792629 | 0.0396314 | − | 0.999214i | \(-0.487382\pi\) | ||||
0.0396314 | + | 0.999214i | \(0.487382\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3467 | 1.08463 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.72063 | −0.484326 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1723 | 1.74358 | 0.871792 | − | 0.489876i | \(-0.162958\pi\) | ||||
0.871792 | + | 0.489876i | \(0.162958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.64738 | −0.366576 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.8929 | 1.78041 | 0.890207 | − | 0.455556i | \(-0.150559\pi\) | ||||
0.890207 | + | 0.455556i | \(0.150559\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.85276 | 0.675222 | 0.337611 | − | 0.941286i | \(-0.390381\pi\) | ||||
0.337611 | + | 0.941286i | \(0.390381\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.13213 | −0.208074 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.0978 | 1.74958 | 0.874792 | − | 0.484499i | \(-0.160998\pi\) | ||||
0.874792 | + | 0.484499i | \(0.160998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.7639 | 1.12678 | 0.563389 | − | 0.826192i | \(-0.309497\pi\) | ||||
0.563389 | + | 0.826192i | \(0.309497\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.588501 | −0.0558581 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.75114 | 0.917310 | 0.458655 | − | 0.888614i | \(-0.348331\pi\) | ||||
0.458655 | + | 0.888614i | \(0.348331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.38079 | −0.595011 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.85276 | 0.448638 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.85200 | 0.353113 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.30341 | 0.209401 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.90806 | −0.803213 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7429 | −1.48569 | −0.742845 | − | 0.669463i | \(-0.766524\pi\) | ||||
−0.742845 | + | 0.669463i | \(0.766524\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.18743 | −0.544773 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.58616 | −0.488065 | −0.244032 | − | 0.969767i | \(-0.578470\pi\) | ||||
−0.244032 | + | 0.969767i | \(0.578470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0650 | 0.872745 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.07090 | −0.176929 | −0.0884646 | − | 0.996079i | \(-0.528196\pi\) | ||||
−0.0884646 | + | 0.996079i | \(0.528196\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.5403 | −1.31811 | −0.659057 | − | 0.752093i | \(-0.729044\pi\) | ||||
−0.659057 | + | 0.752093i | \(0.729044\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.73340 | −0.230194 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.6999 | −1.48014 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.65940 | 0.386942 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.45403 | −0.202405 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.8929 | −1.13815 | −0.569077 | − | 0.822284i | \(-0.692699\pi\) | ||||
−0.569077 | + | 0.822284i | \(0.692699\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1700 | −1.47865 | −0.739326 | − | 0.673348i | \(-0.764856\pi\) | ||||
−0.739326 | + | 0.673348i | \(0.764856\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.80665 | 0.146059 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.80073 | −0.622566 | −0.311283 | − | 0.950317i | \(-0.600759\pi\) | ||||
−0.311283 | + | 0.950317i | \(0.600759\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.9208 | 0.866079 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.6047 | 1.07220 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.1971 | 1.89526 | 0.947632 | − | 0.319364i | \(-0.103469\pi\) | ||||
0.947632 | + | 0.319364i | \(0.103469\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.64738 | 0.283948 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.1687 | 1.71547 | 0.857734 | − | 0.514093i | \(-0.171871\pi\) | ||||
0.857734 | + | 0.514093i | \(0.171871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5492 | 0.811480 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.72063 | 0.360996 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.61329 | −0.426771 | −0.213385 | − | 0.976968i | \(-0.568449\pi\) | ||||
−0.213385 | + | 0.976968i | \(0.568449\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.13213 | 0.161174 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.58616 | −0.419881 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.0991 | 1.35279 | 0.676394 | − | 0.736540i | \(-0.263542\pi\) | ||||
0.676394 | + | 0.736540i | \(0.263542\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9662 | −1.11243 | −0.556214 | − | 0.831039i | \(-0.687747\pi\) | ||||
−0.556214 | + | 0.831039i | \(0.687747\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.92676 | 0.364196 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.588501 | 0.0432675 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.58954 | −0.481875 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.13213 | 0.155089 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.85510 | −0.278945 | −0.139473 | − | 0.990226i | \(-0.544541\pi\) | ||||
−0.139473 | + | 0.990226i | \(0.544541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6438 | −0.910121 | −0.455061 | − | 0.890460i | \(-0.650382\pi\) | ||||
−0.455061 | + | 0.890460i | \(0.650382\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.85276 | −0.347513 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.41488 | −0.599535 | −0.299768 | − | 0.954012i | \(-0.596909\pi\) | ||||
−0.299768 | + | 0.954012i | \(0.596909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.57180 | −0.394974 | −0.197487 | − | 0.980305i | \(-0.563278\pi\) | ||||
−0.197487 | + | 0.980305i | \(0.563278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.9088 | 0.981052 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.93444 | −0.697261 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.90806 | 0.622166 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.38079 | 0.443495 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.2179 | −1.19099 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.5741 | 1.27870 | 0.639348 | − | 0.768917i | \(-0.279204\pi\) | ||||
0.639348 | + | 0.768917i | \(0.279204\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.5710 | −0.998391 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.18743 | 0.421979 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.13213 | 0.144738 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.67218 | −0.180569 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.76722 | 0.589747 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.1536 | 1.81834 | 0.909171 | − | 0.416424i | \(-0.136717\pi\) | ||||
0.909171 | + | 0.416424i | \(0.136717\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 30.0436 | 1.99406 | 0.997031 | − | 0.0770037i | \(-0.0245353\pi\) | ||||
0.997031 | + | 0.0770037i | \(0.0245353\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.03409 | −0.134416 | −0.0672082 | − | 0.997739i | \(-0.521409\pi\) | ||||
−0.0672082 | + | 0.997739i | \(0.521409\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.77669 | −0.511669 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.2156 | −1.45539 | −0.727696 | − | 0.685899i | \(-0.759409\pi\) | ||||
−0.727696 | + | 0.685899i | \(0.759409\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.73340 | 0.178308 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.4845 | 0.940872 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.3798 | −1.51232 | −0.756158 | − | 0.654389i | \(-0.772926\pi\) | ||||
−0.756158 | + | 0.654389i | \(0.772926\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1227 | 0.716478 | 0.358239 | − | 0.933630i | \(-0.383377\pi\) | ||||
0.358239 | + | 0.933630i | \(0.383377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.45403 | 0.156782 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.9081 | 1.45761 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.0282 | 0.635509 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3073 | 0.966186 | 0.483093 | − | 0.875569i | \(-0.339513\pi\) | ||||
0.483093 | + | 0.875569i | \(0.339513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.2732 | −1.46317 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.80665 | −0.113137 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.0115 | −1.43542 | −0.717710 | − | 0.696342i | \(-0.754810\pi\) | ||||
−0.717710 | + | 0.696342i | \(0.754810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.25476 | −0.0779670 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.65940 | −0.288410 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.48578 | 0.153280 | 0.0766398 | − | 0.997059i | \(-0.475581\pi\) | ||||
0.0766398 | + | 0.997059i | \(0.475581\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.9208 | −0.670862 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.747764 | 0.0457624 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1312 | 0.800622 | 0.400311 | − | 0.916379i | \(-0.368902\pi\) | ||||
0.400311 | + | 0.916379i | \(0.368902\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5062 | 1.18492 | 0.592460 | − | 0.805600i | \(-0.298157\pi\) | ||||
0.592460 | + | 0.805600i | \(0.298157\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.3467 | 0.626211 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.64738 | −0.219946 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.1659 | −1.33182 | −0.665910 | − | 0.746032i | \(-0.731957\pi\) | ||||
−0.665910 | + | 0.746032i | \(0.731957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.4007 | 1.87321 | 0.936604 | − | 0.350389i | \(-0.113951\pi\) | ||||
0.936604 | + | 0.350389i | \(0.113951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9138 | −1.00542 | −0.502710 | − | 0.864455i | \(-0.667664\pi\) | ||||
−0.502710 | + | 0.864455i | \(0.667664\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.72063 | −0.279626 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.9931 | −1.12113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.7360 | −0.808002 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.1723 | 1.00666 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.70936 | −0.391965 | −0.195983 | − | 0.980607i | \(-0.562790\pi\) | ||||
−0.195983 | + | 0.980607i | \(0.562790\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.58616 | 0.325239 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.64738 | −0.211643 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.9644 | 1.79072 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.1924 | −0.760397 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.8929 | 1.02792 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.92676 | −0.282105 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.3860 | 1.22056 | 0.610280 | − | 0.792186i | \(-0.291057\pi\) | ||||
0.610280 | + | 0.792186i | \(0.291057\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.85276 | 0.389840 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.2371 | −0.807313 | −0.403657 | − | 0.914911i | \(-0.632261\pi\) | ||||
−0.403657 | + | 0.914911i | \(0.632261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.6826 | −1.33862 | −0.669310 | − | 0.742983i | \(-0.733410\pi\) | ||||
−0.669310 | + | 0.742983i | \(0.733410\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.13213 | −0.120132 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.5754 | 1.77345 | 0.886724 | − | 0.462299i | \(-0.152975\pi\) | ||||
0.886724 | + | 0.462299i | \(0.152975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.9946 | 0.951517 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0978 | 1.01012 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.52851 | 0.474539 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.85276 | 0.269183 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.7639 | 0.650546 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.82796 | −0.321306 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.7643 | −0.921449 | −0.460725 | − | 0.887543i | \(-0.652410\pi\) | ||||
−0.460725 | + | 0.887543i | \(0.652410\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.588501 | −0.0322497 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.9088 | −0.759920 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.6994 | −0.800728 | −0.400364 | − | 0.916356i | \(-0.631116\pi\) | ||||
−0.400364 | + | 0.916356i | \(0.631116\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.75114 | 0.529609 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.64738 | −0.197517 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1572 | −1.08839 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.38079 | −0.343530 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.1364 | −1.13466 | −0.567332 | − | 0.823489i | \(-0.692024\pi\) | ||||
−0.567332 | + | 0.823489i | \(0.692024\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.73491 | −0.146396 | −0.0731982 | − | 0.997317i | \(-0.523321\pi\) | ||||
−0.0731982 | + | 0.997317i | \(0.523321\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.85276 | 0.259021 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.1921 | −1.55374 | −0.776870 | − | 0.629661i | \(-0.783194\pi\) | ||||
−0.776870 | + | 0.629661i | \(0.783194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.5710 | 0.773351 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.85200 | 0.203870 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.743080 | 0.0392183 | 0.0196091 | − | 0.999808i | \(-0.493758\pi\) | ||||
0.0196091 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.28434 | 0.172860 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.30341 | 0.120898 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.67218 | 0.139868 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.8653 | 1.08916 | 0.544581 | − | 0.838708i | \(-0.316689\pi\) | ||||
0.544581 | + | 0.838708i | \(0.316689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.90806 | −0.463735 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.2846 | 1.20888 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.5741 | −1.47951 | −0.739756 | − | 0.672875i | \(-0.765059\pi\) | ||||
−0.739756 | + | 0.672875i | \(0.765059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.6110 | −1.16452 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4579 | 0.742651 | 0.371326 | − | 0.928503i | \(-0.378903\pi\) | ||||
0.371326 | + | 0.928503i | \(0.378903\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.7429 | −0.857764 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.6835 | 0.750293 | 0.375146 | − | 0.926966i | \(-0.377592\pi\) | ||||
0.375146 | + | 0.926966i | \(0.377592\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.77669 | 0.396337 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.18743 | −0.314525 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.1007 | −0.917740 | −0.458870 | − | 0.888503i | \(-0.651746\pi\) | ||||
−0.458870 | + | 0.888503i | \(0.651746\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5278 | 0.582987 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.58616 | −0.281784 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4845 | −0.728797 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.3853 | 1.17367 | 0.586837 | − | 0.809705i | \(-0.300373\pi\) | ||||
0.586837 | + | 0.809705i | \(0.300373\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.0650 | 0.503879 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.8343 | −0.740791 | −0.370396 | − | 0.928874i | \(-0.620778\pi\) | ||||
−0.370396 | + | 0.928874i | \(0.620778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.85276 | 0.241733 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.14649 | 0.106398 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.81584 | −0.337022 | −0.168511 | − | 0.985700i | \(-0.553896\pi\) | ||||
−0.168511 | + | 0.985700i | \(0.553896\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.07090 | −0.102150 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.9104 | −0.586073 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.0282 | −0.492264 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.5403 | −0.761013 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.5247 | −1.34467 | −0.672336 | − | 0.740246i | \(-0.734709\pi\) | ||||
−0.672336 | + | 0.740246i | \(0.734709\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.1204 | −0.883134 | −0.441567 | − | 0.897228i | \(-0.645577\pi\) | ||||
−0.441567 | + | 0.897228i | \(0.645577\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.73340 | −0.132903 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.80665 | 0.0876353 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.5045 | 0.508347 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.6999 | −0.854558 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.8794 | −0.524043 | −0.262022 | − | 0.965062i | \(-0.584389\pi\) | ||||
−0.262022 | + | 0.965062i | \(0.584389\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.76411 | −0.180892 | −0.0904459 | − | 0.995901i | \(-0.528829\pi\) | ||||
−0.0904459 | + | 0.995901i | \(0.528829\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.65940 | 0.223401 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.1213 | 1.44090 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.3749 | −0.972439 | −0.486220 | − | 0.873837i | \(-0.661625\pi\) | ||||
−0.486220 | + | 0.873837i | \(0.661625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.45403 | −0.116859 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.5111 | −1.54465 | −0.772323 | − | 0.635230i | \(-0.780905\pi\) | ||||
−0.772323 | + | 0.635230i | \(0.780905\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.747764 | −0.0354474 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.8929 | −0.657114 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.44463 | 0.398527 | 0.199263 | − | 0.979946i | \(-0.436145\pi\) | ||||
0.199263 | + | 0.979946i | \(0.436145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.4911 | 1.52995 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.1700 | −0.853700 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.3467 | −0.485061 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.5292 | 1.52165 | 0.760827 | − | 0.648955i | \(-0.224794\pi\) | ||||
0.760827 | + | 0.648955i | \(0.224794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.80665 | 0.0843271 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.66091 | −0.123931 | −0.0619655 | − | 0.998078i | \(-0.519737\pi\) | ||||
−0.0619655 | + | 0.998078i | \(0.519737\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.8604 | −0.830042 | −0.415021 | − | 0.909812i | \(-0.636226\pi\) | ||||
−0.415021 | + | 0.909812i | \(0.636226\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.49498 | −0.161728 | −0.0808641 | − | 0.996725i | \(-0.525768\pi\) | ||||
−0.0808641 | + | 0.996725i | \(0.525768\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.6554 | 1.36936 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.80073 | −0.359439 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.5679 | 1.03768 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.72063 | 0.216597 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.9208 | 0.500031 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.0425 | −0.641620 | −0.320810 | − | 0.947144i | \(-0.603955\pi\) | ||||
−0.320810 | + | 0.947144i | \(0.603955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.85585 | −0.130216 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.6047 | 0.619033 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.1723 | −0.779755 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.25175 | 0.373923 | 0.186961 | − | 0.982367i | \(-0.440136\pi\) | ||||
0.186961 | + | 0.982367i | \(0.440136\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.1971 | 1.09423 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.46323 | 0.381940 | 0.190970 | − | 0.981596i | \(-0.438837\pi\) | ||||
0.190970 | + | 0.981596i | \(0.438837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.41790 | −0.379123 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.64738 | 0.163938 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.0673 | −1.39356 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.0944 | 1.61581 | 0.807903 | − | 0.589315i | \(-0.200602\pi\) | ||||
0.807903 | + | 0.589315i | \(0.200602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.1687 | 0.990426 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.7352 | −0.969124 | −0.484562 | − | 0.874757i | \(-0.661021\pi\) | ||||
−0.484562 | + | 0.874757i | \(0.661021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.8929 | −0.796226 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.5492 | 0.468508 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.45121 | 0.330269 | 0.165134 | − | 0.986271i | \(-0.447194\pi\) | ||||
0.165134 | + | 0.986271i | \(0.447194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.69742 | −0.252039 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.72063 | 0.208421 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.85276 | −0.301969 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.96977 | 0.438470 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.61329 | −0.246396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.8825 | 1.09012 | 0.545061 | − | 0.838396i | \(-0.316506\pi\) | ||||
0.545061 | + | 0.838396i | \(0.316506\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.87606 | −0.169488 | −0.0847442 | − | 0.996403i | \(-0.527007\pi\) | ||||
−0.0847442 | + | 0.996403i | \(0.527007\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.13213 | 0.0930537 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.80665 | 0.0786988 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.7144 | 0.770193 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.58616 | −0.242419 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.2287 | −1.87244 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0978 | −0.782438 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0991 | 0.781033 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.95079 | 0.385538 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.9075 | −1.15684 | −0.578422 | − | 0.815738i | \(-0.696331\pi\) | ||||
−0.578422 | + | 0.815738i | \(0.696331\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.9662 | −0.642261 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.7639 | −0.503911 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.6128 | 1.60821 | 0.804104 | − | 0.594489i | \(-0.202645\pi\) | ||||
0.804104 | + | 0.594489i | \(0.202645\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.92676 | 0.210269 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.9953 | −0.937032 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.8829 | 1.31327 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.588501 | 0.0249805 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.4481 | −1.62910 | −0.814550 | − | 0.580094i | \(-0.803016\pi\) | ||||
−0.814550 | + | 0.580094i | \(0.803016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.0261 | −1.26997 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.58954 | −0.278210 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.1516 | −1.18645 | −0.593224 | − | 0.805038i | \(-0.702145\pi\) | ||||
−0.593224 | + | 0.805038i | \(0.702145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.75114 | −0.410234 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.13213 | 0.0895409 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.8587 | −0.916363 | −0.458181 | − | 0.888859i | \(-0.651499\pi\) | ||||
−0.458181 | + | 0.888859i | \(0.651499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0688 | 1.34204 | 0.671020 | − | 0.741440i | \(-0.265857\pi\) | ||||
0.671020 | + | 0.741440i | \(0.265857\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.85510 | −0.161049 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.38079 | 0.266097 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.6342 | −0.817381 | −0.408690 | − | 0.912673i | \(-0.634014\pi\) | ||||
−0.408690 | + | 0.912673i | \(0.634014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6438 | −0.525459 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.3813 | 0.887047 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.8325 | −1.64969 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.85276 | −0.200637 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2586 | 0.505967 | 0.252983 | − | 0.967471i | \(-0.418588\pi\) | ||||
0.252983 | + | 0.967471i | \(0.418588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.72063 | 0.194510 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.41488 | −0.346142 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.0807 | 1.85124 | 0.925620 | − | 0.378453i | \(-0.123544\pi\) | ||||
0.925620 | + | 0.378453i | \(0.123544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.85200 | −0.157917 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.57180 | −0.228038 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.3678 | −0.995642 | −0.497821 | − | 0.867280i | \(-0.665866\pi\) | ||||
−0.497821 | + | 0.867280i | \(0.665866\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.3141 | −0.706258 | −0.353129 | − | 0.935575i | \(-0.614882\pi\) | ||||
−0.353129 | + | 0.935575i | \(0.614882\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.9088 | 0.566411 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.30341 | −0.0936470 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.3044 | 1.02708 | 0.513538 | − | 0.858067i | \(-0.328335\pi\) | ||||
0.513538 | + | 0.858067i | \(0.328335\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.93444 | −0.402564 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.2645 | −0.536626 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.23259 | 0.332511 | 0.166256 | − | 0.986083i | \(-0.446832\pi\) | ||||
0.166256 | + | 0.986083i | \(0.446832\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.90806 | 0.359208 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.4878 | 0.623517 | 0.311759 | − | 0.950161i | \(-0.399082\pi\) | ||||
0.311759 | + | 0.950161i | \(0.399082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.4795 | 1.26527 | 0.632633 | − | 0.774452i | \(-0.281974\pi\) | ||||
0.632633 | + | 0.774452i | \(0.281974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.38079 | 0.256052 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.59433 | 0.0638754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.2179 | −0.687619 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.06321 | −0.0423931 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0092 | −0.637316 | −0.318658 | − | 0.947870i | \(-0.603232\pi\) | ||||
−0.318658 | + | 0.947870i | \(0.603232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.5741 | 0.738256 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.7429 | 0.664421 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.9088 | −0.471844 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.5710 | −0.576422 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.56212 | 0.377681 | 0.188841 | − | 0.982008i | \(-0.439527\pi\) | ||||
0.188841 | + | 0.982008i | \(0.439527\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.5249 | −1.83476 | −0.917382 | − | 0.398008i | \(-0.869702\pi\) | ||||
−0.917382 | + | 0.398008i | \(0.869702\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.18743 | 0.243630 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.25421 | −0.0886220 | −0.0443110 | − | 0.999018i | \(-0.514109\pi\) | ||||
−0.0443110 | + | 0.999018i | \(0.514109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3749 | 0.799784 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.13213 | 0.0835647 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.2189 | −1.61302 | −0.806510 | − | 0.591221i | \(-0.798646\pi\) | ||||
−0.806510 | + | 0.591221i | \(0.798646\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.58616 | 0.218269 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.67218 | −0.104252 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.40200 | −0.0935687 | −0.0467844 | − | 0.998905i | \(-0.514897\pi\) | ||||
−0.0467844 | + | 0.998905i | \(0.514897\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4721 | −0.757375 | −0.378688 | − | 0.925525i | \(-0.623624\pi\) | ||||
−0.378688 | + | 0.925525i | \(0.623624\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.76722 | 0.340491 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.0650 | −0.390303 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.7307 | −1.15118 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.1536 | 1.04982 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.9698 | −0.693715 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.2937 | −1.39902 | −0.699510 | − | 0.714623i | \(-0.746598\pi\) | ||||
−0.699510 | + | 0.714623i | \(0.746598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.4469 | −0.901137 | −0.450568 | − | 0.892742i | \(-0.648779\pi\) | ||||
−0.450568 | + | 0.892742i | \(0.648779\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.6136 | 1.40510 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.0436 | 1.15127 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.1362 | −0.770490 | −0.385245 | − | 0.922814i | \(-0.625883\pi\) | ||||
−0.385245 | + | 0.922814i | \(0.625883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.07090 | 0.0791251 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.03409 | −0.0776054 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 52.9962 | 2.01899 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.5928 | −1.27793 | −0.638965 | − | 0.769235i | \(-0.720637\pi\) | ||||
−0.638965 | + | 0.769235i | \(0.720637\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.77669 | −0.295412 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.5403 | 0.589478 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.0937 | −0.609593 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.2156 | −0.840271 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.67800 | 0.101147 | 0.0505733 | − | 0.998720i | \(-0.483895\pi\) | ||||
0.0505733 | + | 0.998720i | \(0.483895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.77810 | −0.104778 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.73340 | 0.102946 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.1500 | 1.43478 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.0229 | −0.714421 | −0.357211 | − | 0.934024i | \(-0.616272\pi\) | ||||
−0.357211 | + | 0.934024i | \(0.616272\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.4845 | 0.543213 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.38079 | 0.238962 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.6999 | 0.661937 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.3798 | −0.873136 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.6721 | 0.882821 | 0.441410 | − | 0.897305i | \(-0.354478\pi\) | ||||
0.441410 | + | 0.897305i | \(0.354478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.6110 | 0.544140 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.1227 | 0.413659 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.65940 | −0.173046 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.75039 | −0.176182 | −0.0880911 | − | 0.996112i | \(-0.528077\pi\) | ||||
−0.0880911 | + | 0.996112i | \(0.528077\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.1785 | −0.413452 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.9152 | −0.550906 | −0.275453 | − | 0.961315i | \(-0.588828\pi\) | ||||
−0.275453 | + | 0.961315i | \(0.588828\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.45403 | 0.0905183 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.7308 | −1.86869 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.3965 | 1.89065 | 0.945325 | − | 0.326130i | \(-0.105745\pi\) | ||||
0.945325 | + | 0.326130i | \(0.105745\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.9081 | 0.841549 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.3408 | 0.452739 | 0.226370 | − | 0.974041i | \(-0.427314\pi\) | ||||
0.226370 | + | 0.974041i | \(0.427314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.8929 | 0.508998 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.0282 | 0.366912 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.5869 | 1.40993 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.90806 | 0.252079 | 0.126039 | − | 0.992025i | \(-0.459773\pi\) | ||||
0.126039 | + | 0.992025i | \(0.459773\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.3073 | 0.557828 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.1700 | 0.661273 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.5209 | −1.10930 | −0.554650 | − | 0.832084i | \(-0.687148\pi\) | ||||
−0.554650 | + | 0.832084i | \(0.687148\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.2732 | −0.844763 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.83005 | 0.175089 | 0.0875446 | − | 0.996161i | \(-0.472098\pi\) | ||||
0.0875446 | + | 0.996161i | \(0.472098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.0822 | 0.908036 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.80665 | −0.0653195 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.1083 | −0.978823 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.95822 | 0.106676 | 0.0533381 | − | 0.998577i | \(-0.483014\pi\) | ||||
0.0533381 | + | 0.998577i | \(0.483014\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.0115 | −0.828741 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.1208 | 1.80272 | 0.901359 | − | 0.433072i | \(-0.142570\pi\) | ||||
0.901359 | + | 0.433072i | \(0.142570\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.25476 | −0.0450142 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −42.0517 | −1.50666 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53.1462 | 1.90172 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.65940 | −0.166514 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.80073 | 0.278420 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.2447 | 1.57715 | 0.788577 | − | 0.614936i | \(-0.210818\pi\) | ||||
0.788577 | + | 0.614936i | \(0.210818\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.48578 | 0.0884961 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.7907 | 0.739231 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.9083 | 0.849010 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.9208 | −0.387322 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.4333 | −0.652940 | −0.326470 | − | 0.945208i | \(-0.605859\pi\) | ||||
−0.326470 | + | 0.945208i | \(0.605859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.93829 | −0.174704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.747764 | 0.0264210 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.74646 | 0.343945 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.6047 | −0.479501 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.1312 | 0.462239 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.0372 | −1.30216 | −0.651079 | − | 0.759010i | \(-0.725683\pi\) | ||||
−0.651079 | + | 0.759010i | \(0.725683\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.6287 | −0.689257 | −0.344628 | − | 0.938739i | \(-0.611995\pi\) | ||||
−0.344628 | + | 0.938739i | \(0.611995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.5062 | 0.684114 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.1971 | −0.847588 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.2086 | −1.02188 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3467 | 0.361543 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0888 | −1.05011 | −0.525054 | − | 0.851069i | \(-0.675955\pi\) | ||||
−0.525054 | + | 0.851069i | \(0.675955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.1931 | 0.947891 | 0.473946 | − | 0.880554i | \(-0.342829\pi\) | ||||
0.473946 | + | 0.880554i | \(0.342829\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.64738 | −0.126986 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.7986 | 0.792784 | 0.396392 | − | 0.918081i | \(-0.370262\pi\) | ||||
0.396392 | + | 0.918081i | \(0.370262\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.9045 | −0.413460 | −0.206730 | − | 0.978398i | \(-0.566282\pi\) | ||||
−0.206730 | + | 0.978398i | \(0.566282\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.1659 | −0.768927 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.43357 | −0.153614 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.1687 | −0.767181 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.691986 | 0.0238900 | 0.0119450 | − | 0.999929i | \(-0.496198\pi\) | ||||
0.0119450 | + | 0.999929i | \(0.496198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.28996 | −0.251378 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.4007 | 1.08150 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.5492 | −0.362905 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.91117 | 0.168750 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.9138 | −0.580479 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.75510 | −0.128723 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.6664 | −1.05000 | −0.524998 | − | 0.851103i | \(-0.675934\pi\) | ||||
−0.524998 | + | 0.851103i | \(0.675934\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.72063 | −0.161442 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0533 | 0.753327 | 0.376664 | − | 0.926350i | \(-0.377071\pi\) | ||||
0.376664 | + | 0.926350i | \(0.377071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.26932 | 0.0433087 | 0.0216543 | − | 0.999766i | \(-0.493107\pi\) | ||||
0.0216543 | + | 0.999766i | \(0.493107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.9931 | −0.647284 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.1925 | −0.517159 | −0.258579 | − | 0.965990i | \(-0.583254\pi\) | ||||
−0.258579 | + | 0.965990i | \(0.583254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.61329 | 0.190858 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.7360 | −0.466500 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.8307 | −1.79216 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 67.4961 | 2.28702 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.1723 | 0.581195 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.13213 | −0.0720791 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.17081 | 0.107071 | 0.0535353 | − | 0.998566i | \(-0.482951\pi\) | ||||
0.0535353 | + | 0.998566i | \(0.482951\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.70936 | −0.226301 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.3767 | 1.25925 | 0.629627 | − | 0.776897i | \(-0.283208\pi\) | ||||
0.629627 | + | 0.776897i | \(0.283208\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.9178 | −0.905857 | −0.452928 | − | 0.891547i | \(-0.649621\pi\) | ||||
−0.452928 | + | 0.891547i | \(0.649621\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.58616 | 0.187777 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.3214 | 0.648750 | 0.324375 | − | 0.945929i | \(-0.394846\pi\) | ||||
0.324375 | + | 0.945929i | \(0.394846\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.6980 | −1.19727 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.64738 | −0.122192 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.9034 | −0.431795 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.0991 | −0.604985 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.9644 | 1.03387 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.65940 | −0.155400 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7301 | 0.657305 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.1924 | −0.439016 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.9662 | 0.497493 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.7763 | 1.75241 | 0.876204 | − | 0.481940i | \(-0.160068\pi\) | ||||
0.876204 | + | 0.481940i | \(0.160068\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.8929 | 0.593472 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.3026 | −1.60034 | −0.800168 | − | 0.599776i | \(-0.795256\pi\) | ||||
−0.800168 | + | 0.599776i | \(0.795256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.5766 | −1.21051 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.92676 | −0.162874 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.9104 | −0.393316 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.1984 | −1.09512 | −0.547558 | − | 0.836768i | \(-0.684442\pi\) | ||||
−0.547558 | + | 0.836768i | \(0.684442\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.3860 | 0.704691 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −70.7097 | −2.32744 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.588501 | −0.0193498 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.85276 | 0.225074 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.1325 | −0.922999 | −0.461499 | − | 0.887141i | \(-0.652688\pi\) | ||||
−0.461499 | + | 0.887141i | \(0.652688\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.5846 | −0.379669 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.2371 | −0.466102 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.58954 | 0.215501 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.8538 | 0.550589 | 0.275295 | − | 0.961360i | \(-0.411225\pi\) | ||||
0.275295 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.6826 | −0.772853 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.10506 | 0.101222 | 0.0506111 | − | 0.998718i | \(-0.483883\pi\) | ||||
0.0506111 | + | 0.998718i | \(0.483883\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.8404 | −1.85098 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.13213 | −0.0693581 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.2718 | −0.821225 | −0.410612 | − | 0.911810i | \(-0.634685\pi\) | ||||
−0.410612 | + | 0.911810i | \(0.634685\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9674 | −0.420940 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.5754 | 1.02390 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.695354 | −0.0225247 | −0.0112624 | − | 0.999937i | \(-0.503585\pi\) | ||||
−0.0112624 | + | 0.999937i | \(0.503585\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.85510 | 0.124748 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.9946 | 0.549359 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.41543 | −0.142582 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.0978 | 0.583195 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.6438 | 0.407019 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.7734 | −0.764501 | −0.382250 | − | 0.924059i | \(-0.624851\pi\) | ||||
−0.382250 | + | 0.924059i | \(0.624851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.52851 | 0.273975 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.8874 | 0.702400 | 0.351200 | − | 0.936300i | \(-0.385774\pi\) | ||||
0.351200 | + | 0.936300i | \(0.385774\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.1340 | −1.06223 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.85276 | 0.155413 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.1228 | 0.771757 | 0.385879 | − | 0.922550i | \(-0.373898\pi\) | ||||
0.385879 | + | 0.922550i | \(0.373898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.72738 | −0.0871676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.7639 | 0.375593 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.2829 | −0.646926 | −0.323463 | − | 0.946241i | \(-0.604847\pi\) | ||||
−0.323463 | + | 0.946241i | \(0.604847\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.41488 | 0.268120 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.82796 | −0.185506 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.4807 | −1.25541 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4812 | −0.364714 | −0.182357 | − | 0.983232i | \(-0.558373\pi\) | ||||
−0.182357 | + | 0.983232i | \(0.558373\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.7643 | −0.531999 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.57180 | 0.176638 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.3562 | −0.359654 | −0.179827 | − | 0.983698i | \(-0.557554\pi\) | ||||
−0.179827 | + | 0.983698i | \(0.557554\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.588501 | −0.0186194 |
(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 | 3720.2.a.v.1.3 | ✓ | 5 | |
4.3 | odd | 2 | 7440.2.a.cd.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3720.2.a.v.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
7440.2.a.cd.1.3 | 5 | 4.3 | odd | 2 |